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authorrander.wang <rander.wang@intel.com>2017-05-15 14:11:18 +0800
committerYang Rong <rong.r.yang@intel.com>2017-05-17 18:09:25 +0800
commitacd53cffa43da9f92b7e656f1314edc0b4044c0b (patch)
treeed63012fbb24a36e521d98ada4a2ce4ddc721d34
parent98eeab036fc30a036d92bd0e3b63d093aae002c8 (diff)
downloadbeignet-acd53cffa43da9f92b7e656f1314edc0b4044c0b.tar.gz
backend: refine the code structure of math
mov all the common math function to match_common.cl. it is easy to maitain Signed-off-by: rander.wang <rander.wang@intel.com> Tested-by: Yang Rong <rong.r.yang@intel.com>
Diffstat
-rw-r--r--backend/src/libocl/script/ocl_math.def121
-rw-r--r--backend/src/libocl/script/ocl_math_20.def115
-rw-r--r--backend/src/libocl/script/ocl_math_common.def123
-rw-r--r--backend/src/libocl/tmpl/ocl_math.tmpl.cl3610
-rw-r--r--backend/src/libocl/tmpl/ocl_math.tmpl.h172
-rw-r--r--backend/src/libocl/tmpl/ocl_math_20.tmpl.cl3678
-rw-r--r--backend/src/libocl/tmpl/ocl_math_20.tmpl.h177
-rw-r--r--backend/src/libocl/tmpl/ocl_math_common.tmpl.cl3436
-rw-r--r--backend/src/libocl/tmpl/ocl_math_common.tmpl.h179
9 files changed, 4073 insertions, 7538 deletions
diff --git a/backend/src/libocl/script/ocl_math.def b/backend/src/libocl/script/ocl_math.def
index ea4ae8ae..a4e99c35 100644
--- a/backend/src/libocl/script/ocl_math.def
+++ b/backend/src/libocl/script/ocl_math.def
@@ -1,41 +1,4 @@
##math
-gentype acos (gentype)
-gentype acosh (gentype)
-gentype acospi (gentype x)
-gentype asin (gentype)
-gentype asinh (gentype)
-gentype asinpi (gentype x)
-gentype atan (gentype y_over_x)
-gentype atan2 (gentype y, gentype x)
-gentype atanh (gentype)
-gentype atanpi (gentype x)
-gentype atan2pi (gentype y, gentype x)
-gentype cbrt (gentype)
-gentype ceil (gentype)
-gentype copysign (gentype x, gentype y)
-gentype cos (gentype)
-gentype cosh (gentype)
-gentype cospi (gentype x)
-gentype erfc (gentype)
-gentype erf (gentype)
-gentype exp (gentype x)
-gentype exp2 (gentype)
-gentype exp10 (gentype)
-gentype expm1 (gentype x)
-gentype fabs (gentype)
-gentype fdim (gentype x, gentype y)
-gentype floor (gentype)
-# XXX we use madd for fma
-gentype fma (gentype a, gentype b, gentype c)
-gentype fmax (gentype x, gentype y)
-gentypef fmax (gentypef x, float y)
-gentypeh fmax (gentypeh x, half y)
-gentyped fmax (gentyped x, double y)
-gentype fmin (gentype x, gentype y)
-gentypef fmin (gentypef x, float y)
-gentypeh fmin (gentypeh x, half y)
-gentyped fmin (gentyped x, double y)
-gentype fmod (gentype x, gentype y)
gentype fract (gentype x, __global gentype *iptr)
gentype fract (gentype x, __local gentype *iptr)
gentype fract (gentype x, __private gentype *iptr)
@@ -57,20 +20,6 @@ doublen frexp (doublen x, __private intn *exp)
double frexp (double x, __global int *exp)
double frexp (double x, __local int *exp)
double frexp (double x, __private int *exp)
-gentype hypot (gentype x, gentype y)
-intn ilogb (floatn x)
-int ilogb (float x)
-shortn ilogb (halfn x)
-short ilogb (half x)
-int ilogb (double x)
-floatn ldexp (floatn x, intn k)
-floatn ldexp (floatn x, int k)
-float ldexp (float x, int k)
-halfn ldexp (halfn x, intn k)
-halfn ldexp (halfn x, int k)
-half ldexp (half x, int k)
-double ldexp (double x, int k)
-gentype lgamma (gentype x)
floatn lgamma_r (floatn x, __global intn *signp)
floatn lgamma_r (floatn x, __local intn *signp)
floatn lgamma_r (floatn x, __private intn *signp)
@@ -89,31 +38,9 @@ doublen lgamma_r (doublen x, __private intn *signp)
double lgamma_r (double x, __global int *signp)
double lgamma_r (double x, __local int *signp)
double lgamma_r (double x, __private int *signp)
-gentype log (gentype)
-gentype log2 (gentype)
-gentype log10 (gentype)
-gentype log1p (gentype x)
-gentype logb (gentype x)
-gentype mad (gentype a, gentype b, gentype c)
-gentype maxmag (gentype x, gentype y)
-gentype minmag (gentype x, gentype y)
gentype modf (gentype x, __global gentype *iptr)
gentype modf (gentype x, __local gentype *iptr)
gentype modf (gentype x, __private gentype *iptr)
-floatn nan (uintn nancode)
-float nan (uint nancode)
-halfn nan (ushortn nancode)
-half nan (ushort nancode)
-double nan (ulong nancode)
-gentype nextafter (gentype x, gentype y)
-gentype pow (gentype x, gentype y)
-floatn pown (floatn x, intn y)
-float pown (float x, int y)
-halfn pown (halfn x, intn y)
-half pown (half x, int y)
-double pown (double x, int y)
-gentype powr (gentype x, gentype y)
-gentype remainder (gentype x, gentype y)
floatn remquo (floatn x, floatn y, __global intn *quo)
floatn remquo (floatn x, floatn y, __local intn *quo)
floatn remquo (floatn x, floatn y, __private intn *quo)
@@ -132,55 +59,7 @@ doublen remquo (doublen x, doublen y, __private intn *quo)
double remquo (double x, double y, __global int *quo)
double remquo (double x, double y, __local int *quo)
double remquo (double x, double y, __private int *quo)
-gentype rint (gentype)
-floatn rootn (floatn x, intn y)
-halfn rootn (halfn x, intn y)
-gentype round (gentype x)
-gentype rsqrt (gentype)
-gentype sin (gentype)
gentype sincos (gentype x, __global gentype *cosval)
gentype sincos (gentype x, __local gentype *cosval)
gentype sincos (gentype x, __private gentype *cosval)
-gentype sinh (gentype)
-gentype sinpi (gentype x)
-gentype sqrt (gentype)
-gentype tan (gentype)
-gentype tanh (gentype)
-gentype tanpi (gentype x)
-gentype tgamma (gentype)
-gentype trunc (gentype)
-
-# XXX we already defined all native and non-native
-# functions to the same one.
-gentype native_cos (gentype x)
-gentype native_divide (gentype x, gentype y)
-gentype native_exp (gentype x)
-gentype native_exp2 (gentype x)
-gentype native_exp10 (gentype x)
-gentype native_log (gentype x)
-gentype native_log2 (gentype x)
-gentype native_log10 (gentype x)
-gentype native_powr (gentype x, gentype y)
-gentype native_recip (gentype x)
-gentype native_rsqrt (gentype x)
-gentype native_sin (gentype x)
-gentype native_sqrt (gentype x)
-gentype native_tan (gentype x)
-
-
-##half_native_math
-gentype half_cos (gentype x)
-gentype half_divide (gentype x, gentype y)
-gentype half_exp (gentype x)
-gentype half_exp2 (gentype x)
-gentype half_exp10 (gentype x)
-gentype half_log (gentype x)
-gentype half_log2 (gentype x)
-gentype half_log10 (gentype x)
-gentype half_powr (gentype x, gentype y)
-gentype half_recip (gentype x)
-gentype half_rsqrt (gentype x)
-gentype half_sin (gentype x)
-gentype half_sqrt (gentype x)
-gentype half_tan (gentype x)
diff --git a/backend/src/libocl/script/ocl_math_20.def b/backend/src/libocl/script/ocl_math_20.def
index b0e9d890..71558d16 100644
--- a/backend/src/libocl/script/ocl_math_20.def
+++ b/backend/src/libocl/script/ocl_math_20.def
@@ -1,39 +1,4 @@
##math
-gentype acos (gentype)
-gentype acosh (gentype)
-gentype acospi (gentype x)
-gentype asin (gentype)
-gentype asinh (gentype)
-gentype asinpi (gentype x)
-gentype atan (gentype y_over_x)
-gentype atan2 (gentype y, gentype x)
-gentype atanh (gentype)
-gentype atanpi (gentype x)
-gentype atan2pi (gentype y, gentype x)
-gentype cbrt (gentype)
-gentype ceil (gentype)
-gentype copysign (gentype x, gentype y)
-gentype cos (gentype)
-gentype cosh (gentype)
-gentype cospi (gentype x)
-gentype erfc (gentype)
-gentype erf (gentype)
-gentype exp (gentype x)
-gentype exp2 (gentype)
-gentype exp10 (gentype)
-gentype expm1 (gentype x)
-gentype fabs (gentype)
-gentype fdim (gentype x, gentype y)
-gentype floor (gentype)
-# XXX we use madd for fma
-gentype fma (gentype a, gentype b, gentype c)
-gentype fmax (gentype x, gentype y)
-gentypef fmax (gentypef x, float y)
-gentypeh fmax (gentypeh x, half y)
-gentype fmin (gentype x, gentype y)
-gentypef fmin (gentypef x, float y)
-gentypeh fmin (gentypeh x, half y)
-gentype fmod (gentype x, gentype y)
gentype fract (gentype x, __generic gentype *iptr)
floatn frexp (floatn x, __generic intn *exp)
float frexp (float x, __generic int *exp)
@@ -41,98 +6,18 @@ halfn frexp (halfn x, __generic intn *exp)
half frexp (half x, __generic int *exp)
doublen frexp (doublen x, __generic intn *exp)
double frexp (double x, __generic int *exp)
-gentype hypot (gentype x, gentype y)
-intn ilogb (floatn x)
-int ilogb (float x)
-shortn ilogb (halfn x)
-short ilogb (half x)
-floatn ldexp (floatn x, intn k)
-floatn ldexp (floatn x, int k)
-float ldexp (float x, int k)
-halfn ldexp (halfn x, intn k)
-halfn ldexp (halfn x, int k)
-half ldexp (half x, int k)
-gentype lgamma (gentype x)
floatn lgamma_r (floatn x, __generic intn *signp)
float lgamma_r (float x, __generic int *signp)
halfn lgamma_r (halfn x, __generic intn *signp)
half lgamma_r (half x, __generic int *signp)
doublen lgamma_r (doublen x, __generic intn *signp)
double lgamma_r (double x, __generic int *signp)
-gentype log (gentype)
-gentype log2 (gentype)
-gentype log10 (gentype)
-gentype log1p (gentype x)
-gentype logb (gentype x)
-gentype mad (gentype a, gentype b, gentype c)
-gentype maxmag (gentype x, gentype y)
-gentype minmag (gentype x, gentype y)
gentype modf (gentype x, __generic gentype *iptr)
-floatn nan (uintn nancode)
-float nan (uint nancode)
-halfn nan (ushortn nancode)
-half nan (ushort nancode)
-gentype nextafter (gentype x, gentype y)
-gentype pow (gentype x, gentype y)
-floatn pown (floatn x, intn y)
-float pown (float x, int y)
-halfn pown (halfn x, intn y)
-half pown (half x, int y)
-gentype powr (gentype x, gentype y)
-gentype remainder (gentype x, gentype y)
floatn remquo (floatn x, floatn y, __generic intn *quo)
float remquo (float x, float y, __generic int *quo)
halfn remquo (halfn x, halfn y, __generic intn *quo)
half remquo (half x, half y, __generic int *quo)
doublen remquo (doublen x, doublen y, __generic intn *quo)
double remquo (double x, double y, __generic int *quo)
-gentype rint (gentype)
-floatn rootn (floatn x, intn y)
-halfn rootn (halfn x, intn y)
-gentype round (gentype x)
-gentype rsqrt (gentype)
-gentype sin (gentype)
gentype sincos (gentype x, __generic gentype *cosval)
-gentype sinh (gentype)
-gentype sinpi (gentype x)
-gentype sqrt (gentype)
-gentype tan (gentype)
-gentype tanh (gentype)
-gentype tanpi (gentype x)
-gentype tgamma (gentype)
-gentype trunc (gentype)
-
-# XXX we already defined all native and non-native
-# functions to the same one.
-gentype native_cos (gentype x)
-gentype native_divide (gentype x, gentype y)
-gentype native_exp (gentype x)
-gentype native_exp2 (gentype x)
-gentype native_exp10 (gentype x)
-gentype native_log (gentype x)
-gentype native_log2 (gentype x)
-gentype native_log10 (gentype x)
-gentype native_powr (gentype x, gentype y)
-gentype native_recip (gentype x)
-gentype native_rsqrt (gentype x)
-gentype native_sin (gentype x)
-gentype native_sqrt (gentype x)
-gentype native_tan (gentype x)
-
-
-##half_native_math
-gentype half_cos (gentype x)
-gentype half_divide (gentype x, gentype y)
-gentype half_exp (gentype x)
-gentype half_exp2 (gentype x)
-gentype half_exp10 (gentype x)
-gentype half_log (gentype x)
-gentype half_log2 (gentype x)
-gentype half_log10 (gentype x)
-gentype half_powr (gentype x, gentype y)
-gentype half_recip (gentype x)
-gentype half_rsqrt (gentype x)
-gentype half_sin (gentype x)
-gentype half_sqrt (gentype x)
-gentype half_tan (gentype x)
diff --git a/backend/src/libocl/script/ocl_math_common.def b/backend/src/libocl/script/ocl_math_common.def
index b28f8af4..77829235 100644
--- a/backend/src/libocl/script/ocl_math_common.def
+++ b/backend/src/libocl/script/ocl_math_common.def
@@ -1,4 +1,127 @@
##math
+gentype acos (gentype)
+gentype acosh (gentype)
+gentype acospi (gentype x)
+gentype asin (gentype)
+gentype asinh (gentype)
+gentype asinpi (gentype x)
+gentype atan (gentype y_over_x)
+gentype atan2 (gentype y, gentype x)
+gentype atanh (gentype)
+gentype atanpi (gentype x)
+gentype atan2pi (gentype y, gentype x)
+gentype cbrt (gentype)
+gentype ceil (gentype)
+gentype copysign (gentype x, gentype y)
+gentype cos (gentype)
+gentype cosh (gentype)
+gentype cospi (gentype x)
+gentype erfc (gentype)
+gentype erf (gentype)
+gentype exp (gentype x)
+gentype exp2 (gentype)
+gentype exp10 (gentype)
+gentype expm1 (gentype x)
+gentype fabs (gentype)
+gentype fdim (gentype x, gentype y)
+gentype floor (gentype)
+# XXX we use madd for fma
+gentype fma (gentype a, gentype b, gentype c)
+gentype fmax (gentype x, gentype y)
+gentypef fmax (gentypef x, float y)
+gentypeh fmax (gentypeh x, half y)
+gentyped fmax (gentyped x, double y)
+gentype fmin (gentype x, gentype y)
+gentypef fmin (gentypef x, float y)
+gentypeh fmin (gentypeh x, half y)
+gentyped fmin (gentyped x, double y)
+gentype fmod (gentype x, gentype y)
+gentype hypot (gentype x, gentype y)
+intn ilogb (floatn x)
+int ilogb (float x)
+shortn ilogb (halfn x)
+short ilogb (half x)
+int ilogb (double x)
+floatn ldexp (floatn x, intn k)
+floatn ldexp (floatn x, int k)
+float ldexp (float x, int k)
+halfn ldexp (halfn x, intn k)
+halfn ldexp (halfn x, int k)
+half ldexp (half x, int k)
+double ldexp (double x, int k)
+gentype lgamma (gentype x)
+gentype log (gentype)
+gentype log2 (gentype)
+gentype log10 (gentype)
+gentype log1p (gentype x)
+gentype logb (gentype x)
+gentype mad (gentype a, gentype b, gentype c)
+gentype maxmag (gentype x, gentype y)
+gentype minmag (gentype x, gentype y)
+floatn nan (uintn nancode)
+float nan (uint nancode)
+halfn nan (ushortn nancode)
+half nan (ushort nancode)
+double nan (ulong nancode)
+gentype nextafter (gentype x, gentype y)
+gentype pow (gentype x, gentype y)
+floatn pown (floatn x, intn y)
+float pown (float x, int y)
+halfn pown (halfn x, intn y)
+half pown (half x, int y)
+double pown (double x, int y)
+gentype powr (gentype x, gentype y)
+gentype remainder (gentype x, gentype y)
+gentype rint (gentype)
+floatn rootn (floatn x, intn y)
+halfn rootn (halfn x, intn y)
+gentype round (gentype x)
+gentype rsqrt (gentype)
+gentype sin (gentype)
+gentype sinh (gentype)
+gentype sinpi (gentype x)
+gentype sqrt (gentype)
+gentype tan (gentype)
+gentype tanh (gentype)
+gentype tanpi (gentype x)
+gentype tgamma (gentype)
+gentype trunc (gentype)
+
+# XXX we already defined all native and non-native
+# functions to the same one.
+gentype native_cos (gentype x)
+gentype native_divide (gentype x, gentype y)
+gentype native_exp (gentype x)
+gentype native_exp2 (gentype x)
+gentype native_exp10 (gentype x)
+gentype native_log (gentype x)
+gentype native_log2 (gentype x)
+gentype native_log10 (gentype x)
+gentype native_powr (gentype x, gentype y)
+gentype native_recip (gentype x)
+gentype native_rsqrt (gentype x)
+gentype native_sin (gentype x)
+gentype native_sqrt (gentype x)
+gentype native_tan (gentype x)
+
+
+##half_native_math
+gentype half_cos (gentype x)
+gentype half_divide (gentype x, gentype y)
+gentype half_exp (gentype x)
+gentype half_exp2 (gentype x)
+gentype half_exp10 (gentype x)
+gentype half_log (gentype x)
+gentype half_log2 (gentype x)
+gentype half_log10 (gentype x)
+gentype half_powr (gentype x, gentype y)
+gentype half_recip (gentype x)
+gentype half_rsqrt (gentype x)
+gentype half_sin (gentype x)
+gentype half_sqrt (gentype x)
+gentype half_tan (gentype x)
+
+
double acos (double)
double acosh (double)
double acospi (double x)
diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.cl b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
index 98e295a1..594b7125 100644
--- a/backend/src/libocl/tmpl/ocl_math.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
@@ -21,7 +21,6 @@
#include "ocl_common.h"
#include "ocl_integer.h"
#include "ocl_convert.h"
-#include "ocl_printf.h"
extern constant int __ocl_math_fastpath_flag;
@@ -39,96 +38,6 @@ CONST float __gen_ocl_rnde(float x) __asm("llvm.rint" ".f32");
CONST float __gen_ocl_rndu(float x) __asm("llvm.ceil" ".f32");
CONST float __gen_ocl_rndd(float x) __asm("llvm.floor" ".f32");
-
-/* native functions */
-OVERLOADABLE float native_cos(float x) { return __gen_ocl_cos(x); }
-OVERLOADABLE float native_sin(float x) { return __gen_ocl_sin(x); }
-OVERLOADABLE float native_sqrt(float x) { return __gen_ocl_sqrt(x); }
-OVERLOADABLE float native_rsqrt(float x) { return __gen_ocl_rsqrt(x); }
-OVERLOADABLE float native_log2(float x) { return __gen_ocl_log(x); }
-OVERLOADABLE float native_log(float x) {
- return native_log2(x) * 0.6931472002f;
-}
-OVERLOADABLE float native_log10(float x) {
- return native_log2(x) * 0.3010299956f;
-}
-OVERLOADABLE float native_powr(float x, float y) { return __gen_ocl_pow(x,y); }
-OVERLOADABLE float native_recip(float x) { return __gen_ocl_rcp(x); }
-OVERLOADABLE float native_tan(float x) {
- return native_sin(x) / native_cos(x);
-}
-OVERLOADABLE float native_exp2(float x) { return __gen_ocl_exp(x); }
-OVERLOADABLE float native_exp(float x) { return __gen_ocl_exp(M_LOG2E_F*x); }
-OVERLOADABLE float native_exp10(float x) { return __gen_ocl_exp(M_LOG210_F*x); }
-OVERLOADABLE float native_divide(float x, float y) { return x/y; }
-
-/* Fast path */
-OVERLOADABLE float __gen_ocl_internal_fastpath_acosh (float x) {
- return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_asinh (float x) {
- return native_log(x + native_sqrt(x * x + 1));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_atanh (float x) {
- return 0.5f * native_log((1 + x) / (1 - x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cbrt (float x) {
- return __gen_ocl_pow(x, 0.3333333333f);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cos (float x) {
- return native_cos(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cosh (float x) {
- return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cospi (float x) {
- return __gen_ocl_cos(x * M_PI_F);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_exp (float x) {
- return native_exp(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_exp10 (float x) {
- return native_exp10(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_expm1 (float x) {
- return __gen_ocl_pow(M_E_F, x) - 1;
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_fmod (float x, float y) {
- return x-y*__gen_ocl_rndz(x/y);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_hypot (float x, float y) {
- return __gen_ocl_sqrt(x*x + y*y);
-}
-OVERLOADABLE int __gen_ocl_internal_fastpath_ilogb (float x) {
- return __gen_ocl_rndd(native_log2(x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_ldexp (float x, int n) {
- return __gen_ocl_pow(2, n) * x;
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log (float x) {
- return native_log(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log2 (float x) {
- return native_log2(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log10 (float x) {
- return native_log10(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log1p (float x) {
- return native_log(x + 1);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_logb (float x) {
- return __gen_ocl_rndd(native_log2(x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_remainder (float x, float y) {
- return x-y*__gen_ocl_rnde(x/y);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_rootn(float x, int n) {
- return __gen_ocl_pow(x, 1.f / n);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sin (float x) {
- return native_sin(x);
-}
OVERLOADABLE float __gen_ocl_internal_fastpath_sincos (float x, __global float *cosval) {
*cosval = native_cos(x);
return native_sin(x);
@@ -141,320 +50,8 @@ OVERLOADABLE float __gen_ocl_internal_fastpath_sincos (float x, __private float
*cosval = native_cos(x);
return native_sin(x);
}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sinh (float x) {
- return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sinpi (float x) {
- return __gen_ocl_sin(x * M_PI_F);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_tan (float x) {
- return native_tan(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_tanh (float x) {
- float y = native_exp(-2 * x);
- return (1 - y) / (1 + y);
-}
-
-/* Internal implement, high accuracy. */
-OVERLOADABLE float __gen_ocl_internal_floor(float x) { return __gen_ocl_rndd(x); }
-OVERLOADABLE float __gen_ocl_internal_copysign(float x, float y) {
- union { unsigned u; float f; } ux, uy;
- ux.f = x;
- uy.f = y;
- ux.u = (ux.u & 0x7fffffff) | (uy.u & 0x80000000u);
- return ux.f;
-}
-
-OVERLOADABLE float inline __gen_ocl_internal_log_valid(float x) {
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- union { unsigned int i; float f; } u;
- const float
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- two25 = 3.355443200e+07, /* 0x4c000000 */
- Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
- Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
- Lg3 = 2.8571429849e-01, /* 3E924925 */
- Lg4 = 2.2222198546e-01; /* 3E638E29 */
-
- const float zero = 0.0;
- float fsq, f, s, z, R, w, t1, t2, partial;
- int k, ix, i, j;
-
- u.f = x; ix = u.i;
- k = 0;
-
- k += (ix>>23) - 127;
- ix &= 0x007fffff;
- i = (ix + (0x95f64<<3)) & 0x800000;
- u.i = ix | (i^0x3f800000); x = u.f;
- k += (i>>23);
- f = x - 1.0f;
- fsq = f * f;
-
- if((0x007fffff & (15 + ix)) < 16) { /* |f| < 2**-20 */
- R = fsq * (0.5f - 0.33333333333333333f * f);
- return k * ln2_hi + k * ln2_lo + f - R;
- }
-
- s = f / (2.0f + f);
- z = s * s;
- i = ix - (0x6147a << 3);
- w = z * z;
- j = (0x6b851 << 3) - ix;
- t1= w * mad(w, Lg4, Lg2);
- t2= z * mad(w, Lg3, Lg1);
- i |= j;
- R = t2 + t1;
- partial = (i > 0) ? -mad(s, 0.5f * fsq, -0.5f * fsq) : (s * f);
-
- return mad(s, R, f) - partial + k * ln2_hi + k * ln2_lo;;
-}
-
-OVERLOADABLE float __gen_ocl_internal_log(float x)
-{
- union { unsigned int i; float f; } u;
- u.f = x;
- int ix = u.i;
-
- if (ix < 0 )
- return NAN; /* log(-#) = NaN */
- if (ix >= 0x7f800000)
- return NAN;
-
- return __gen_ocl_internal_log_valid(x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_log10(float x)
-{
- union { float f; unsigned i; } u;
- const float
- ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
- log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
- log10_2lo = 7.9034151668e-07; /* 0x355427db */
-
- float y, z;
- int i, k, hx;
-
- u.f = x; hx = u.i;
-
- if (hx<0)
- return NAN; /* log(-#) = NaN */
- if (hx >= 0x7f800000)
- return NAN;
-
- k = (hx >> 23) - 127;
- i = ((unsigned)k & 0x80000000) >> 31;
- hx = (hx&0x007fffff) | ((0x7f-i) << 23);
- y = (float)(k + i);
- u.i = hx; x = u.f;
-
- return y * log10_2lo + y * log10_2hi + ivln10 * __gen_ocl_internal_log_valid(x);
-}
-
-
-OVERLOADABLE float __gen_ocl_internal_log2(float x)
-{
- const float zero = 0.0,
- invln2 = 0x1.715476p+0f;
- int ix;
-
- union { float f; int i; } u;
- u.f = x; ix = u.i;
-
- if (ix < 0)
- return NAN; /** log(-#) = NaN */
- if (ix >= 0x7f800000)
- return NAN;
-
- return invln2 * __gen_ocl_internal_log_valid(x);
-}
-
-
-float __gen_ocl_scalbnf (float x, int n){
- /* copy from fdlibm */
- float two25 = 3.355443200e+07, /* 0x4c000000 */
- twom25 = 2.9802322388e-08, /* 0x33000000 */
- huge = 1.0e+30,
- tiny = 1.0e-30;
- int k,ix;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- k = (ix&0x7f800000)>>23; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((ix&0x7fffffff)==0) return x; /* +-0 */
- x *= two25;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- k = ((ix&0x7f800000)>>23) - 25;
- }
- if (k==0xff) return x+x; /* NaN or Inf */
- if (n< -50000)
- return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
- if (n> 50000 || k+n > 0xfe)
- return huge*__gen_ocl_internal_copysign(huge,x); /* overflow */
- /* Now k and n are bounded we know that k = k+n does not overflow. */
- k = k+n;
- if (k > 0) { /* normal result */
- GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
- return x;
- }
- if (k <= -25)
- return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
- k += 25; /* subnormal result */
- GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
- return x*twom25;
-}
-
-const __constant unsigned int two_over_pi[] = {
-0, 0, 0xA2F, 0x983, 0x6E4, 0xe44, 0x152, 0x9FC,
-0x275, 0x7D1, 0xF53, 0x4DD, 0xC0D, 0xB62,
-0x959, 0x93C, 0x439, 0x041, 0xFE5, 0x163,
-};
-
-// The main idea is from "Radian Reduction for Trigonometric Functions"
-// written by Mary H. Payne and Robert N. Hanek. Also another reference
-// is "A Continued-Fraction Analysis of Trigonometric Argument Reduction"
-// written by Roger Alan Smith, who gave the worst case in this paper.
-// for single float, worst x = 0x1.47d0fep34, and there are 29 bit
-// leading zeros in the fraction part of x*(2.0/pi). so we need at least
-// 29 (leading zero)+ 24 (fraction )+12 (integer) + guard bits. that is,
-// 65 + guard bits, as we calculate in 12*7 = 84bits, which means we have
-// about 19 guard bits. If we need further precision, we may need more
-// guard bits
-// Note we place two 0 in two_over_pi, which is used to handle input less
-// than 0x1.0p23
-
-int payne_hanek(float x, float *y) {
- union { float f; unsigned u;} ieee;
- ieee.f = x;
- unsigned u = ieee.u;
- int k = ((u & 0x7f800000) >> 23)-127;
- int ma = (u & 0x7fffff) | 0x800000;
- unsigned high, low;
- high = (ma & 0xfff000) >> 12;
- low = ma & 0xfff;
-
- // Two tune below macro, you need to fully understand the algorithm
-#define CALC_BLOCKS 7
-#define ZERO_BITS 2
-
- unsigned result[CALC_BLOCKS];
-
- // round down, note we need 2 bits integer precision
- int index = (k-23-2) < 0 ? (k-23-2-11)/12 : (k-23-2)/12;
-
- for (int i = 0; i < CALC_BLOCKS; i++) {
- result[i] = low * two_over_pi[index+i+ZERO_BITS] ;
- result[i] += high * two_over_pi[index+i+1+ZERO_BITS];
- }
-
- for (int i = CALC_BLOCKS-1; i > 0; i--) {
- int temp = result[i] >> 12;
- result[i] -= temp << 12;
- result[i-1] += temp;
- }
-#undef CALC_BLOCKS
-#undef ZERO_BITS
-
- // get number of integer digits in result[0], note we only consider 12 valid bits
- // and also it means the fraction digits in result[0] is (12-intDigit)
-
- int intDigit = index*(-12) + (k-23);
-
- // As the integer bits may be all included in result[0], and also maybe
- // some bits in result[0], and some in result[1]. So we merge succesive bits,
- // which makes easy coding.
-
- unsigned b0 = (result[0] << 12) | result[1];
- unsigned b1 = (result[2] << 12) | result[3];
- unsigned b2 = (result[4] << 12) | result[5];
- unsigned b3 = (result[6] << 12);
-
- unsigned intPart = b0 >> (24-intDigit);
-
- unsigned fract1 = ((b0 << intDigit) | (b1 >> (24-intDigit))) & 0xffffff;
- unsigned fract2 = ((b1 << intDigit) | (b2 >> (24-intDigit))) & 0xffffff;
- unsigned fract3 = ((b2 << intDigit) | (b3 >> (24-intDigit))) & 0xffffff;
-
- // larger than 0.5? which mean larger than pi/4, we need
- // transform from [0,pi/2] to [-pi/4, pi/4] through -(1.0-fract)
- int largerPiBy4 = ((fract1 & 0x800000) != 0);
- int sign = largerPiBy4 ? 1 : 0;
- intPart = largerPiBy4 ? (intPart+1) : intPart;
-
- fract1 = largerPiBy4 ? (fract1 ^ 0x00ffffff) : fract1;
- fract2 = largerPiBy4 ? (fract2 ^ 0x00ffffff) : fract2;
- fract3 = largerPiBy4 ? (fract3 ^ 0x00ffffff) : fract3;
-
- int leadingZero = (fract1 == 0);
-
- // +1 is for the hidden bit 1 in floating-point format
- int exponent = leadingZero ? -(24+1) : -(0+1);
-
- fract1 = leadingZero ? fract2 : fract1;
- fract2 = leadingZero ? fract3 : fract2;
-
- // fract1 may have leading zeros, add it
- int shift = clz(fract1)-8;
- exponent += -shift;
-
- float pio2 = 0x1.921fb6p+0;
- unsigned fdigit = ((fract1 << shift) | (fract2 >> (24-shift))) & 0xffffff;
-
- // we know that denormal number will not appear here
- ieee.u = (sign << 31) | ((exponent+127) << 23) | (fdigit & 0x7fffff);
- *y = ieee.f * pio2;
- return intPart;
-}
-
-int argumentReduceSmall(float x, float * remainder) {
- union {
- float f;
- unsigned u;
- } ieee;
-
- float twoByPi = 2.0f/3.14159265f;
- float piBy2_1h = (float) 0xc90/0x1.0p11,
- piBy2_1l = (float) 0xfda/0x1.0p23,
- piBy2_2h = (float) 0xa22/0x1.0p35,
- piBy2_2l = (float) 0x168/0x1.0p47,
- piBy2_3h = (float) 0xc23/0x1.0p59,
- piBy2_3l = (float) 0x4c4/0x1.0p71;
-
- float y = (float)(int)(twoByPi * x + 0.5f);
- ieee.f = y;
- ieee.u = ieee.u & 0xfffff000;
-
- float yh = ieee.f;
- float yl = y - yh;
- float rem = x - yh*piBy2_1h - yh*piBy2_1l - yl*piBy2_1h - yl*piBy2_1l;
- rem = rem - yh*piBy2_2h - yh*piBy2_2l + yl*piBy2_2h + yl*piBy2_2l;
- rem = rem - yh*piBy2_3h - yh*piBy2_3l - yl*piBy2_3h - yl*piBy2_3l;
-
- *remainder = rem;
- return (int)y;
-}
-
-
-int __ieee754_rem_pio2f(float x, float *y) {
- if (x < 4000.0f) {
- return argumentReduceSmall(x, y);
- } else {
- return payne_hanek(x, y);
- }
-}
-
-OVERLOADABLE float __kernel_sinf(float x)
+OVERLOADABLE float __kernel_sinf_12(float x)
{
/* copied from fdlibm */
const float
@@ -470,7 +67,7 @@ OVERLOADABLE float __kernel_sinf(float x)
return mad(v, r, x);
}
-float __kernel_cosf(float x, float y)
+float __kernel_cosf_12(float x, float y)
{
/* copied from fdlibm */
const float
@@ -495,402 +92,153 @@ float __kernel_cosf(float x, float y)
}
}
-OVERLOADABLE float sin(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sin(x);
-
- const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
- float y,z=0.0;
- int n, ix;
-
- float negative = x < 0.0f? -1.0f : 1.0f;
- x = fabs(x);
-
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
-
- /* sin(Inf or NaN) is NaN */
- if (ix >= 0x7f800000) return x-x;
-
- if(x <= pio4)
- return negative * __kernel_sinf(x);
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- float s = __kernel_sinf(y);
- float c = __kernel_cosf(y,0.0f);
- float ret = (n&1) ? negative*c : negative*s;
- return (n&3)> 1? -1.0f*ret : ret;
- }
-}
-
-OVERLOADABLE float cos(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cos(x);
-
- const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
- float y,z=0.0;
- int n, ix;
- x = __gen_ocl_fabs(x);
- GEN_OCL_GET_FLOAT_WORD(ix,x);
-
- ix &= 0x7fffffff;
-
- /* cos(Inf or NaN) is NaN */
- if (ix >= 0x7f800000) return x-x;
-
- if(x <= pio4)
- return __kernel_cosf(x, 0.f);
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- n &= 3;
- float c = __kernel_cosf(y, 0.0f);
- float s = __kernel_sinf(y);
- float v = (n&1) ? s : c;
- /* n&3 return
- 0 cos(y)
- 1 -sin(y)
- 2 -cos(y)
- 3 sin(y)
- */
- int mask = (n>>1) ^ n;
- float sign = (mask&1) ? -1.0f : 1.0f;
- return sign * v;
- }
-}
-
-float __kernel_tanf(float x, float y, int iy)
-{
- /* copied from fdlibm */
- float z,r,v,w,s;
- int ix,hx;
- const float
- one = 1.0000000000e+00, /* 0x3f800000 */
- pio4 = 7.8539812565e-01, /* 0x3f490fda */
- pio4lo= 3.7748947079e-08; /* 0x33222168 */
- float T[13];// = {
- T[0] = 3.3333334327e-01; /* 0x3eaaaaab */
- T[1] = 1.3333334029e-01; /* 0x3e088889 */
- T[2] = 5.3968254477e-02; /* 0x3d5d0dd1 */
- T[3] = 2.1869488060e-02; /* 0x3cb327a4 */
- T[4] = 8.8632395491e-03; /* 0x3c11371f */
- T[5] = 3.5920790397e-03; /* 0x3b6b6916 */
- T[6] = 1.4562094584e-03; /* 0x3abede48 */
- T[7] = 5.8804126456e-04; /* 0x3a1a26c8 */
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff; /* high word of |x| */
- if(ix<0x31800000) /* x < 2**-28 */
- {if((int)x==0) { /* generate inexact */
- if((ix|(iy+1))==0) return one/__gen_ocl_fabs(x);
- else return (iy==1)? x: -one/x;
- }
- }
- if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
- if(hx<0) {x = -x; y = -y;}
- z = pio4-x;
- w = pio4lo-y;
- x = z+w; y = 0.0;
- }
- z = x*x;
- w = z*z;
- /* Break x^5*(T[1]+x^2*T[2]+...) into
- * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
- * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
- */
-
- r = mad(w, mad(w, mad(w, T[7], T[5]), T[3]), T[1]);
- v = z* mad(w, mad(w, T[6], T[4]), T[2]);
-
- s = z*x;
- r = mad(z, mad(s, r + v, y), y);
- r += T[0]*s;
- w = x+r;
- if(ix>=0x3f2ca140) {
- v = (float)iy;
- return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
- }
- if(iy==1) return w;
- else
- return -1.0/(x+r);
-}
-
-OVERLOADABLE float tan(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_tan(x);
-
- float y,z=0.0;
- int n, ix;
- float negative = x < 0.0f? -1.0f : 1.0f;
- x = negative * x;
-
- GEN_OCL_GET_FLOAT_WORD(ix,x);
-
- ix &= 0x7fffffff;
-
- /* tan(Inf or NaN) is NaN */
- if (ix>=0x7f800000) return x-x; /* NaN */
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- return negative * __kernel_tanf(y,0.0f,1-((n&1)<<1)); /* 1 -- n even
- -1 -- n odd */
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_cospi(float x) {
- int ix;
- if(isinf(x) || isnan(x)) { return NAN; }
- if(x < 0.0f) { x = -x; }
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- if(x> 0x1.0p24) return 1.0f;
- float m = __gen_ocl_internal_floor(x);
- ix = (int)m;
- m = x-m;
- if((ix&0x1) != 0) m+=1.0f;
- ix = __gen_ocl_internal_floor(m*4.0f);
-
- switch(ix) {
- case 0:
- return __kernel_cosf(m*M_PI_F, 0.0f);
- case 1:
- case 2:
- return __kernel_sinf((0.5f-m)*M_PI_F);
- case 3:
- case 4:
- return -__kernel_cosf((m-1.0f)*M_PI_F, 0.0f);
- case 5:
- case 6:
- return __kernel_sinf((m-1.5f)*M_PI_F);
- default:
- return __kernel_cosf((2.0f-m)*M_PI_F, 0.0f);
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_sinpi(float x) {
+OVERLOADABLE float __gen_ocl_internal_floor_12(float x) { return __gen_ocl_rndd(x); }
+OVERLOADABLE float __gen_ocl_internal_sinpi_12(float x) {
float sign = 1.0f;
int ix;
if(isinf(x)) return NAN;
if(x < 0.0f) { x = -x; sign = -1.0f; }
GEN_OCL_GET_FLOAT_WORD(ix, x);
if(x> 0x1.0p24) return 0.0f;
- float m = __gen_ocl_internal_floor(x);
+ float m = __gen_ocl_internal_floor_12(x);
ix = (int)m;
m = x-m;
if((ix&0x1) != 0) m+=1.0f;
- ix = __gen_ocl_internal_floor(m*4.0f);
+ ix = __gen_ocl_internal_floor_12(m*4.0f);
switch(ix) {
case 0:
- return sign*__kernel_sinf(m*M_PI_F);
+ return sign*__kernel_sinf_12(m*M_PI_F);
case 1:
case 2:
- return sign*__kernel_cosf((m-0.5f)*M_PI_F, 0.0f);
+ return sign*__kernel_cosf_12((m-0.5f)*M_PI_F, 0.0f);
case 3:
case 4:
- return -sign*__kernel_sinf((m-1.0f)*M_PI_F);
+ return -sign*__kernel_sinf_12((m-1.0f)*M_PI_F);
case 5:
case 6:
- return -sign*__kernel_cosf((m-1.5f)*M_PI_F, 0.0f);
+ return -sign*__kernel_cosf_12((m-1.5f)*M_PI_F, 0.0f);
default:
- return -sign*__kernel_sinf((2.0f-m)*M_PI_F);
+ return -sign*__kernel_sinf_12((2.0f-m)*M_PI_F);
}
}
-OVERLOADABLE float lgamma(float x) {
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- const float
- zero= 0.,
- one = 1.0000000000e+00,
- pi = 3.1415927410e+00,
- a0 = 7.7215664089e-02,
- a1 = 3.2246702909e-01,
- a2 = 6.7352302372e-02,
- a3 = 2.0580807701e-02,
- a4 = 7.3855509982e-03,
- a5 = 2.8905137442e-03,
- a6 = 1.1927076848e-03,
- a7 = 5.1006977446e-04,
- a8 = 2.2086278477e-04,
- a9 = 1.0801156895e-04,
- a10 = 2.5214456400e-05,
- a11 = 4.4864096708e-05,
- tc = 1.4616321325e+00,
- tf = -1.2148628384e-01,
- tt = 6.6971006518e-09,
- t0 = 4.8383611441e-01,
- t1 = -1.4758771658e-01,
- t2 = 6.4624942839e-02,
- t3 = -3.2788541168e-02,
- t4 = 1.7970675603e-02,
- t5 = -1.0314224288e-02,
- t6 = 6.1005386524e-03,
- t7 = -3.6845202558e-03,
- t8 = 2.2596477065e-03,
- t9 = -1.4034647029e-03,
- t10 = 8.8108185446e-04,
- t11 = -5.3859531181e-04,
- t12 = 3.1563205994e-04,
- t13 = -3.1275415677e-04,
- t14 = 3.3552918467e-04,
- u0 = -7.7215664089e-02,
- u1 = 6.3282704353e-01,
- u2 = 1.4549225569e+00,
- u3 = 9.7771751881e-01,
- u4 = 2.2896373272e-01,
- u5 = 1.3381091878e-02,
- v1 = 2.4559779167e+00,
- v2 = 2.1284897327e+00,
- v3 = 7.6928514242e-01,
- v4 = 1.0422264785e-01,
- v5 = 3.2170924824e-03,
- s0 = -7.7215664089e-02,
- s1 = 2.1498242021e-01,
- s2 = 3.2577878237e-01,
- s3 = 1.4635047317e-01,
- s4 = 2.6642270386e-02,
- s5 = 1.8402845599e-03,
- s6 = 3.1947532989e-05,
- r1 = 1.3920053244e+00,
- r2 = 7.2193557024e-01,
- r3 = 1.7193385959e-01,
- r4 = 1.8645919859e-02,
- r5 = 7.7794247773e-04,
- r6 = 7.3266842264e-06,
- w0 = 4.1893854737e-01,
- w1 = 8.3333335817e-02,
- w2 = -2.7777778450e-03,
- w3 = 7.9365057172e-04,
- w4 = -5.9518753551e-04,
- w5 = 8.3633989561e-04,
- w6 = -1.6309292987e-03;
- float t, y, z, nadj, p, p1, p2, p3, q, r, w;
- int i, hx, ix;
- nadj = 0;
- hx = *(int *)&x;
- ix = hx & 0x7fffffff;
- if (ix >= 0x7f800000)
- return x * x;
- if (ix == 0)
- return ((x + one) / zero);
- if (ix < 0x1c800000) {
- if (hx < 0) {
- return -native_log(-x);
- } else
- return -native_log(x);
- }
- if (hx < 0) {
- if (ix >= 0x4b000000)
- return ((-x) / zero);
- t = __gen_ocl_internal_sinpi(x);
- if (t == zero)
- return ((-x) / zero);
- nadj = native_log(pi / __gen_ocl_fabs(t * x));
- x = -x;
- }
- if (ix == 0x3f800000 || ix == 0x40000000)
- r = 0;
- else if (ix < 0x40000000) {
- if (ix <= 0x3f666666) {
- r = -native_log(x);
- if (ix >= 0x3f3b4a20) {
- y = one - x;
- i = 0;
- } else if (ix >= 0x3e6d3308) {
- y = x - (tc - one);
- i = 1;
- } else {
- y = x;
- i = 2;
- }
- } else {
- r = zero;
- if (ix >= 0x3fdda618) {
- y = (float) 2.0 - x;
- i = 0;
- }
- else if (ix >= 0x3F9da620) {
- y = x - tc;
- i = 1;
- }
- else {
- y = x - one;
- i = 2;
- }
- }
- switch (i) {
- case 0:
- z = y * y;
- p1 = mad(z, mad(z, mad(z, mad(z, mad(z, a10, a8), a6), a4), a2), a0);
- p2 = z * mad(z, mad(z, mad(z, mad(z, mad(z, a11, a9), a7), a5), a3), a1);
- p = mad(y, p1, p2);
- r += (p - (float) 0.5 * y);
- break;
- case 1:
- z = y * y;
- w = z * y;
- p1 = mad(w, mad(w, mad(w, mad(w, t12, t9), t6), t3), t0);
- p2 = mad(w, mad(w, mad(w, mad(w, t13, t10), t7), t4), t1);
- p3 = mad(w, mad(w, mad(w, mad(w, t14, t11), t8), t5), t2);
- p = mad(p1, z, mad(w, mad(y, p3, p2), -tt));
- r += (tf + p);
- break;
- case 2:
- p1 = y * mad(y, mad(y, mad(y, mad(y, mad(y, u5, u4), u3), u2), u1), u0);
- p2 = mad(y, mad(y, mad(y, mad(y, mad(y, v5, v4), v3), v2), v1), one);
- r += (-(float) 0.5 * y + p1 / p2);
- }
- } else if (ix < 0x41000000) {
- i = (int) x;
- t = zero;
- y = x - (float) i;
+#define BODY \
+ if (isnan(x)) { \
+ *p = x; \
+ return x; \
+ } \
+ *p = __gen_ocl_rndd(x); \
+ if (isinf(x)) { \
+ return x > 0 ? +0. : -0.; \
+ } \
+ return min(x - *p, 0x1.FFFFFep-1F);
+OVERLOADABLE float fract(float x, global float *p) { BODY; }
+OVERLOADABLE float fract(float x, local float *p) { BODY; }
+OVERLOADABLE float fract(float x, private float *p) { BODY; }
+#undef BODY
+
+OVERLOADABLE half fract(half x, global half *p) {
+ float _x = (float)x;
+ float _p;
+ half ret = (half)fract(_x, &_p);
+ *p = (half)_p;
+ return ret;
+}
+OVERLOADABLE half fract(half x, local half *p) {
+ float _x = (float)x;
+ float _p;
+ half ret = (half)fract(_x, &_p);
+ *p = (half)_p;
+ return ret;
+}
+OVERLOADABLE half fract(half x, private half *p) {
+ float _x = (float)x;
+ float _p;
+ half ret = (half)fract(_x, &_p);
+ *p = (half)_p;
+ return ret;
+}
- p =y * mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, s6, s5), s4), s3), s2), s1), s0);
- q = mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, r6, r5), r4), r3), r2), r1), one);
- r = .5f * y + p / q;
- z = one;
+#define BODY \
+ if (isnan(x) || isinf(x)) { \
+ *exp = 0; \
+ return x; \
+ } \
+ uint u = as_uint(x); \
+ uint a = u & 0x7FFFFFFFu; \
+ if (a == 0) { \
+ *exp = 0; \
+ return x; \
+ } \
+ if (a >= 0x800000) { \
+ *exp = (a >> 23) - 126; \
+ return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
+ } \
+ int e = -126; \
+ while (a < 0x400000) { \
+ e --; \
+ a <<= 1; \
+ } \
+ a <<= 1; \
+ *exp = e; \
+ return as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
+OVERLOADABLE float frexp(float x, global int *exp) { BODY; }
+OVERLOADABLE float frexp(float x, local int *exp) { BODY; }
+OVERLOADABLE float frexp(float x, private int *exp) { BODY; }
+#undef BODY
- switch (i) {
- case 7:
- z *= (y + 6.0f);
- case 6:
- z *= (y + 5.0f);
- case 5:
- z *= (y + 4.0f);
- case 4:
- z *= (y + 3.0f);
- case 3:
- z *= (y + 2.0f);
- r += native_log(z);
- break;
- }
+OVERLOADABLE half frexp(half x, global int *exp) {
+ float _x = (float)x;
+ return (half)frexp(_x, exp);
+}
+OVERLOADABLE half frexp(half x, local int *exp) {
+ float _x = (float)x;
+ return (half)frexp(_x, exp);
+}
+OVERLOADABLE half frexp(half x, private int *exp) {
+ float _x = (float)x;
+ return (half)frexp(_x, exp);
+}
- } else if (ix < 0x5c800000) {
- t = native_log(x);
- z = one / x;
- y = z * z;
- w = mad(z, mad(y, mad(y, mad(y, mad(y, mad(y, w6, w5), w4), w3), w2), w1), w0);
- r = (x - .5f) * (t - one) + w;
- } else
- r = x * (native_log(x) - one);
- if (hx < 0)
- r = nadj - r;
- return r;
+#define BODY \
+ uint hx = as_uint(x), ix = hx & 0x7FFFFFFF; \
+ if (ix > 0x7F800000) { \
+ *i = nan(0u); \
+ return nan(0u); \
+ } \
+ if (ix == 0x7F800000) { \
+ *i = x; \
+ return as_float(hx & 0x80000000u); \
+ } \
+ *i = __gen_ocl_rndz(x); \
+ return x - *i;
+OVERLOADABLE float modf(float x, global float *i) { BODY; }
+OVERLOADABLE float modf(float x, local float *i) { BODY; }
+OVERLOADABLE float modf(float x, private float *i) { BODY; }
+#undef BODY
+
+OVERLOADABLE half modf(half x, global half *i) {
+ float _x = (float)x;
+ float _i;
+ half ret = (half)modf(_x, &_i);
+ *i = (half)_i;
+ return ret;
+}
+OVERLOADABLE half modf(half x, local half *i) {
+ float _x = (float)x;
+ float _i;
+ half ret = (half)modf(_x, &_i);
+ *i = (half)_i;
+ return ret;
+}
+OVERLOADABLE half modf(half x, private half *i) {
+ float _x = (float)x;
+ float _i;
+ half ret = (half)modf(_x, &_i);
+ *i = (half)_i;
+ return ret;
}
/*
@@ -989,7 +337,7 @@ OVERLOADABLE float lgamma(float x) {
if (hx < 0) { \
if (ix >= 0x4b000000) \
return ((-x) / zero); \
- t = __gen_ocl_internal_sinpi(x); \
+ t = __gen_ocl_internal_sinpi_12(x); \
if (t == zero) \
return ((-x) / zero); \
nadj = native_log(pi / __gen_ocl_fabs(t * x)); \
@@ -1088,2089 +436,20 @@ OVERLOADABLE float lgamma_r(float x, local int *signgamp) { BODY; }
OVERLOADABLE float lgamma_r(float x, private int *signgamp) { BODY; }
#undef BODY
-OVERLOADABLE float log1p(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log1p(x);
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- const float
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- two25 = 3.355443200e+07, /* 0x4c000000 */
- Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
- Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
- Lp3 = 2.8571429849e-01, /* 3E924925 */
- Lp4 = 2.2222198546e-01; /* 3E638E29 */
- const float zero = 0.0;
- float hfsq,f,c,s,z,R,u;
- int k,hx,hu,ax;
- union {float f; unsigned i;} un;
- un.f = x; hx = un.i;
- ax = hx&0x7fffffff;
-
- k = 1;
- if (hx < 0x3ed413d7) { /* x < 0.41422 */
- if(ax>=0x3f800000) { /* x <= -1.0 */
- if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
- else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
- }
- if(ax<0x31000000) { /* |x| < 2**-29 */
- if(two25+x>zero /* raise inexact */
- &&ax<0x24800000) /* |x| < 2**-54 */
- return x;
- else
- return x - x*x*(float)0.5;
- }
- if(hx>0||hx<=((int)0xbe95f61f)) {
- k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
- }
- if (hx >= 0x7f800000) return x+x;
- if(k!=0) {
- if(hx<0x5a000000) {
- u = (float)1.0+x;
-
- un.f = u; hu = un.i;
- k = (hu>>23)-127;
- /* correction term */
- c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
- c /= u;
- } else {
- u = x;
- un.f = u; hu = un.i;
- k = (hu>>23)-127;
- c = 0;
- }
- hu &= 0x007fffff;
- if(hu<0x3504f7) {
- un.i = hu|0x3f800000; u = un.f;/* normalize u */
- } else {
- k += 1;
- un.i = hu|0x3f000000; u = un.f; /* normalize u/2 */
- hu = (0x00800000-hu)>>2;
- }
- f = u-(float)1.0;
- }
- hfsq=(float)0.5*f*f;
- if(hu==0)
- { /* |f| < 2**-20 */
- if(f==zero)
- {
- if(k==0) return zero;
- else {c = mad(k , ln2_lo, c); return mad(k, ln2_hi, c);}
- }
- R = mad(hfsq, 1.0f, -0.66666666666666666f * f);
- if(k==0) return f-R; else
- return k * ln2_hi - (R - mad(k, ln2_lo, c) - f);
- }
- s = f/((float)2.0+f);
- z = s*s;
- R = z * mad(z, mad(z, mad(z, Lp4, Lp3), Lp2), Lp1);
- if(k==0)
- return f + mad(hfsq + R, s, -hfsq);
- else
- return k*ln2_hi-( (hfsq - mad(s, hfsq + R, mad(k, ln2_lo, c))) - f);
-}
-
-OVERLOADABLE float logb(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_logb(x);
-
- union {float f; unsigned i;} u;
- u.f = x;
- int e = ((u.i & 0x7f800000) >> 23);
- float r1 = e-127;
- float r2 = -INFINITY;
- float r3 = x*x;
- /* sub normal or +/-0 */
- float r = e == 0 ? r2 : r1;
- /* inf & nan */
- return e == 0xff ? r3 : r;
-}
-
-OVERLOADABLE int ilogb(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_ilogb(x);
-
- union { int i; float f; } u;
- if (isnan(x))
- return FP_ILOGBNAN;
- if (isinf(x))
- return 0x7FFFFFFF;
- u.f = x;
- u.i &= 0x7fffffff;
- if (u.i == 0)
- return FP_ILOGB0;
- if (u.i >= 0x800000)
- return (u.i >> 23) - 127;
- int r = -126;
- int a = u.i & 0x7FFFFF;
- while(a < 0x800000) {
- a <<= 1;
- r --;
- }
- return r;
-}
-OVERLOADABLE float nan(uint code) {
- return NAN;
-}
-OVERLOADABLE float __gen_ocl_internal_tanpi(float x) {
- float sign = 1.0f;
- int ix;
- if(isinf(x)) return NAN;
- if(x < 0.0f) { x = -x; sign = -1.0f; }
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- if(x> 0x1.0p24) return 0.0f;
- float m = __gen_ocl_internal_floor(x);
- ix = (int)m;
- m = x-m;
- int n = __gen_ocl_internal_floor(m*4.0f);
- if(m == 0.5f) {
- return (ix&0x1) == 0 ? sign*INFINITY : sign*-INFINITY;
- }
- if(m == 0.0f) {
- return (ix&0x1) == 0 ? 0.0f : -0.0f;
- }
-
- switch(n) {
- case 0:
- return sign * __kernel_tanf(m*M_PI_F, 0.0f, 1);
- case 1:
- return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
- case 2:
- return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
- default:
- return sign * -1.0f*__kernel_tanf((1.0f-m)*M_PI_F, 0.0f, 1);
- }
-}
-OVERLOADABLE float __gen_ocl_internal_cbrt(float x) {
- /* copied from fdlibm */
- const unsigned
- B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
- B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
-
- const float
- C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
- D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
- E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
- F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
- G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
-
- float r,s,t, w;
- int hx;
- uint sign;
- uint high;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- sign=hx&0x80000000; /* sign= sign(x) */
- hx ^=sign;
- if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
- if(hx==0)
- return(x); /* cbrt(0) is itself */
-
- GEN_OCL_SET_FLOAT_WORD(x,hx); /* x <- |x| */
- /* rough cbrt to 5 bits */
- if(hx<0x00800000) /* subnormal number */
- {
- //SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
- //t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
- t = (sign = 0) ? 0.0f : -0.0f;
- return t;
- }
- else
- GEN_OCL_SET_FLOAT_WORD(t,hx/3+B1);
-
-
- /* new cbrt to 23 bits */
- r=t*t/x;
- s=mad(r, t, C);
- t*=G+F/(s+E+D/s);
- /* one step newton iteration to 53 bits with error less than 0.667 ulps */
- s=t*t; /* t*t is exact */
- r=x/s;
- w=t+t;
- r=(r-t)/(w+r); /* r-s is exact */
- t=mad(t, r, t);
-
- /* retore the sign bit */
- GEN_OCL_GET_FLOAT_WORD(high,t);
- GEN_OCL_SET_FLOAT_WORD(t,high|sign);
- return(t);
-}
-
-#define BODY \
- *cosval = cos(x); \
- return sin(x);
-
-OVERLOADABLE float sincos(float x, global float *cosval) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sincos(x, cosval);
- BODY;
-}
-OVERLOADABLE float sincos(float x, local float *cosval) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sincos(x, cosval);
- BODY;
-}
-OVERLOADABLE float sincos(float x, private float *cosval) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sincos(x, cosval);
- BODY;
-}
-#undef BODY
-
-INLINE float __gen_ocl_asin_util(float x) {
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunSoft, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- float
- pS0 = 1.66666666666666657415e-01,
- pS1 = -3.25565818622400915405e-01,
- pS2 = 2.01212532134862925881e-01,
- pS3 = -4.00555345006794114027e-02,
- pS4 = 7.91534994289814532176e-04,
- qS1 = -2.40339491173441421878e+00,
- qS2 = 2.02094576023350569471e+00,
- qS3 = -6.88283971605453293030e-01,
- qS4 = 7.70381505559019352791e-02;
-
- float t = x*x;
- float p = t * mad(t, mad(t, mad(t, mad(t, pS4, pS3), pS2), pS1), pS0);
- float q = mad(t, mad(t, mad(t, mad(t, qS4, qS3), qS2), qS1), 1.0f);
- float w = p / q;
- return mad(x, w, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_asin(float x) {
- uint ix;
- union { uint i; float f; } u;
- u.f = x;
- ix = u.i & 0x7fffffff;
- if(ix == 0x3f800000) {
- return x * M_PI_2_F; /* asin(|1|)=+-pi/2 with inexact */
- }
- if(ix > 0x3f800000) { /* |x|>= 1 */
- return NAN; /* asin(|x|>1) is NaN */
- }
-
- if(ix < 0x32000000) { /* if |x| < 2**-27 */
- if(HUGE_VALF + x > FLT_ONE) return x; /* return x with inexact if x!=0*/
- }
-
- if(x < -0.5) {
- return 2 * __gen_ocl_asin_util(native_sqrt((1+x) / 2)) - M_PI_2_F;
- } else if(x > 0.5) {
- return M_PI_2_F - 2 * __gen_ocl_asin_util(native_sqrt((1-x) / 2));
- } else {
- return __gen_ocl_asin_util(x);
- }
-}
-OVERLOADABLE float __gen_ocl_internal_asinpi(float x) {
- return __gen_ocl_internal_asin(x) / M_PI_F;
-}
-OVERLOADABLE float __gen_ocl_internal_acos(float x) {
- if(x > 0.5)
- return 2 * __gen_ocl_asin_util(native_sqrt((1-x)/2));
- else
- return M_PI_2_F - __gen_ocl_internal_asin(x);
-}
-OVERLOADABLE float __gen_ocl_internal_acospi(float x) {
- return __gen_ocl_internal_acos(x) / M_PI_F;
-}
-__constant float atanhi[4] = {
- 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
- 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
- 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
- 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
-};
-__constant float atanlo[4] = {
- 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
- 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
- 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
- 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
-};
-
-OVERLOADABLE float __gen_ocl_internal_atan(float x) {
- /* copied from fdlibm */
- float aT[11];
- aT[0] = 3.3333334327e-01; /* 0x3eaaaaaa */
- aT[1] = -2.0000000298e-01; /* 0xbe4ccccd */
- aT[2] = 1.4285714924e-01; /* 0x3e124925 */
- aT[3] = -1.1111110449e-01; /* 0xbde38e38 */
- aT[4] = 9.0908870101e-02; /* 0x3dba2e6e */
- aT[5] = -7.6918758452e-02; /* 0xbd9d8795 */
- aT[6] = 6.6610731184e-02; /* 0x3d886b35 */
- const float one = 1.0, huge = 1.0e30;
-
- float w,s1,s2,z;
- int ix,hx,id;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x50800000) { /* if |x| >= 2^34 */
- if(ix>0x7f800000)
- return x+x; /* NaN */
- if(hx>0) return atanhi[3]+atanlo[3];
- else return -atanhi[3]-atanlo[3];
- } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
- if (ix < 0x31000000) { /* |x| < 2^-29 */
- if(huge+x>one) return x; /* raise inexact */
- }
- id = -1;
- } else {
- x = __gen_ocl_fabs(x);
- if (ix < 0x3f980000) { /* |x| < 1.1875 */
- if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
- id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
- } else { /* 11/16<=|x|< 19/16 */
- id = 1; x = (x-one)/(x+one);
- }
- } else {
- if (ix < 0x401c0000) { /* |x| < 2.4375 */
- id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
- } else { /* 2.4375 <= |x| < 2^66 */
- id = 3; x = -(float)1.0/x;
- }
- }}
- /* end of argument reduction */
- z = x*x;
- w = z*z;
- /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
- s1 = z * mad(w, mad(w, mad(w, aT[6], aT[4]), aT[2]), aT[0]);
- s2 = w * mad(w, mad(w, aT[5], aT[3]), aT[1]);
- if (id<0) return x - x*(s1+s2);
- else {
- z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
- return (hx<0)? -z:z;
- }
-
-}
-OVERLOADABLE float __gen_ocl_internal_atanpi(float x) {
- return __gen_ocl_internal_atan(x) / M_PI_F;
-}
-
-// XXX work-around PTX profile
-OVERLOADABLE float sqrt(float x) { return native_sqrt(x); }
-OVERLOADABLE float rsqrt(float x) { return native_rsqrt(x); }
-OVERLOADABLE float __gen_ocl_internal_atan2(float y, float x) {
- /* copied from fdlibm */
- float z;
- int k,m,hx,hy,ix,iy;
- const float
- tiny = 1.0e-30,
- zero = 0.0,
- pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
- pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
- pi = 3.1415927410e+00, /* 0x40490fdb */
- pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- iy = hy&0x7fffffff;
-
- if((ix>0x7f800000)||
- (iy>0x7f800000)) /* x or y is NaN */
- return x+y;
- if(hx==0x3f800000) return z=__gen_ocl_internal_atan(y); /* x=1.0 */
- m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
-
- /* when y = 0 */
- if(iy==0) {
- switch(m) {
- case 0:
- case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny;/* atan(+0,-anything) = pi */
- case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
- }
- }
- /* when x = 0 */
- if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
-
- /* both are denorms. Gen does not support denorm, so we convert to normal float number*/
- if(ix <= 0x7fffff && iy <= 0x7fffff) {
- x = (float)(ix) * (1.0f - ((hx>>30) & 0x2));
- y = (float)(iy) * (1.0f - ((hy>>30) & 0x2));
- }
-
- /* when x is INF */
- if(ix==0x7f800000) {
- if(iy==0x7f800000) {
- switch(m) {
- case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
- case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
- case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
- case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
- }
- } else {
- switch(m) {
- case 0: return zero ; /* atan(+...,+INF) */
- case 1: return -zero ; /* atan(-...,+INF) */
- case 2: return pi+tiny ; /* atan(+...,-INF) */
- case 3: return -pi-tiny ; /* atan(-...,-INF) */
- }
- }
- }
- /* when y is INF */
- if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
-
- /* compute y/x */
- k = (iy-ix)>>23;
- if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
- else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
- else z=__gen_ocl_internal_atan(__gen_ocl_fabs(y/x)); /* safe to do y/x */
- switch (m) {
- case 0: return z ; /* atan(+,+) */
- case 1: {
- uint zh;
- GEN_OCL_GET_FLOAT_WORD(zh,z);
- GEN_OCL_SET_FLOAT_WORD(z,zh ^ 0x80000000);
- }
- return z ; /* atan(-,+) */
- case 2: return pi-(z-pi_lo);/* atan(+,-) */
- default: /* case 3 */
- return (z-pi_lo)-pi;/* atan(-,-) */
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_atan2pi(float y, float x) {
- return __gen_ocl_internal_atan2(y, x) / M_PI_F;
-}
-OVERLOADABLE float __gen_ocl_internal_fabs(float x) { return __gen_ocl_fabs(x); }
-OVERLOADABLE float __gen_ocl_internal_trunc(float x) { return __gen_ocl_rndz(x); }
-OVERLOADABLE float __gen_ocl_internal_round(float x) {
- float y = __gen_ocl_rndz(x);
- if (__gen_ocl_fabs(x - y) >= 0.5f)
- y += __gen_ocl_internal_copysign(1.f, x);
- return y;
-}
-OVERLOADABLE float __gen_ocl_internal_ceil(float x) { return __gen_ocl_rndu(x); }
-OVERLOADABLE float __gen_ocl_internal_rint(float x) {
- return __gen_ocl_rnde(x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_exp(float x) {
- float o_threshold = 8.8721679688e+01, /* 0x42b17180 */
- u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
- twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- one = 1.0,
- huge = 1.0e+30,
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03; /* 0xbb360b61 */
- float y,hi=0.0,lo=0.0,c,t;
- int k=0,xsb;
- unsigned hx;
- float ln2HI_0 = 6.9313812256e-01; /* 0x3f317180 */
- float ln2HI_1 = -6.9313812256e-01; /* 0xbf317180 */
- float ln2LO_0 = 9.0580006145e-06; /* 0x3717f7d1 */
- float ln2LO_1 = -9.0580006145e-06; /* 0xb717f7d1 */
- float half_0 = 0.5;
- float half_1 = -0.5;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- xsb = (hx>>31)&1; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |x| */
-
- /* filter out non-finite argument */
- if(hx >= 0x42b17218) { /* if |x|>=88.721... */
- if(hx>0x7f800000)
- return x+x; /* NaN */
- if(hx==0x7f800000)
- return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
- if(x > o_threshold) return huge*huge; /* overflow */
- if(x < u_threshold) return twom100*twom100; /* underflow */
- }
- /* argument reduction */
- if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
- if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
- hi = x-(xsb ==1 ? ln2HI_1 : ln2HI_0); lo= xsb == 1? ln2LO_1 : ln2LO_0; k = 1-xsb-xsb;
- } else {
- float tmp = xsb == 1 ? half_1 : half_0;
- k = ivln2*x+tmp;
- t = k;
- hi = x - t*ln2HI_0; /* t*ln2HI is exact here */
- lo = t*ln2LO_0;
- }
- x = hi - lo;
- }
- else if(hx < 0x31800000) { /* when |x|<2**-28 */
- if(huge+x>one) return one+x;/* trigger inexact */
- }
- else k = 0;
-
- /* x is now in primary range */
- t = x*x;
- c = x - t*(P1+t*P2);
- if(k==0)
- return one-((x*c)/(c-(float)2.0)-x);
- else
- y = one-((lo-(x*c)/((float)2.0-c))-hi);
- if(k >= -125) {
- unsigned hy;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- GEN_OCL_SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
- return y;
- } else {
- unsigned hy;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- GEN_OCL_SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
- return y*twom100;
- }
-}
-
-/* erf,erfc from glibc s_erff.c -- float version of s_erf.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-INLINE_OVERLOADABLE float __gen_ocl_internal_erf(float x) {
-/*...*/
-const float
-tiny = 1.0e-30,
-half_val= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
- /* c = (subfloat)0.84506291151 */
-erx = 8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to erf on [0,0.84375]
- */
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
-efx8= 1.0270333290e+00, /* 0x3f8375d4 */
-pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
-pp1 = -3.2504209876e-01, /* 0xbea66beb */
-pp2 = -2.8481749818e-02, /* 0xbce9528f */
-pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
-qq2 = 6.5022252500e-02, /* 0x3d852a63 */
-qq3 = 5.0813062117e-03, /* 0x3ba68116 */
-qq4 = 1.3249473704e-04, /* 0x390aee49 */
-qq5 = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1 = 4.1485610604e-01, /* 0x3ed46805 */
-pa2 = -3.7220788002e-01, /* 0xbebe9208 */
-pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
-pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
-pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
-qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
-qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
-qa4 = 1.2617121637e-01, /* 0x3e013307 */
-qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
-qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
- /*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
- */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
-ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2 = -1.0558626175e+01, /* 0xc128f022 */
-ra3 = -6.2375331879e+01, /* 0xc2798057 */
-ra4 = -1.6239666748e+02, /* 0xc322658c */
-ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6 = -8.1287437439e+01, /* 0xc2a2932b */
-ra7 = -9.8143291473e+00, /* 0xc11d077e */
-sa1 = 1.9651271820e+01, /* 0x419d35ce */
-sa2 = 1.3765776062e+02, /* 0x4309a863 */
-sa3 = 4.3456588745e+02, /* 0x43d9486f */
-sa4 = 6.4538726807e+02, /* 0x442158c9 */
-sa5 = 4.2900814819e+02, /* 0x43d6810b */
-sa6 = 1.0863500214e+02, /* 0x42d9451f */
-sa7 = 6.5702495575e+00, /* 0x40d23f7c */
-sa8 = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to erfc in [1/.35,28]
- */
-rb0 = -9.8649431020e-03, /* 0xbc21a092 */
-rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2 = -1.7757955551e+01, /* 0xc18e104b */
-rb3 = -1.6063638306e+02, /* 0xc320a2ea */
-rb4 = -6.3756646729e+02, /* 0xc41f6441 */
-rb5 = -1.0250950928e+03, /* 0xc480230b */
-rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1 = 3.0338060379e+01, /* 0x41f2b459 */
-sb2 = 3.2579251099e+02, /* 0x43a2e571 */
-sb3 = 1.5367296143e+03, /* 0x44c01759 */
-sb4 = 3.1998581543e+03, /* 0x4547fdbb */
-sb5 = 2.5530502930e+03, /* 0x451f90ce */
-sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
-sb7 = -2.2440952301e+01; /* 0xc1b38712 */
-
- int hx,ix,i;
- float R,S,P,Q,s,y,z,r;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erf(nan)=nan */
- i = ((unsigned int)hx>>31)<<1;
- return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
- }
-
- if(ix < 0x3f580000) { /* |x|<0.84375 */
- if(ix < 0x31800000) { /* |x|<2**-28 */
- if (ix < 0x04000000)
- /*avoid underflow */
- return (float)0.125*((float)8.0*x+efx8*x);
- return x + efx*x;
- }
- z = x*x;
- r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
- s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5,qq4), qq3), qq2), qq1), one);
- y = r / s;
- return mad(x, y, x);
- }
- if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = __gen_ocl_internal_fabs(x)-one;
- P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
- Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
- if(hx>=0) return erx + P/Q; else return -erx - P/Q;
- }
- if (ix >= 0x40c00000) { /* inf>|x|>=6 */
- if(hx>=0) return one-tiny; else return tiny-one;
- }
- x = __gen_ocl_internal_fabs(x);
- s = one/(x*x);
- if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
- } else { /* |x| >= 1/0.35 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- rb6, rb5), rb4), rb3), rb2), rb1), rb0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
- }
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- GEN_OCL_SET_FLOAT_WORD(z,ix&0xfffff000);
- r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*__gen_ocl_internal_exp((z-x)*(z+x)+R/S);
- if(hx>=0) return one-r/x; else return r/x-one;
-}
-INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
-/*...*/
-const float
-tiny = 1.0e-30,
-half_val= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
- /* c = (subfloat)0.84506291151 */
-erx = 8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to erf on [0,0.84375]
- */
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
-efx8= 1.0270333290e+00, /* 0x3f8375d4 */
-pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
-pp1 = -3.2504209876e-01, /* 0xbea66beb */
-pp2 = -2.8481749818e-02, /* 0xbce9528f */
-pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
-qq2 = 6.5022252500e-02, /* 0x3d852a63 */
-qq3 = 5.0813062117e-03, /* 0x3ba68116 */
-qq4 = 1.3249473704e-04, /* 0x390aee49 */
-qq5 = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1 = 4.1485610604e-01, /* 0x3ed46805 */
-pa2 = -3.7220788002e-01, /* 0xbebe9208 */
-pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
-pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
-pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
-qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
-qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
-qa4 = 1.2617121637e-01, /* 0x3e013307 */
-qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
-qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
- /*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
- */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
-ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2 = -1.0558626175e+01, /* 0xc128f022 */
-ra3 = -6.2375331879e+01, /* 0xc2798057 */
-ra4 = -1.6239666748e+02, /* 0xc322658c */
-ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6 = -8.1287437439e+01, /* 0xc2a2932b */
-ra7 = -9.8143291473e+00, /* 0xc11d077e */
-sa1 = 1.9651271820e+01, /* 0x419d35ce */
-sa2 = 1.3765776062e+02, /* 0x4309a863 */
-sa3 = 4.3456588745e+02, /* 0x43d9486f */
-sa4 = 6.4538726807e+02, /* 0x442158c9 */
-sa5 = 4.2900814819e+02, /* 0x43d6810b */
-sa6 = 1.0863500214e+02, /* 0x42d9451f */
-sa7 = 6.5702495575e+00, /* 0x40d23f7c */
-sa8 = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to erfc in [1/.35,28]
- */
-rb0 = -9.8649431020e-03, /* 0xbc21a092 */
-rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2 = -1.7757955551e+01, /* 0xc18e104b */
-rb3 = -1.6063638306e+02, /* 0xc320a2ea */
-rb4 = -6.3756646729e+02, /* 0xc41f6441 */
-rb5 = -1.0250950928e+03, /* 0xc480230b */
-rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1 = 3.0338060379e+01, /* 0x41f2b459 */
-sb2 = 3.2579251099e+02, /* 0x43a2e571 */
-sb3 = 1.5367296143e+03, /* 0x44c01759 */
-sb4 = 3.1998581543e+03, /* 0x4547fdbb */
-sb5 = 2.5530502930e+03, /* 0x451f90ce */
-sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
-sb7 = -2.2440952301e+01; /* 0xc1b38712 */
- int hx,ix;
- float R,S,P,Q,s,y,z,r;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erfc(nan)=nan */
- /* erfc(+-inf)=0,2 */
- return (float)(((unsigned int)hx>>31)<<1)+one/x;
- }
-
- if(ix < 0x3f580000) { /* |x|<0.84375 */
- if(ix < 0x23800000) /* |x|<2**-56 */
- return one-x;
- z = x*x;
- r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
- s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5, qq4), qq3), qq2), qq1), one);
- y = r/s;
- if(hx < 0x3e800000) { /* x<1/4 */
- return one-(x+x*y);
- } else {
- r = x*y;
- r += (x-half_val);
- return half_val - r ;
- }
- }
- if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = __gen_ocl_internal_fabs(x)-one;
- P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
- Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
- if(hx>=0) {
- z = one-erx; return z - P/Q;
- } else {
- z = erx+P/Q; return one+z;
- }
- }
- if (ix < 0x41e00000) { /* |x|<28 */
- x = __gen_ocl_internal_fabs(x);
- s = one/(x*x);
- if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
- } else { /* |x| >= 1/.35 ~ 2.857143 */
- if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- rb6, rb5), rb4), rb3), rb2), rb1), rb0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
- }
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- GEN_OCL_SET_FLOAT_WORD(z,ix&0xffffe000);
- r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*
- __gen_ocl_internal_exp((z-x)*(z+x)+R/S);
- if(hx>0) {
- float ret = r/x;
- return ret;
- } else
- return two-r/x;
- } else {
- if(hx>0) {
- return tiny*tiny;
- } else
- return two-tiny;
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_fmod (float x, float y) {
- //return x-y*__gen_ocl_rndz(x/y);
- float one = 1.0;
- float Zero[2];
- int n,hx,hy,hz,ix,iy,sx,i;
- Zero[0] = 0.0;
- Zero[1] = -0.0;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- sx = hx&0x80000000; /* sign of x */
- hx ^=sx; /* |x| */
- hy &= 0x7fffffff; /* |y| */
- /* purge off exception values */
- if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
- (hy>0x7f800000)) /* or y is NaN */
- return (x*y)/(x*y);
- if(hx<hy) return x; /* |x|<|y| return x */
- if(hx==hy)
- return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
-
- /* determine ix = ilogb(x) */
- if(hx<0x00800000) { /* subnormal x */
- for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
- } else ix = (hx>>23)-127;
-
- /* determine iy = ilogb(y) */
- if(hy<0x00800000) { /* subnormal y */
- for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
- } else iy = (hy>>23)-127;
-
- /* set up {hx,lx}, {hy,ly} and align y to x */
- if(ix >= -126)
- hx = 0x00800000|(0x007fffff&hx);
- else { /* subnormal x, shift x to normal */
- n = -126-ix;
- hx = hx<<n;
- }
- if(iy >= -126)
- hy = 0x00800000|(0x007fffff&hy);
- else { /* subnormal y, shift y to normal */
- n = -126-iy;
- hy = hy<<n;
- }
- /* fix point fmod */
- n = ix - iy;
- while(n--) {
- hz=hx-hy;
- if(hz<0){hx = hx+hx;}
- else {
- if(hz==0) /* return sign(x)*0 */
- return Zero[(unsigned)sx>>31];
- hx = hz+hz;
- }
- }
- hz=hx-hy;
- if(hz>=0) {hx=hz;}
-
- /* convert back to floating value and restore the sign */
- if(hx==0) /* return sign(x)*0 */
- return Zero[(unsigned)sx>>31];
- while(hx<0x00800000) { /* normalize x */
- hx = hx+hx;
- iy -= 1;
- }
- if(iy>= -126) { /* normalize output */
- hx = ((hx-0x00800000)|((iy+127)<<23));
- GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
- } else { /* subnormal output */
- n = -126 - iy;
- hx >>= n;
- GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
- x *= one; /* create necessary signal */
- }
- return x; /* exact output */
-}
-
-OVERLOADABLE float __gen_ocl_internal_expm1(float x) {
- //return __gen_ocl_pow(M_E_F, x) - 1;
- float Q1 = -3.3333335072e-02, /* 0xbd088889 */
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- one = 1.0,
- o_threshold= 8.8721679688e+01; /* 0x42b17180 */
- float y,hi,lo,c,t,e,hxs,hfx,r1;
- int k,xsb;
- int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- xsb = hx&0x80000000;
- /* sign bit of x */
- //if(xsb==0)
- //y=x;
- //else
- //y= -x; /* y = |x| */
- y = __gen_ocl_internal_fabs(x);
- hx &= 0x7fffffff; /* high word of |x| */
- /* filter out huge and non-finite argument */
- if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
- if(hx >= 0x42b17218) { /* if |x|>=88.721... */
- if(hx>0x7f800000)
- return x+x; /* NaN */
- if(hx==0x7f800000)
- return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
- if(x > o_threshold)
- return huge*huge; /* overflow */
- }
- if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
- if(x+tiny<(float)0.0) /* raise inexact */
- return tiny-one; /* return -1 */
- }
- }
- /* argument reduction */
- if(hx > 0x3eb17218) {/* if |x| > 0.5 ln2 */
- if(hx < 0x3F851592) {/* and |x| < 1.5 ln2 */
- if(xsb==0){
- hi = x - ln2_hi; lo = ln2_lo; k = 1;
- } else {
- hi = x + ln2_hi; lo = -ln2_lo; k = -1;
- }
- } else {
- k = ivln2*x+((xsb==0)?(float)0.5:(float)-0.5);
- t = k;
- hi = x - t*ln2_hi;/* t*ln2_hi is exact here */
- lo = t*ln2_lo;
- }
- x = hi - lo;
- c = (hi-x)-lo;
- } else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
- //t = huge+x; /* return x with inexact flags when x!=0 */
- //return x - (t-(huge+x));
- return x;
- } else k = 0;
- /* x is now in primary range */
- hfx = (float)0.5*x;
- hxs = x*hfx;
- r1 = one+hxs*(Q1+hxs*Q2);
- t = (float)3.0-r1*hfx;
- e = hxs*((r1-t)/((float)6.0 - x*t));
- if(k==0)
- return x - (x*e-hxs); /* c is 0 */
- else{
- e = (x*(e-c)-c);
- e -= hxs;
- if(k== -1)return (float)0.5*(x-e)-(float)0.5;
- if(k==1){
- if(x < (float)-0.25)
- return -(float)2.0*(e-(x+(float)0.5));
- else
- return (one+(float)2.0*(x-e));
- }
- if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
- int i;
- y = one-(e-x);
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- return y-one;
- }
- t = one;
- if(k<23) {
- int i;
- GEN_OCL_SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
- y = t-(e-x);
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- } else {
- int i;
- GEN_OCL_SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
- y = x-(e+t);
- y += one;
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- }
- }
- return y;
-}
-
-OVERLOADABLE float __gen_ocl_internal_acosh(float x) {
- //return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
- float one = 1.0,
- ln2 = 6.9314718246e-01;/* 0x3f317218 */
- float t;
- int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- if(hx<0x3f800000) { /* x < 1 */
- return (x-x)/(x-x);
- } else if(hx >=0x4d800000) { /* x > 2**28 */
- if(hx >=0x7f800000) {/* x is inf of NaN */
- return x+x;
- } else
- return __gen_ocl_internal_log(x)+ln2;/* acosh(huge)=log(2x) */
- } else if (hx==0x3f800000) {
- return 0.0; /* acosh(1) = 0 */
- } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
- t=x*x;
- return __gen_ocl_internal_log((float)2.0*x-one/(x+__gen_ocl_sqrt(t-one)));
- } else { /* 1<x<2 */
- t = x-one;
- return log1p(t+__gen_ocl_sqrt((float)2.0*t+t*t));
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_asinh(float x){
- //return native_log(x + native_sqrt(x * x + 1));
- float one = 1.0000000000e+00, /* 0x3F800000 */
- ln2 = 6.9314718246e-01, /* 0x3f317218 */
- huge= 1.0000000000e+30;
- float w;
- int hx,ix;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix< 0x38000000) { /* |x|<2**-14 */
- if(huge+x>one) return x; /* return x inexact except 0 */
- }
- if(ix>0x47000000) {/* |x| > 2**14 */
- if(ix>=0x7f800000) return x+x;/* x is inf or NaN */
- w = __gen_ocl_internal_log(__gen_ocl_internal_fabs(x))+ln2;
- } else {
- float xa = __gen_ocl_internal_fabs(x);
- if (ix>0x40000000) {/* 2**14 > |x| > 2.0 */
- w = __gen_ocl_internal_log(mad(xa, 2.0f, one / (__gen_ocl_sqrt(mad(xa, xa, one)) + xa)));
- } else { /* 2.0 > |x| > 2**-14 */
- float t = xa*xa;
- w =log1p(xa+t/(one+__gen_ocl_sqrt(one+t)));
- }
- }
- return __gen_ocl_internal_copysign(w, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_sinh(float x){
- //return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
- float one = 1.0,
- shuge = 1.0e37;
- float t,w,h;
- int ix,jx;
- GEN_OCL_GET_FLOAT_WORD(jx,x);
- ix = jx&0x7fffffff;
- /* x is INF or NaN */
- if(ix>=0x7f800000) return x+x;
- h = 0.5;
- if (jx<0) h = -h;
- /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix < 0x41b00000) { /* |x|<22 */
- if (ix<0x31800000) /* |x|<2**-28 */
- if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
- t = __gen_ocl_internal_expm1(__gen_ocl_internal_fabs(x));
- if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
- return h*(t+t/(t+one));
- }
- /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix < 0x42b17180) return h*__gen_ocl_internal_exp(__gen_ocl_internal_fabs(x));
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix<=0x42b2d4fc) {
- w = __gen_ocl_internal_exp((float)0.5*__gen_ocl_internal_fabs(x));
- t = h*w;
- return t*w;
- }
- /* |x| > overflowthresold, sinh(x) overflow */
- return x*shuge;
-}
-
-OVERLOADABLE float __gen_ocl_internal_tanh(float x) {
- //float y = native_exp(-2 * x);
- //return (1 - y) / (1 + y);
- float one=1.0, two=2.0, tiny = 1.0e-30;
- float t,z;
- int jx,ix;
- GEN_OCL_GET_FLOAT_WORD(jx,x);
- ix = jx&0x7fffffff;
- /* x is INF or NaN */
- if(ix>=0x7f800000) {
- if (jx>=0)
- return one/x+one; /* tanh(+-inf)=+-1 */
- else
- return one/x-one; /* tanh(NaN) = NaN */
- }
-
- if (ix < 0x41b00000) { /* |x|<22 */
- if (ix == 0)
- return x; /* x == +-0 */
- if (ix<0x24000000) /* |x|<2**-55 */
- return x*(one+x); /* tanh(small) = small */
- if (ix>=0x3f800000) { /* |x|>=1 */
- t = __gen_ocl_internal_expm1(two*__gen_ocl_internal_fabs(x));
- z = one - two/(t+two);
- } else {
- t = __gen_ocl_internal_expm1(-two*__gen_ocl_internal_fabs(x));
- z= -t/(t+two);
- }
- } else { /* |x| > 22, return +-1 */
- z = one - tiny; /* raised inexact flag */
- }
- return (jx>=0)? z: -z;
-}
-
-OVERLOADABLE float __gen_ocl_internal_cosh(float x) {
- //return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
- float halF = 0.5,
- huge = 1.0e+30,
- tiny = 1.0e-30,
- one = 1.0;
- float t,w;
- int ix;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
- /* |x| in [0,22] */
- if (ix < 0x41b00000) {
- /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
- if(ix<0x3eb17218) {
- t = __gen_ocl_internal_expm1(__gen_ocl_fabs(x));
- w = one+t;
- if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
- return one+(t*t)/(w+w);
- }
- /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
- t = __gen_ocl_internal_exp(__gen_ocl_fabs(x));
- return halF*t+halF/t;
- }
- /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
- if (ix < 0x42b17180) return halF*__gen_ocl_internal_exp(__gen_ocl_fabs(x));
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix<=0x42b2d4fc) {
- w = __gen_ocl_internal_exp(halF*__gen_ocl_fabs(x));
- t = halF*w;
- return t*w;
- }
- /* x is INF or NaN */
- if(ix>=0x7f800000) return x*x;
- /* |x| > overflowthresold, cosh(x) overflow */
- return huge*huge;
-}
-
-OVERLOADABLE float __gen_ocl_internal_remainder(float x, float p){
- //return x-y*__gen_ocl_rnde(x/y);
- float zero = 0.0;
- int hx,hp;
- unsigned sx;
- float p_half;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hp,p);
- sx = hx&0x80000000;
- hp &= 0x7fffffff;
- hx &= 0x7fffffff;
- /* purge off exception values */
- if(hp==0) return (x*p)/(x*p); /* p = 0 */
- if((hx>=0x7f800000)|| /* x not finite */
- ((hp>0x7f800000))) /* p is NaN */
- return (x*p)/(x*p);
- if (hp<=0x7effffff) x = __gen_ocl_internal_fmod(x,p+p); /* now x < 2p */
- if ((hx-hp)==0) return zero*x;
- x = __gen_ocl_fabs(x);
- p = __gen_ocl_fabs(p);
- if (hp<0x01000000) {
- if(x+x>p) {
- x-=p;
- if(x+x>=p) x -= p;
- }
- } else {
- p_half = (float)0.5*p;
- if(x>p_half) {
- x-=p;
- if(x>=p_half) x -= p;
- }
- }
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_SET_FLOAT_WORD(x,hx^sx);
- return x;
-}
-
-OVERLOADABLE float __gen_ocl_internal_ldexp(float x, int n) {
- x = __gen_ocl_scalbnf(x,n);
- return x;
-}
-
-OVERLOADABLE float __gen_ocl_internal_atanh(float x) {
- //return 0.5f * native_sqrt((1 + x) / (1 - x));
- float xa = __gen_ocl_fabs (x);
- float t;
- if (isless (xa, 0.5f)){
- if (xa < 0x1.0p-28f) return x;
- t = xa + xa;
- t = 0.5f * log1p (t + t * xa / (1.0f - xa));
- } else if (isless (xa, 1.0f)){
- t = 0.5f * log1p ((xa + xa) / (1.0f - xa));
- } else{
- if (isgreater (xa, 1.0f)) return (x - x) / (x - x);
- return x / 0.0f;
- }
- return __gen_ocl_internal_copysign(t, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_exp10(float x){
- float px, qx,ans;
- short n;
- int i;
- float*p;
- float MAXL10 = 38.230809449325611792;
- float LOG210 = 3.32192809488736234787e0;
- float LG102A = 3.00781250000000000000E-1;
- float LG102B = 2.48745663981195213739E-4;
- float P[6];
- P[0] = 2.063216740311022E-001;
- P[1] = 5.420251702225484E-001;
- P[2] = 1.171292686296281E+000;
- P[3] = 2.034649854009453E+000;
- P[4] = 2.650948748208892E+000;
- P[5] = 2.302585167056758E+000;
-
- if( x < -MAXL10 ) return 0.0;
-
- if( isinf(x)) return INFINITY;
- /* The following is necessary because range reduction blows up: */
- if( x == 0 )return 1.0;
-
- /* Express 10**x = 10**g 2**n
- * = 10**g 10**( n log10(2) )
- * = 10**( g + n log10(2) )
- */
- px = x * LOG210;
- qx = __gen_ocl_internal_floor( px + 0.5 );
- n = qx;
- x -= qx * LG102A;
- x -= qx * LG102B;
-
- /* rational approximation for exponential
- * of the fractional part:
- * 10**x - 1 = 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
- p = P;
- ans = *p++;
- i = 5;
- do{
- ans = ans * x + *p++;
- }
- while( --i );
- px = 1.0 + x * ans;
-
- /* multiply by power of 2 */
- x = __gen_ocl_internal_ldexp( px, n );
- return x;
-}
-
-OVERLOADABLE float cospi(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cospi(x);
-
- return __gen_ocl_internal_cospi(x);
-}
-
-OVERLOADABLE float cosh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cosh(x);
-
- return __gen_ocl_internal_cosh(x);
-}
-
-OVERLOADABLE float acos(float x) {
- return __gen_ocl_internal_acos(x);
-}
-
-OVERLOADABLE float acospi(float x) {
- return __gen_ocl_internal_acospi(x);
-}
-
-OVERLOADABLE float acosh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_acosh(x);
-
- return __gen_ocl_internal_acosh(x);
-}
-
-OVERLOADABLE float sinpi(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sinpi(x);
-
- return __gen_ocl_internal_sinpi(x);
-}
-
-OVERLOADABLE float sinh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sinh(x);
-
- return __gen_ocl_internal_sinh(x);
-}
-
-OVERLOADABLE float asin(float x) {
- return __gen_ocl_internal_asin(x);
-}
-
-OVERLOADABLE float asinpi(float x) {
- return __gen_ocl_internal_asinpi(x);
-}
-
-OVERLOADABLE float asinh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_asinh(x);
-
- return __gen_ocl_internal_asinh(x);
-}
-
-OVERLOADABLE float tanpi(float x) {
- return __gen_ocl_internal_tanpi(x);
-}
-
-OVERLOADABLE float tanh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_tanh(x);
-
- return __gen_ocl_internal_tanh(x);
-}
-
-OVERLOADABLE float atan(float x) {
- return __gen_ocl_internal_atan(x);
-}
-
-OVERLOADABLE float atan2(float y, float x) {
- return __gen_ocl_internal_atan2(y, x);
-}
-
-OVERLOADABLE float atan2pi(float y, float x) {
- return __gen_ocl_internal_atan2pi(y, x);
-}
-
-OVERLOADABLE float atanpi(float x) {
- return __gen_ocl_internal_atanpi(x);
-}
-
-OVERLOADABLE float atanh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_atanh(x);
-
- return __gen_ocl_internal_atanh(x);
-}
-
-OVERLOADABLE float cbrt(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cbrt(x);
-
- return __gen_ocl_internal_cbrt(x);
-}
-
-OVERLOADABLE float rint(float x) {
- return __gen_ocl_internal_rint(x);
-}
-
-OVERLOADABLE float copysign(float x, float y) {
- return __gen_ocl_internal_copysign(x, y);
-}
-
-OVERLOADABLE float erf(float x) {
- return __gen_ocl_internal_erf(x);
-}
-
-OVERLOADABLE float erfc(float x) {
- return __gen_ocl_internal_erfc(x);
-}
-
-OVERLOADABLE float fmod (float x, float y) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_fmod(x, y);
-
- return __gen_ocl_internal_fmod(x, y);
-}
-
-OVERLOADABLE float remainder(float x, float p) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_remainder(x, p);
-
- return __gen_ocl_internal_remainder(x, p);
-}
-
-OVERLOADABLE float ldexp(float x, int n) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_ldexp(x, n);
-
- if (x == (float)0.0f) x = 0.0f;
- return __gen_ocl_internal_ldexp(x, n);
-}
-
-CONST OVERLOADABLE float __gen_ocl_mad(float a, float b, float c) __asm("llvm.fma" ".f32");
-CONST OVERLOADABLE half __gen_ocl_mad(half a, half b, half c) __asm("llvm.fma" ".f16");
-PURE CONST float __gen_ocl_fmax(float a, float b);
-PURE CONST float __gen_ocl_fmin(float a, float b);
-
-OVERLOADABLE float mad(float a, float b, float c) {
- return __gen_ocl_mad(a, b, c);
-}
-
-
-#define BODY \
- if (isnan(x) || isinf(x)) { \
- *exp = 0; \
- return x; \
- } \
- uint u = as_uint(x); \
- uint a = u & 0x7FFFFFFFu; \
- if (a == 0) { \
- *exp = 0; \
- return x; \
- } \
- if (a >= 0x800000) { \
- *exp = (a >> 23) - 126; \
- return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
- } \
- int e = -126; \
- while (a < 0x400000) { \
- e --; \
- a <<= 1; \
- } \
- a <<= 1; \
- *exp = e; \
- return as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
-OVERLOADABLE float frexp(float x, global int *exp) { BODY; }
-OVERLOADABLE float frexp(float x, local int *exp) { BODY; }
-OVERLOADABLE float frexp(float x, private int *exp) { BODY; }
-#undef BODY
-
-OVERLOADABLE float nextafter(float x, float y) {
- int hx, hy, ix, iy;
- hx = as_int(x);
- hy = as_int(y);
- ix = hx & 0x7fffffff;
- iy = hy & 0x7fffffff;
- if(ix == 0)
- ix = hx & 0x7fffff;
- if(iy == 0)
- iy = hy & 0x7fffff;
- if(ix>0x7f800000 || iy>0x7f800000)
- return x+y;
- if(hx == hy)
- return y;
- if(ix == 0) {
- if(iy == 0)
- return y;
- else
- return as_float((hy&0x80000000) | 1);
- }
- if(hx >= 0) {
- if(hx > hy) {
- hx -= 1;
- } else {
- hx += 1;
- }
- } else {
- if(hy >= 0 || hx > hy){
- hx -= 1;
- } else {
- hx += 1;
- }
- }
- return as_float(hx);
-}
-
-#define BODY \
- uint hx = as_uint(x), ix = hx & 0x7FFFFFFF; \
- if (ix > 0x7F800000) { \
- *i = nan(0u); \
- return nan(0u); \
- } \
- if (ix == 0x7F800000) { \
- *i = x; \
- return as_float(hx & 0x80000000u); \
- } \
- *i = __gen_ocl_rndz(x); \
- return x - *i;
-OVERLOADABLE float modf(float x, global float *i) { BODY; }
-OVERLOADABLE float modf(float x, local float *i) { BODY; }
-OVERLOADABLE float modf(float x, private float *i) { BODY; }
-#undef BODY
-
-OVERLOADABLE float __gen_ocl_internal_fmax(float a, float b) { return max(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmin(float a, float b) { return min(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmax(half a, half b) { return max(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmin(half a, half b) { return min(a,b); }
-OVERLOADABLE float __gen_ocl_internal_maxmag(float x, float y) {
- float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
- return a > b ? x : b > a ? y : max(x, y);
-}
-OVERLOADABLE float __gen_ocl_internal_minmag(float x, float y) {
- float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
- return a < b ? x : b < a ? y : min(x, y);
-}
-OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) {
- if(isnan(x))
- return x;
- if(isnan(y))
- return y;
- return x > y ? (x - y) : +0.f;
-}
-/*
- * the pow/pown high precision implementation are copied from msun library.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) {
- float z,ax,z_h,z_l,p_h,p_l;
- float y1,t1,t2,r,s,sn,t,u,v,w;
- int i,j,k,yisint,n;
- int hx,hy,ix,iy,is;
- float bp[2],dp_h[2],dp_l[2],
- zero = 0.0,
- one = 1.0,
- two = 2.0,
- two24 = 16777216.0, /* 0x4b800000 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
- L1 = 6.0000002384e-01, /* 0x3f19999a */
- L2 = 4.2857143283e-01, /* 0x3edb6db7 */
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03, /* 0xbb360b61 */
- lg2 = 6.9314718246e-01, /* 0x3f317218 */
- lg2_h = 6.93145752e-01, /* 0x3f317200 */
- lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
- ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
- cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
- cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
- cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
- ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
- bp[0] = 1.0,bp[1] = 1.5,
- dp_h[0] = 0.0,dp_h[1] = 5.84960938e-01,
- dp_l[0] = 0.0,dp_l[1] = 1.56322085e-06;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- ix = hx&0x7fffffff; iy = hy&0x7fffffff;
- if (ix < 0x00800000) { /* x < 2**-126 */
- ix = 0;/* Gen does not support subnormal number now */
- }
- if (iy < 0x00800000) { /* y < 2**-126 */
- iy = 0;/* Gen does not support subnormal number now */
- }
- /* y==zero: x**0 = 1 */
- if(iy==0) return one;
- /* pow(+1, y) returns 1 for any y, even a NAN */
- if(hx==0x3f800000) return one;
- /* +-NaN return x+y */
- if(ix > 0x7f800000 || iy > 0x7f800000)
- return (x+0.0f)+y+(0.0f);
- /* determine if y is an odd int when x < 0
- * yisint = 0 ... y is not an integer
- * yisint = 1 ... y is an odd int
- * yisint = 2 ... y is an even int
- */
- yisint = 0;
- if(hx<0) {
- if(iy>=0x4b800000) yisint = 2; /* even integer y */
- else if(iy>=0x3f800000) {
- k = (iy>>23)-0x7f; /* exponent */
- j = iy>>(23-k);
- if((j<<(23-k))==iy) yisint = 2-(j&1);
- }
- }
- /* special value of y */
- if (iy==0x7f800000) { /* y is +-inf */
- if (ix==0x3f800000)
- //return y - y; /* inf**+-1 is NaN */
- return one;
- else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
- return (hy>=0)? y: zero;
- else /* (|x|<1)**-,+inf = inf,0 */
- return (hy<0)?-y: zero;
- }
- if(iy==0x3f800000) { /* y is +-1 */
- if(hy<0) return one/x; else return x;
- }
- if(hy==0x40000000) return x*x; /* y is 2 */
- if(hy==0x3f000000) { /* y is 0.5 */
- if(hx>=0)return __gen_ocl_sqrt(x);
- }
-
- ax = __gen_ocl_fabs(x);
- /* special value of x */
- if(ix==0x7f800000||ix==0||ix==0x3f800000){
- z = ax; /*x is +-0,+-inf,+-1*/
- if(hy<0) z = one/z; /* z = (1/|x|) */
- if(hx<0) {
- if(((ix-0x3f800000)|yisint)==0) {
- z = (z-z)/(z-z); /* (-1)**non-int is NaN */
- } else if(yisint==1)
- z = -z; /* (x<0)**odd = -(|x|**odd) */
- }
- return z;
- }
- n = ((uint)hx>>31)-1;
-
- /* (x<0)**(non-int) is NaN */
- if((n|yisint)==0) return (x-x)/(x-x);
-
- sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
-
- /* |y| is huge */
- if(iy>0x4d000000) { /* if |y| > 2**27 */
- /* over/underflow if x is not close to one */
- if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
- if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = ax-1; /* t has 20 trailing zeros */
- w = (t*t)*((float)0.5-t*(0.333333333333f-t*0.25f));
- u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
- v = t*ivln2_l-w*ivln2;
- t1 = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
- t2 = v-(t1-u);
- } else {
- float s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
- //if(ix<0x00800000)
- //{ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
- n += ((ix)>>23)-0x7f;
- j = ix&0x007fffff;
- /* determine interval */
- ix = j|0x3f800000; /* normalize ix */
- if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
- else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
- else {k=0;n+=1;ix -= 0x00800000;}
- GEN_OCL_SET_FLOAT_WORD(ax,ix);
-
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
- s = u*v;
- s_h = s;
- GEN_OCL_GET_FLOAT_WORD(is,s_h);
- GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
- /* t_h=ax+bp[k] High */
- is = ((ix>>1)&0xfffff000)|0x20000000;
- GEN_OCL_SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
- t_l = ax - (t_h-bp[k]);
- s_l = v*((u-s_h*t_h)-s_h*t_l);
-
- /* compute log(ax) */
- s2 = s*s;
- r = s2*s2*(L1+s2*L2);
- r += s_l*(s_h+s);
- s2 = s_h*s_h;
- t_h = 3.0f+s2+r;
- GEN_OCL_GET_FLOAT_WORD(is,t_h);
- GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
- t_l = r-((t_h-3.0f)-s2);
- /* u+v = s*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h+t_l*s;
- /* 2/(3log2)*(s+...) */
- p_h = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,p_h);
- GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
- p_l = v-(p_h-u);
- z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
- z_l = cp_l*p_h+p_l*cp+dp_l[k];
- /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (float)n;
- t1 = (((z_h+z_l)+dp_h[k])+t);
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);
- }
-
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
- GEN_OCL_GET_FLOAT_WORD(is,y);
- GEN_OCL_SET_FLOAT_WORD(y1,is&0xffffe000);
- p_l = (y-y1)*t1+y*t2;
- p_h = y1*t1;
- z = p_l+p_h;
- GEN_OCL_GET_FLOAT_WORD(j,z);
- if (j>0x43000000) /* if z > 128 */
- return sn*huge*huge; /* overflow */
- else if (j==0x43000000) { /* if z == 128 */
- if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
- }
- else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
- return sn*tiny*tiny; /* underflow */
- else if (j==0xc3160000){ /* z == -150 */
- if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
- }
-
- /*
- * compute 2**(p_h+p_l)
- */
- i = j&0x7fffffff;
- k = (i>>23)-0x7f;
- n = 0;
- if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
- n = j+(0x00800000>>(k+1));
- k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
- GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
- n = ((n&0x007fffff)|0x00800000)>>(23-k);
- if(j<0) n = -n;
- p_h -= t;
- }
- t = p_l+p_h;
- GEN_OCL_GET_FLOAT_WORD(is,t);
- GEN_OCL_SET_FLOAT_WORD(t,is&0xffff8000);
- u = t*lg2_h;
- v = (p_l-(t-p_h))*lg2+t*lg2_l;
- z = u+v;
- w = v-(z-u);
- t = z*z;
- t1 = z - t*(P1+t*P2);
- r = (z*t1)/(t1-two)-(w+z*w);
- z = one-(r-z);
- GEN_OCL_GET_FLOAT_WORD(j,z);
- j += (n<<23);
- if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
- else GEN_OCL_SET_FLOAT_WORD(z,j);
- return sn*z;
-}
-
-OVERLOADABLE float tgamma (float x)
-{
- /* based on glibc __ieee754_gammaf_r by Ulrich Drepper <drepper@cygnus.com> */
-
- unsigned int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- if (hx == 0xff800000)
- {
- /* x == -Inf. According to ISO this is NaN. */
- return NAN;
- }
- if ((hx & 0x7f800000) == 0x7f800000)
- {
- /* Positive infinity (return positive infinity) or NaN (return
- NaN). */
- return x;
- }
- if (x < 0.0f && __gen_ocl_internal_floor (x) == x)
- {
- /* integer x < 0 */
- return NAN;
- }
-
- if (x >= 36.0f)
- {
- /* Overflow. */
- return INFINITY;
- }
- else if (x <= 0.0f && x >= -FLT_EPSILON / 4.0f)
- {
- return 1.0f / x;
- }
- else
- {
- float sinpix = __gen_ocl_internal_sinpi(x);
- if (x <= -42.0f)
- /* Underflow. */
- {return 0.0f * sinpix /*for sign*/;}
- int exp2_adj = 0;
- float x_abs = __gen_ocl_fabs(x);
- float gam0;
-
- if (x_abs < 4.0f) {
- /* gamma = exp(lgamma) is only accurate for small lgamma */
- float prod,x_adj;
- if (x_abs < 0.5f) {
- prod = 1.0f / x_abs;
- x_adj = x_abs + 1.0f;
- } else if (x_abs <= 1.5f) {
- prod = 1.0f;
- x_adj = x_abs;
- } else if (x_abs < 2.5f) {
- x_adj = x_abs - 1.0f;
- prod = x_adj;
- } else {
- x_adj = x_abs - 2.0f;
- prod = x_adj * (x_abs - 1.0f);
- }
- gam0 = __gen_ocl_internal_exp (lgamma (x_adj)) * prod;
- }
- else {
- /* Compute gamma (X) using Stirling's approximation,
- starting by computing pow (X, X) with a power of 2
- factored out to avoid intermediate overflow. */
- float x_int = __gen_ocl_internal_round (x_abs);
- float x_frac = x_abs - x_int;
- int x_log2;
- float x_mant = frexp (x_abs, &x_log2);
- if (x_mant < M_SQRT1_2_F)
- {
- x_log2--;
- x_mant *= 2.0f;
- }
- exp2_adj = x_log2 * (int) x_int;
- float ret = (__gen_ocl_internal_pow(x_mant, x_abs)
- * exp2 (x_log2 * x_frac)
- * __gen_ocl_internal_exp (-x_abs)
- * sqrt (2.0f * M_PI_F / x_abs) );
-
- float x2 = x_abs * x_abs;
- float bsum = (0x3.403404p-12f / x2 -0xb.60b61p-12f) / x2 + 0x1.555556p-4f;
- gam0 = ret + ret * __gen_ocl_internal_expm1 (bsum / x_abs);
- }
- if (x > 0.0f) {return __gen_ocl_internal_ldexp (gam0, exp2_adj);}
- float gam1 = M_PI_F / (-x * sinpix * gam0);
- return __gen_ocl_internal_ldexp (gam1, -exp2_adj);
- }
+OVERLOADABLE half lgamma_r(half x, global int *signgamp) {
+ float _x = (float)x;
+ return (half)lgamma_r(_x, signgamp);
}
-
-float __gen_ocl_internal_pown(float x, int y) {
- const float
- bp[] = {1.0, 1.5,},
- dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
- dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
- zero = 0.0,
- one = 1.0,
- two = 2.0,
- two24 = 16777216.0, /* 0x4b800000 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
- L1 = 6.0000002384e-01, /* 0x3f19999a */
- L2 = 4.2857143283e-01, /* 0x3edb6db7 */
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03, /* 0xbb360b61 */
- lg2 = 6.9314718246e-01, /* 0x3f317218 */
- lg2_h = 0x1.62ep-1,
- lg2_l = 0x1.0bfbe8p-15,
- ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
- cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
- cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
- cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
- ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
-
- float z,ax,z_h,z_l,p_h,p_l;
- float y1,t1,t2,r,s,t,u,v,w;
- int i,j,k,yisint,n;
- int hx,ix,iy,is;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- iy = y > 0 ? y&0x7fffffff : (-y)&0x7fffffff;
- /* y==zero: x**0 = 1 */
- if(y==0) return one;
-
- /* +-NaN return NAN */
- if(ix > 0x7f800000)
- return NAN;
-
- /* determine if y is an odd int
- * yisint = 1 ... y is an odd int
- * yisint = 2 ... y is an even int
- */
- yisint = y&1 ? 1 : 2;
-
- if (y == 1) return x;
- if (y == -1) return one/x;
- if (y == 2) return x*x;
-
- ax = __gen_ocl_fabs(x);
-
- /* special value of x */
- if(ix==0x7f800000||ix==0||ix==0x3f800000){
- z = ax; /*x is +-0,+-inf,+-1*/
- if(y<0) z = one/z; /* z = (1/|x|) */
- if(hx<0) {
- if(yisint==1)
- z = -z; /* (x<0)**odd = -(|x|**odd) */
- }
- return z;
- }
-
- float sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if(((((unsigned)hx>>31)-1)|(yisint-1))==0)
- sn = -one; /* (-ve)**(odd int) */
-
- /* |y| is huge */
- if(iy>0x08000000) { /* if |y| > 2**27 */
- /* over/underflow if x is not close to one */
- if(ix<0x3f7ffff8) return (y<0)? sn*huge*huge:tiny*tiny;
- if(ix>0x3f800007) return (y>0)? sn*huge*huge:tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = ax-1; /* t has 20 trailing zeros */
- w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
- u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
- v = t*ivln2_l-w*ivln2;
- t1 = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
- t2 = v-(t1-u);
- } else {
- float s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
-// if(ix<0x00800000)
-// {ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
- n += ((ix)>>23)-0x7f;
- j = ix&0x007fffff;
- /* determine interval */
- ix = j|0x3f800000; /* normalize ix */
- if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
- else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
- else {k=0;n+=1;ix -= 0x00800000;}
- GEN_OCL_SET_FLOAT_WORD(ax,ix);
-
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
- s = u*v;
- s_h = s;
- GEN_OCL_GET_FLOAT_WORD(is,s_h);
- GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
-
- /* t_h=ax+bp[k] High */
- GEN_OCL_SET_FLOAT_WORD(t_h, (((ix>>1)|0x20000000)+0x00400000+(k<<21)) &0xfffff000);
- t_l = ax - (t_h-bp[k]);
- s_l = v*((u-s_h*t_h)-s_h*t_l);
-
-
- /* compute log(ax) */
- s2 = s*s;
- r = s2*s2*(L1+s2*L2);
- r += s_l*(s_h+s);
- s2 = s_h*s_h;
- t_h = (float)3.0+s2+r;
- GEN_OCL_GET_FLOAT_WORD(is,t_h);
- GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
- t_l = r-((t_h-(float)3.0)-s2);
- /* u+v = s*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h+t_l*s;
- /* 2/(3log2)*(s+...) */
- p_h = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,p_h);
- GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
- p_l = v-(p_h-u);
- z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
- z_l = cp_l*p_h+p_l*cp+dp_l[k];
- /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (float)n;
- t1 = (((z_h+z_l)+dp_h[k])+t);
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);
- }
-
- /* split up y into y1+y2+y3 and compute (y1+y2+y3)*(t1+t2) */
-
- float fy = (float)y;
- float y3 = (float)(y-(int)fy);
- GEN_OCL_GET_FLOAT_WORD(is,fy);
- GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000);
-
- p_l = (fy-y1)*t1 + y3*t1 + fy*t2 + y3*t2;
- p_h = y1*t1;
- z = p_l+p_h;
-
- GEN_OCL_GET_FLOAT_WORD(j,z);
- if (j>0x43000000) /* if z > 128 */
- return sn*huge*huge; /* overflow */
- else if (j==0x43000000) { /* if z == 128 */
- if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
- }
- else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
- return sn*tiny*tiny; /* underflow */
- else if (j==0xc3160000){ /* z == -150 */
- if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
- }
- /*
- * compute 2**(p_h+p_l)
- */
- i = j&0x7fffffff;
- k = (i>>23)-0x7f;
- n = 0;
- if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
- n = j+(0x00800000>>(k+1));
- k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
- GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
- n = ((n&0x007fffff)|0x00800000)>>(23-k);
- if(j<0) n = -n;
- p_h -= t;
-
- z -= n;
- }
-
- t = z;
- GEN_OCL_GET_FLOAT_WORD(is,t);
- GEN_OCL_SET_FLOAT_WORD(t,is&0xfffff000);
- u = t*lg2_h;
- v = (p_l-(t-p_h))*lg2+t*lg2_l;
- z = u+v;
- w = v-(z-u);
- t = z*z;
- t1 = z - t*(P1+t*P2);
- r = (z*t1)/(t1-two)-(w+z*w);
- z = one-(r-z);
- GEN_OCL_GET_FLOAT_WORD(j,z);
- j += (n<<23);
- if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
- else GEN_OCL_SET_FLOAT_WORD(z,j);
- return sn*z;
+OVERLOADABLE half lgamma_r(half x, local int *signgamp) {
+ float _x = (float)x;
+ return (half)lgamma_r(_x, signgamp);
}
-
-OVERLOADABLE float hypot(float x, float y) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_hypot(x, y);
-
- //return __gen_ocl_sqrt(x*x + y*y);
- float a,b,an,bn,cn;
- int e;
- if (isfinite (x) && isfinite (y)){ /* Determine absolute values. */
- x = __gen_ocl_fabs (x);
- y = __gen_ocl_fabs (y);
- /* Find the bigger and the smaller one. */
- a = max(x,y);
- b = min(x,y);
- /* Now 0 <= b <= a. */
- /* Write a = an * 2^e, b = bn * 2^e with 0 <= bn <= an < 1. */
- an = frexp (a, &e);
- bn = ldexp (b, - e);
- /* Through the normalization, no unneeded overflow or underflow will occur here. */
- cn = __gen_ocl_sqrt (an * an + bn * bn);
- return ldexp (cn, e);
- }else{
- if (isinf (x) || isinf (y)) /* x or y is infinite. Return +Infinity. */
- return INFINITY;
- else /* x or y is NaN. Return NaN. */
- return x + y;
- }
+OVERLOADABLE half lgamma_r(half x, private int *signgamp) {
+ float _x = (float)x;
+ return (half)lgamma_r(_x, signgamp);
}
#define BODY \
- if (isnan(x)) { \
- *p = x; \
- return x; \
- } \
- *p = __gen_ocl_internal_floor(x); \
- if (isinf(x)) { \
- return x > 0 ? +0. : -0.; \
- } \
- return __gen_ocl_internal_fmin(x - *p, 0x1.FFFFFep-1F);
-OVERLOADABLE float fract(float x, global float *p) { BODY; }
-OVERLOADABLE float fract(float x, local float *p) { BODY; }
-OVERLOADABLE float fract(float x, private float *p) { BODY; }
-#undef BODY
-
-#define BODY \
float Zero[2]; \
int n,hx,hy,hz,ix,iy,sx,i,sy; \
uint q,sxy; \
@@ -3256,523 +535,41 @@ OVERLOADABLE float remquo(float x, float y, local int *quo) { BODY; }
OVERLOADABLE float remquo(float x, float y, private int *quo) { BODY; }
#undef BODY
-OVERLOADABLE float powr(float x, float y) {
- unsigned int hx, sx, hy, sy;
-
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_pow(x,y);
- else {
- if (isnan(x) || isnan(y)) return NAN;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- sx = (hx & 0x80000000) >> 31;
- sy = (hy & 0x80000000) >> 31;
-
- if ((hx&0x7fffffff) < 0x00800000) { /* x < 2**-126 */
- x = 0.0f;/* Gen does not support subnormal number now */
- hx = hx &0x80000000;
- }
- if ((hy&0x7fffffff) < 0x00800000) { /* y < 2**-126 */
- y = 0.0;/* Gen does not support subnormal number now */
- hy = hy &0x80000000;
- }
-
- // (x < 0) ** y = NAN (y!=0)
- if ((sx && (hx & 0x7fffffff))) return NAN;
-
- // +/-0 ** +/-0 = NAN
- if ( !(hx&0x7fffffff) && !(hy&0x7fffffff)) return NAN;
-
- // +inf ** +/-0 = NAN
- if ( ((hx & 0x7f800000) ==0x7f800000) && !(hy&0x7fffffff)) return NAN;
-
- // others except nan/inf/0 ** 0 = 1.0
- if (!(hy&0x7fffffff)) return 1.0f;
-
- // +1 ** inf = NAN; +1 ** finite = 1;
- if (hx == 0x3f800000) {
- return isinf(y) ? NAN : 1.0f;
- }
-
- if ( !(hx & 0x7fffffff)) {
- // +/-0 ** y<0 = +inf
- // +/-0 ** y>0 = +0
- return sy ? INFINITY : 0.0f;
- }
-
- return __gen_ocl_internal_pow(x,y);
- }
-}
-
-OVERLOADABLE float pown(float x, int n) {
- if (__ocl_math_fastpath_flag) {
- if (x == 0.f && n == 0)
- return 1.f;
- if (x < 0.f && (n&1) )
- return -powr(-x, n);
- return powr(x, n);
- } else {
- int ix;
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- float sign = ix < 0 ? -1.0f : 1.0f;
- if (x == 0.0f) x = sign * 0.0f;
-
- return __gen_ocl_internal_pown(x, n);
- }
-}
-
-OVERLOADABLE float pow(float x, float y) {
- if (!__ocl_math_fastpath_flag)
- return __gen_ocl_internal_pow(x,y);
- else {
- int n;
- if (x == 0.f && y == 0.f)
- return 1.f;
- if (x >= 0.f)
- return powr(x, y);
- n = y;
- if ((float)n == y)//is exact integer
- return pown(x, n);
- return NAN;
- }
-}
-
-OVERLOADABLE float rootn(float x, int n) {
- float ax,re;
- int sign = 0;
- int hx;
- if( n == 0 )return NAN;
-
- GEN_OCL_GET_FLOAT_WORD(hx, x);
- // Gen does not support denorm, flush to zero
- if ((hx & 0x7fffffff) < 0x00800000) {
- x = hx < 0 ? -0.0f : 0.0f;
- }
-
- //rootn ( x, n ) returns a NaN for x < 0 and n is even.
- if( x < 0 && 0 == (n&1) )
- return NAN;
- if( x == 0.0 ){
- switch( n & 0x80000001 ){
- //rootn ( +-0, n ) is +0 for even n > 0.
- case 0:
- return 0.0f;
- //rootn ( +-0, n ) is +-0 for odd n > 0.
- case 1:
- return x;
- //rootn ( +-0, n ) is +inf for even n < 0.
- case 0x80000000:
- return INFINITY;
-
- //rootn ( +-0, n ) is +-inf for odd n < 0.
- case 0x80000001:
- return __gen_ocl_internal_copysign(INFINITY, x);
- }
- }
- ax = __gen_ocl_fabs(x);
- if(x <0.0f && (n&1))
- sign = 1;
- if (__ocl_math_fastpath_flag)
- re = __gen_ocl_pow(ax, 1.f/n);
- else
- re = __gen_ocl_internal_pow(ax,1.f/n);
- if(sign)
- re = -re;
- return re;
-}
-
-OVERLOADABLE float fabs(float x) {
- return __gen_ocl_internal_fabs(x);
-}
-
-OVERLOADABLE float trunc(float x) {
- return __gen_ocl_internal_trunc(x);
-}
-
-OVERLOADABLE float round(float x) {
- return __gen_ocl_internal_round(x);
-}
-
-OVERLOADABLE float floor(float x) {
- return __gen_ocl_internal_floor(x);
-}
-
-OVERLOADABLE float ceil(float x) {
- return __gen_ocl_internal_ceil(x);
-}
-
-OVERLOADABLE float log(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log(x);
-
- return __gen_ocl_internal_log(x);
-}
-
-OVERLOADABLE float log2(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log2(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log2(x);
-
- return __gen_ocl_internal_log2(x);
-}
-
-OVERLOADABLE float log10(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log10(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log10(x);
-
- return __gen_ocl_internal_log10(x);
-}
+#define BODY \
+ *cosval = cos(x); \
+ return sin(x);
-OVERLOADABLE float exp(float x) {
+OVERLOADABLE float sincos(float x, global float *cosval) {
if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_exp(x);
-
- /* Use native instruction when it has enough precision */
- if (x > -0x1.6p1 && x < 0x1.6p1)
- return __gen_ocl_internal_fastpath_exp(x);
-
- return __gen_ocl_internal_exp(x);
-}
-
-OVERLOADABLE float exp2(float x) {
- /* Use native instruction when it has enough precision, exp2 always */
- return native_exp2(x);
+ return __gen_ocl_internal_fastpath_sincos(x, cosval);
+ BODY;
}
-
-OVERLOADABLE float exp10(float x) {
+OVERLOADABLE float sincos(float x, local float *cosval) {
if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_exp10(x);
-
- return __gen_ocl_internal_exp10(x);
+ return __gen_ocl_internal_fastpath_sincos(x, cosval);
+ BODY;
}
-
-OVERLOADABLE float expm1(float x) {
+OVERLOADABLE float sincos(float x, private float *cosval) {
if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_expm1(x);
-
- return __gen_ocl_internal_expm1(x);
-}
-
-OVERLOADABLE float fmin(float a, float b) {
- return __gen_ocl_internal_fmin(a, b);
-}
-
-OVERLOADABLE float fmax(float a, float b) {
- return __gen_ocl_internal_fmax(a, b);
-}
-
-OVERLOADABLE float fma(float a, float b, float c) {
- return mad(a, b, c);
-}
-
-OVERLOADABLE float fdim(float x, float y) {
- return __gen_ocl_internal_fdim(x, y);
-}
-
-OVERLOADABLE float maxmag(float x, float y) {
- return __gen_ocl_internal_maxmag(x, y);
-}
-
-OVERLOADABLE float minmag(float x, float y) {
- return __gen_ocl_internal_minmag(x, y);
+ return __gen_ocl_internal_fastpath_sincos(x, cosval);
+ BODY;
}
+#undef BODY
-
-/* So far, the HW do not support half float math function.
- We just do the conversion and call the float version here. */
-OVERLOADABLE half cospi(half x) {
- float _x = (float)x;
- return (half)cospi(_x);
-}
-OVERLOADABLE half cosh(half x) {
- float _x = (float)x;
- return (half)cosh(_x);
-}
-OVERLOADABLE half acos(half x) {
- float _x = (float)x;
- return (half)acos(_x);
-}
-OVERLOADABLE float half_cos(float x) {
- return (float)cos(x);
-}
-OVERLOADABLE float half_divide(float x, float y) {
- return (float)native_divide(x, y);
-}
-OVERLOADABLE float half_exp(float x) {
- return (float)native_exp(x);
-}
-OVERLOADABLE float half_exp2(float x){
- return (float)native_exp2(x);
-}
-OVERLOADABLE float half_exp10(float x){
- return (float)native_exp10(x);
-}
-OVERLOADABLE float half_log(float x){
- return (float)native_log(x);
-}
-OVERLOADABLE float half_log2(float x){
- return (float)native_log2(x);
-}
-OVERLOADABLE float half_log10(float x){
- return (float)native_log10(x);
-}
-OVERLOADABLE float half_powr(float x, float y){
- return (float)powr(x, y);
-}
-OVERLOADABLE float half_recip(float x){
- return (float)native_recip(x);
-}
-OVERLOADABLE float half_rsqrt(float x){
- return (float)native_rsqrt(x);
-}
-OVERLOADABLE float half_sin(float x){
- return (float)sin(x);
-}
-OVERLOADABLE float half_sqrt(float x){
- return (float)native_sqrt(x);
-}
-OVERLOADABLE float half_tan(float x){
- return (float)tan(x);
-}
-OVERLOADABLE half acospi(half x) {
- float _x = (float)x;
- return (half)acospi(_x);
-}
-OVERLOADABLE half acosh(half x) {
- float _x = (float)x;
- return (half)acosh(_x);
-}
-OVERLOADABLE half sinpi(half x) {
- float _x = (float)x;
- return (half)sinpi(_x);
-}
-OVERLOADABLE half sinh(half x) {
- float _x = (float)x;
- return (half)sinh(_x);
-}
-OVERLOADABLE half asin(half x) {
- float _x = (float)x;
- return (half)asin(_x);
-}
-OVERLOADABLE half asinpi(half x) {
- float _x = (float)x;
- return (half)asinpi(_x);
-}
-OVERLOADABLE half asinh(half x) {
- float _x = (float)x;
- return (half)asinh(_x);
-}
-OVERLOADABLE half tanpi(half x) {
- float _x = (float)x;
- return (half)tanpi(_x);
-}
-OVERLOADABLE half tanh(half x) {
- float _x = (float)x;
- return (half)tanh(_x);
-}
-OVERLOADABLE half atan(half x) {
- float _x = (float)x;
- return (half)atan(_x);
-}
-OVERLOADABLE half atan2(half y, half x) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)atan2(_x, _y);
-}
-OVERLOADABLE half atan2pi(half y, half x) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)atan2pi(_x, _y);
-}
-OVERLOADABLE half atanpi(half x) {
- float _x = (float)x;
- return (half)atanpi(_x);
-}
-OVERLOADABLE half atanh(half x) {
- float _x = (float)x;
- return (half)atanh(_x);
-}
-OVERLOADABLE half cbrt(half x) {
- float _x = (float)x;
- return (half)cbrt(_x);
-}
-OVERLOADABLE half rint(half x) {
- float _x = (float)x;
- return (half)rint(_x);
-}
-OVERLOADABLE half copysign(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)copysign(_x, _y);
-}
-OVERLOADABLE half erf(half x) {
- float _x = (float)x;
- return (half)erf(_x);
-}
-OVERLOADABLE half erfc(half x) {
- float _x = (float)x;
- return (half)erfc(_x);
-}
-OVERLOADABLE half fmod(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)fmod(_x, _y);
-}
-OVERLOADABLE half remainder(half x, half p) {
- float _x = (float)x;
- float _p = (float)p;
- return (half)remainder(_x, _p);
-}
-OVERLOADABLE half ldexp(half x, int n) {
- float _x = (float)x;
- return (half)ldexp(_x, n);
-}
-OVERLOADABLE half powr(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)powr(_x, _y);
-}
-OVERLOADABLE half pow(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)pow(_x, _y);
-}
-//no pow, we use powr instead
-OVERLOADABLE half fabs(half x) {
- float _x = (float)x;
- return (half)fabs(_x);
-}
-OVERLOADABLE half trunc(half x) {
- float _x = (float)x;
- return (half)trunc(_x);
-}
-OVERLOADABLE half round(half x) {
- float _x = (float)x;
- return (half)round(_x);
-}
-OVERLOADABLE half floor(half x) {
- float _x = (float)x;
- return (half)floor(_x);
-}
-OVERLOADABLE half ceil(half x) {
- float _x = (float)x;
- return (half)ceil(_x);
-}
-OVERLOADABLE half log(half x) {
- float _x = (float)x;
- return (half)log(_x);
-}
-OVERLOADABLE half log2(half x) {
- float _x = (float)x;
- return (half)log2(_x);
-}
-OVERLOADABLE half log10(half x) {
- float _x = (float)x;
- return (half)log10(_x);
-}
-OVERLOADABLE half exp(half x) {
- float _x = (float)x;
- return (half)exp(_x);
-}
-OVERLOADABLE half exp10(half x) {
- float _x = (float)x;
- return (half)exp10(_x);
-}
-OVERLOADABLE half expm1(half x) {
- float _x = (float)x;
- return (half)expm1(_x);
-}
-OVERLOADABLE half fmin(half a, half b) {
- return __gen_ocl_internal_fmin(a, b);
-}
-OVERLOADABLE half fmax(half a, half b) {
- return __gen_ocl_internal_fmax(a, b);
-}
-OVERLOADABLE half fma(half a, half b, half c) {
- float _a = (float)a;
- float _b = (float)b;
- float _c = (float)c;
- return (half)fma(_a, _b, _c);
-}
-OVERLOADABLE half fdim(half x, half y) {
+OVERLOADABLE half remquo(half x, half y, global int *quo) {
float _x = (float)x;
float _y = (float)y;
- return (half)fdim(_x, _y);
+ return (half)remquo(_x, _y, quo);
}
-OVERLOADABLE half maxmag(half x, half y) {
+OVERLOADABLE half remquo(half x, half y, local int *quo) {
float _x = (float)x;
float _y = (float)y;
- return (half)maxmag(_x, _y);
+ return (half)remquo(_x, _y, quo);
}
-OVERLOADABLE half minmag(half x, half y) {
+OVERLOADABLE half remquo(half x, half y, private int *quo) {
float _x = (float)x;
float _y = (float)y;
- return (half)minmag(_x, _y);
-}
-OVERLOADABLE half exp2(half x) {
- float _x = (float)x;
- return (half)exp2(_x);
-}
-OVERLOADABLE half mad(half a, half b, half c) {
- return __gen_ocl_mad(a,b,c);
-}
-OVERLOADABLE half sin(half x) {
- float _x = (float)x;
- return (half)sin(_x);
-}
-OVERLOADABLE half cos(half x) {
- float _x = (float)x;
- return (half)cos(_x);
-}
-OVERLOADABLE half tan(half x) {
- float _x = (float)x;
- return (half)tan(_x);
-}
-OVERLOADABLE half tgamma(half x) {
- float _x = (float)x;
- return (half)tgamma(_x);
-}
-OVERLOADABLE half lgamma(half x) {
- float _x = (float)x;
- return (half)lgamma(_x);
-}
-OVERLOADABLE half lgamma_r(half x, global int *signgamp) {
- float _x = (float)x;
- return (half)lgamma_r(_x, signgamp);
-}
-OVERLOADABLE half lgamma_r(half x, local int *signgamp) {
- float _x = (float)x;
- return (half)lgamma_r(_x, signgamp);
-}
-OVERLOADABLE half lgamma_r(half x, private int *signgamp) {
- float _x = (float)x;
- return (half)lgamma_r(_x, signgamp);
-}
-OVERLOADABLE half log1p(half x) {
- float _x = (float)x;
- return (half)log1p(_x);
-}
-OVERLOADABLE half logb(half x) {
- float _x = (float)x;
- return (half)logb(_x);
-}
-OVERLOADABLE int ilogb(half x) {
- float _x = (float)x;
- return ilogb(_x);
-}
-OVERLOADABLE half nan(ushort code) {
- return (half)NAN;
+ return (half)remquo(_x, _y, quo);
}
OVERLOADABLE half sincos(half x, global half *cosval) {
@@ -3797,109 +594,6 @@ OVERLOADABLE half sincos(half x, private half *cosval) {
return ret;
}
-OVERLOADABLE half sqrt(half x) {
- float _x = (float)x;
- return (half)sqrt(_x);
-}
-OVERLOADABLE half rsqrt(half x) {
- float _x = (float)x;
- return (half)rsqrt(_x);
-}
-OVERLOADABLE half frexp(half x, global int *exp) {
- float _x = (float)x;
- return (half)frexp(_x, exp);
-}
-OVERLOADABLE half frexp(half x, local int *exp) {
- float _x = (float)x;
- return (half)frexp(_x, exp);
-}
-OVERLOADABLE half frexp(half x, private int *exp) {
- float _x = (float)x;
- return (half)frexp(_x, exp);
-}
-OVERLOADABLE half nextafter(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)nextafter(_x, _y);
-}
-
-OVERLOADABLE half modf(half x, global half *i) {
- float _x = (float)x;
- float _i;
- half ret = (half)modf(_x, &_i);
- *i = (half)_i;
- return ret;
-}
-OVERLOADABLE half modf(half x, local half *i) {
- float _x = (float)x;
- float _i;
- half ret = (half)modf(_x, &_i);
- *i = (half)_i;
- return ret;
-}
-OVERLOADABLE half modf(half x, private half *i) {
- float _x = (float)x;
- float _i;
- half ret = (half)modf(_x, &_i);
- *i = (half)_i;
- return ret;
-}
-
-OVERLOADABLE half hypot(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)hypot(_x, _y);
-}
-
-OVERLOADABLE half fract(half x, global half *p) {
- float _x = (float)x;
- float _p;
- half ret = (half)fract(_x, &_p);
- *p = (half)_p;
- return ret;
-}
-OVERLOADABLE half fract(half x, local half *p) {
- float _x = (float)x;
- float _p;
- half ret = (half)fract(_x, &_p);
- *p = (half)_p;
- return ret;
-}
-OVERLOADABLE half fract(half x, private half *p) {
- float _x = (float)x;
- float _p;
- half ret = (half)fract(_x, &_p);
- *p = (half)_p;
- return ret;
-}
-
-OVERLOADABLE half remquo(half x, half y, global int *quo) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)remquo(_x, _y, quo);
-}
-OVERLOADABLE half remquo(half x, half y, local int *quo) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)remquo(_x, _y, quo);
-}
-OVERLOADABLE half remquo(half x, half y, private int *quo) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)remquo(_x, _y, quo);
-}
-
-OVERLOADABLE half pown(half x, int n) {
- float _x = (float)x;
- return (half)pown(_x, n);
-}
-OVERLOADABLE half rootn(half x, int n) {
- float _x = (float)x;
- return (half)rootn(_x, n);
-}
-
-
-
//-----------------double -----------------------
INLINE int __HI(double x){
long x64 = as_long(x);
diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.h b/backend/src/libocl/tmpl/ocl_math.tmpl.h
index ca11b25d..cafb7678 100644
--- a/backend/src/libocl/tmpl/ocl_math.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math.tmpl.h
@@ -21,217 +21,47 @@
#include "ocl_types.h"
#include "ocl_math_common.h"
-OVERLOADABLE float cospi(float x);
-OVERLOADABLE float cosh(float x);
-OVERLOADABLE float acos(float x);
-OVERLOADABLE float acospi(float x);
-OVERLOADABLE float acosh(float x);
-OVERLOADABLE float sinpi(float x);
-OVERLOADABLE float sinh(float x);
-OVERLOADABLE float asin(float x);
-OVERLOADABLE float asinpi(float x);
-OVERLOADABLE float asinh(float x);
-OVERLOADABLE float tanpi(float x);
-OVERLOADABLE float tanh(float x);
-OVERLOADABLE float atan(float x);
-OVERLOADABLE float atan2(float y, float x);
-OVERLOADABLE float atan2pi(float y, float x);
-OVERLOADABLE float atanpi(float x);
-OVERLOADABLE float atanh(float x);
-OVERLOADABLE float cbrt(float x);
-OVERLOADABLE float rint(float x);
-OVERLOADABLE float copysign(float x, float y);
-OVERLOADABLE float erf(float x);
-OVERLOADABLE float erfc(float x);
-OVERLOADABLE float fmod (float x, float y);
-OVERLOADABLE float remainder(float x, float p);
-OVERLOADABLE float ldexp(float x, int n);
-OVERLOADABLE float powr(float x, float y);
-OVERLOADABLE float pow(float x, float y);
-//no pow, we use powr instead
-OVERLOADABLE float fabs(float x);
-OVERLOADABLE float trunc(float x);
-OVERLOADABLE float round(float x);
-OVERLOADABLE float floor(float x);
-OVERLOADABLE float ceil(float x);
-OVERLOADABLE float log(float x);
-OVERLOADABLE float log2(float x);
-OVERLOADABLE float log10(float x);
-OVERLOADABLE float exp(float x);
-OVERLOADABLE float exp10(float x);
-OVERLOADABLE float expm1(float x);
-OVERLOADABLE float fmin(float a, float b);
-OVERLOADABLE float fmax(float a, float b);
-OVERLOADABLE float fma(float a, float b, float c);
-OVERLOADABLE float fdim(float x, float y);
-OVERLOADABLE float maxmag(float x, float y);
-OVERLOADABLE float minmag(float x, float y);
-OVERLOADABLE float exp2(float x);
-OVERLOADABLE float mad(float a, float b, float c);
-OVERLOADABLE float sin(float x);
-OVERLOADABLE float cos(float x);
-OVERLOADABLE float tan(float x);
-OVERLOADABLE float tgamma(float x);
-OVERLOADABLE float lgamma(float x);
+
OVERLOADABLE float lgamma_r(float x, global int *signgamp);
OVERLOADABLE float lgamma_r(float x, local int *signgamp);
OVERLOADABLE float lgamma_r(float x, private int *signgamp);
-OVERLOADABLE float log1p(float x);
-OVERLOADABLE float logb(float x);
-OVERLOADABLE int ilogb(float x);
-OVERLOADABLE float nan(uint code);
OVERLOADABLE float sincos(float x, global float *cosval);
OVERLOADABLE float sincos(float x, local float *cosval);
OVERLOADABLE float sincos(float x, private float *cosval);
-OVERLOADABLE float sqrt(float x);
-OVERLOADABLE float rsqrt(float x);
OVERLOADABLE float frexp(float x, global int *exp);
OVERLOADABLE float frexp(float x, local int *exp);
OVERLOADABLE float frexp(float x, private int *exp);
-OVERLOADABLE float nextafter(float x, float y);
OVERLOADABLE float modf(float x, global float *i);
OVERLOADABLE float modf(float x, local float *i);
OVERLOADABLE float modf(float x, private float *i);
-OVERLOADABLE float hypot(float x, float y);
OVERLOADABLE float fract(float x, global float *p);
OVERLOADABLE float fract(float x, local float *p);
OVERLOADABLE float fract(float x, private float *p);
OVERLOADABLE float remquo(float x, float y, global int *quo);
OVERLOADABLE float remquo(float x, float y, local int *quo);
OVERLOADABLE float remquo(float x, float y, private int *quo);
-OVERLOADABLE float pown(float x, int n);
-OVERLOADABLE float rootn(float x, int n);
-
-// native
-OVERLOADABLE float native_cos(float x);
-OVERLOADABLE float native_divide(float x, float y);
-OVERLOADABLE float native_exp(float x);
-OVERLOADABLE float native_exp2(float x);
-OVERLOADABLE float native_exp10(float x);
-OVERLOADABLE float native_log(float x);
-OVERLOADABLE float native_log2(float x);
-OVERLOADABLE float native_log10(float x);
-OVERLOADABLE float native_powr(float x, float y);
-OVERLOADABLE float native_recip(float x);
-OVERLOADABLE float native_rsqrt(float x);
-OVERLOADABLE float native_sin(float x);
-OVERLOADABLE float native_sqrt(float x);
-OVERLOADABLE float native_tan(float x);
-// Half float version.
-OVERLOADABLE half cospi(half x);
-OVERLOADABLE half cosh(half x);
-OVERLOADABLE half acos(half x);
-OVERLOADABLE half acospi(half x);
-OVERLOADABLE half acosh(half x);
-OVERLOADABLE half sinpi(half x);
-OVERLOADABLE half sinh(half x);
-OVERLOADABLE half asin(half x);
-OVERLOADABLE half asinpi(half x);
-OVERLOADABLE half asinh(half x);
-OVERLOADABLE half tanpi(half x);
-OVERLOADABLE half tanh(half x);
-OVERLOADABLE half atan(half x);
-OVERLOADABLE half atan2(half y, half x);
-OVERLOADABLE half atan2pi(half y, half x);
-OVERLOADABLE half atanpi(half x);
-OVERLOADABLE half atanh(half x);
-OVERLOADABLE half cbrt(half x);
-OVERLOADABLE half rint(half x);
-OVERLOADABLE half copysign(half x, half y);
-OVERLOADABLE half erf(half x);
-OVERLOADABLE half erfc(half x);
-OVERLOADABLE half fmod (half x, half y);
-OVERLOADABLE half remainder(half x, half p);
-OVERLOADABLE half ldexp(half x, int n);
-OVERLOADABLE half powr(half x, half y);
-OVERLOADABLE half pow(half x, half y);
-//no pow, we use powr instead
-OVERLOADABLE half fabs(half x);
-OVERLOADABLE half trunc(half x);
-OVERLOADABLE half round(half x);
-OVERLOADABLE half floor(half x);
-OVERLOADABLE half ceil(half x);
-OVERLOADABLE half log(half x);
-OVERLOADABLE half log2(half x);
-OVERLOADABLE half log10(half x);
-OVERLOADABLE half exp(half x);
-OVERLOADABLE half exp10(half x);
-OVERLOADABLE half expm1(half x);
-OVERLOADABLE half fmin(half a, half b);
-OVERLOADABLE half fmax(half a, half b);
-OVERLOADABLE half fma(half a, half b, half c);
-OVERLOADABLE half fdim(half x, half y);
-OVERLOADABLE half maxmag(half x, half y);
-OVERLOADABLE half minmag(half x, half y);
-OVERLOADABLE half exp2(half x);
-OVERLOADABLE half mad(half a, half b, half c);
-OVERLOADABLE half sin(half x);
-OVERLOADABLE half cos(half x);
-OVERLOADABLE half tan(half x);
-OVERLOADABLE half tgamma(half x);
-OVERLOADABLE half lgamma(half x);
OVERLOADABLE half lgamma_r(half x, global int *signgamp);
OVERLOADABLE half lgamma_r(half x, local int *signgamp);
OVERLOADABLE half lgamma_r(half x, private int *signgamp);
-OVERLOADABLE half log1p(half x);
-OVERLOADABLE half logb(half x);
-OVERLOADABLE int ilogb(half x);
-OVERLOADABLE half nan(ushort code);
OVERLOADABLE half sincos(half x, global half *cosval);
OVERLOADABLE half sincos(half x, local half *cosval);
OVERLOADABLE half sincos(half x, private half *cosval);
-OVERLOADABLE half sqrt(half x);
-OVERLOADABLE half rsqrt(half x);
OVERLOADABLE half frexp(half x, global int *exp);
OVERLOADABLE half frexp(half x, local int *exp);
OVERLOADABLE half frexp(half x, private int *exp);
-OVERLOADABLE half nextafter(half x, half y);
OVERLOADABLE half modf(half x, global half *i);
OVERLOADABLE half modf(half x, local half *i);
OVERLOADABLE half modf(half x, private half *i);
-OVERLOADABLE half hypot(half x, half y);
OVERLOADABLE half fract(half x, global half *p);
OVERLOADABLE half fract(half x, local half *p);
OVERLOADABLE half fract(half x, private half *p);
OVERLOADABLE half remquo(half x, half y, global int *quo);
OVERLOADABLE half remquo(half x, half y, local int *quo);
OVERLOADABLE half remquo(half x, half y, private int *quo);
-OVERLOADABLE half pown(half x, int n);
-OVERLOADABLE half rootn(half x, int n);
-// native half
-OVERLOADABLE half native_cos(half x);
-OVERLOADABLE half native_divide(half x, half y);
-OVERLOADABLE half native_exp(half x);
-OVERLOADABLE half native_exp2(half x);
-OVERLOADABLE half native_exp10(half x);
-OVERLOADABLE half native_log(half x);
-OVERLOADABLE half native_log2(half x);
-OVERLOADABLE half native_log10(half x);
-OVERLOADABLE half native_powr(half x, half y);
-OVERLOADABLE half native_recip(half x);
-OVERLOADABLE half native_rsqrt(half x);
-OVERLOADABLE half native_sin(half x);
-OVERLOADABLE half native_sqrt(half x);
-OVERLOADABLE half native_tan(half x);
-// half accuracy
-OVERLOADABLE float half_cos(float x);
-OVERLOADABLE float half_divide(float x, float y);
-OVERLOADABLE float half_exp(float x);
-OVERLOADABLE float half_exp2(float x);
-OVERLOADABLE float half_exp10(float x);
-OVERLOADABLE float half_log(float x);
-OVERLOADABLE float half_log2(float x);
-OVERLOADABLE float half_log10(float x);
-OVERLOADABLE float half_powr(float x, float y);
-OVERLOADABLE float half_recip(float x);
-OVERLOADABLE float half_rsqrt(float x);
-OVERLOADABLE float half_sin(float x);
-OVERLOADABLE float half_sqrt(float x);
-OVERLOADABLE float half_tan(float x);
//------- double -----------
OVERLOADABLE double fract(double x, global double *p);
diff --git a/backend/src/libocl/tmpl/ocl_math_20.tmpl.cl b/backend/src/libocl/tmpl/ocl_math_20.tmpl.cl
index ba35ddd5..c6b52a31 100644
--- a/backend/src/libocl/tmpl/ocl_math_20.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_20.tmpl.cl
@@ -37,414 +37,200 @@ CONST float __gen_ocl_rnde(float x) __asm("llvm.rint" ".f32");
CONST float __gen_ocl_rndu(float x) __asm("llvm.ceil" ".f32");
CONST float __gen_ocl_rndd(float x) __asm("llvm.floor" ".f32");
+#define BODY \
+ if (isnan(x)) { \
+ *p = x; \
+ return x; \
+ } \
+ *p = __gen_ocl_rndd(x); \
+ if (isinf(x)) { \
+ return x > 0 ? +0. : -0.; \
+ } \
+ return min(x - *p, 0x1.FFFFFep-1F);
+OVERLOADABLE float fract(float x, float *p) { BODY; }
+#undef BODY
-/* native functions */
-OVERLOADABLE float native_cos(float x) { return __gen_ocl_cos(x); }
-OVERLOADABLE float native_sin(float x) { return __gen_ocl_sin(x); }
-OVERLOADABLE float native_sqrt(float x) { return __gen_ocl_sqrt(x); }
-OVERLOADABLE float native_rsqrt(float x) { return __gen_ocl_rsqrt(x); }
-OVERLOADABLE float native_log2(float x) { return __gen_ocl_log(x); }
-OVERLOADABLE float native_log(float x) {
- return native_log2(x) * 0.6931472002f;
-}
-OVERLOADABLE float native_log10(float x) {
- return native_log2(x) * 0.3010299956f;
-}
-OVERLOADABLE float native_powr(float x, float y) { return __gen_ocl_pow(x,y); }
-OVERLOADABLE float native_recip(float x) { return __gen_ocl_rcp(x); }
-OVERLOADABLE float native_tan(float x) {
- return native_sin(x) / native_cos(x);
-}
-OVERLOADABLE float native_exp2(float x) { return __gen_ocl_exp(x); }
-OVERLOADABLE float native_exp(float x) { return __gen_ocl_exp(M_LOG2E_F*x); }
-OVERLOADABLE float native_exp10(float x) { return __gen_ocl_exp(M_LOG210_F*x); }
-OVERLOADABLE float native_divide(float x, float y) { return x/y; }
+#define BODY \
+ float Zero[2]; \
+ int n,hx,hy,hz,ix,iy,sx,i,sy; \
+ uint q,sxy; \
+ Zero[0] = 0.0;Zero[1] = -0.0; \
+ if (x == 0.0f) { x = 0.0f; }; \
+ if (y == 0.0f) { y = 0.0f; }\
+ GEN_OCL_GET_FLOAT_WORD(hx,x);GEN_OCL_GET_FLOAT_WORD(hy,y); \
+ sxy = (hx ^ hy) & 0x80000000;sx = hx&0x80000000;sy = hy&0x80000000; \
+ hx ^=sx; hy &= 0x7fffffff; \
+ if (hx < 0x00800000)hx = 0;if (hy < 0x00800000)hy = 0; \
+ if(hy==0||hx>=0x7f800000||hy>0x7f800000){ \
+ *quo = 0;return NAN; \
+ } \
+ if( hy == 0x7F800000 || hx == 0 ) { \
+ *quo = 0;return x; \
+ } \
+ if( hx == hy ) { \
+ *quo = (x == y) ? 1 : -1; \
+ return sx ? -0.0 : 0.0; \
+ } \
+ if(hx<hy) { \
+ q = 0; \
+ goto fixup; \
+ } else if(hx==hy) { \
+ *quo = (sxy ? -1 : 1); \
+ return Zero[(uint)sx>>31]; \
+ } \
+ ix = (hx>>23)-127; \
+ iy = (hy>>23)-127; \
+ hx = 0x00800000|(0x007fffff&hx); \
+ hy = 0x00800000|(0x007fffff&hy); \
+ n = ix - iy; \
+ q = 0; \
+ while(n--) { \
+ hz=hx-hy; \
+ if(hz<0) hx = hx << 1; \
+ else {hx = hz << 1; q++;} \
+ q <<= 1; \
+ } \
+ hz=hx-hy; \
+ if(hz>=0) {hx=hz;q++;} \
+ if(hx==0) { \
+ q &= 0x0000007f; \
+ *quo = (sxy ? -q : q); \
+ return Zero[(uint)sx>>31]; \
+ } \
+ while(hx<0x00800000) { \
+ hx <<= 1;iy -= 1; \
+ } \
+ if(iy>= -126) { \
+ hx = ((hx-0x00800000)|((iy+127)<<23)); \
+ } else {\
+ n = -126 - iy; \
+ hx >>= n; \
+ } \
+fixup: \
+ GEN_OCL_SET_FLOAT_WORD(x,hx); \
+ if(hx<0x00800000){ \
+ GEN_OCL_GET_FLOAT_WORD(hy,y); \
+ hy &= 0x7fffffff; \
+ if(hx+hx > hy ||(hx+hx==hy && (q & 1)))q++; \
+ x = 0; \
+ }else{ \
+ y = __gen_ocl_fabs(y); \
+ if (y < 0x1p-125f) { \
+ if (x+x>y || (x+x==y && (q & 1))) { \
+ q++;x-=y; \
+ } \
+ }else if (x>0.5f*y || (x==0.5f*y && (q & 1))) { \
+ q++;x-=y; \
+ } \
+ GEN_OCL_GET_FLOAT_WORD(hx,x);GEN_OCL_SET_FLOAT_WORD(x,hx^sx); \
+ } \
+ int sign = sx==sy?0:1; \
+ q &= 0x0000007f; \
+ *quo = (sign ? -q : q); \
+ return x;
-/* Fast path */
-OVERLOADABLE float __gen_ocl_internal_fastpath_acosh (float x) {
- return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_asinh (float x) {
- return native_log(x + native_sqrt(x * x + 1));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_atanh (float x) {
- return 0.5f * native_log((1 + x) / (1 - x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cbrt (float x) {
- return __gen_ocl_pow(x, 0.3333333333f);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cos (float x) {
- return native_cos(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cosh (float x) {
- return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_cospi (float x) {
- return __gen_ocl_cos(x * M_PI_F);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_exp (float x) {
- return native_exp(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_exp10 (float x) {
- return native_exp10(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_expm1 (float x) {
- return __gen_ocl_pow(M_E_F, x) - 1;
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_fmod (float x, float y) {
- return x-y*__gen_ocl_rndz(x/y);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_hypot (float x, float y) {
- return __gen_ocl_sqrt(x*x + y*y);
-}
-OVERLOADABLE int __gen_ocl_internal_fastpath_ilogb (float x) {
- return __gen_ocl_rndd(native_log2(x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_ldexp (float x, int n) {
- return __gen_ocl_pow(2, n) * x;
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log (float x) {
- return native_log(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log2 (float x) {
- return native_log2(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log10 (float x) {
- return native_log10(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_log1p (float x) {
- return native_log(x + 1);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_logb (float x) {
- return __gen_ocl_rndd(native_log2(x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_remainder (float x, float y) {
- return x-y*__gen_ocl_rnde(x/y);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_rootn(float x, int n) {
- return __gen_ocl_pow(x, 1.f / n);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sin (float x) {
- return native_sin(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sincos (float x, float *cosval) {
- *cosval = native_cos(x);
- return native_sin(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sinh (float x) {
- return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_sinpi (float x) {
- return __gen_ocl_sin(x * M_PI_F);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_tan (float x) {
- return native_tan(x);
-}
-OVERLOADABLE float __gen_ocl_internal_fastpath_tanh (float x) {
- float y = native_exp(-2 * x);
- return (1 - y) / (1 + y);
+OVERLOADABLE float remquo(float x, float y, int *quo) {
+ BODY;
}
+#undef BODY
+#define BODY \
+ if (isnan(x) || isinf(x)) { \
+ *exp = 0; \
+ return x; \
+ } \
+ uint u = as_uint(x); \
+ uint a = u & 0x7FFFFFFFu; \
+ if (a == 0) { \
+ *exp = 0; \
+ return x; \
+ } \
+ if (a >= 0x800000) { \
+ *exp = (a >> 23) - 126; \
+ return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
+ } \
+ int e = -126; \
+ while (a < 0x400000) { \
+ e --; \
+ a <<= 1; \
+ } \
+ a <<= 1; \
+ *exp = e; \
+ return as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
+OVERLOADABLE float frexp(float x, int *exp) { BODY; }
+#undef BODY
-/* Internal implement, high accuracy. */
-OVERLOADABLE float __gen_ocl_internal_floor(float x) { return __gen_ocl_rndd(x); }
-OVERLOADABLE float __gen_ocl_internal_copysign(float x, float y) {
- union { unsigned u; float f; } ux, uy;
- ux.f = x;
- uy.f = y;
- ux.u = (ux.u & 0x7fffffff) | (uy.u & 0x80000000u);
- return ux.f;
+OVERLOADABLE half fract(half x, half *p) {
+ float _x = (float)x;
+ float _p;
+ half ret = (half)fract(_x, &_p);
+ *p = (half)_p;
+ return ret;
}
-OVERLOADABLE float inline __gen_ocl_internal_log_valid(float x) {
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- union { unsigned int i; float f; } u;
- const float
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- two25 = 3.355443200e+07, /* 0x4c000000 */
- Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
- Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
- Lg3 = 2.8571429849e-01, /* 3E924925 */
- Lg4 = 2.2222198546e-01; /* 3E638E29 */
-
- const float zero = 0.0;
- float fsq, f, s, z, R, w, t1, t2, partial;
- int k, ix, i, j;
-
- u.f = x; ix = u.i;
- k = 0;
-
- k += (ix>>23) - 127;
- ix &= 0x007fffff;
- i = (ix + (0x95f64<<3)) & 0x800000;
- u.i = ix | (i^0x3f800000); x = u.f;
- k += (i>>23);
- f = x - 1.0f;
- fsq = f * f;
-
- if((0x007fffff & (15 + ix)) < 16) { /* |f| < 2**-20 */
- R = fsq * (0.5f - 0.33333333333333333f * f);
- return k * ln2_hi + k * ln2_lo + f - R;
- }
-
- s = f / (2.0f + f);
- z = s * s;
- i = ix - (0x6147a << 3);
- w = z * z;
- j = (0x6b851 << 3) - ix;
- t1= w * mad(w, Lg4, Lg2);
- t2= z * mad(w, Lg3, Lg1);
- i |= j;
- R = t2 + t1;
- partial = (i > 0) ? -mad(s, 0.5f * fsq, -0.5f * fsq) : (s * f);
-
- return mad(s, R, f) - partial + k * ln2_hi + k * ln2_lo;;
+OVERLOADABLE half remquo(half x, half y, int *quo) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)remquo(_x, _y, quo);
}
-OVERLOADABLE float __gen_ocl_internal_log(float x)
-{
- union { unsigned int i; float f; } u;
- u.f = x;
- int ix = u.i;
-
- if (ix < 0 )
- return NAN; /* log(-#) = NaN */
- if (ix >= 0x7f800000)
- return NAN;
-
- return __gen_ocl_internal_log_valid(x);
+OVERLOADABLE half modf(half x, half *i) {
+ float _x = (float)x;
+ float _i;
+ half ret = (half)modf(_x, &_i);
+ *i = (half)_i;
+ return ret;
}
-OVERLOADABLE float __gen_ocl_internal_log10(float x)
-{
- union { float f; unsigned i; } u;
- const float
- ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
- log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
- log10_2lo = 7.9034151668e-07; /* 0x355427db */
-
- float y, z;
- int i, k, hx;
-
- u.f = x; hx = u.i;
-
- if (hx<0)
- return NAN; /* log(-#) = NaN */
- if (hx >= 0x7f800000)
- return NAN;
-
- k = (hx >> 23) - 127;
- i = ((unsigned)k & 0x80000000) >> 31;
- hx = (hx&0x007fffff) | ((0x7f-i) << 23);
- y = (float)(k + i);
- u.i = hx; x = u.f;
-
- return y * log10_2lo + y * log10_2hi + ivln10 * __gen_ocl_internal_log_valid(x);
+OVERLOADABLE half frexp(half x, int *exp) {
+ float _x = (float)x;
+ return (half)frexp(_x, exp);
}
-
-OVERLOADABLE float __gen_ocl_internal_log2(float x)
-{
- const float zero = 0.0,
- invln2 = 0x1.715476p+0f;
- int ix;
-
- union { float f; int i; } u;
- u.f = x; ix = u.i;
-
- if (ix < 0)
- return NAN; /** log(-#) = NaN */
- if (ix >= 0x7f800000)
- return NAN;
-
- return invln2 * __gen_ocl_internal_log_valid(x);
+OVERLOADABLE half sincos(half x, half *cosval) {
+ float _x = (float)x;
+ float _cosval;
+ half ret = (half)sincos(_x, &_cosval);
+ *cosval = (half)_cosval;
+ return ret;
}
-
-float __gen_ocl_scalbnf (float x, int n){
- /* copy from fdlibm */
- float two25 = 3.355443200e+07, /* 0x4c000000 */
- twom25 = 2.9802322388e-08, /* 0x33000000 */
- huge = 1.0e+30,
- tiny = 1.0e-30;
- int k,ix;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- k = (ix&0x7f800000)>>23; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((ix&0x7fffffff)==0) return x; /* +-0 */
- x *= two25;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- k = ((ix&0x7f800000)>>23) - 25;
- }
- if (k==0xff) return x+x; /* NaN or Inf */
- if (n< -50000)
- return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
- if (n> 50000 || k+n > 0xfe)
- return huge*__gen_ocl_internal_copysign(huge,x); /* overflow */
- /* Now k and n are bounded we know that k = k+n does not overflow. */
- k = k+n;
- if (k > 0) { /* normal result */
- GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
- return x;
- }
- if (k <= -25)
- return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
- k += 25; /* subnormal result */
- GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
- return x*twom25;
+OVERLOADABLE half lgamma_r(half x, int *signgamp) {
+ float _x = (float)x;
+ return (half)lgamma_r(_x, signgamp);
}
-const __constant unsigned int two_over_pi[] = {
-0, 0, 0xA2F, 0x983, 0x6E4, 0xe44, 0x152, 0x9FC,
-0x275, 0x7D1, 0xF53, 0x4DD, 0xC0D, 0xB62,
-0x959, 0x93C, 0x439, 0x041, 0xFE5, 0x163,
-};
-
-// The main idea is from "Radian Reduction for Trigonometric Functions"
-// written by Mary H. Payne and Robert N. Hanek. Also another reference
-// is "A Continued-Fraction Analysis of Trigonometric Argument Reduction"
-// written by Roger Alan Smith, who gave the worst case in this paper.
-// for single float, worst x = 0x1.47d0fep34, and there are 29 bit
-// leading zeros in the fraction part of x*(2.0/pi). so we need at least
-// 29 (leading zero)+ 24 (fraction )+12 (integer) + guard bits. that is,
-// 65 + guard bits, as we calculate in 12*7 = 84bits, which means we have
-// about 19 guard bits. If we need further precision, we may need more
-// guard bits
-// Note we place two 0 in two_over_pi, which is used to handle input less
-// than 0x1.0p23
-
-int payne_hanek(float x, float *y) {
- union { float f; unsigned u;} ieee;
- ieee.f = x;
- unsigned u = ieee.u;
- int k = ((u & 0x7f800000) >> 23)-127;
- int ma = (u & 0x7fffff) | 0x800000;
- unsigned high, low;
- high = (ma & 0xfff000) >> 12;
- low = ma & 0xfff;
-
- // Two tune below macro, you need to fully understand the algorithm
-#define CALC_BLOCKS 7
-#define ZERO_BITS 2
-
- unsigned result[CALC_BLOCKS];
-
- // round down, note we need 2 bits integer precision
- int index = (k-23-2) < 0 ? (k-23-2-11)/12 : (k-23-2)/12;
+#define BODY \
+ uint hx = as_uint(x), ix = hx & 0x7FFFFFFF; \
+ if (ix > 0x7F800000) { \
+ *i = nan(0u); \
+ return nan(0u); \
+ } \
+ if (ix == 0x7F800000) { \
+ *i = x; \
+ return as_float(hx & 0x80000000u); \
+ } \
+ *i = __gen_ocl_rndz(x); \
+ return x - *i;
+OVERLOADABLE float modf(float x, float *i) { BODY; }
+#undef BODY
- for (int i = 0; i < CALC_BLOCKS; i++) {
- result[i] = low * two_over_pi[index+i+ZERO_BITS] ;
- result[i] += high * two_over_pi[index+i+1+ZERO_BITS];
- }
+#define BODY \
+ *cosval = cos(x); \
+ return sin(x);
- for (int i = CALC_BLOCKS-1; i > 0; i--) {
- int temp = result[i] >> 12;
- result[i] -= temp << 12;
- result[i-1] += temp;
+OVERLOADABLE float sincos(float x, float *cosval) {
+ if (__ocl_math_fastpath_flag)
+ {
+ *cosval = native_cos(x);
+ return native_sin(x);
}
-#undef CALC_BLOCKS
-#undef ZERO_BITS
-
- // get number of integer digits in result[0], note we only consider 12 valid bits
- // and also it means the fraction digits in result[0] is (12-intDigit)
-
- int intDigit = index*(-12) + (k-23);
-
- // As the integer bits may be all included in result[0], and also maybe
- // some bits in result[0], and some in result[1]. So we merge succesive bits,
- // which makes easy coding.
-
- unsigned b0 = (result[0] << 12) | result[1];
- unsigned b1 = (result[2] << 12) | result[3];
- unsigned b2 = (result[4] << 12) | result[5];
- unsigned b3 = (result[6] << 12);
-
- unsigned intPart = b0 >> (24-intDigit);
-
- unsigned fract1 = ((b0 << intDigit) | (b1 >> (24-intDigit))) & 0xffffff;
- unsigned fract2 = ((b1 << intDigit) | (b2 >> (24-intDigit))) & 0xffffff;
- unsigned fract3 = ((b2 << intDigit) | (b3 >> (24-intDigit))) & 0xffffff;
-
- // larger than 0.5? which mean larger than pi/4, we need
- // transform from [0,pi/2] to [-pi/4, pi/4] through -(1.0-fract)
- int largerPiBy4 = ((fract1 & 0x800000) != 0);
- int sign = largerPiBy4 ? 1 : 0;
- intPart = largerPiBy4 ? (intPart+1) : intPart;
-
- fract1 = largerPiBy4 ? (fract1 ^ 0x00ffffff) : fract1;
- fract2 = largerPiBy4 ? (fract2 ^ 0x00ffffff) : fract2;
- fract3 = largerPiBy4 ? (fract3 ^ 0x00ffffff) : fract3;
-
- int leadingZero = (fract1 == 0);
-
- // +1 is for the hidden bit 1 in floating-point format
- int exponent = leadingZero ? -(24+1) : -(0+1);
-
- fract1 = leadingZero ? fract2 : fract1;
- fract2 = leadingZero ? fract3 : fract2;
-
- // fract1 may have leading zeros, add it
- int shift = clz(fract1)-8;
- exponent += -shift;
-
- float pio2 = 0x1.921fb6p+0;
- unsigned fdigit = ((fract1 << shift) | (fract2 >> (24-shift))) & 0xffffff;
-
- // we know that denormal number will not appear here
- ieee.u = (sign << 31) | ((exponent+127) << 23) | (fdigit & 0x7fffff);
- *y = ieee.f * pio2;
- return intPart;
-}
-int argumentReduceSmall(float x, float * remainder) {
- union {
- float f;
- unsigned u;
- } ieee;
-
- float twoByPi = 2.0f/3.14159265f;
- float piBy2_1h = (float) 0xc90/0x1.0p11,
- piBy2_1l = (float) 0xfda/0x1.0p23,
- piBy2_2h = (float) 0xa22/0x1.0p35,
- piBy2_2l = (float) 0x168/0x1.0p47,
- piBy2_3h = (float) 0xc23/0x1.0p59,
- piBy2_3l = (float) 0x4c4/0x1.0p71;
-
- float y = (float)(int)(twoByPi * x + 0.5f);
- ieee.f = y;
- ieee.u = ieee.u & 0xfffff000;
-
- float yh = ieee.f;
- float yl = y - yh;
- float rem = x - yh*piBy2_1h - yh*piBy2_1l - yl*piBy2_1h - yl*piBy2_1l;
- rem = rem - yh*piBy2_2h - yh*piBy2_2l + yl*piBy2_2h + yl*piBy2_2l;
- rem = rem - yh*piBy2_3h - yh*piBy2_3l - yl*piBy2_3h - yl*piBy2_3l;
-
- *remainder = rem;
- return (int)y;
-}
-
-
-int __ieee754_rem_pio2f(float x, float *y) {
- if (x < 4000.0f) {
- return argumentReduceSmall(x, y);
- } else {
- return payne_hanek(x, y);
- }
+ BODY;
}
+#undef BODY
-OVERLOADABLE float __kernel_sinf(float x)
+OVERLOADABLE float __kernel_sinf_20(float x)
{
/* copied from fdlibm */
const float
@@ -460,7 +246,7 @@ OVERLOADABLE float __kernel_sinf(float x)
return mad(v, r, x);
}
-float __kernel_cosf(float x, float y)
+float __kernel_cosf_20(float x, float y)
{
/* copied from fdlibm */
const float
@@ -485,414 +271,38 @@ float __kernel_cosf(float x, float y)
}
}
-OVERLOADABLE float sin(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sin(x);
-
- const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
- float y,z=0.0;
- int n, ix;
-
- float negative = x < 0.0f? -1.0f : 1.0f;
- x = fabs(x);
-
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
-
- /* sin(Inf or NaN) is NaN */
- if (ix >= 0x7f800000) return x-x;
-
- if(x <= pio4)
- return negative * __kernel_sinf(x);
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- float s = __kernel_sinf(y);
- float c = __kernel_cosf(y,0.0f);
- float ret = (n&1) ? negative*c : negative*s;
- return (n&3)> 1? -1.0f*ret : ret;
- }
-}
-
-OVERLOADABLE float cos(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cos(x);
-
- const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
- float y,z=0.0;
- int n, ix;
- x = __gen_ocl_fabs(x);
- GEN_OCL_GET_FLOAT_WORD(ix,x);
-
- ix &= 0x7fffffff;
-
- /* cos(Inf or NaN) is NaN */
- if (ix >= 0x7f800000) return x-x;
-
- if(x <= pio4)
- return __kernel_cosf(x, 0.f);
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- n &= 3;
- float c = __kernel_cosf(y, 0.0f);
- float s = __kernel_sinf(y);
- float v = (n&1) ? s : c;
- /* n&3 return
- 0 cos(y)
- 1 -sin(y)
- 2 -cos(y)
- 3 sin(y)
- */
- int mask = (n>>1) ^ n;
- float sign = (mask&1) ? -1.0f : 1.0f;
- return sign * v;
- }
-}
-
-float __kernel_tanf(float x, float y, int iy)
-{
- /* copied from fdlibm */
- float z,r,v,w,s;
- int ix,hx;
- const float
- one = 1.0000000000e+00, /* 0x3f800000 */
- pio4 = 7.8539812565e-01, /* 0x3f490fda */
- pio4lo= 3.7748947079e-08; /* 0x33222168 */
- float T[13];// = {
- T[0] = 3.3333334327e-01; /* 0x3eaaaaab */
- T[1] = 1.3333334029e-01; /* 0x3e088889 */
- T[2] = 5.3968254477e-02; /* 0x3d5d0dd1 */
- T[3] = 2.1869488060e-02; /* 0x3cb327a4 */
- T[4] = 8.8632395491e-03; /* 0x3c11371f */
- T[5] = 3.5920790397e-03; /* 0x3b6b6916 */
- T[6] = 1.4562094584e-03; /* 0x3abede48 */
- T[7] = 5.8804126456e-04; /* 0x3a1a26c8 */
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff; /* high word of |x| */
- if(ix<0x31800000) /* x < 2**-28 */
- {if((int)x==0) { /* generate inexact */
- if((ix|(iy+1))==0) return one/__gen_ocl_fabs(x);
- else return (iy==1)? x: -one/x;
- }
- }
- if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
- if(hx<0) {x = -x; y = -y;}
- z = pio4-x;
- w = pio4lo-y;
- x = z+w; y = 0.0;
- }
- z = x*x;
- w = z*z;
- /* Break x^5*(T[1]+x^2*T[2]+...) into
- * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
- * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
- */
-
- r = mad(w, mad(w, mad(w, T[7], T[5]), T[3]), T[1]);
- v = z* mad(w, mad(w, T[6], T[4]), T[2]);
-
- s = z*x;
- r = mad(z, mad(s, r + v, y), y);
- r += T[0]*s;
- w = x+r;
- if(ix>=0x3f2ca140) {
- v = (float)iy;
- return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
- }
- if(iy==1) return w;
- else
- return -1.0/(x+r);
-}
-
-OVERLOADABLE float tan(float x)
-{
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_tan(x);
-
- float y,z=0.0;
- int n, ix;
- float negative = x < 0.0f? -1.0f : 1.0f;
- x = negative * x;
-
- GEN_OCL_GET_FLOAT_WORD(ix,x);
-
- ix &= 0x7fffffff;
-
- /* tan(Inf or NaN) is NaN */
- if (ix>=0x7f800000) return x-x; /* NaN */
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,&y);
- return negative * __kernel_tanf(y,0.0f,1-((n&1)<<1)); /* 1 -- n even
- -1 -- n odd */
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_cospi(float x) {
- int ix;
- if(isinf(x) || isnan(x)) { return NAN; }
- if(x < 0.0f) { x = -x; }
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- if(x> 0x1.0p24) return 1.0f;
- float m = __gen_ocl_internal_floor(x);
- ix = (int)m;
- m = x-m;
- if((ix&0x1) != 0) m+=1.0f;
- ix = __gen_ocl_internal_floor(m*4.0f);
-
- switch(ix) {
- case 0:
- return __kernel_cosf(m*M_PI_F, 0.0f);
- case 1:
- case 2:
- return __kernel_sinf((0.5f-m)*M_PI_F);
- case 3:
- case 4:
- return -__kernel_cosf((m-1.0f)*M_PI_F, 0.0f);
- case 5:
- case 6:
- return __kernel_sinf((m-1.5f)*M_PI_F);
- default:
- return __kernel_cosf((2.0f-m)*M_PI_F, 0.0f);
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_sinpi(float x) {
+OVERLOADABLE float __gen_ocl_internal_floor_20(float x) { return __gen_ocl_rndd(x); }
+OVERLOADABLE float __gen_ocl_internal_sinpi_20(float x) {
float sign = 1.0f;
int ix;
if(isinf(x)) return NAN;
if(x < 0.0f) { x = -x; sign = -1.0f; }
GEN_OCL_GET_FLOAT_WORD(ix, x);
if(x> 0x1.0p24) return 0.0f;
- float m = __gen_ocl_internal_floor(x);
+ float m = __gen_ocl_internal_floor_20(x);
ix = (int)m;
m = x-m;
if((ix&0x1) != 0) m+=1.0f;
- ix = __gen_ocl_internal_floor(m*4.0f);
+ ix = __gen_ocl_internal_floor_20(m*4.0f);
switch(ix) {
case 0:
- return sign*__kernel_sinf(m*M_PI_F);
+ return sign*__kernel_sinf_20(m*M_PI_F);
case 1:
case 2:
- return sign*__kernel_cosf((m-0.5f)*M_PI_F, 0.0f);
+ return sign*__kernel_cosf_20((m-0.5f)*M_PI_F, 0.0f);
case 3:
case 4:
- return -sign*__kernel_sinf((m-1.0f)*M_PI_F);
+ return -sign*__kernel_sinf_20((m-1.0f)*M_PI_F);
case 5:
case 6:
- return -sign*__kernel_cosf((m-1.5f)*M_PI_F, 0.0f);
+ return -sign*__kernel_cosf_20((m-1.5f)*M_PI_F, 0.0f);
default:
- return -sign*__kernel_sinf((2.0f-m)*M_PI_F);
+ return -sign*__kernel_sinf_20((2.0f-m)*M_PI_F);
}
}
-OVERLOADABLE float lgamma(float x) {
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- const float
- zero= 0.,
- one = 1.0000000000e+00,
- pi = 3.1415927410e+00,
- a0 = 7.7215664089e-02,
- a1 = 3.2246702909e-01,
- a2 = 6.7352302372e-02,
- a3 = 2.0580807701e-02,
- a4 = 7.3855509982e-03,
- a5 = 2.8905137442e-03,
- a6 = 1.1927076848e-03,
- a7 = 5.1006977446e-04,
- a8 = 2.2086278477e-04,
- a9 = 1.0801156895e-04,
- a10 = 2.5214456400e-05,
- a11 = 4.4864096708e-05,
- tc = 1.4616321325e+00,
- tf = -1.2148628384e-01,
- tt = 6.6971006518e-09,
- t0 = 4.8383611441e-01,
- t1 = -1.4758771658e-01,
- t2 = 6.4624942839e-02,
- t3 = -3.2788541168e-02,
- t4 = 1.7970675603e-02,
- t5 = -1.0314224288e-02,
- t6 = 6.1005386524e-03,
- t7 = -3.6845202558e-03,
- t8 = 2.2596477065e-03,
- t9 = -1.4034647029e-03,
- t10 = 8.8108185446e-04,
- t11 = -5.3859531181e-04,
- t12 = 3.1563205994e-04,
- t13 = -3.1275415677e-04,
- t14 = 3.3552918467e-04,
- u0 = -7.7215664089e-02,
- u1 = 6.3282704353e-01,
- u2 = 1.4549225569e+00,
- u3 = 9.7771751881e-01,
- u4 = 2.2896373272e-01,
- u5 = 1.3381091878e-02,
- v1 = 2.4559779167e+00,
- v2 = 2.1284897327e+00,
- v3 = 7.6928514242e-01,
- v4 = 1.0422264785e-01,
- v5 = 3.2170924824e-03,
- s0 = -7.7215664089e-02,
- s1 = 2.1498242021e-01,
- s2 = 3.2577878237e-01,
- s3 = 1.4635047317e-01,
- s4 = 2.6642270386e-02,
- s5 = 1.8402845599e-03,
- s6 = 3.1947532989e-05,
- r1 = 1.3920053244e+00,
- r2 = 7.2193557024e-01,
- r3 = 1.7193385959e-01,
- r4 = 1.8645919859e-02,
- r5 = 7.7794247773e-04,
- r6 = 7.3266842264e-06,
- w0 = 4.1893854737e-01,
- w1 = 8.3333335817e-02,
- w2 = -2.7777778450e-03,
- w3 = 7.9365057172e-04,
- w4 = -5.9518753551e-04,
- w5 = 8.3633989561e-04,
- w6 = -1.6309292987e-03;
- float t, y, z, nadj, p, p1, p2, p3, q, r, w;
- int i, hx, ix;
- nadj = 0;
- hx = *(int *)&x;
- ix = hx & 0x7fffffff;
- if (ix >= 0x7f800000)
- return x * x;
- if (ix == 0)
- return ((x + one) / zero);
- if (ix < 0x1c800000) {
- if (hx < 0) {
- return -native_log(-x);
- } else
- return -native_log(x);
- }
- if (hx < 0) {
- if (ix >= 0x4b000000)
- return ((-x) / zero);
- t = __gen_ocl_internal_sinpi(x);
- if (t == zero)
- return ((-x) / zero);
- nadj = native_log(pi / __gen_ocl_fabs(t * x));
- x = -x;
- }
- if (ix == 0x3f800000 || ix == 0x40000000)
- r = 0;
- else if (ix < 0x40000000) {
- if (ix <= 0x3f666666) {
- r = -native_log(x);
- if (ix >= 0x3f3b4a20) {
- y = one - x;
- i = 0;
- } else if (ix >= 0x3e6d3308) {
- y = x - (tc - one);
- i = 1;
- } else {
- y = x;
- i = 2;
- }
- } else {
- r = zero;
- if (ix >= 0x3fdda618) {
- y = (float) 2.0 - x;
- i = 0;
- }
- else if (ix >= 0x3F9da620) {
- y = x - tc;
- i = 1;
- }
- else {
- y = x - one;
- i = 2;
- }
- }
- switch (i) {
- case 0:
- z = y * y;
- p1 = mad(z, mad(z, mad(z, mad(z, mad(z, a10, a8), a6), a4), a2), a0);
- p2 = z * mad(z, mad(z, mad(z, mad(z, mad(z, a11, a9), a7), a5), a3), a1);
- p = mad(y, p1, p2);
- r += (p - (float) 0.5 * y);
- break;
- case 1:
- z = y * y;
- w = z * y;
- p1 = mad(w, mad(w, mad(w, mad(w, t12, t9), t6), t3), t0);
- p2 = mad(w, mad(w, mad(w, mad(w, t13, t10), t7), t4), t1);
- p3 = mad(w, mad(w, mad(w, mad(w, t14, t11), t8), t5), t2);
- p = mad(p1, z, mad(w, mad(y, p3, p2), -tt));
- r += (tf + p);
- break;
- case 2:
- p1 = y * mad(y, mad(y, mad(y, mad(y, mad(y, u5, u4), u3), u2), u1), u0);
- p2 = mad(y, mad(y, mad(y, mad(y, mad(y, v5, v4), v3), v2), v1), one);
- r += (-(float) 0.5 * y + p1 / p2);
- }
- } else if (ix < 0x41000000) {
- i = (int) x;
- t = zero;
- y = x - (float) i;
-
- p =y * mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, s6, s5), s4), s3), s2), s1), s0);
- q = mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, r6, r5), r4), r3), r2), r1), one);
- r = .5f * y + p / q;
- z = one;
-
- switch (i) {
- case 7:
- z *= (y + 6.0f);
- case 6:
- z *= (y + 5.0f);
- case 5:
- z *= (y + 4.0f);
- case 4:
- z *= (y + 3.0f);
- case 3:
- z *= (y + 2.0f);
- r += native_log(z);
- break;
- }
-
- } else if (ix < 0x5c800000) {
- t = native_log(x);
- z = one / x;
- y = z * z;
- w = mad(z, mad(y, mad(y, mad(y, mad(y, mad(y, w6, w5), w4), w3), w2), w1), w0);
- r = (x - .5f) * (t - one) + w;
- } else
- r = x * (native_log(x) - one);
- if (hx < 0)
- r = nadj - r;
- return r;
-}
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
#define BODY \
const float \
zero= 0., \
@@ -979,7 +389,7 @@ OVERLOADABLE float lgamma(float x) {
if (hx < 0) { \
if (ix >= 0x4b000000) \
return ((-x) / zero); \
- t = __gen_ocl_internal_sinpi(x); \
+ t = __gen_ocl_internal_sinpi_20(x); \
if (t == zero) \
return ((-x) / zero); \
nadj = native_log(pi / __gen_ocl_fabs(t * x)); \
@@ -1076,2730 +486,6 @@ OVERLOADABLE float lgamma(float x) {
OVERLOADABLE float lgamma_r(float x, int *signgamp) { BODY; }
#undef BODY
-OVERLOADABLE float log1p(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log1p(x);
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- const float
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- two25 = 3.355443200e+07, /* 0x4c000000 */
- Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
- Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
- Lp3 = 2.8571429849e-01, /* 3E924925 */
- Lp4 = 2.2222198546e-01; /* 3E638E29 */
- const float zero = 0.0;
- float hfsq,f,c,s,z,R,u;
- int k,hx,hu,ax;
- union {float f; unsigned i;} un;
- un.f = x; hx = un.i;
- ax = hx&0x7fffffff;
-
- k = 1;
- if (hx < 0x3ed413d7) { /* x < 0.41422 */
- if(ax>=0x3f800000) { /* x <= -1.0 */
- if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
- else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
- }
- if(ax<0x31000000) { /* |x| < 2**-29 */
- if(two25+x>zero /* raise inexact */
- &&ax<0x24800000) /* |x| < 2**-54 */
- return x;
- else
- return x - x*x*(float)0.5;
- }
- if(hx>0||hx<=((int)0xbe95f61f)) {
- k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
- }
- if (hx >= 0x7f800000) return x+x;
- if(k!=0) {
- if(hx<0x5a000000) {
- u = (float)1.0+x;
-
- un.f = u; hu = un.i;
- k = (hu>>23)-127;
- /* correction term */
- c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
- c /= u;
- } else {
- u = x;
- un.f = u; hu = un.i;
- k = (hu>>23)-127;
- c = 0;
- }
- hu &= 0x007fffff;
- if(hu<0x3504f7) {
- un.i = hu|0x3f800000; u = un.f;/* normalize u */
- } else {
- k += 1;
- un.i = hu|0x3f000000; u = un.f; /* normalize u/2 */
- hu = (0x00800000-hu)>>2;
- }
- f = u-(float)1.0;
- }
- hfsq=(float)0.5*f*f;
- if(hu==0)
- { /* |f| < 2**-20 */
- if(f==zero)
- {
- if(k==0) return zero;
- else {c = mad(k , ln2_lo, c); return mad(k, ln2_hi, c);}
- }
- R = mad(hfsq, 1.0f, -0.66666666666666666f * f);
- if(k==0) return f-R; else
- return k * ln2_hi - (R - mad(k, ln2_lo, c) - f);
- }
- s = f/((float)2.0+f);
- z = s*s;
- R = z * mad(z, mad(z, mad(z, Lp4, Lp3), Lp2), Lp1);
- if(k==0)
- return f + mad(hfsq + R, s, -hfsq);
- else
- return k*ln2_hi-( (hfsq - mad(s, hfsq + R, mad(k, ln2_lo, c))) - f);
-}
-
-OVERLOADABLE float logb(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_logb(x);
-
- union {float f; unsigned i;} u;
- u.f = x;
- int e = ((u.i & 0x7f800000) >> 23);
- float r1 = e-127;
- float r2 = -INFINITY;
- float r3 = x*x;
- /* sub normal or +/-0 */
- float r = e == 0 ? r2 : r1;
- /* inf & nan */
- return e == 0xff ? r3 : r;
-}
-
-OVERLOADABLE int ilogb(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_ilogb(x);
-
- union { int i; float f; } u;
- if (isnan(x))
- return FP_ILOGBNAN;
- if (isinf(x))
- return 0x7FFFFFFF;
- u.f = x;
- u.i &= 0x7fffffff;
- if (u.i == 0)
- return FP_ILOGB0;
- if (u.i >= 0x800000)
- return (u.i >> 23) - 127;
- int r = -126;
- int a = u.i & 0x7FFFFF;
- while(a < 0x800000) {
- a <<= 1;
- r --;
- }
- return r;
-}
-OVERLOADABLE float nan(uint code) {
- return NAN;
-}
-OVERLOADABLE float __gen_ocl_internal_tanpi(float x) {
- float sign = 1.0f;
- int ix;
- if(isinf(x)) return NAN;
- if(x < 0.0f) { x = -x; sign = -1.0f; }
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- if(x> 0x1.0p24) return 0.0f;
- float m = __gen_ocl_internal_floor(x);
- ix = (int)m;
- m = x-m;
- int n = __gen_ocl_internal_floor(m*4.0f);
- if(m == 0.5f) {
- return (ix&0x1) == 0 ? sign*INFINITY : sign*-INFINITY;
- }
- if(m == 0.0f) {
- return (ix&0x1) == 0 ? 0.0f : -0.0f;
- }
-
- switch(n) {
- case 0:
- return sign * __kernel_tanf(m*M_PI_F, 0.0f, 1);
- case 1:
- return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
- case 2:
- return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
- default:
- return sign * -1.0f*__kernel_tanf((1.0f-m)*M_PI_F, 0.0f, 1);
- }
-}
-OVERLOADABLE float __gen_ocl_internal_cbrt(float x) {
- /* copied from fdlibm */
- const unsigned
- B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
- B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
-
- const float
- C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
- D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
- E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
- F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
- G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
-
- float r,s,t, w;
- int hx;
- uint sign;
- uint high;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- sign=hx&0x80000000; /* sign= sign(x) */
- hx ^=sign;
- if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
- if(hx==0)
- return(x); /* cbrt(0) is itself */
-
- GEN_OCL_SET_FLOAT_WORD(x,hx); /* x <- |x| */
- /* rough cbrt to 5 bits */
- if(hx<0x00800000) /* subnormal number */
- {
- //SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
- //t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
- t = (sign = 0) ? 0.0f : -0.0f;
- return t;
- }
- else
- GEN_OCL_SET_FLOAT_WORD(t,hx/3+B1);
-
-
- /* new cbrt to 23 bits */
- r=t*t/x;
- s=mad(r, t, C);
- t*=G+F/(s+E+D/s);
- /* one step newton iteration to 53 bits with error less than 0.667 ulps */
- s=t*t; /* t*t is exact */
- r=x/s;
- w=t+t;
- r=(r-t)/(w+r); /* r-s is exact */
- t=mad(t, r, t);
-
- /* retore the sign bit */
- GEN_OCL_GET_FLOAT_WORD(high,t);
- GEN_OCL_SET_FLOAT_WORD(t,high|sign);
- return(t);
-}
-
-#define BODY \
- *cosval = cos(x); \
- return sin(x);
-
-OVERLOADABLE float sincos(float x, float *cosval) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sincos(x, cosval);
- BODY;
-}
-#undef BODY
-
-INLINE float __gen_ocl_asin_util(float x) {
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunSoft, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- float
- pS0 = 1.66666666666666657415e-01,
- pS1 = -3.25565818622400915405e-01,
- pS2 = 2.01212532134862925881e-01,
- pS3 = -4.00555345006794114027e-02,
- pS4 = 7.91534994289814532176e-04,
- qS1 = -2.40339491173441421878e+00,
- qS2 = 2.02094576023350569471e+00,
- qS3 = -6.88283971605453293030e-01,
- qS4 = 7.70381505559019352791e-02;
-
- float t = x*x;
- float p = t * mad(t, mad(t, mad(t, mad(t, pS4, pS3), pS2), pS1), pS0);
- float q = mad(t, mad(t, mad(t, mad(t, qS4, qS3), qS2), qS1), 1.0f);
- float w = p / q;
- return mad(x, w, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_asin(float x) {
- uint ix;
- union { uint i; float f; } u;
- u.f = x;
- ix = u.i & 0x7fffffff;
- if(ix == 0x3f800000) {
- return x * M_PI_2_F; /* asin(|1|)=+-pi/2 with inexact */
- }
- if(ix > 0x3f800000) { /* |x|>= 1 */
- return NAN; /* asin(|x|>1) is NaN */
- }
-
- if(ix < 0x32000000) { /* if |x| < 2**-27 */
- if(HUGE_VALF + x > FLT_ONE) return x; /* return x with inexact if x!=0*/
- }
-
- if(x < -0.5) {
- return 2 * __gen_ocl_asin_util(native_sqrt((1+x) / 2)) - M_PI_2_F;
- } else if(x > 0.5) {
- return M_PI_2_F - 2 * __gen_ocl_asin_util(native_sqrt((1-x) / 2));
- } else {
- return __gen_ocl_asin_util(x);
- }
-}
-OVERLOADABLE float __gen_ocl_internal_asinpi(float x) {
- return __gen_ocl_internal_asin(x) / M_PI_F;
-}
-OVERLOADABLE float __gen_ocl_internal_acos(float x) {
- if(x > 0.5)
- return 2 * __gen_ocl_asin_util(native_sqrt((1-x)/2));
- else
- return M_PI_2_F - __gen_ocl_internal_asin(x);
-}
-OVERLOADABLE float __gen_ocl_internal_acospi(float x) {
- return __gen_ocl_internal_acos(x) / M_PI_F;
-}
-__constant float atanhi[4] = {
- 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
- 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
- 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
- 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
-};
-__constant float atanlo[4] = {
- 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
- 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
- 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
- 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
-};
-
-OVERLOADABLE float __gen_ocl_internal_atan(float x) {
- /* copied from fdlibm */
- float aT[11];
- aT[0] = 3.3333334327e-01; /* 0x3eaaaaaa */
- aT[1] = -2.0000000298e-01; /* 0xbe4ccccd */
- aT[2] = 1.4285714924e-01; /* 0x3e124925 */
- aT[3] = -1.1111110449e-01; /* 0xbde38e38 */
- aT[4] = 9.0908870101e-02; /* 0x3dba2e6e */
- aT[5] = -7.6918758452e-02; /* 0xbd9d8795 */
- aT[6] = 6.6610731184e-02; /* 0x3d886b35 */
- const float one = 1.0, huge = 1.0e30;
-
- float w,s1,s2,z;
- int ix,hx,id;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x50800000) { /* if |x| >= 2^34 */
- if(ix>0x7f800000)
- return x+x; /* NaN */
- if(hx>0) return atanhi[3]+atanlo[3];
- else return -atanhi[3]-atanlo[3];
- } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
- if (ix < 0x31000000) { /* |x| < 2^-29 */
- if(huge+x>one) return x; /* raise inexact */
- }
- id = -1;
- } else {
- x = __gen_ocl_fabs(x);
- if (ix < 0x3f980000) { /* |x| < 1.1875 */
- if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
- id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
- } else { /* 11/16<=|x|< 19/16 */
- id = 1; x = (x-one)/(x+one);
- }
- } else {
- if (ix < 0x401c0000) { /* |x| < 2.4375 */
- id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
- } else { /* 2.4375 <= |x| < 2^66 */
- id = 3; x = -(float)1.0/x;
- }
- }}
- /* end of argument reduction */
- z = x*x;
- w = z*z;
- /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
- s1 = z * mad(w, mad(w, mad(w, aT[6], aT[4]), aT[2]), aT[0]);
- s2 = w * mad(w, mad(w, aT[5], aT[3]), aT[1]);
- if (id<0) return x - x*(s1+s2);
- else {
- z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
- return (hx<0)? -z:z;
- }
-
-}
-OVERLOADABLE float __gen_ocl_internal_atanpi(float x) {
- return __gen_ocl_internal_atan(x) / M_PI_F;
-}
-
-// XXX work-around PTX profile
-OVERLOADABLE float sqrt(float x) { return native_sqrt(x); }
-OVERLOADABLE float rsqrt(float x) { return native_rsqrt(x); }
-OVERLOADABLE float __gen_ocl_internal_atan2(float y, float x) {
- /* copied from fdlibm */
- float z;
- int k,m,hx,hy,ix,iy;
- const float
- tiny = 1.0e-30,
- zero = 0.0,
- pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
- pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
- pi = 3.1415927410e+00, /* 0x40490fdb */
- pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- iy = hy&0x7fffffff;
-
- if((ix>0x7f800000)||
- (iy>0x7f800000)) /* x or y is NaN */
- return x+y;
- if(hx==0x3f800000) return z=__gen_ocl_internal_atan(y); /* x=1.0 */
- m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
-
- /* when y = 0 */
- if(iy==0) {
- switch(m) {
- case 0:
- case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny;/* atan(+0,-anything) = pi */
- case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
- }
- }
- /* when x = 0 */
- if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
-
- /* both are denorms. Gen does not support denorm, so we convert to normal float number*/
- if(ix <= 0x7fffff && iy <= 0x7fffff) {
- x = (float)(ix) * (1.0f - ((hx>>30) & 0x2));
- y = (float)(iy) * (1.0f - ((hy>>30) & 0x2));
- }
-
- /* when x is INF */
- if(ix==0x7f800000) {
- if(iy==0x7f800000) {
- switch(m) {
- case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
- case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
- case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
- case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
- }
- } else {
- switch(m) {
- case 0: return zero ; /* atan(+...,+INF) */
- case 1: return -zero ; /* atan(-...,+INF) */
- case 2: return pi+tiny ; /* atan(+...,-INF) */
- case 3: return -pi-tiny ; /* atan(-...,-INF) */
- }
- }
- }
- /* when y is INF */
- if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
-
- /* compute y/x */
- k = (iy-ix)>>23;
- if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
- else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
- else z=__gen_ocl_internal_atan(__gen_ocl_fabs(y/x)); /* safe to do y/x */
- switch (m) {
- case 0: return z ; /* atan(+,+) */
- case 1: {
- uint zh;
- GEN_OCL_GET_FLOAT_WORD(zh,z);
- GEN_OCL_SET_FLOAT_WORD(z,zh ^ 0x80000000);
- }
- return z ; /* atan(-,+) */
- case 2: return pi-(z-pi_lo);/* atan(+,-) */
- default: /* case 3 */
- return (z-pi_lo)-pi;/* atan(-,-) */
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_atan2pi(float y, float x) {
- return __gen_ocl_internal_atan2(y, x) / M_PI_F;
-}
-OVERLOADABLE float __gen_ocl_internal_fabs(float x) { return __gen_ocl_fabs(x); }
-OVERLOADABLE float __gen_ocl_internal_trunc(float x) { return __gen_ocl_rndz(x); }
-OVERLOADABLE float __gen_ocl_internal_round(float x) {
- float y = __gen_ocl_rndz(x);
- if (__gen_ocl_fabs(x - y) >= 0.5f)
- y += __gen_ocl_internal_copysign(1.f, x);
- return y;
-}
-OVERLOADABLE float __gen_ocl_internal_ceil(float x) { return __gen_ocl_rndu(x); }
-OVERLOADABLE float __gen_ocl_internal_rint(float x) {
- return __gen_ocl_rnde(x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_exp(float x) {
- float o_threshold = 8.8721679688e+01, /* 0x42b17180 */
- u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
- twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- one = 1.0,
- huge = 1.0e+30,
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03; /* 0xbb360b61 */
- float y,hi=0.0,lo=0.0,c,t;
- int k=0,xsb;
- unsigned hx;
- float ln2HI_0 = 6.9313812256e-01; /* 0x3f317180 */
- float ln2HI_1 = -6.9313812256e-01; /* 0xbf317180 */
- float ln2LO_0 = 9.0580006145e-06; /* 0x3717f7d1 */
- float ln2LO_1 = -9.0580006145e-06; /* 0xb717f7d1 */
- float half_0 = 0.5;
- float half_1 = -0.5;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- xsb = (hx>>31)&1; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |x| */
-
- /* filter out non-finite argument */
- if(hx >= 0x42b17218) { /* if |x|>=88.721... */
- if(hx>0x7f800000)
- return x+x; /* NaN */
- if(hx==0x7f800000)
- return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
- if(x > o_threshold) return huge*huge; /* overflow */
- if(x < u_threshold) return twom100*twom100; /* underflow */
- }
- /* argument reduction */
- if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
- if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
- hi = x-(xsb ==1 ? ln2HI_1 : ln2HI_0); lo= xsb == 1? ln2LO_1 : ln2LO_0; k = 1-xsb-xsb;
- } else {
- float tmp = xsb == 1 ? half_1 : half_0;
- k = ivln2*x+tmp;
- t = k;
- hi = x - t*ln2HI_0; /* t*ln2HI is exact here */
- lo = t*ln2LO_0;
- }
- x = hi - lo;
- }
- else if(hx < 0x31800000) { /* when |x|<2**-28 */
- if(huge+x>one) return one+x;/* trigger inexact */
- }
- else k = 0;
-
- /* x is now in primary range */
- t = x*x;
- c = x - t*(P1+t*P2);
- if(k==0)
- return one-((x*c)/(c-(float)2.0)-x);
- else
- y = one-((lo-(x*c)/((float)2.0-c))-hi);
- if(k >= -125) {
- unsigned hy;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- GEN_OCL_SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
- return y;
- } else {
- unsigned hy;
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- GEN_OCL_SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
- return y*twom100;
- }
-}
-
-/* erf,erfc from glibc s_erff.c -- float version of s_erf.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-INLINE_OVERLOADABLE float __gen_ocl_internal_erf(float x) {
-/*...*/
-const float
-tiny = 1.0e-30,
-half_val= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
- /* c = (subfloat)0.84506291151 */
-erx = 8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to erf on [0,0.84375]
- */
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
-efx8= 1.0270333290e+00, /* 0x3f8375d4 */
-pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
-pp1 = -3.2504209876e-01, /* 0xbea66beb */
-pp2 = -2.8481749818e-02, /* 0xbce9528f */
-pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
-qq2 = 6.5022252500e-02, /* 0x3d852a63 */
-qq3 = 5.0813062117e-03, /* 0x3ba68116 */
-qq4 = 1.3249473704e-04, /* 0x390aee49 */
-qq5 = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1 = 4.1485610604e-01, /* 0x3ed46805 */
-pa2 = -3.7220788002e-01, /* 0xbebe9208 */
-pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
-pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
-pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
-qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
-qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
-qa4 = 1.2617121637e-01, /* 0x3e013307 */
-qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
-qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
- /*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
- */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
-ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2 = -1.0558626175e+01, /* 0xc128f022 */
-ra3 = -6.2375331879e+01, /* 0xc2798057 */
-ra4 = -1.6239666748e+02, /* 0xc322658c */
-ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6 = -8.1287437439e+01, /* 0xc2a2932b */
-ra7 = -9.8143291473e+00, /* 0xc11d077e */
-sa1 = 1.9651271820e+01, /* 0x419d35ce */
-sa2 = 1.3765776062e+02, /* 0x4309a863 */
-sa3 = 4.3456588745e+02, /* 0x43d9486f */
-sa4 = 6.4538726807e+02, /* 0x442158c9 */
-sa5 = 4.2900814819e+02, /* 0x43d6810b */
-sa6 = 1.0863500214e+02, /* 0x42d9451f */
-sa7 = 6.5702495575e+00, /* 0x40d23f7c */
-sa8 = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to erfc in [1/.35,28]
- */
-rb0 = -9.8649431020e-03, /* 0xbc21a092 */
-rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2 = -1.7757955551e+01, /* 0xc18e104b */
-rb3 = -1.6063638306e+02, /* 0xc320a2ea */
-rb4 = -6.3756646729e+02, /* 0xc41f6441 */
-rb5 = -1.0250950928e+03, /* 0xc480230b */
-rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1 = 3.0338060379e+01, /* 0x41f2b459 */
-sb2 = 3.2579251099e+02, /* 0x43a2e571 */
-sb3 = 1.5367296143e+03, /* 0x44c01759 */
-sb4 = 3.1998581543e+03, /* 0x4547fdbb */
-sb5 = 2.5530502930e+03, /* 0x451f90ce */
-sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
-sb7 = -2.2440952301e+01; /* 0xc1b38712 */
-
- int hx,ix,i;
- float R,S,P,Q,s,y,z,r;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erf(nan)=nan */
- i = ((unsigned int)hx>>31)<<1;
- return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
- }
-
- if(ix < 0x3f580000) { /* |x|<0.84375 */
- if(ix < 0x31800000) { /* |x|<2**-28 */
- if (ix < 0x04000000)
- /*avoid underflow */
- return (float)0.125*((float)8.0*x+efx8*x);
- return x + efx*x;
- }
- z = x*x;
- r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
- s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5,qq4), qq3), qq2), qq1), one);
- y = r / s;
- return mad(x, y, x);
- }
- if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = __gen_ocl_internal_fabs(x)-one;
- P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
- Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
- if(hx>=0) return erx + P/Q; else return -erx - P/Q;
- }
- if (ix >= 0x40c00000) { /* inf>|x|>=6 */
- if(hx>=0) return one-tiny; else return tiny-one;
- }
- x = __gen_ocl_internal_fabs(x);
- s = one/(x*x);
- if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
- } else { /* |x| >= 1/0.35 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- rb6, rb5), rb4), rb3), rb2), rb1), rb0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
- }
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- GEN_OCL_SET_FLOAT_WORD(z,ix&0xfffff000);
- r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*__gen_ocl_internal_exp((z-x)*(z+x)+R/S);
- if(hx>=0) return one-r/x; else return r/x-one;
-}
-INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
-/*...*/
-const float
-tiny = 1.0e-30,
-half_val= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
- /* c = (subfloat)0.84506291151 */
-erx = 8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to erf on [0,0.84375]
- */
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
-efx8= 1.0270333290e+00, /* 0x3f8375d4 */
-pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
-pp1 = -3.2504209876e-01, /* 0xbea66beb */
-pp2 = -2.8481749818e-02, /* 0xbce9528f */
-pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
-qq2 = 6.5022252500e-02, /* 0x3d852a63 */
-qq3 = 5.0813062117e-03, /* 0x3ba68116 */
-qq4 = 1.3249473704e-04, /* 0x390aee49 */
-qq5 = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1 = 4.1485610604e-01, /* 0x3ed46805 */
-pa2 = -3.7220788002e-01, /* 0xbebe9208 */
-pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
-pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
-pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
-qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
-qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
-qa4 = 1.2617121637e-01, /* 0x3e013307 */
-qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
-qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
- /*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
- */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
-ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2 = -1.0558626175e+01, /* 0xc128f022 */
-ra3 = -6.2375331879e+01, /* 0xc2798057 */
-ra4 = -1.6239666748e+02, /* 0xc322658c */
-ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6 = -8.1287437439e+01, /* 0xc2a2932b */
-ra7 = -9.8143291473e+00, /* 0xc11d077e */
-sa1 = 1.9651271820e+01, /* 0x419d35ce */
-sa2 = 1.3765776062e+02, /* 0x4309a863 */
-sa3 = 4.3456588745e+02, /* 0x43d9486f */
-sa4 = 6.4538726807e+02, /* 0x442158c9 */
-sa5 = 4.2900814819e+02, /* 0x43d6810b */
-sa6 = 1.0863500214e+02, /* 0x42d9451f */
-sa7 = 6.5702495575e+00, /* 0x40d23f7c */
-sa8 = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to erfc in [1/.35,28]
- */
-rb0 = -9.8649431020e-03, /* 0xbc21a092 */
-rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2 = -1.7757955551e+01, /* 0xc18e104b */
-rb3 = -1.6063638306e+02, /* 0xc320a2ea */
-rb4 = -6.3756646729e+02, /* 0xc41f6441 */
-rb5 = -1.0250950928e+03, /* 0xc480230b */
-rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1 = 3.0338060379e+01, /* 0x41f2b459 */
-sb2 = 3.2579251099e+02, /* 0x43a2e571 */
-sb3 = 1.5367296143e+03, /* 0x44c01759 */
-sb4 = 3.1998581543e+03, /* 0x4547fdbb */
-sb5 = 2.5530502930e+03, /* 0x451f90ce */
-sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
-sb7 = -2.2440952301e+01; /* 0xc1b38712 */
- int hx,ix;
- float R,S,P,Q,s,y,z,r;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erfc(nan)=nan */
- /* erfc(+-inf)=0,2 */
- return (float)(((unsigned int)hx>>31)<<1)+one/x;
- }
-
- if(ix < 0x3f580000) { /* |x|<0.84375 */
- if(ix < 0x23800000) /* |x|<2**-56 */
- return one-x;
- z = x*x;
- r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
- s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5, qq4), qq3), qq2), qq1), one);
- y = r/s;
- if(hx < 0x3e800000) { /* x<1/4 */
- return one-(x+x*y);
- } else {
- r = x*y;
- r += (x-half_val);
- return half_val - r ;
- }
- }
- if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = __gen_ocl_internal_fabs(x)-one;
- P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
- Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
- if(hx>=0) {
- z = one-erx; return z - P/Q;
- } else {
- z = erx+P/Q; return one+z;
- }
- }
- if (ix < 0x41e00000) { /* |x|<28 */
- x = __gen_ocl_internal_fabs(x);
- s = one/(x*x);
- if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
- } else { /* |x| >= 1/.35 ~ 2.857143 */
- if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
- R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- rb6, rb5), rb4), rb3), rb2), rb1), rb0);
- S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
- sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
- }
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- GEN_OCL_SET_FLOAT_WORD(z,ix&0xffffe000);
- r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*
- __gen_ocl_internal_exp((z-x)*(z+x)+R/S);
- if(hx>0) {
- float ret = r/x;
- return ret;
- } else
- return two-r/x;
- } else {
- if(hx>0) {
- return tiny*tiny;
- } else
- return two-tiny;
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_fmod (float x, float y) {
- //return x-y*__gen_ocl_rndz(x/y);
- float one = 1.0;
- float Zero[2];
- int n,hx,hy,hz,ix,iy,sx,i;
- Zero[0] = 0.0;
- Zero[1] = -0.0;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- sx = hx&0x80000000; /* sign of x */
- hx ^=sx; /* |x| */
- hy &= 0x7fffffff; /* |y| */
- /* purge off exception values */
- if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
- (hy>0x7f800000)) /* or y is NaN */
- return (x*y)/(x*y);
- if(hx<hy) return x; /* |x|<|y| return x */
- if(hx==hy)
- return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
-
- /* determine ix = ilogb(x) */
- if(hx<0x00800000) { /* subnormal x */
- for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
- } else ix = (hx>>23)-127;
-
- /* determine iy = ilogb(y) */
- if(hy<0x00800000) { /* subnormal y */
- for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
- } else iy = (hy>>23)-127;
-
- /* set up {hx,lx}, {hy,ly} and align y to x */
- if(ix >= -126)
- hx = 0x00800000|(0x007fffff&hx);
- else { /* subnormal x, shift x to normal */
- n = -126-ix;
- hx = hx<<n;
- }
- if(iy >= -126)
- hy = 0x00800000|(0x007fffff&hy);
- else { /* subnormal y, shift y to normal */
- n = -126-iy;
- hy = hy<<n;
- }
- /* fix point fmod */
- n = ix - iy;
- while(n--) {
- hz=hx-hy;
- if(hz<0){hx = hx+hx;}
- else {
- if(hz==0) /* return sign(x)*0 */
- return Zero[(unsigned)sx>>31];
- hx = hz+hz;
- }
- }
- hz=hx-hy;
- if(hz>=0) {hx=hz;}
-
- /* convert back to floating value and restore the sign */
- if(hx==0) /* return sign(x)*0 */
- return Zero[(unsigned)sx>>31];
- while(hx<0x00800000) { /* normalize x */
- hx = hx+hx;
- iy -= 1;
- }
- if(iy>= -126) { /* normalize output */
- hx = ((hx-0x00800000)|((iy+127)<<23));
- GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
- } else { /* subnormal output */
- n = -126 - iy;
- hx >>= n;
- GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
- x *= one; /* create necessary signal */
- }
- return x; /* exact output */
-}
-
-OVERLOADABLE float __gen_ocl_internal_expm1(float x) {
- //return __gen_ocl_pow(M_E_F, x) - 1;
- float Q1 = -3.3333335072e-02, /* 0xbd088889 */
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- one = 1.0,
- o_threshold= 8.8721679688e+01; /* 0x42b17180 */
- float y,hi,lo,c,t,e,hxs,hfx,r1;
- int k,xsb;
- int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- xsb = hx&0x80000000;
- /* sign bit of x */
- //if(xsb==0)
- //y=x;
- //else
- //y= -x; /* y = |x| */
- y = __gen_ocl_internal_fabs(x);
- hx &= 0x7fffffff; /* high word of |x| */
- /* filter out huge and non-finite argument */
- if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
- if(hx >= 0x42b17218) { /* if |x|>=88.721... */
- if(hx>0x7f800000)
- return x+x; /* NaN */
- if(hx==0x7f800000)
- return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
- if(x > o_threshold)
- return huge*huge; /* overflow */
- }
- if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
- if(x+tiny<(float)0.0) /* raise inexact */
- return tiny-one; /* return -1 */
- }
- }
- /* argument reduction */
- if(hx > 0x3eb17218) {/* if |x| > 0.5 ln2 */
- if(hx < 0x3F851592) {/* and |x| < 1.5 ln2 */
- if(xsb==0){
- hi = x - ln2_hi; lo = ln2_lo; k = 1;
- } else {
- hi = x + ln2_hi; lo = -ln2_lo; k = -1;
- }
- } else {
- k = ivln2*x+((xsb==0)?(float)0.5:(float)-0.5);
- t = k;
- hi = x - t*ln2_hi;/* t*ln2_hi is exact here */
- lo = t*ln2_lo;
- }
- x = hi - lo;
- c = (hi-x)-lo;
- } else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
- //t = huge+x; /* return x with inexact flags when x!=0 */
- //return x - (t-(huge+x));
- return x;
- } else k = 0;
- /* x is now in primary range */
- hfx = (float)0.5*x;
- hxs = x*hfx;
- r1 = one+hxs*(Q1+hxs*Q2);
- t = (float)3.0-r1*hfx;
- e = hxs*((r1-t)/((float)6.0 - x*t));
- if(k==0)
- return x - (x*e-hxs); /* c is 0 */
- else{
- e = (x*(e-c)-c);
- e -= hxs;
- if(k== -1)return (float)0.5*(x-e)-(float)0.5;
- if(k==1){
- if(x < (float)-0.25)
- return -(float)2.0*(e-(x+(float)0.5));
- else
- return (one+(float)2.0*(x-e));
- }
- if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
- int i;
- y = one-(e-x);
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- return y-one;
- }
- t = one;
- if(k<23) {
- int i;
- GEN_OCL_SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
- y = t-(e-x);
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- } else {
- int i;
- GEN_OCL_SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
- y = x-(e+t);
- y += one;
- GEN_OCL_GET_FLOAT_WORD(i,y);
- GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
- }
- }
- return y;
-}
-
-OVERLOADABLE float __gen_ocl_internal_acosh(float x) {
- //return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
- float one = 1.0,
- ln2 = 6.9314718246e-01;/* 0x3f317218 */
- float t;
- int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- if(hx<0x3f800000) { /* x < 1 */
- return (x-x)/(x-x);
- } else if(hx >=0x4d800000) { /* x > 2**28 */
- if(hx >=0x7f800000) {/* x is inf of NaN */
- return x+x;
- } else
- return __gen_ocl_internal_log(x)+ln2;/* acosh(huge)=log(2x) */
- } else if (hx==0x3f800000) {
- return 0.0; /* acosh(1) = 0 */
- } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
- t=x*x;
- return __gen_ocl_internal_log((float)2.0*x-one/(x+__gen_ocl_sqrt(t-one)));
- } else { /* 1<x<2 */
- t = x-one;
- return log1p(t+__gen_ocl_sqrt((float)2.0*t+t*t));
- }
-}
-
-OVERLOADABLE float __gen_ocl_internal_asinh(float x){
- //return native_log(x + native_sqrt(x * x + 1));
- float one = 1.0000000000e+00, /* 0x3F800000 */
- ln2 = 6.9314718246e-01, /* 0x3f317218 */
- huge= 1.0000000000e+30;
- float w;
- int hx,ix;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix< 0x38000000) { /* |x|<2**-14 */
- if(huge+x>one) return x; /* return x inexact except 0 */
- }
- if(ix>0x47000000) {/* |x| > 2**14 */
- if(ix>=0x7f800000) return x+x;/* x is inf or NaN */
- w = __gen_ocl_internal_log(__gen_ocl_internal_fabs(x))+ln2;
- } else {
- float xa = __gen_ocl_internal_fabs(x);
- if (ix>0x40000000) {/* 2**14 > |x| > 2.0 */
- w = __gen_ocl_internal_log(mad(xa, 2.0f, one / (__gen_ocl_sqrt(mad(xa, xa, one)) + xa)));
- } else { /* 2.0 > |x| > 2**-14 */
- float t = xa*xa;
- w =log1p(xa+t/(one+__gen_ocl_sqrt(one+t)));
- }
- }
- return __gen_ocl_internal_copysign(w, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_sinh(float x){
- //return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
- float one = 1.0,
- shuge = 1.0e37;
- float t,w,h;
- int ix,jx;
- GEN_OCL_GET_FLOAT_WORD(jx,x);
- ix = jx&0x7fffffff;
- /* x is INF or NaN */
- if(ix>=0x7f800000) return x+x;
- h = 0.5;
- if (jx<0) h = -h;
- /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix < 0x41b00000) { /* |x|<22 */
- if (ix<0x31800000) /* |x|<2**-28 */
- if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
- t = __gen_ocl_internal_expm1(__gen_ocl_internal_fabs(x));
- if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
- return h*(t+t/(t+one));
- }
- /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix < 0x42b17180) return h*__gen_ocl_internal_exp(__gen_ocl_internal_fabs(x));
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix<=0x42b2d4fc) {
- w = __gen_ocl_internal_exp((float)0.5*__gen_ocl_internal_fabs(x));
- t = h*w;
- return t*w;
- }
- /* |x| > overflowthresold, sinh(x) overflow */
- return x*shuge;
-}
-
-OVERLOADABLE float __gen_ocl_internal_tanh(float x) {
- //float y = native_exp(-2 * x);
- //return (1 - y) / (1 + y);
- float one=1.0, two=2.0, tiny = 1.0e-30;
- float t,z;
- int jx,ix;
- GEN_OCL_GET_FLOAT_WORD(jx,x);
- ix = jx&0x7fffffff;
- /* x is INF or NaN */
- if(ix>=0x7f800000) {
- if (jx>=0)
- return one/x+one; /* tanh(+-inf)=+-1 */
- else
- return one/x-one; /* tanh(NaN) = NaN */
- }
-
- if (ix < 0x41b00000) { /* |x|<22 */
- if (ix == 0)
- return x; /* x == +-0 */
- if (ix<0x24000000) /* |x|<2**-55 */
- return x*(one+x); /* tanh(small) = small */
- if (ix>=0x3f800000) { /* |x|>=1 */
- t = __gen_ocl_internal_expm1(two*__gen_ocl_internal_fabs(x));
- z = one - two/(t+two);
- } else {
- t = __gen_ocl_internal_expm1(-two*__gen_ocl_internal_fabs(x));
- z= -t/(t+two);
- }
- } else { /* |x| > 22, return +-1 */
- z = one - tiny; /* raised inexact flag */
- }
- return (jx>=0)? z: -z;
-}
-
-OVERLOADABLE float __gen_ocl_internal_cosh(float x) {
- //return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
- float halF = 0.5,
- huge = 1.0e+30,
- tiny = 1.0e-30,
- one = 1.0;
- float t,w;
- int ix;
- GEN_OCL_GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
- /* |x| in [0,22] */
- if (ix < 0x41b00000) {
- /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
- if(ix<0x3eb17218) {
- t = __gen_ocl_internal_expm1(__gen_ocl_fabs(x));
- w = one+t;
- if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
- return one+(t*t)/(w+w);
- }
- /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
- t = __gen_ocl_internal_exp(__gen_ocl_fabs(x));
- return halF*t+halF/t;
- }
- /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
- if (ix < 0x42b17180) return halF*__gen_ocl_internal_exp(__gen_ocl_fabs(x));
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix<=0x42b2d4fc) {
- w = __gen_ocl_internal_exp(halF*__gen_ocl_fabs(x));
- t = halF*w;
- return t*w;
- }
- /* x is INF or NaN */
- if(ix>=0x7f800000) return x*x;
- /* |x| > overflowthresold, cosh(x) overflow */
- return huge*huge;
-}
-
-OVERLOADABLE float __gen_ocl_internal_remainder(float x, float p){
- //return x-y*__gen_ocl_rnde(x/y);
- float zero = 0.0;
- int hx,hp;
- unsigned sx;
- float p_half;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hp,p);
- sx = hx&0x80000000;
- hp &= 0x7fffffff;
- hx &= 0x7fffffff;
- /* purge off exception values */
- if(hp==0) return (x*p)/(x*p); /* p = 0 */
- if((hx>=0x7f800000)|| /* x not finite */
- ((hp>0x7f800000))) /* p is NaN */
- return (x*p)/(x*p);
- if (hp<=0x7effffff) x = __gen_ocl_internal_fmod(x,p+p); /* now x < 2p */
- if ((hx-hp)==0) return zero*x;
- x = __gen_ocl_fabs(x);
- p = __gen_ocl_fabs(p);
- if (hp<0x01000000) {
- if(x+x>p) {
- x-=p;
- if(x+x>=p) x -= p;
- }
- } else {
- p_half = (float)0.5*p;
- if(x>p_half) {
- x-=p;
- if(x>=p_half) x -= p;
- }
- }
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_SET_FLOAT_WORD(x,hx^sx);
- return x;
-}
-
-OVERLOADABLE float __gen_ocl_internal_ldexp(float x, int n) {
- x = __gen_ocl_scalbnf(x,n);
- return x;
-}
-
-OVERLOADABLE float __gen_ocl_internal_atanh(float x) {
- //return 0.5f * native_sqrt((1 + x) / (1 - x));
- float xa = __gen_ocl_fabs (x);
- float t;
- if (isless (xa, 0.5f)){
- if (xa < 0x1.0p-28f) return x;
- t = xa + xa;
- t = 0.5f * log1p (t + t * xa / (1.0f - xa));
- } else if (isless (xa, 1.0f)){
- t = 0.5f * log1p ((xa + xa) / (1.0f - xa));
- } else{
- if (isgreater (xa, 1.0f)) return (x - x) / (x - x);
- return x / 0.0f;
- }
- return __gen_ocl_internal_copysign(t, x);
-}
-
-OVERLOADABLE float __gen_ocl_internal_exp10(float x){
- float px, qx,ans;
- short n;
- int i;
- float*p;
- float MAXL10 = 38.230809449325611792;
- float LOG210 = 3.32192809488736234787e0;
- float LG102A = 3.00781250000000000000E-1;
- float LG102B = 2.48745663981195213739E-4;
- float P[6];
- P[0] = 2.063216740311022E-001;
- P[1] = 5.420251702225484E-001;
- P[2] = 1.171292686296281E+000;
- P[3] = 2.034649854009453E+000;
- P[4] = 2.650948748208892E+000;
- P[5] = 2.302585167056758E+000;
-
- if( x < -MAXL10 ) return 0.0;
-
- if( isinf(x)) return INFINITY;
- /* The following is necessary because range reduction blows up: */
- if( x == 0 )return 1.0;
-
- /* Express 10**x = 10**g 2**n
- * = 10**g 10**( n log10(2) )
- * = 10**( g + n log10(2) )
- */
- px = x * LOG210;
- qx = __gen_ocl_internal_floor( px + 0.5 );
- n = qx;
- x -= qx * LG102A;
- x -= qx * LG102B;
-
- /* rational approximation for exponential
- * of the fractional part:
- * 10**x - 1 = 2x P(x**2)/( Q(x**2) - P(x**2) )
- */
- p = P;
- ans = *p++;
- i = 5;
- do{
- ans = ans * x + *p++;
- }
- while( --i );
- px = 1.0 + x * ans;
-
- /* multiply by power of 2 */
- x = __gen_ocl_internal_ldexp( px, n );
- return x;
-}
-
-OVERLOADABLE float cospi(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cospi(x);
-
- return __gen_ocl_internal_cospi(x);
-}
-
-OVERLOADABLE float cosh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cosh(x);
-
- return __gen_ocl_internal_cosh(x);
-}
-
-OVERLOADABLE float acos(float x) {
- return __gen_ocl_internal_acos(x);
-}
-
-OVERLOADABLE float acospi(float x) {
- return __gen_ocl_internal_acospi(x);
-}
-
-OVERLOADABLE float acosh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_acosh(x);
-
- return __gen_ocl_internal_acosh(x);
-}
-
-OVERLOADABLE float sinpi(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sinpi(x);
-
- return __gen_ocl_internal_sinpi(x);
-}
-
-OVERLOADABLE float sinh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_sinh(x);
-
- return __gen_ocl_internal_sinh(x);
-}
-
-OVERLOADABLE float asin(float x) {
- return __gen_ocl_internal_asin(x);
-}
-
-OVERLOADABLE float asinpi(float x) {
- return __gen_ocl_internal_asinpi(x);
-}
-
-OVERLOADABLE float asinh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_asinh(x);
-
- return __gen_ocl_internal_asinh(x);
-}
-
-OVERLOADABLE float tanpi(float x) {
- return __gen_ocl_internal_tanpi(x);
-}
-
-OVERLOADABLE float tanh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_tanh(x);
-
- return __gen_ocl_internal_tanh(x);
-}
-
-OVERLOADABLE float atan(float x) {
- return __gen_ocl_internal_atan(x);
-}
-
-OVERLOADABLE float atan2(float y, float x) {
- return __gen_ocl_internal_atan2(y, x);
-}
-
-OVERLOADABLE float atan2pi(float y, float x) {
- return __gen_ocl_internal_atan2pi(y, x);
-}
-
-OVERLOADABLE float atanpi(float x) {
- return __gen_ocl_internal_atanpi(x);
-}
-
-OVERLOADABLE float atanh(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_atanh(x);
-
- return __gen_ocl_internal_atanh(x);
-}
-
-OVERLOADABLE float cbrt(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_cbrt(x);
-
- return __gen_ocl_internal_cbrt(x);
-}
-
-OVERLOADABLE float rint(float x) {
- return __gen_ocl_internal_rint(x);
-}
-
-OVERLOADABLE float copysign(float x, float y) {
- return __gen_ocl_internal_copysign(x, y);
-}
-
-OVERLOADABLE float erf(float x) {
- return __gen_ocl_internal_erf(x);
-}
-
-OVERLOADABLE float erfc(float x) {
- return __gen_ocl_internal_erfc(x);
-}
-
-OVERLOADABLE float fmod (float x, float y) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_fmod(x, y);
-
- return __gen_ocl_internal_fmod(x, y);
-}
-
-OVERLOADABLE float remainder(float x, float p) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_remainder(x, p);
-
- return __gen_ocl_internal_remainder(x, p);
-}
-
-OVERLOADABLE float ldexp(float x, int n) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_ldexp(x, n);
-
- if (x == (float)0.0f) x = 0.0f;
- return __gen_ocl_internal_ldexp(x, n);
-}
-
-CONST OVERLOADABLE float __gen_ocl_mad(float a, float b, float c) __asm("llvm.fma" ".f32");
-CONST OVERLOADABLE half __gen_ocl_mad(half a, half b, half c) __asm("llvm.fma" ".f16");
-PURE CONST float __gen_ocl_fmax(float a, float b);
-PURE CONST float __gen_ocl_fmin(float a, float b);
-
-OVERLOADABLE float mad(float a, float b, float c) {
- return __gen_ocl_mad(a, b, c);
-}
-
-
-#define BODY \
- if (isnan(x) || isinf(x)) { \
- *exp = 0; \
- return x; \
- } \
- uint u = as_uint(x); \
- uint a = u & 0x7FFFFFFFu; \
- if (a == 0) { \
- *exp = 0; \
- return x; \
- } \
- if (a >= 0x800000) { \
- *exp = (a >> 23) - 126; \
- return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
- } \
- int e = -126; \
- while (a < 0x400000) { \
- e --; \
- a <<= 1; \
- } \
- a <<= 1; \
- *exp = e; \
- return as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
-OVERLOADABLE float frexp(float x, int *exp) { BODY; }
-#undef BODY
-
-OVERLOADABLE float nextafter(float x, float y) {
- int hx, hy, ix, iy;
- hx = as_int(x);
- hy = as_int(y);
- ix = hx & 0x7fffffff;
- iy = hy & 0x7fffffff;
- if(ix == 0)
- ix = hx & 0x7fffff;
- if(iy == 0)
- iy = hy & 0x7fffff;
- if(ix>0x7f800000 || iy>0x7f800000)
- return x+y;
- if(hx == hy)
- return y;
- if(ix == 0) {
- if(iy == 0)
- return y;
- else
- return as_float((hy&0x80000000) | 1);
- }
- if(hx >= 0) {
- if(hx > hy) {
- hx -= 1;
- } else {
- hx += 1;
- }
- } else {
- if(hy >= 0 || hx > hy){
- hx -= 1;
- } else {
- hx += 1;
- }
- }
- return as_float(hx);
-}
-
-#define BODY \
- uint hx = as_uint(x), ix = hx & 0x7FFFFFFF; \
- if (ix > 0x7F800000) { \
- *i = nan(0u); \
- return nan(0u); \
- } \
- if (ix == 0x7F800000) { \
- *i = x; \
- return as_float(hx & 0x80000000u); \
- } \
- *i = __gen_ocl_rndz(x); \
- return x - *i;
-OVERLOADABLE float modf(float x, float *i) { BODY; }
-#undef BODY
-
-OVERLOADABLE float __gen_ocl_internal_fmax(float a, float b) { return max(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmin(float a, float b) { return min(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmax(half a, half b) { return max(a,b); }
-OVERLOADABLE float __gen_ocl_internal_fmin(half a, half b) { return min(a,b); }
-OVERLOADABLE float __gen_ocl_internal_maxmag(float x, float y) {
- float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
- return a > b ? x : b > a ? y : max(x, y);
-}
-OVERLOADABLE float __gen_ocl_internal_minmag(float x, float y) {
- float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
- return a < b ? x : b < a ? y : min(x, y);
-}
-OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) {
- if(isnan(x))
- return x;
- if(isnan(y))
- return y;
- return x > y ? (x - y) : +0.f;
-}
-/*
- * the pow/pown high precision implementation are copied from msun library.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) {
- float z,ax,z_h,z_l,p_h,p_l;
- float y1,t1,t2,r,s,sn,t,u,v,w;
- int i,j,k,yisint,n;
- int hx,hy,ix,iy,is;
- float bp[2],dp_h[2],dp_l[2],
- zero = 0.0,
- one = 1.0,
- two = 2.0,
- two24 = 16777216.0, /* 0x4b800000 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
- L1 = 6.0000002384e-01, /* 0x3f19999a */
- L2 = 4.2857143283e-01, /* 0x3edb6db7 */
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03, /* 0xbb360b61 */
- lg2 = 6.9314718246e-01, /* 0x3f317218 */
- lg2_h = 6.93145752e-01, /* 0x3f317200 */
- lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
- ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
- cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
- cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
- cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
- ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
- bp[0] = 1.0,bp[1] = 1.5,
- dp_h[0] = 0.0,dp_h[1] = 5.84960938e-01,
- dp_l[0] = 0.0,dp_l[1] = 1.56322085e-06;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- ix = hx&0x7fffffff; iy = hy&0x7fffffff;
- if (ix < 0x00800000) { /* x < 2**-126 */
- ix = 0;/* Gen does not support subnormal number now */
- }
- if (iy < 0x00800000) { /* y < 2**-126 */
- iy = 0;/* Gen does not support subnormal number now */
- }
- /* y==zero: x**0 = 1 */
- if(iy==0) return one;
- /* pow(+1, y) returns 1 for any y, even a NAN */
- if(hx==0x3f800000) return one;
- /* +-NaN return x+y */
- if(ix > 0x7f800000 || iy > 0x7f800000)
- return (x+0.0f)+y+(0.0f);
- /* determine if y is an odd int when x < 0
- * yisint = 0 ... y is not an integer
- * yisint = 1 ... y is an odd int
- * yisint = 2 ... y is an even int
- */
- yisint = 0;
- if(hx<0) {
- if(iy>=0x4b800000) yisint = 2; /* even integer y */
- else if(iy>=0x3f800000) {
- k = (iy>>23)-0x7f; /* exponent */
- j = iy>>(23-k);
- if((j<<(23-k))==iy) yisint = 2-(j&1);
- }
- }
- /* special value of y */
- if (iy==0x7f800000) { /* y is +-inf */
- if (ix==0x3f800000)
- //return y - y; /* inf**+-1 is NaN */
- return one;
- else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
- return (hy>=0)? y: zero;
- else /* (|x|<1)**-,+inf = inf,0 */
- return (hy<0)?-y: zero;
- }
- if(iy==0x3f800000) { /* y is +-1 */
- if(hy<0) return one/x; else return x;
- }
- if(hy==0x40000000) return x*x; /* y is 2 */
- if(hy==0x3f000000) { /* y is 0.5 */
- if(hx>=0)return __gen_ocl_sqrt(x);
- }
-
- ax = __gen_ocl_fabs(x);
- /* special value of x */
- if(ix==0x7f800000||ix==0||ix==0x3f800000){
- z = ax; /*x is +-0,+-inf,+-1*/
- if(hy<0) z = one/z; /* z = (1/|x|) */
- if(hx<0) {
- if(((ix-0x3f800000)|yisint)==0) {
- z = (z-z)/(z-z); /* (-1)**non-int is NaN */
- } else if(yisint==1)
- z = -z; /* (x<0)**odd = -(|x|**odd) */
- }
- return z;
- }
- n = ((uint)hx>>31)-1;
-
- /* (x<0)**(non-int) is NaN */
- if((n|yisint)==0) return (x-x)/(x-x);
-
- sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
-
- /* |y| is huge */
- if(iy>0x4d000000) { /* if |y| > 2**27 */
- /* over/underflow if x is not close to one */
- if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
- if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = ax-1; /* t has 20 trailing zeros */
- w = (t*t)*((float)0.5-t*(0.333333333333f-t*0.25f));
- u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
- v = t*ivln2_l-w*ivln2;
- t1 = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
- t2 = v-(t1-u);
- } else {
- float s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
- //if(ix<0x00800000)
- //{ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
- n += ((ix)>>23)-0x7f;
- j = ix&0x007fffff;
- /* determine interval */
- ix = j|0x3f800000; /* normalize ix */
- if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
- else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
- else {k=0;n+=1;ix -= 0x00800000;}
- GEN_OCL_SET_FLOAT_WORD(ax,ix);
-
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
- s = u*v;
- s_h = s;
- GEN_OCL_GET_FLOAT_WORD(is,s_h);
- GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
- /* t_h=ax+bp[k] High */
- is = ((ix>>1)&0xfffff000)|0x20000000;
- GEN_OCL_SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
- t_l = ax - (t_h-bp[k]);
- s_l = v*((u-s_h*t_h)-s_h*t_l);
-
- /* compute log(ax) */
- s2 = s*s;
- r = s2*s2*(L1+s2*L2);
- r += s_l*(s_h+s);
- s2 = s_h*s_h;
- t_h = 3.0f+s2+r;
- GEN_OCL_GET_FLOAT_WORD(is,t_h);
- GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
- t_l = r-((t_h-3.0f)-s2);
- /* u+v = s*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h+t_l*s;
- /* 2/(3log2)*(s+...) */
- p_h = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,p_h);
- GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
- p_l = v-(p_h-u);
- z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
- z_l = cp_l*p_h+p_l*cp+dp_l[k];
- /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (float)n;
- t1 = (((z_h+z_l)+dp_h[k])+t);
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);
- }
-
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
- GEN_OCL_GET_FLOAT_WORD(is,y);
- GEN_OCL_SET_FLOAT_WORD(y1,is&0xffffe000);
- p_l = (y-y1)*t1+y*t2;
- p_h = y1*t1;
- z = p_l+p_h;
- GEN_OCL_GET_FLOAT_WORD(j,z);
- if (j>0x43000000) /* if z > 128 */
- return sn*huge*huge; /* overflow */
- else if (j==0x43000000) { /* if z == 128 */
- if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
- }
- else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
- return sn*tiny*tiny; /* underflow */
- else if (j==0xc3160000){ /* z == -150 */
- if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
- }
-
- /*
- * compute 2**(p_h+p_l)
- */
- i = j&0x7fffffff;
- k = (i>>23)-0x7f;
- n = 0;
- if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
- n = j+(0x00800000>>(k+1));
- k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
- GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
- n = ((n&0x007fffff)|0x00800000)>>(23-k);
- if(j<0) n = -n;
- p_h -= t;
- }
- t = p_l+p_h;
- GEN_OCL_GET_FLOAT_WORD(is,t);
- GEN_OCL_SET_FLOAT_WORD(t,is&0xffff8000);
- u = t*lg2_h;
- v = (p_l-(t-p_h))*lg2+t*lg2_l;
- z = u+v;
- w = v-(z-u);
- t = z*z;
- t1 = z - t*(P1+t*P2);
- r = (z*t1)/(t1-two)-(w+z*w);
- z = one-(r-z);
- GEN_OCL_GET_FLOAT_WORD(j,z);
- j += (n<<23);
- if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
- else GEN_OCL_SET_FLOAT_WORD(z,j);
- return sn*z;
-}
-
-OVERLOADABLE float tgamma (float x)
-{
- /* based on glibc __ieee754_gammaf_r by Ulrich Drepper <drepper@cygnus.com> */
-
- unsigned int hx;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- if (hx == 0xff800000)
- {
- /* x == -Inf. According to ISO this is NaN. */
- return NAN;
- }
- if ((hx & 0x7f800000) == 0x7f800000)
- {
- /* Positive infinity (return positive infinity) or NaN (return
- NaN). */
- return x;
- }
- if (x < 0.0f && __gen_ocl_internal_floor (x) == x)
- {
- /* integer x < 0 */
- return NAN;
- }
-
- if (x >= 36.0f)
- {
- /* Overflow. */
- return INFINITY;
- }
- else if (x <= 0.0f && x >= -FLT_EPSILON / 4.0f)
- {
- return 1.0f / x;
- }
- else
- {
- float sinpix = __gen_ocl_internal_sinpi(x);
- if (x <= -42.0f)
- /* Underflow. */
- {return 0.0f * sinpix /*for sign*/;}
- int exp2_adj = 0;
- float x_abs = __gen_ocl_fabs(x);
- float gam0;
-
- if (x_abs < 4.0f) {
- /* gamma = exp(lgamma) is only accurate for small lgamma */
- float prod,x_adj;
- if (x_abs < 0.5f) {
- prod = 1.0f / x_abs;
- x_adj = x_abs + 1.0f;
- } else if (x_abs <= 1.5f) {
- prod = 1.0f;
- x_adj = x_abs;
- } else if (x_abs < 2.5f) {
- x_adj = x_abs - 1.0f;
- prod = x_adj;
- } else {
- x_adj = x_abs - 2.0f;
- prod = x_adj * (x_abs - 1.0f);
- }
- gam0 = __gen_ocl_internal_exp (lgamma (x_adj)) * prod;
- }
- else {
- /* Compute gamma (X) using Stirling's approximation,
- starting by computing pow (X, X) with a power of 2
- factored out to avoid intermediate overflow. */
- float x_int = __gen_ocl_internal_round (x_abs);
- float x_frac = x_abs - x_int;
- int x_log2;
- float x_mant = frexp (x_abs, &x_log2);
- if (x_mant < M_SQRT1_2_F)
- {
- x_log2--;
- x_mant *= 2.0f;
- }
- exp2_adj = x_log2 * (int) x_int;
- float ret = (__gen_ocl_internal_pow(x_mant, x_abs)
- * exp2 (x_log2 * x_frac)
- * __gen_ocl_internal_exp (-x_abs)
- * sqrt (2.0f * M_PI_F / x_abs) );
-
- float x2 = x_abs * x_abs;
- float bsum = (0x3.403404p-12f / x2 -0xb.60b61p-12f) / x2 + 0x1.555556p-4f;
- gam0 = ret + ret * __gen_ocl_internal_expm1 (bsum / x_abs);
- }
- if (x > 0.0f) {return __gen_ocl_internal_ldexp (gam0, exp2_adj);}
- float gam1 = M_PI_F / (-x * sinpix * gam0);
- return __gen_ocl_internal_ldexp (gam1, -exp2_adj);
- }
-}
-
-float __gen_ocl_internal_pown(float x, int y) {
- const float
- bp[] = {1.0, 1.5,},
- dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
- dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
- zero = 0.0,
- one = 1.0,
- two = 2.0,
- two24 = 16777216.0, /* 0x4b800000 */
- huge = 1.0e30,
- tiny = 1.0e-30,
- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
- L1 = 6.0000002384e-01, /* 0x3f19999a */
- L2 = 4.2857143283e-01, /* 0x3edb6db7 */
- P1 = 1.6666667163e-01, /* 0x3e2aaaab */
- P2 = -2.7777778450e-03, /* 0xbb360b61 */
- lg2 = 6.9314718246e-01, /* 0x3f317218 */
- lg2_h = 0x1.62ep-1,
- lg2_l = 0x1.0bfbe8p-15,
- ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
- cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
- cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
- cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
- ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
- ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
- ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
-
- float z,ax,z_h,z_l,p_h,p_l;
- float y1,t1,t2,r,s,t,u,v,w;
- int i,j,k,yisint,n;
- int hx,ix,iy,is;
-
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- iy = y > 0 ? y&0x7fffffff : (-y)&0x7fffffff;
- /* y==zero: x**0 = 1 */
- if(y==0) return one;
-
- /* +-NaN return NAN */
- if(ix > 0x7f800000)
- return NAN;
-
- /* determine if y is an odd int
- * yisint = 1 ... y is an odd int
- * yisint = 2 ... y is an even int
- */
- yisint = y&1 ? 1 : 2;
-
- if (y == 1) return x;
- if (y == -1) return one/x;
- if (y == 2) return x*x;
-
- ax = __gen_ocl_fabs(x);
-
- /* special value of x */
- if(ix==0x7f800000||ix==0||ix==0x3f800000){
- z = ax; /*x is +-0,+-inf,+-1*/
- if(y<0) z = one/z; /* z = (1/|x|) */
- if(hx<0) {
- if(yisint==1)
- z = -z; /* (x<0)**odd = -(|x|**odd) */
- }
- return z;
- }
-
- float sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if(((((unsigned)hx>>31)-1)|(yisint-1))==0)
- sn = -one; /* (-ve)**(odd int) */
-
- /* |y| is huge */
- if(iy>0x08000000) { /* if |y| > 2**27 */
- /* over/underflow if x is not close to one */
- if(ix<0x3f7ffff8) return (y<0)? sn*huge*huge:tiny*tiny;
- if(ix>0x3f800007) return (y>0)? sn*huge*huge:tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = ax-1; /* t has 20 trailing zeros */
- w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
- u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
- v = t*ivln2_l-w*ivln2;
- t1 = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
- t2 = v-(t1-u);
- } else {
- float s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
-// if(ix<0x00800000)
-// {ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
- n += ((ix)>>23)-0x7f;
- j = ix&0x007fffff;
- /* determine interval */
- ix = j|0x3f800000; /* normalize ix */
- if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
- else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
- else {k=0;n+=1;ix -= 0x00800000;}
- GEN_OCL_SET_FLOAT_WORD(ax,ix);
-
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
- s = u*v;
- s_h = s;
- GEN_OCL_GET_FLOAT_WORD(is,s_h);
- GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
-
- /* t_h=ax+bp[k] High */
- GEN_OCL_SET_FLOAT_WORD(t_h, (((ix>>1)|0x20000000)+0x00400000+(k<<21)) &0xfffff000);
- t_l = ax - (t_h-bp[k]);
- s_l = v*((u-s_h*t_h)-s_h*t_l);
-
-
- /* compute log(ax) */
- s2 = s*s;
- r = s2*s2*(L1+s2*L2);
- r += s_l*(s_h+s);
- s2 = s_h*s_h;
- t_h = (float)3.0+s2+r;
- GEN_OCL_GET_FLOAT_WORD(is,t_h);
- GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
- t_l = r-((t_h-(float)3.0)-s2);
- /* u+v = s*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h+t_l*s;
- /* 2/(3log2)*(s+...) */
- p_h = u+v;
- GEN_OCL_GET_FLOAT_WORD(is,p_h);
- GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
- p_l = v-(p_h-u);
- z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
- z_l = cp_l*p_h+p_l*cp+dp_l[k];
- /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (float)n;
- t1 = (((z_h+z_l)+dp_h[k])+t);
- GEN_OCL_GET_FLOAT_WORD(is,t1);
- GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);
- }
-
- /* split up y into y1+y2+y3 and compute (y1+y2+y3)*(t1+t2) */
-
- float fy = (float)y;
- float y3 = (float)(y-(int)fy);
- GEN_OCL_GET_FLOAT_WORD(is,fy);
- GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000);
-
- p_l = (fy-y1)*t1 + y3*t1 + fy*t2 + y3*t2;
- p_h = y1*t1;
- z = p_l+p_h;
-
- GEN_OCL_GET_FLOAT_WORD(j,z);
- if (j>0x43000000) /* if z > 128 */
- return sn*huge*huge; /* overflow */
- else if (j==0x43000000) { /* if z == 128 */
- if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
- }
- else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
- return sn*tiny*tiny; /* underflow */
- else if (j==0xc3160000){ /* z == -150 */
- if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
- }
- /*
- * compute 2**(p_h+p_l)
- */
- i = j&0x7fffffff;
- k = (i>>23)-0x7f;
- n = 0;
- if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
- n = j+(0x00800000>>(k+1));
- k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
- GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
- n = ((n&0x007fffff)|0x00800000)>>(23-k);
- if(j<0) n = -n;
- p_h -= t;
-
- z -= n;
- }
-
- t = z;
- GEN_OCL_GET_FLOAT_WORD(is,t);
- GEN_OCL_SET_FLOAT_WORD(t,is&0xfffff000);
- u = t*lg2_h;
- v = (p_l-(t-p_h))*lg2+t*lg2_l;
- z = u+v;
- w = v-(z-u);
- t = z*z;
- t1 = z - t*(P1+t*P2);
- r = (z*t1)/(t1-two)-(w+z*w);
- z = one-(r-z);
- GEN_OCL_GET_FLOAT_WORD(j,z);
- j += (n<<23);
- if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
- else GEN_OCL_SET_FLOAT_WORD(z,j);
- return sn*z;
-}
-
-OVERLOADABLE float hypot(float x, float y) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_hypot(x, y);
-
- //return __gen_ocl_sqrt(x*x + y*y);
- float a,b,an,bn,cn;
- int e;
- if (isfinite (x) && isfinite (y)){ /* Determine absolute values. */
- x = __gen_ocl_fabs (x);
- y = __gen_ocl_fabs (y);
- /* Find the bigger and the smaller one. */
- a = max(x,y);
- b = min(x,y);
- /* Now 0 <= b <= a. */
- /* Write a = an * 2^e, b = bn * 2^e with 0 <= bn <= an < 1. */
- an = frexp (a, &e);
- bn = ldexp (b, - e);
- /* Through the normalization, no unneeded overflow or underflow will occur here. */
- cn = __gen_ocl_sqrt (an * an + bn * bn);
- return ldexp (cn, e);
- }else{
- if (isinf (x) || isinf (y)) /* x or y is infinite. Return +Infinity. */
- return INFINITY;
- else /* x or y is NaN. Return NaN. */
- return x + y;
- }
-}
-
-#define BODY \
- if (isnan(x)) { \
- *p = x; \
- return x; \
- } \
- *p = __gen_ocl_internal_floor(x); \
- if (isinf(x)) { \
- return x > 0 ? +0. : -0.; \
- } \
- return __gen_ocl_internal_fmin(x - *p, 0x1.FFFFFep-1F);
-OVERLOADABLE float fract(float x, float *p) { BODY; }
-#undef BODY
-
-#define BODY \
- float Zero[2]; \
- int n,hx,hy,hz,ix,iy,sx,i,sy; \
- uint q,sxy; \
- Zero[0] = 0.0;Zero[1] = -0.0; \
- if (x == 0.0f) { x = 0.0f; }; \
- if (y == 0.0f) { y = 0.0f; }\
- GEN_OCL_GET_FLOAT_WORD(hx,x);GEN_OCL_GET_FLOAT_WORD(hy,y); \
- sxy = (hx ^ hy) & 0x80000000;sx = hx&0x80000000;sy = hy&0x80000000; \
- hx ^=sx; hy &= 0x7fffffff; \
- if (hx < 0x00800000)hx = 0;if (hy < 0x00800000)hy = 0; \
- if(hy==0||hx>=0x7f800000||hy>0x7f800000){ \
- *quo = 0;return NAN; \
- } \
- if( hy == 0x7F800000 || hx == 0 ) { \
- *quo = 0;return x; \
- } \
- if( hx == hy ) { \
- *quo = (x == y) ? 1 : -1; \
- return sx ? -0.0 : 0.0; \
- } \
- if(hx<hy) { \
- q = 0; \
- goto fixup; \
- } else if(hx==hy) { \
- *quo = (sxy ? -1 : 1); \
- return Zero[(uint)sx>>31]; \
- } \
- ix = (hx>>23)-127; \
- iy = (hy>>23)-127; \
- hx = 0x00800000|(0x007fffff&hx); \
- hy = 0x00800000|(0x007fffff&hy); \
- n = ix - iy; \
- q = 0; \
- while(n--) { \
- hz=hx-hy; \
- if(hz<0) hx = hx << 1; \
- else {hx = hz << 1; q++;} \
- q <<= 1; \
- } \
- hz=hx-hy; \
- if(hz>=0) {hx=hz;q++;} \
- if(hx==0) { \
- q &= 0x0000007f; \
- *quo = (sxy ? -q : q); \
- return Zero[(uint)sx>>31]; \
- } \
- while(hx<0x00800000) { \
- hx <<= 1;iy -= 1; \
- } \
- if(iy>= -126) { \
- hx = ((hx-0x00800000)|((iy+127)<<23)); \
- } else {\
- n = -126 - iy; \
- hx >>= n; \
- } \
-fixup: \
- GEN_OCL_SET_FLOAT_WORD(x,hx); \
- if(hx<0x00800000){ \
- GEN_OCL_GET_FLOAT_WORD(hy,y); \
- hy &= 0x7fffffff; \
- if(hx+hx > hy ||(hx+hx==hy && (q & 1)))q++; \
- x = 0; \
- }else{ \
- y = __gen_ocl_fabs(y); \
- if (y < 0x1p-125f) { \
- if (x+x>y || (x+x==y && (q & 1))) { \
- q++;x-=y; \
- } \
- }else if (x>0.5f*y || (x==0.5f*y && (q & 1))) { \
- q++;x-=y; \
- } \
- GEN_OCL_GET_FLOAT_WORD(hx,x);GEN_OCL_SET_FLOAT_WORD(x,hx^sx); \
- } \
- int sign = sx==sy?0:1; \
- q &= 0x0000007f; \
- *quo = (sign ? -q : q); \
- return x;
-
-OVERLOADABLE float remquo(float x, float y, int *quo) {
- BODY;
-}
-#undef BODY
-
-OVERLOADABLE float powr(float x, float y) {
- unsigned int hx, sx, hy, sy;
-
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_pow(x,y);
- else {
- if (isnan(x) || isnan(y)) return NAN;
- GEN_OCL_GET_FLOAT_WORD(hx,x);
- GEN_OCL_GET_FLOAT_WORD(hy,y);
- sx = (hx & 0x80000000) >> 31;
- sy = (hy & 0x80000000) >> 31;
-
- if ((hx&0x7fffffff) < 0x00800000) { /* x < 2**-126 */
- x = 0.0f;/* Gen does not support subnormal number now */
- hx = hx &0x80000000;
- }
- if ((hy&0x7fffffff) < 0x00800000) { /* y < 2**-126 */
- y = 0.0;/* Gen does not support subnormal number now */
- hy = hy &0x80000000;
- }
-
- // (x < 0) ** y = NAN (y!=0)
- if ((sx && (hx & 0x7fffffff))) return NAN;
-
- // +/-0 ** +/-0 = NAN
- if ( !(hx&0x7fffffff) && !(hy&0x7fffffff)) return NAN;
-
- // +inf ** +/-0 = NAN
- if ( ((hx & 0x7f800000) ==0x7f800000) && !(hy&0x7fffffff)) return NAN;
-
- // others except nan/inf/0 ** 0 = 1.0
- if (!(hy&0x7fffffff)) return 1.0f;
-
- // +1 ** inf = NAN; +1 ** finite = 1;
- if (hx == 0x3f800000) {
- return isinf(y) ? NAN : 1.0f;
- }
-
- if ( !(hx & 0x7fffffff)) {
- // +/-0 ** y<0 = +inf
- // +/-0 ** y>0 = +0
- return sy ? INFINITY : 0.0f;
- }
-
- return __gen_ocl_internal_pow(x,y);
- }
-}
-
-OVERLOADABLE float pown(float x, int n) {
- if (__ocl_math_fastpath_flag) {
- if (x == 0.f && n == 0)
- return 1.f;
- if (x < 0.f && (n&1) )
- return -powr(-x, n);
- return powr(x, n);
- } else {
- int ix;
- GEN_OCL_GET_FLOAT_WORD(ix, x);
- float sign = ix < 0 ? -1.0f : 1.0f;
- if (x == 0.0f) x = sign * 0.0f;
-
- return __gen_ocl_internal_pown(x, n);
- }
-}
-
-OVERLOADABLE float pow(float x, float y) {
- if (!__ocl_math_fastpath_flag)
- return __gen_ocl_internal_pow(x,y);
- else {
- int n;
- if (x == 0.f && y == 0.f)
- return 1.f;
- if (x >= 0.f)
- return powr(x, y);
- n = y;
- if ((float)n == y)//is exact integer
- return pown(x, n);
- return NAN;
- }
-}
-
-OVERLOADABLE float rootn(float x, int n) {
- float ax,re;
- int sign = 0;
- int hx;
- if( n == 0 )return NAN;
-
- GEN_OCL_GET_FLOAT_WORD(hx, x);
- // Gen does not support denorm, flush to zero
- if ((hx & 0x7fffffff) < 0x00800000) {
- x = hx < 0 ? -0.0f : 0.0f;
- }
-
- //rootn ( x, n ) returns a NaN for x < 0 and n is even.
- if( x < 0 && 0 == (n&1) )
- return NAN;
- if( x == 0.0 ){
- switch( n & 0x80000001 ){
- //rootn ( +-0, n ) is +0 for even n > 0.
- case 0:
- return 0.0f;
- //rootn ( +-0, n ) is +-0 for odd n > 0.
- case 1:
- return x;
- //rootn ( +-0, n ) is +inf for even n < 0.
- case 0x80000000:
- return INFINITY;
-
- //rootn ( +-0, n ) is +-inf for odd n < 0.
- case 0x80000001:
- return __gen_ocl_internal_copysign(INFINITY, x);
- }
- }
- ax = __gen_ocl_fabs(x);
- if(x <0.0f && (n&1))
- sign = 1;
- if (__ocl_math_fastpath_flag)
- re = __gen_ocl_pow(ax, 1.f/n);
- else
- re = __gen_ocl_internal_pow(ax,1.f/n);
- if(sign)
- re = -re;
- return re;
-}
-
-OVERLOADABLE float fabs(float x) {
- return __gen_ocl_internal_fabs(x);
-}
-
-OVERLOADABLE float trunc(float x) {
- return __gen_ocl_internal_trunc(x);
-}
-
-OVERLOADABLE float round(float x) {
- return __gen_ocl_internal_round(x);
-}
-
-OVERLOADABLE float floor(float x) {
- return __gen_ocl_internal_floor(x);
-}
-
-OVERLOADABLE float ceil(float x) {
- return __gen_ocl_internal_ceil(x);
-}
-
-OVERLOADABLE float log(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log(x);
-
- return __gen_ocl_internal_log(x);
-}
-
-OVERLOADABLE float log2(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log2(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log2(x);
-
- return __gen_ocl_internal_log2(x);
-}
-
-OVERLOADABLE float log10(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_log10(x);
-
- /* Use native instruction when it has enough precision */
- if((x > 0x1.1p0) || (x <= 0))
- return __gen_ocl_internal_fastpath_log10(x);
-
- return __gen_ocl_internal_log10(x);
-}
-
-OVERLOADABLE float exp(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_exp(x);
-
- /* Use native instruction when it has enough precision */
- if (x > -0x1.6p1 && x < 0x1.6p1)
- return __gen_ocl_internal_fastpath_exp(x);
-
- return __gen_ocl_internal_exp(x);
-}
-
-OVERLOADABLE float exp2(float x) {
- /* Use native instruction when it has enough precision, exp2 always */
- return native_exp2(x);
-}
-
-OVERLOADABLE float exp10(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_exp10(x);
-
- return __gen_ocl_internal_exp10(x);
-}
-
-OVERLOADABLE float expm1(float x) {
- if (__ocl_math_fastpath_flag)
- return __gen_ocl_internal_fastpath_expm1(x);
-
- return __gen_ocl_internal_expm1(x);
-}
-
-OVERLOADABLE float fmin(float a, float b) {
- return __gen_ocl_internal_fmin(a, b);
-}
-
-OVERLOADABLE float fmax(float a, float b) {
- return __gen_ocl_internal_fmax(a, b);
-}
-
-OVERLOADABLE float fma(float a, float b, float c) {
- return mad(a, b, c);
-}
-
-OVERLOADABLE float fdim(float x, float y) {
- return __gen_ocl_internal_fdim(x, y);
-}
-
-OVERLOADABLE float maxmag(float x, float y) {
- return __gen_ocl_internal_maxmag(x, y);
-}
-
-OVERLOADABLE float minmag(float x, float y) {
- return __gen_ocl_internal_minmag(x, y);
-}
-
-
-/* So far, the HW do not support half float math function.
- We just do the conversion and call the float version here. */
-OVERLOADABLE half cospi(half x) {
- float _x = (float)x;
- return (half)cospi(_x);
-}
-OVERLOADABLE half cosh(half x) {
- float _x = (float)x;
- return (half)cosh(_x);
-}
-OVERLOADABLE half acos(half x) {
- float _x = (float)x;
- return (half)acos(_x);
-}
-OVERLOADABLE float half_cos(float x) {
- return (float)cos(x);
-}
-OVERLOADABLE float half_divide(float x, float y) {
- return (float)native_divide(x, y);
-}
-OVERLOADABLE float half_exp(float x) {
- return (float)native_exp(x);
-}
-OVERLOADABLE float half_exp2(float x){
- return (float)native_exp2(x);
-}
-OVERLOADABLE float half_exp10(float x){
- return (float)native_exp10(x);
-}
-OVERLOADABLE float half_log(float x){
- return (float)native_log(x);
-}
-OVERLOADABLE float half_log2(float x){
- return (float)native_log2(x);
-}
-OVERLOADABLE float half_log10(float x){
- return (float)native_log10(x);
-}
-OVERLOADABLE float half_powr(float x, float y){
- return (float)powr(x, y);
-}
-OVERLOADABLE float half_recip(float x){
- return (float)native_recip(x);
-}
-OVERLOADABLE float half_rsqrt(float x){
- return (float)native_rsqrt(x);
-}
-OVERLOADABLE float half_sin(float x){
- return (float)sin(x);
-}
-OVERLOADABLE float half_sqrt(float x){
- return (float)native_sqrt(x);
-}
-OVERLOADABLE float half_tan(float x){
- return (float)tan(x);
-}
-OVERLOADABLE half acospi(half x) {
- float _x = (float)x;
- return (half)acospi(_x);
-}
-OVERLOADABLE half acosh(half x) {
- float _x = (float)x;
- return (half)acosh(_x);
-}
-OVERLOADABLE half sinpi(half x) {
- float _x = (float)x;
- return (half)sinpi(_x);
-}
-OVERLOADABLE half sinh(half x) {
- float _x = (float)x;
- return (half)sinh(_x);
-}
-OVERLOADABLE half asin(half x) {
- float _x = (float)x;
- return (half)asin(_x);
-}
-OVERLOADABLE half asinpi(half x) {
- float _x = (float)x;
- return (half)asinpi(_x);
-}
-OVERLOADABLE half asinh(half x) {
- float _x = (float)x;
- return (half)asinh(_x);
-}
-OVERLOADABLE half tanpi(half x) {
- float _x = (float)x;
- return (half)tanpi(_x);
-}
-OVERLOADABLE half tanh(half x) {
- float _x = (float)x;
- return (half)tanh(_x);
-}
-OVERLOADABLE half atan(half x) {
- float _x = (float)x;
- return (half)atan(_x);
-}
-OVERLOADABLE half atan2(half y, half x) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)atan2(_x, _y);
-}
-OVERLOADABLE half atan2pi(half y, half x) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)atan2pi(_x, _y);
-}
-OVERLOADABLE half atanpi(half x) {
- float _x = (float)x;
- return (half)atanpi(_x);
-}
-OVERLOADABLE half atanh(half x) {
- float _x = (float)x;
- return (half)atanh(_x);
-}
-OVERLOADABLE half cbrt(half x) {
- float _x = (float)x;
- return (half)cbrt(_x);
-}
-OVERLOADABLE half rint(half x) {
- float _x = (float)x;
- return (half)rint(_x);
-}
-OVERLOADABLE half copysign(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)copysign(_x, _y);
-}
-OVERLOADABLE half erf(half x) {
- float _x = (float)x;
- return (half)erf(_x);
-}
-OVERLOADABLE half erfc(half x) {
- float _x = (float)x;
- return (half)erfc(_x);
-}
-OVERLOADABLE half fmod(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)fmod(_x, _y);
-}
-OVERLOADABLE half remainder(half x, half p) {
- float _x = (float)x;
- float _p = (float)p;
- return (half)remainder(_x, _p);
-}
-OVERLOADABLE half ldexp(half x, int n) {
- float _x = (float)x;
- return (half)ldexp(_x, n);
-}
-OVERLOADABLE half powr(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)powr(_x, _y);
-}
-OVERLOADABLE half pow(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)pow(_x, _y);
-}
-//no pow, we use powr instead
-OVERLOADABLE half fabs(half x) {
- float _x = (float)x;
- return (half)fabs(_x);
-}
-OVERLOADABLE half trunc(half x) {
- float _x = (float)x;
- return (half)trunc(_x);
-}
-OVERLOADABLE half round(half x) {
- float _x = (float)x;
- return (half)round(_x);
-}
-OVERLOADABLE half floor(half x) {
- float _x = (float)x;
- return (half)floor(_x);
-}
-OVERLOADABLE half ceil(half x) {
- float _x = (float)x;
- return (half)ceil(_x);
-}
-OVERLOADABLE half log(half x) {
- float _x = (float)x;
- return (half)log(_x);
-}
-OVERLOADABLE half log2(half x) {
- float _x = (float)x;
- return (half)log2(_x);
-}
-OVERLOADABLE half log10(half x) {
- float _x = (float)x;
- return (half)log10(_x);
-}
-OVERLOADABLE half exp(half x) {
- float _x = (float)x;
- return (half)exp(_x);
-}
-OVERLOADABLE half exp10(half x) {
- float _x = (float)x;
- return (half)exp10(_x);
-}
-OVERLOADABLE half expm1(half x) {
- float _x = (float)x;
- return (half)expm1(_x);
-}
-OVERLOADABLE half fmin(half a, half b) {
- return __gen_ocl_internal_fmin(a, b);
-}
-OVERLOADABLE half fmax(half a, half b) {
- return __gen_ocl_internal_fmax(a, b);
-}
-OVERLOADABLE half fma(half a, half b, half c) {
- float _a = (float)a;
- float _b = (float)b;
- float _c = (float)c;
- return (half)fma(_a, _b, _c);
-}
-OVERLOADABLE half fdim(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)fdim(_x, _y);
-}
-OVERLOADABLE half maxmag(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)maxmag(_x, _y);
-}
-OVERLOADABLE half minmag(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)minmag(_x, _y);
-}
-OVERLOADABLE half exp2(half x) {
- float _x = (float)x;
- return (half)exp2(_x);
-}
-OVERLOADABLE half mad(half a, half b, half c) {
- return __gen_ocl_mad(a,b,c);
-}
-OVERLOADABLE half sin(half x) {
- float _x = (float)x;
- return (half)sin(_x);
-}
-OVERLOADABLE half cos(half x) {
- float _x = (float)x;
- return (half)cos(_x);
-}
-OVERLOADABLE half tan(half x) {
- float _x = (float)x;
- return (half)tan(_x);
-}
-OVERLOADABLE half tgamma(half x) {
- float _x = (float)x;
- return (half)tgamma(_x);
-}
-OVERLOADABLE half lgamma(half x) {
- float _x = (float)x;
- return (half)lgamma(_x);
-}
-OVERLOADABLE half lgamma_r(half x, int *signgamp) {
- float _x = (float)x;
- return (half)lgamma_r(_x, signgamp);
-}
-OVERLOADABLE half log1p(half x) {
- float _x = (float)x;
- return (half)log1p(_x);
-}
-OVERLOADABLE half logb(half x) {
- float _x = (float)x;
- return (half)logb(_x);
-}
-OVERLOADABLE int ilogb(half x) {
- float _x = (float)x;
- return ilogb(_x);
-}
-OVERLOADABLE half nan(ushort code) {
- return (half)NAN;
-}
-
-OVERLOADABLE half sincos(half x, half *cosval) {
- float _x = (float)x;
- float _cosval;
- half ret = (half)sincos(_x, &_cosval);
- *cosval = (half)_cosval;
- return ret;
-}
-
-OVERLOADABLE half sqrt(half x) {
- float _x = (float)x;
- return (half)sqrt(_x);
-}
-OVERLOADABLE half rsqrt(half x) {
- float _x = (float)x;
- return (half)rsqrt(_x);
-}
-OVERLOADABLE half frexp(half x, int *exp) {
- float _x = (float)x;
- return (half)frexp(_x, exp);
-}
-OVERLOADABLE half nextafter(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)nextafter(_x, _y);
-}
-
-OVERLOADABLE half modf(half x, half *i) {
- float _x = (float)x;
- float _i;
- half ret = (half)modf(_x, &_i);
- *i = (half)_i;
- return ret;
-}
-
-OVERLOADABLE half hypot(half x, half y) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)hypot(_x, _y);
-}
-
-OVERLOADABLE half fract(half x, half *p) {
- float _x = (float)x;
- float _p;
- half ret = (half)fract(_x, &_p);
- *p = (half)_p;
- return ret;
-}
-
-OVERLOADABLE half remquo(half x, half y, int *quo) {
- float _x = (float)x;
- float _y = (float)y;
- return (half)remquo(_x, _y, quo);
-}
-
-OVERLOADABLE half pown(half x, int n) {
- float _x = (float)x;
- return (half)pown(_x, n);
-}
-OVERLOADABLE half rootn(half x, int n) {
- float _x = (float)x;
- return (half)rootn(_x, n);
-}
-
//-----------------double -----------------------
INLINE int __HI(double x){
diff --git a/backend/src/libocl/tmpl/ocl_math_20.tmpl.h b/backend/src/libocl/tmpl/ocl_math_20.tmpl.h
index c384b51b..ad68de42 100644
--- a/backend/src/libocl/tmpl/ocl_math_20.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_20.tmpl.h
@@ -21,194 +21,19 @@
#include "ocl_types.h"
#include "ocl_math_common.h"
-OVERLOADABLE float cospi(float x);
-OVERLOADABLE float cosh(float x);
-OVERLOADABLE float acos(float x);
-OVERLOADABLE float acospi(float x);
-OVERLOADABLE float acosh(float x);
-OVERLOADABLE float sinpi(float x);
-OVERLOADABLE float sinh(float x);
-OVERLOADABLE float asin(float x);
-OVERLOADABLE float asinpi(float x);
-OVERLOADABLE float asinh(float x);
-OVERLOADABLE float tanpi(float x);
-OVERLOADABLE float tanh(float x);
-OVERLOADABLE float atan(float x);
-OVERLOADABLE float atan2(float y, float x);
-OVERLOADABLE float atan2pi(float y, float x);
-OVERLOADABLE float atanpi(float x);
-OVERLOADABLE float atanh(float x);
-OVERLOADABLE float cbrt(float x);
-OVERLOADABLE float rint(float x);
-OVERLOADABLE float copysign(float x, float y);
-OVERLOADABLE float erf(float x);
-OVERLOADABLE float erfc(float x);
-OVERLOADABLE float fmod (float x, float y);
-OVERLOADABLE float remainder(float x, float p);
-OVERLOADABLE float ldexp(float x, int n);
-OVERLOADABLE float powr(float x, float y);
-OVERLOADABLE float pow(float x, float y);
-//no pow, we use powr instead
-OVERLOADABLE float fabs(float x);
-OVERLOADABLE float trunc(float x);
-OVERLOADABLE float round(float x);
-OVERLOADABLE float floor(float x);
-OVERLOADABLE float ceil(float x);
-OVERLOADABLE float log(float x);
-OVERLOADABLE float log2(float x);
-OVERLOADABLE float log10(float x);
-OVERLOADABLE float exp(float x);
-OVERLOADABLE float exp10(float x);
-OVERLOADABLE float expm1(float x);
-OVERLOADABLE float fmin(float a, float b);
-OVERLOADABLE float fmax(float a, float b);
-OVERLOADABLE float fma(float a, float b, float c);
-OVERLOADABLE float fdim(float x, float y);
-OVERLOADABLE float maxmag(float x, float y);
-OVERLOADABLE float minmag(float x, float y);
-OVERLOADABLE float exp2(float x);
-OVERLOADABLE float mad(float a, float b, float c);
-OVERLOADABLE float sin(float x);
-OVERLOADABLE float cos(float x);
-OVERLOADABLE float tan(float x);
-OVERLOADABLE float tgamma(float x);
-OVERLOADABLE float lgamma(float x);
OVERLOADABLE float lgamma_r(float x, int *signgamp);
-OVERLOADABLE float log1p(float x);
-OVERLOADABLE float logb(float x);
-OVERLOADABLE int ilogb(float x);
-OVERLOADABLE float nan(uint code);
OVERLOADABLE float sincos(float x, float *cosval);
-OVERLOADABLE float sqrt(float x);
-OVERLOADABLE float rsqrt(float x);
-OVERLOADABLE float frexp(float x, int *exp);
-OVERLOADABLE float nextafter(float x, float y);
OVERLOADABLE float modf(float x, float *i);
-OVERLOADABLE float hypot(float x, float y);
+OVERLOADABLE float frexp(float x, int *exp);
OVERLOADABLE float fract(float x, float *p);
OVERLOADABLE float remquo(float x, float y, int *quo);
-OVERLOADABLE float pown(float x, int n);
-OVERLOADABLE float rootn(float x, int n);
-
-// native
-OVERLOADABLE float native_cos(float x);
-OVERLOADABLE float native_divide(float x, float y);
-OVERLOADABLE float native_exp(float x);
-OVERLOADABLE float native_exp2(float x);
-OVERLOADABLE float native_exp10(float x);
-OVERLOADABLE float native_log(float x);
-OVERLOADABLE float native_log2(float x);
-OVERLOADABLE float native_log10(float x);
-OVERLOADABLE float native_powr(float x, float y);
-OVERLOADABLE float native_recip(float x);
-OVERLOADABLE float native_rsqrt(float x);
-OVERLOADABLE float native_sin(float x);
-OVERLOADABLE float native_sqrt(float x);
-OVERLOADABLE float native_tan(float x);
-
-// Half float version.
-OVERLOADABLE half cospi(half x);
-OVERLOADABLE half cosh(half x);
-OVERLOADABLE half acos(half x);
-OVERLOADABLE half acospi(half x);
-OVERLOADABLE half acosh(half x);
-OVERLOADABLE half sinpi(half x);
-OVERLOADABLE half sinh(half x);
-OVERLOADABLE half asin(half x);
-OVERLOADABLE half asinpi(half x);
-OVERLOADABLE half asinh(half x);
-OVERLOADABLE half tanpi(half x);
-OVERLOADABLE half tanh(half x);
-OVERLOADABLE half atan(half x);
-OVERLOADABLE half atan2(half y, half x);
-OVERLOADABLE half atan2pi(half y, half x);
-OVERLOADABLE half atanpi(half x);
-OVERLOADABLE half atanh(half x);
-OVERLOADABLE half cbrt(half x);
-OVERLOADABLE half rint(half x);
-OVERLOADABLE half copysign(half x, half y);
-OVERLOADABLE half erf(half x);
-OVERLOADABLE half erfc(half x);
-OVERLOADABLE half fmod (half x, half y);
-OVERLOADABLE half remainder(half x, half p);
-OVERLOADABLE half ldexp(half x, int n);
-OVERLOADABLE half powr(half x, half y);
-OVERLOADABLE half pow(half x, half y);
-//no pow, we use powr instead
-OVERLOADABLE half fabs(half x);
-OVERLOADABLE half trunc(half x);
-OVERLOADABLE half round(half x);
-OVERLOADABLE half floor(half x);
-OVERLOADABLE half ceil(half x);
-OVERLOADABLE half log(half x);
-OVERLOADABLE half log2(half x);
-OVERLOADABLE half log10(half x);
-OVERLOADABLE half exp(half x);
-OVERLOADABLE half exp10(half x);
-OVERLOADABLE half expm1(half x);
-OVERLOADABLE half fmin(half a, half b);
-OVERLOADABLE half fmax(half a, half b);
-OVERLOADABLE half fma(half a, half b, half c);
-OVERLOADABLE half fdim(half x, half y);
-OVERLOADABLE half maxmag(half x, half y);
-OVERLOADABLE half minmag(half x, half y);
-OVERLOADABLE half exp2(half x);
-OVERLOADABLE half mad(half a, half b, half c);
-OVERLOADABLE half sin(half x);
-OVERLOADABLE half cos(half x);
-OVERLOADABLE half tan(half x);
-OVERLOADABLE half tgamma(half x);
-OVERLOADABLE half lgamma(half x);
OVERLOADABLE half lgamma_r(half x, int *signgamp);
-OVERLOADABLE half log1p(half x);
-OVERLOADABLE half logb(half x);
-OVERLOADABLE int ilogb(half x);
-OVERLOADABLE half nan(ushort code);
OVERLOADABLE half sincos(half x, half *cosval);
-OVERLOADABLE half sqrt(half x);
-OVERLOADABLE half rsqrt(half x);
OVERLOADABLE half frexp(half x, int *exp);
-OVERLOADABLE half nextafter(half x, half y);
OVERLOADABLE half modf(half x, half *i);
-OVERLOADABLE half hypot(half x, half y);
OVERLOADABLE half fract(half x, half *p);
OVERLOADABLE half remquo(half x, half y, int *quo);
-OVERLOADABLE half pown(half x, int n);
-OVERLOADABLE half rootn(half x, int n);
-
-// native half
-OVERLOADABLE half native_cos(half x);
-OVERLOADABLE half native_divide(half x, half y);
-OVERLOADABLE half native_exp(half x);
-OVERLOADABLE half native_exp2(half x);
-OVERLOADABLE half native_exp10(half x);
-OVERLOADABLE half native_log(half x);
-OVERLOADABLE half native_log2(half x);
-OVERLOADABLE half native_log10(half x);
-OVERLOADABLE half native_powr(half x, half y);
-OVERLOADABLE half native_recip(half x);
-OVERLOADABLE half native_rsqrt(half x);
-OVERLOADABLE half native_sin(half x);
-OVERLOADABLE half native_sqrt(half x);
-OVERLOADABLE half native_tan(half x);
-
-// half accuracy
-OVERLOADABLE float half_cos(float x);
-OVERLOADABLE float half_divide(float x, float y);
-OVERLOADABLE float half_exp(float x);
-OVERLOADABLE float half_exp2(float x);
-OVERLOADABLE float half_exp10(float x);
-OVERLOADABLE float half_log(float x);
-OVERLOADABLE float half_log2(float x);
-OVERLOADABLE float half_log10(float x);
-OVERLOADABLE float half_powr(float x, float y);
-OVERLOADABLE float half_recip(float x);
-OVERLOADABLE float half_rsqrt(float x);
-OVERLOADABLE float half_sin(float x);
-OVERLOADABLE float half_sqrt(float x);
-OVERLOADABLE float half_tan(float x);
-
//------- double -----------
OVERLOADABLE double fract(double x, double *p);
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
index 63dd202d..e82b7f55 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl
@@ -1,5 +1,5 @@
/*
- * Copyright © 2012 - 2014 Intel Corporation
+ * Copyright © 2012 - 2017 Intel Corporation
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
@@ -32,6 +32,3440 @@
* is preserved.
* ====================================================
*/
+
+extern constant int __ocl_math_fastpath_flag;
+
+CONST float __gen_ocl_fabs(float x) __asm("llvm.fabs" ".f32");
+CONST float __gen_ocl_sin(float x) __asm("llvm.sin" ".f32");
+CONST float __gen_ocl_cos(float x) __asm("llvm.cos" ".f32");
+CONST float __gen_ocl_sqrt(float x) __asm("llvm.sqrt" ".f32");
+PURE CONST float __gen_ocl_rsqrt(float x);
+CONST float __gen_ocl_log(float x) __asm("llvm.log2" ".f32");
+CONST float __gen_ocl_exp(float x) __asm("llvm.exp2" ".f32");
+PURE CONST float __gen_ocl_pow(float x, float y) __asm("llvm.pow" ".f32");
+PURE CONST float __gen_ocl_rcp(float x);
+CONST float __gen_ocl_rndz(float x) __asm("llvm.trunc" ".f32");
+CONST float __gen_ocl_rnde(float x) __asm("llvm.rint" ".f32");
+CONST float __gen_ocl_rndu(float x) __asm("llvm.ceil" ".f32");
+CONST float __gen_ocl_rndd(float x) __asm("llvm.floor" ".f32");
+
+
+/* native functions */
+OVERLOADABLE float native_cos(float x) { return __gen_ocl_cos(x); }
+OVERLOADABLE float native_sin(float x) { return __gen_ocl_sin(x); }
+OVERLOADABLE float native_sqrt(float x) { return __gen_ocl_sqrt(x); }
+OVERLOADABLE float native_rsqrt(float x) { return __gen_ocl_rsqrt(x); }
+OVERLOADABLE float native_log2(float x) { return __gen_ocl_log(x); }
+OVERLOADABLE float native_log(float x) {
+ return native_log2(x) * 0.6931472002f;
+}
+OVERLOADABLE float native_log10(float x) {
+ return native_log2(x) * 0.3010299956f;
+}
+OVERLOADABLE float native_powr(float x, float y) { return __gen_ocl_pow(x,y); }
+OVERLOADABLE float native_recip(float x) { return __gen_ocl_rcp(x); }
+OVERLOADABLE float native_tan(float x) {
+ return native_sin(x) / native_cos(x);
+}
+OVERLOADABLE float native_exp2(float x) { return __gen_ocl_exp(x); }
+OVERLOADABLE float native_exp(float x) { return __gen_ocl_exp(M_LOG2E_F*x); }
+OVERLOADABLE float native_exp10(float x) { return __gen_ocl_exp(M_LOG210_F*x); }
+OVERLOADABLE float native_divide(float x, float y) { return x/y; }
+
+/* Fast path */
+OVERLOADABLE float __gen_ocl_internal_fastpath_acosh (float x) {
+ return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_asinh (float x) {
+ return native_log(x + native_sqrt(x * x + 1));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_atanh (float x) {
+ return 0.5f * native_log((1 + x) / (1 - x));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_cbrt (float x) {
+ return __gen_ocl_pow(x, 0.3333333333f);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_cos (float x) {
+ return native_cos(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_cosh (float x) {
+ return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_cospi (float x) {
+ return __gen_ocl_cos(x * M_PI_F);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_exp (float x) {
+ return native_exp(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_exp10 (float x) {
+ return native_exp10(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_expm1 (float x) {
+ return __gen_ocl_pow(M_E_F, x) - 1;
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_fmod (float x, float y) {
+ return x-y*__gen_ocl_rndz(x/y);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_hypot (float x, float y) {
+ return __gen_ocl_sqrt(x*x + y*y);
+}
+OVERLOADABLE int __gen_ocl_internal_fastpath_ilogb (float x) {
+ return __gen_ocl_rndd(native_log2(x));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_ldexp (float x, int n) {
+ return __gen_ocl_pow(2, n) * x;
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_log (float x) {
+ return native_log(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_log2 (float x) {
+ return native_log2(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_log10 (float x) {
+ return native_log10(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_log1p (float x) {
+ return native_log(x + 1);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_logb (float x) {
+ return __gen_ocl_rndd(native_log2(x));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_remainder (float x, float y) {
+ return x-y*__gen_ocl_rnde(x/y);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_rootn(float x, int n) {
+ return __gen_ocl_pow(x, 1.f / n);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_sin (float x) {
+ return native_sin(x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_fastpath_sinh (float x) {
+ return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_sinpi (float x) {
+ return __gen_ocl_sin(x * M_PI_F);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_tan (float x) {
+ return native_tan(x);
+}
+OVERLOADABLE float __gen_ocl_internal_fastpath_tanh (float x) {
+ float y = native_exp(-2 * x);
+ return (1 - y) / (1 + y);
+}
+
+
+/* Internal implement, high accuracy. */
+OVERLOADABLE float __gen_ocl_internal_floor(float x) { return __gen_ocl_rndd(x); }
+OVERLOADABLE float __gen_ocl_internal_copysign(float x, float y) {
+ union { unsigned u; float f; } ux, uy;
+ ux.f = x;
+ uy.f = y;
+ ux.u = (ux.u & 0x7fffffff) | (uy.u & 0x80000000u);
+ return ux.f;
+}
+
+OVERLOADABLE float inline __gen_ocl_internal_log_valid(float x) {
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+ union { unsigned int i; float f; } u;
+ const float
+ ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
+ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
+ two25 = 3.355443200e+07, /* 0x4c000000 */
+ Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
+ Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
+ Lg3 = 2.8571429849e-01, /* 3E924925 */
+ Lg4 = 2.2222198546e-01; /* 3E638E29 */
+
+ const float zero = 0.0;
+ float fsq, f, s, z, R, w, t1, t2, partial;
+ int k, ix, i, j;
+
+ u.f = x; ix = u.i;
+ k = 0;
+
+ k += (ix>>23) - 127;
+ ix &= 0x007fffff;
+ i = (ix + (0x95f64<<3)) & 0x800000;
+ u.i = ix | (i^0x3f800000); x = u.f;
+ k += (i>>23);
+ f = x - 1.0f;
+ fsq = f * f;
+
+ if((0x007fffff & (15 + ix)) < 16) { /* |f| < 2**-20 */
+ R = fsq * (0.5f - 0.33333333333333333f * f);
+ return k * ln2_hi + k * ln2_lo + f - R;
+ }
+
+ s = f / (2.0f + f);
+ z = s * s;
+ i = ix - (0x6147a << 3);
+ w = z * z;
+ j = (0x6b851 << 3) - ix;
+ t1= w * mad(w, Lg4, Lg2);
+ t2= z * mad(w, Lg3, Lg1);
+ i |= j;
+ R = t2 + t1;
+ partial = (i > 0) ? -mad(s, 0.5f * fsq, -0.5f * fsq) : (s * f);
+
+ return mad(s, R, f) - partial + k * ln2_hi + k * ln2_lo;;
+}
+
+OVERLOADABLE float __gen_ocl_internal_log(float x)
+{
+ union { unsigned int i; float f; } u;
+ u.f = x;
+ int ix = u.i;
+
+ if (ix < 0 )
+ return NAN; /* log(-#) = NaN */
+ if (ix >= 0x7f800000)
+ return NAN;
+
+ return __gen_ocl_internal_log_valid(x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_log10(float x)
+{
+ union { float f; unsigned i; } u;
+ const float
+ ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
+ log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
+ log10_2lo = 7.9034151668e-07; /* 0x355427db */
+
+ float y, z;
+ int i, k, hx;
+
+ u.f = x; hx = u.i;
+
+ if (hx<0)
+ return NAN; /* log(-#) = NaN */
+ if (hx >= 0x7f800000)
+ return NAN;
+
+ k = (hx >> 23) - 127;
+ i = ((unsigned)k & 0x80000000) >> 31;
+ hx = (hx&0x007fffff) | ((0x7f-i) << 23);
+ y = (float)(k + i);
+ u.i = hx; x = u.f;
+
+ return y * log10_2lo + y * log10_2hi + ivln10 * __gen_ocl_internal_log_valid(x);
+}
+
+
+OVERLOADABLE float __gen_ocl_internal_log2(float x)
+{
+ const float zero = 0.0,
+ invln2 = 0x1.715476p+0f;
+ int ix;
+
+ union { float f; int i; } u;
+ u.f = x; ix = u.i;
+
+ if (ix < 0)
+ return NAN; /** log(-#) = NaN */
+ if (ix >= 0x7f800000)
+ return NAN;
+
+ return invln2 * __gen_ocl_internal_log_valid(x);
+}
+
+
+float __gen_ocl_scalbnf (float x, int n){
+ /* copy from fdlibm */
+ float two25 = 3.355443200e+07, /* 0x4c000000 */
+ twom25 = 2.9802322388e-08, /* 0x33000000 */
+ huge = 1.0e+30,
+ tiny = 1.0e-30;
+ int k,ix;
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ k = (ix&0x7f800000)>>23; /* extract exponent */
+ if (k==0) { /* 0 or subnormal x */
+ if ((ix&0x7fffffff)==0) return x; /* +-0 */
+ x *= two25;
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ k = ((ix&0x7f800000)>>23) - 25;
+ }
+ if (k==0xff) return x+x; /* NaN or Inf */
+ if (n< -50000)
+ return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
+ if (n> 50000 || k+n > 0xfe)
+ return huge*__gen_ocl_internal_copysign(huge,x); /* overflow */
+ /* Now k and n are bounded we know that k = k+n does not overflow. */
+ k = k+n;
+ if (k > 0) { /* normal result */
+ GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
+ return x;
+ }
+ if (k <= -25)
+ return tiny*__gen_ocl_internal_copysign(tiny,x); /*underflow*/
+ k += 25; /* subnormal result */
+ GEN_OCL_SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
+ return x*twom25;
+}
+
+const __constant unsigned int two_over_pi[] = {
+0, 0, 0xA2F, 0x983, 0x6E4, 0xe44, 0x152, 0x9FC,
+0x275, 0x7D1, 0xF53, 0x4DD, 0xC0D, 0xB62,
+0x959, 0x93C, 0x439, 0x041, 0xFE5, 0x163,
+};
+
+// The main idea is from "Radian Reduction for Trigonometric Functions"
+// written by Mary H. Payne and Robert N. Hanek. Also another reference
+// is "A Continued-Fraction Analysis of Trigonometric Argument Reduction"
+// written by Roger Alan Smith, who gave the worst case in this paper.
+// for single float, worst x = 0x1.47d0fep34, and there are 29 bit
+// leading zeros in the fraction part of x*(2.0/pi). so we need at least
+// 29 (leading zero)+ 24 (fraction )+12 (integer) + guard bits. that is,
+// 65 + guard bits, as we calculate in 12*7 = 84bits, which means we have
+// about 19 guard bits. If we need further precision, we may need more
+// guard bits
+// Note we place two 0 in two_over_pi, which is used to handle input less
+// than 0x1.0p23
+
+int payne_hanek(float x, float *y) {
+ union { float f; unsigned u;} ieee;
+ ieee.f = x;
+ unsigned u = ieee.u;
+ int k = ((u & 0x7f800000) >> 23)-127;
+ int ma = (u & 0x7fffff) | 0x800000;
+ unsigned high, low;
+ high = (ma & 0xfff000) >> 12;
+ low = ma & 0xfff;
+
+ // Two tune below macro, you need to fully understand the algorithm
+#define CALC_BLOCKS 7
+#define ZERO_BITS 2
+
+ unsigned result[CALC_BLOCKS];
+
+ // round down, note we need 2 bits integer precision
+ int index = (k-23-2) < 0 ? (k-23-2-11)/12 : (k-23-2)/12;
+
+ for (int i = 0; i < CALC_BLOCKS; i++) {
+ result[i] = low * two_over_pi[index+i+ZERO_BITS] ;
+ result[i] += high * two_over_pi[index+i+1+ZERO_BITS];
+ }
+
+ for (int i = CALC_BLOCKS-1; i > 0; i--) {
+ int temp = result[i] >> 12;
+ result[i] -= temp << 12;
+ result[i-1] += temp;
+ }
+#undef CALC_BLOCKS
+#undef ZERO_BITS
+
+ // get number of integer digits in result[0], note we only consider 12 valid bits
+ // and also it means the fraction digits in result[0] is (12-intDigit)
+
+ int intDigit = index*(-12) + (k-23);
+
+ // As the integer bits may be all included in result[0], and also maybe
+ // some bits in result[0], and some in result[1]. So we merge succesive bits,
+ // which makes easy coding.
+
+ unsigned b0 = (result[0] << 12) | result[1];
+ unsigned b1 = (result[2] << 12) | result[3];
+ unsigned b2 = (result[4] << 12) | result[5];
+ unsigned b3 = (result[6] << 12);
+
+ unsigned intPart = b0 >> (24-intDigit);
+
+ unsigned fract1 = ((b0 << intDigit) | (b1 >> (24-intDigit))) & 0xffffff;
+ unsigned fract2 = ((b1 << intDigit) | (b2 >> (24-intDigit))) & 0xffffff;
+ unsigned fract3 = ((b2 << intDigit) | (b3 >> (24-intDigit))) & 0xffffff;
+
+ // larger than 0.5? which mean larger than pi/4, we need
+ // transform from [0,pi/2] to [-pi/4, pi/4] through -(1.0-fract)
+ int largerPiBy4 = ((fract1 & 0x800000) != 0);
+ int sign = largerPiBy4 ? 1 : 0;
+ intPart = largerPiBy4 ? (intPart+1) : intPart;
+
+ fract1 = largerPiBy4 ? (fract1 ^ 0x00ffffff) : fract1;
+ fract2 = largerPiBy4 ? (fract2 ^ 0x00ffffff) : fract2;
+ fract3 = largerPiBy4 ? (fract3 ^ 0x00ffffff) : fract3;
+
+ int leadingZero = (fract1 == 0);
+
+ // +1 is for the hidden bit 1 in floating-point format
+ int exponent = leadingZero ? -(24+1) : -(0+1);
+
+ fract1 = leadingZero ? fract2 : fract1;
+ fract2 = leadingZero ? fract3 : fract2;
+
+ // fract1 may have leading zeros, add it
+ int shift = clz(fract1)-8;
+ exponent += -shift;
+
+ float pio2 = 0x1.921fb6p+0;
+ unsigned fdigit = ((fract1 << shift) | (fract2 >> (24-shift))) & 0xffffff;
+
+ // we know that denormal number will not appear here
+ ieee.u = (sign << 31) | ((exponent+127) << 23) | (fdigit & 0x7fffff);
+ *y = ieee.f * pio2;
+ return intPart;
+}
+
+int argumentReduceSmall(float x, float * remainder) {
+ union {
+ float f;
+ unsigned u;
+ } ieee;
+
+ float twoByPi = 2.0f/3.14159265f;
+ float piBy2_1h = (float) 0xc90/0x1.0p11,
+ piBy2_1l = (float) 0xfda/0x1.0p23,
+ piBy2_2h = (float) 0xa22/0x1.0p35,
+ piBy2_2l = (float) 0x168/0x1.0p47,
+ piBy2_3h = (float) 0xc23/0x1.0p59,
+ piBy2_3l = (float) 0x4c4/0x1.0p71;
+
+ float y = (float)(int)(twoByPi * x + 0.5f);
+ ieee.f = y;
+ ieee.u = ieee.u & 0xfffff000;
+
+ float yh = ieee.f;
+ float yl = y - yh;
+ float rem = x - yh*piBy2_1h - yh*piBy2_1l - yl*piBy2_1h - yl*piBy2_1l;
+ rem = rem - yh*piBy2_2h - yh*piBy2_2l + yl*piBy2_2h + yl*piBy2_2l;
+ rem = rem - yh*piBy2_3h - yh*piBy2_3l - yl*piBy2_3h - yl*piBy2_3l;
+
+ *remainder = rem;
+ return (int)y;
+}
+
+
+int __ieee754_rem_pio2f(float x, float *y) {
+ if (x < 4000.0f) {
+ return argumentReduceSmall(x, y);
+ } else {
+ return payne_hanek(x, y);
+ }
+}
+
+OVERLOADABLE float __kernel_sinf(float x)
+{
+ /* copied from fdlibm */
+ const float
+ S1 = -1.6666667163e-01, /* 0xbe2aaaab */
+ S2 = 8.3333337680e-03, /* 0x3c088889 */
+ S3 = -1.9841270114e-04, /* 0xb9500d01 */
+ S4 = 2.7557314297e-06; /* 0x3638ef1b */
+ float z,r,v;
+ z = x*x;
+ v = z*x;
+ r = mad(z, mad(z, mad(z, S4, S3), S2), S1);
+
+ return mad(v, r, x);
+}
+
+float __kernel_cosf(float x, float y)
+{
+ /* copied from fdlibm */
+ const float
+ one = 1.0000000000e+00, /* 0x3f800000 */
+ C1 = 4.1666667908e-02, /* 0x3d2aaaab */
+ C2 = -1.3888889225e-03, /* 0xbab60b61 */
+ C3 = 2.4801587642e-05; /* 0x37d00d01 */
+ float a,hz,z,r,qx;
+ int ix;
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ ix &= 0x7fffffff; /* ix = |x|'s high word*/
+ z = x*x;
+ r = z * mad(z, mad(z, C3, C2), C1);
+
+ if(ix < 0x3e99999a) /* if |x| < 0.3 */
+ return one - ((float)0.5*z - (z*r - x*y));
+ else {
+ GEN_OCL_SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
+ hz = (float)0.5*z-qx;
+ a = one-qx;
+ return a - (hz - (z*r-x*y));
+ }
+}
+
+OVERLOADABLE float sin(float x)
+{
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_sin(x);
+
+ const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
+ float y,z=0.0;
+ int n, ix;
+
+ float negative = x < 0.0f? -1.0f : 1.0f;
+ x = fabs(x);
+
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ ix &= 0x7fffffff;
+
+ /* sin(Inf or NaN) is NaN */
+ if (ix >= 0x7f800000) return x-x;
+
+ if(x <= pio4)
+ return negative * __kernel_sinf(x);
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2f(x,&y);
+ float s = __kernel_sinf(y);
+ float c = __kernel_cosf(y,0.0f);
+ float ret = (n&1) ? negative*c : negative*s;
+ return (n&3)> 1? -1.0f*ret : ret;
+ }
+}
+
+OVERLOADABLE float cos(float x)
+{
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_cos(x);
+
+ const float pio4 = 7.8539812565e-01; /* 0x3f490fda */
+ float y,z=0.0;
+ int n, ix;
+ x = __gen_ocl_fabs(x);
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+
+ ix &= 0x7fffffff;
+
+ /* cos(Inf or NaN) is NaN */
+ if (ix >= 0x7f800000) return x-x;
+
+ if(x <= pio4)
+ return __kernel_cosf(x, 0.f);
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2f(x,&y);
+ n &= 3;
+ float c = __kernel_cosf(y, 0.0f);
+ float s = __kernel_sinf(y);
+ float v = (n&1) ? s : c;
+ /* n&3 return
+ 0 cos(y)
+ 1 -sin(y)
+ 2 -cos(y)
+ 3 sin(y)
+ */
+ int mask = (n>>1) ^ n;
+ float sign = (mask&1) ? -1.0f : 1.0f;
+ return sign * v;
+ }
+}
+
+float __kernel_tanf(float x, float y, int iy)
+{
+ /* copied from fdlibm */
+ float z,r,v,w,s;
+ int ix,hx;
+ const float
+ one = 1.0000000000e+00, /* 0x3f800000 */
+ pio4 = 7.8539812565e-01, /* 0x3f490fda */
+ pio4lo= 3.7748947079e-08; /* 0x33222168 */
+ float T[13];// = {
+ T[0] = 3.3333334327e-01; /* 0x3eaaaaab */
+ T[1] = 1.3333334029e-01; /* 0x3e088889 */
+ T[2] = 5.3968254477e-02; /* 0x3d5d0dd1 */
+ T[3] = 2.1869488060e-02; /* 0x3cb327a4 */
+ T[4] = 8.8632395491e-03; /* 0x3c11371f */
+ T[5] = 3.5920790397e-03; /* 0x3b6b6916 */
+ T[6] = 1.4562094584e-03; /* 0x3abede48 */
+ T[7] = 5.8804126456e-04; /* 0x3a1a26c8 */
+
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff; /* high word of |x| */
+ if(ix<0x31800000) /* x < 2**-28 */
+ {if((int)x==0) { /* generate inexact */
+ if((ix|(iy+1))==0) return one/__gen_ocl_fabs(x);
+ else return (iy==1)? x: -one/x;
+ }
+ }
+ if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
+ if(hx<0) {x = -x; y = -y;}
+ z = pio4-x;
+ w = pio4lo-y;
+ x = z+w; y = 0.0;
+ }
+ z = x*x;
+ w = z*z;
+ /* Break x^5*(T[1]+x^2*T[2]+...) into
+ * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+ * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+ */
+
+ r = mad(w, mad(w, mad(w, T[7], T[5]), T[3]), T[1]);
+ v = z* mad(w, mad(w, T[6], T[4]), T[2]);
+
+ s = z*x;
+ r = mad(z, mad(s, r + v, y), y);
+ r += T[0]*s;
+ w = x+r;
+ if(ix>=0x3f2ca140) {
+ v = (float)iy;
+ return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
+ }
+ if(iy==1) return w;
+ else
+ return -1.0/(x+r);
+}
+
+OVERLOADABLE float tan(float x)
+{
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_tan(x);
+
+ float y,z=0.0;
+ int n, ix;
+ float negative = x < 0.0f? -1.0f : 1.0f;
+ x = negative * x;
+
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+
+ ix &= 0x7fffffff;
+
+ /* tan(Inf or NaN) is NaN */
+ if (ix>=0x7f800000) return x-x; /* NaN */
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2f(x,&y);
+ return negative * __kernel_tanf(y,0.0f,1-((n&1)<<1)); /* 1 -- n even
+ -1 -- n odd */
+ }
+}
+
+OVERLOADABLE float __gen_ocl_internal_cospi(float x) {
+ int ix;
+ if(isinf(x) || isnan(x)) { return NAN; }
+ if(x < 0.0f) { x = -x; }
+ GEN_OCL_GET_FLOAT_WORD(ix, x);
+ if(x> 0x1.0p24) return 1.0f;
+ float m = __gen_ocl_internal_floor(x);
+ ix = (int)m;
+ m = x-m;
+ if((ix&0x1) != 0) m+=1.0f;
+ ix = __gen_ocl_internal_floor(m*4.0f);
+
+ switch(ix) {
+ case 0:
+ return __kernel_cosf(m*M_PI_F, 0.0f);
+ case 1:
+ case 2:
+ return __kernel_sinf((0.5f-m)*M_PI_F);
+ case 3:
+ case 4:
+ return -__kernel_cosf((m-1.0f)*M_PI_F, 0.0f);
+ case 5:
+ case 6:
+ return __kernel_sinf((m-1.5f)*M_PI_F);
+ default:
+ return __kernel_cosf((2.0f-m)*M_PI_F, 0.0f);
+ }
+}
+
+OVERLOADABLE float __gen_ocl_internal_sinpi(float x) {
+ float sign = 1.0f;
+ int ix;
+ if(isinf(x)) return NAN;
+ if(x < 0.0f) { x = -x; sign = -1.0f; }
+ GEN_OCL_GET_FLOAT_WORD(ix, x);
+ if(x> 0x1.0p24) return 0.0f;
+ float m = __gen_ocl_internal_floor(x);
+ ix = (int)m;
+ m = x-m;
+ if((ix&0x1) != 0) m+=1.0f;
+ ix = __gen_ocl_internal_floor(m*4.0f);
+
+ switch(ix) {
+ case 0:
+ return sign*__kernel_sinf(m*M_PI_F);
+ case 1:
+ case 2:
+ return sign*__kernel_cosf((m-0.5f)*M_PI_F, 0.0f);
+ case 3:
+ case 4:
+ return -sign*__kernel_sinf((m-1.0f)*M_PI_F);
+ case 5:
+ case 6:
+ return -sign*__kernel_cosf((m-1.5f)*M_PI_F, 0.0f);
+ default:
+ return -sign*__kernel_sinf((2.0f-m)*M_PI_F);
+ }
+
+}
+
+OVERLOADABLE float lgamma(float x) {
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+ const float
+ zero= 0.,
+ one = 1.0000000000e+00,
+ pi = 3.1415927410e+00,
+ a0 = 7.7215664089e-02,
+ a1 = 3.2246702909e-01,
+ a2 = 6.7352302372e-02,
+ a3 = 2.0580807701e-02,
+ a4 = 7.3855509982e-03,
+ a5 = 2.8905137442e-03,
+ a6 = 1.1927076848e-03,
+ a7 = 5.1006977446e-04,
+ a8 = 2.2086278477e-04,
+ a9 = 1.0801156895e-04,
+ a10 = 2.5214456400e-05,
+ a11 = 4.4864096708e-05,
+ tc = 1.4616321325e+00,
+ tf = -1.2148628384e-01,
+ tt = 6.6971006518e-09,
+ t0 = 4.8383611441e-01,
+ t1 = -1.4758771658e-01,
+ t2 = 6.4624942839e-02,
+ t3 = -3.2788541168e-02,
+ t4 = 1.7970675603e-02,
+ t5 = -1.0314224288e-02,
+ t6 = 6.1005386524e-03,
+ t7 = -3.6845202558e-03,
+ t8 = 2.2596477065e-03,
+ t9 = -1.4034647029e-03,
+ t10 = 8.8108185446e-04,
+ t11 = -5.3859531181e-04,
+ t12 = 3.1563205994e-04,
+ t13 = -3.1275415677e-04,
+ t14 = 3.3552918467e-04,
+ u0 = -7.7215664089e-02,
+ u1 = 6.3282704353e-01,
+ u2 = 1.4549225569e+00,
+ u3 = 9.7771751881e-01,
+ u4 = 2.2896373272e-01,
+ u5 = 1.3381091878e-02,
+ v1 = 2.4559779167e+00,
+ v2 = 2.1284897327e+00,
+ v3 = 7.6928514242e-01,
+ v4 = 1.0422264785e-01,
+ v5 = 3.2170924824e-03,
+ s0 = -7.7215664089e-02,
+ s1 = 2.1498242021e-01,
+ s2 = 3.2577878237e-01,
+ s3 = 1.4635047317e-01,
+ s4 = 2.6642270386e-02,
+ s5 = 1.8402845599e-03,
+ s6 = 3.1947532989e-05,
+ r1 = 1.3920053244e+00,
+ r2 = 7.2193557024e-01,
+ r3 = 1.7193385959e-01,
+ r4 = 1.8645919859e-02,
+ r5 = 7.7794247773e-04,
+ r6 = 7.3266842264e-06,
+ w0 = 4.1893854737e-01,
+ w1 = 8.3333335817e-02,
+ w2 = -2.7777778450e-03,
+ w3 = 7.9365057172e-04,
+ w4 = -5.9518753551e-04,
+ w5 = 8.3633989561e-04,
+ w6 = -1.6309292987e-03;
+ float t, y, z, nadj, p, p1, p2, p3, q, r, w;
+ int i, hx, ix;
+ nadj = 0;
+ hx = *(int *)&x;
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x7f800000)
+ return x * x;
+ if (ix == 0)
+ return ((x + one) / zero);
+ if (ix < 0x1c800000) {
+ if (hx < 0) {
+ return -native_log(-x);
+ } else
+ return -native_log(x);
+ }
+ if (hx < 0) {
+ if (ix >= 0x4b000000)
+ return ((-x) / zero);
+ t = __gen_ocl_internal_sinpi(x);
+ if (t == zero)
+ return ((-x) / zero);
+ nadj = native_log(pi / __gen_ocl_fabs(t * x));
+ x = -x;
+ }
+ if (ix == 0x3f800000 || ix == 0x40000000)
+ r = 0;
+ else if (ix < 0x40000000) {
+ if (ix <= 0x3f666666) {
+ r = -native_log(x);
+ if (ix >= 0x3f3b4a20) {
+ y = one - x;
+ i = 0;
+ } else if (ix >= 0x3e6d3308) {
+ y = x - (tc - one);
+ i = 1;
+ } else {
+ y = x;
+ i = 2;
+ }
+ } else {
+ r = zero;
+ if (ix >= 0x3fdda618) {
+ y = (float) 2.0 - x;
+ i = 0;
+ }
+ else if (ix >= 0x3F9da620) {
+ y = x - tc;
+ i = 1;
+ }
+ else {
+ y = x - one;
+ i = 2;
+ }
+ }
+ switch (i) {
+ case 0:
+ z = y * y;
+ p1 = mad(z, mad(z, mad(z, mad(z, mad(z, a10, a8), a6), a4), a2), a0);
+ p2 = z * mad(z, mad(z, mad(z, mad(z, mad(z, a11, a9), a7), a5), a3), a1);
+ p = mad(y, p1, p2);
+ r += (p - (float) 0.5 * y);
+ break;
+ case 1:
+ z = y * y;
+ w = z * y;
+ p1 = mad(w, mad(w, mad(w, mad(w, t12, t9), t6), t3), t0);
+ p2 = mad(w, mad(w, mad(w, mad(w, t13, t10), t7), t4), t1);
+ p3 = mad(w, mad(w, mad(w, mad(w, t14, t11), t8), t5), t2);
+ p = mad(p1, z, mad(w, mad(y, p3, p2), -tt));
+ r += (tf + p);
+ break;
+ case 2:
+ p1 = y * mad(y, mad(y, mad(y, mad(y, mad(y, u5, u4), u3), u2), u1), u0);
+ p2 = mad(y, mad(y, mad(y, mad(y, mad(y, v5, v4), v3), v2), v1), one);
+ r += (-(float) 0.5 * y + p1 / p2);
+ }
+ } else if (ix < 0x41000000) {
+ i = (int) x;
+ t = zero;
+ y = x - (float) i;
+
+ p =y * mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, s6, s5), s4), s3), s2), s1), s0);
+ q = mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, r6, r5), r4), r3), r2), r1), one);
+ r = .5f * y + p / q;
+ z = one;
+
+ switch (i) {
+ case 7:
+ z *= (y + 6.0f);
+ case 6:
+ z *= (y + 5.0f);
+ case 5:
+ z *= (y + 4.0f);
+ case 4:
+ z *= (y + 3.0f);
+ case 3:
+ z *= (y + 2.0f);
+ r += native_log(z);
+ break;
+ }
+
+ } else if (ix < 0x5c800000) {
+ t = native_log(x);
+ z = one / x;
+ y = z * z;
+ w = mad(z, mad(y, mad(y, mad(y, mad(y, mad(y, w6, w5), w4), w3), w2), w1), w0);
+ r = (x - .5f) * (t - one) + w;
+ } else
+ r = x * (native_log(x) - one);
+ if (hx < 0)
+ r = nadj - r;
+ return r;
+}
+
+OVERLOADABLE float log1p(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_log1p(x);
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+ const float
+ ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
+ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
+ two25 = 3.355443200e+07, /* 0x4c000000 */
+ Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
+ Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
+ Lp3 = 2.8571429849e-01, /* 3E924925 */
+ Lp4 = 2.2222198546e-01; /* 3E638E29 */
+ const float zero = 0.0;
+ float hfsq,f,c,s,z,R,u;
+ int k,hx,hu,ax;
+ union {float f; unsigned i;} un;
+ un.f = x; hx = un.i;
+ ax = hx&0x7fffffff;
+
+ k = 1;
+ if (hx < 0x3ed413d7) { /* x < 0.41422 */
+ if(ax>=0x3f800000) { /* x <= -1.0 */
+ if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
+ else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
+ }
+ if(ax<0x31000000) { /* |x| < 2**-29 */
+ if(two25+x>zero /* raise inexact */
+ &&ax<0x24800000) /* |x| < 2**-54 */
+ return x;
+ else
+ return x - x*x*(float)0.5;
+ }
+ if(hx>0||hx<=((int)0xbe95f61f)) {
+ k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
+ }
+ if (hx >= 0x7f800000) return x+x;
+ if(k!=0) {
+ if(hx<0x5a000000) {
+ u = (float)1.0+x;
+
+ un.f = u; hu = un.i;
+ k = (hu>>23)-127;
+ /* correction term */
+ c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
+ c /= u;
+ } else {
+ u = x;
+ un.f = u; hu = un.i;
+ k = (hu>>23)-127;
+ c = 0;
+ }
+ hu &= 0x007fffff;
+ if(hu<0x3504f7) {
+ un.i = hu|0x3f800000; u = un.f;/* normalize u */
+ } else {
+ k += 1;
+ un.i = hu|0x3f000000; u = un.f; /* normalize u/2 */
+ hu = (0x00800000-hu)>>2;
+ }
+ f = u-(float)1.0;
+ }
+ hfsq=(float)0.5*f*f;
+ if(hu==0)
+ { /* |f| < 2**-20 */
+ if(f==zero)
+ {
+ if(k==0) return zero;
+ else {c = mad(k , ln2_lo, c); return mad(k, ln2_hi, c);}
+ }
+ R = mad(hfsq, 1.0f, -0.66666666666666666f * f);
+ if(k==0) return f-R; else
+ return k * ln2_hi - (R - mad(k, ln2_lo, c) - f);
+ }
+ s = f/((float)2.0+f);
+ z = s*s;
+ R = z * mad(z, mad(z, mad(z, Lp4, Lp3), Lp2), Lp1);
+ if(k==0)
+ return f + mad(hfsq + R, s, -hfsq);
+ else
+ return k*ln2_hi-( (hfsq - mad(s, hfsq + R, mad(k, ln2_lo, c))) - f);
+}
+
+OVERLOADABLE float logb(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_logb(x);
+
+ union {float f; unsigned i;} u;
+ u.f = x;
+ int e = ((u.i & 0x7f800000) >> 23);
+ float r1 = e-127;
+ float r2 = -INFINITY;
+ float r3 = x*x;
+ /* sub normal or +/-0 */
+ float r = e == 0 ? r2 : r1;
+ /* inf & nan */
+ return e == 0xff ? r3 : r;
+}
+
+OVERLOADABLE int ilogb(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_ilogb(x);
+
+ union { int i; float f; } u;
+ if (isnan(x))
+ return FP_ILOGBNAN;
+ if (isinf(x))
+ return 0x7FFFFFFF;
+ u.f = x;
+ u.i &= 0x7fffffff;
+ if (u.i == 0)
+ return FP_ILOGB0;
+ if (u.i >= 0x800000)
+ return (u.i >> 23) - 127;
+ int r = -126;
+ int a = u.i & 0x7FFFFF;
+ while(a < 0x800000) {
+ a <<= 1;
+ r --;
+ }
+ return r;
+}
+OVERLOADABLE float nan(uint code) {
+ return NAN;
+}
+OVERLOADABLE float __gen_ocl_internal_tanpi(float x) {
+ float sign = 1.0f;
+ int ix;
+ if(isinf(x)) return NAN;
+ if(x < 0.0f) { x = -x; sign = -1.0f; }
+ GEN_OCL_GET_FLOAT_WORD(ix, x);
+ if(x> 0x1.0p24) return 0.0f;
+ float m = __gen_ocl_internal_floor(x);
+ ix = (int)m;
+ m = x-m;
+ int n = __gen_ocl_internal_floor(m*4.0f);
+ if(m == 0.5f) {
+ return (ix&0x1) == 0 ? sign*INFINITY : sign*-INFINITY;
+ }
+ if(m == 0.0f) {
+ return (ix&0x1) == 0 ? 0.0f : -0.0f;
+ }
+
+ switch(n) {
+ case 0:
+ return sign * __kernel_tanf(m*M_PI_F, 0.0f, 1);
+ case 1:
+ return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
+ case 2:
+ return sign * 1.0f/__kernel_tanf((0.5f-m)*M_PI_F, 0.0f, 1);
+ default:
+ return sign * -1.0f*__kernel_tanf((1.0f-m)*M_PI_F, 0.0f, 1);
+ }
+}
+OVERLOADABLE float __gen_ocl_internal_cbrt(float x) {
+ /* copied from fdlibm */
+ const unsigned
+ B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
+ B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
+
+ const float
+ C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
+ D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
+ E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
+ F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
+ G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
+
+ float r,s,t, w;
+ int hx;
+ uint sign;
+ uint high;
+
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ sign=hx&0x80000000; /* sign= sign(x) */
+ hx ^=sign;
+ if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
+ if(hx==0)
+ return(x); /* cbrt(0) is itself */
+
+ GEN_OCL_SET_FLOAT_WORD(x,hx); /* x <- |x| */
+ /* rough cbrt to 5 bits */
+ if(hx<0x00800000) /* subnormal number */
+ {
+ //SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
+ //t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
+ t = (sign = 0) ? 0.0f : -0.0f;
+ return t;
+ }
+ else
+ GEN_OCL_SET_FLOAT_WORD(t,hx/3+B1);
+
+
+ /* new cbrt to 23 bits */
+ r=t*t/x;
+ s=mad(r, t, C);
+ t*=G+F/(s+E+D/s);
+ /* one step newton iteration to 53 bits with error less than 0.667 ulps */
+ s=t*t; /* t*t is exact */
+ r=x/s;
+ w=t+t;
+ r=(r-t)/(w+r); /* r-s is exact */
+ t=mad(t, r, t);
+
+ /* retore the sign bit */
+ GEN_OCL_GET_FLOAT_WORD(high,t);
+ GEN_OCL_SET_FLOAT_WORD(t,high|sign);
+ return(t);
+}
+
+INLINE float __gen_ocl_asin_util(float x) {
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+ float
+ pS0 = 1.66666666666666657415e-01,
+ pS1 = -3.25565818622400915405e-01,
+ pS2 = 2.01212532134862925881e-01,
+ pS3 = -4.00555345006794114027e-02,
+ pS4 = 7.91534994289814532176e-04,
+ qS1 = -2.40339491173441421878e+00,
+ qS2 = 2.02094576023350569471e+00,
+ qS3 = -6.88283971605453293030e-01,
+ qS4 = 7.70381505559019352791e-02;
+
+ float t = x*x;
+ float p = t * mad(t, mad(t, mad(t, mad(t, pS4, pS3), pS2), pS1), pS0);
+ float q = mad(t, mad(t, mad(t, mad(t, qS4, qS3), qS2), qS1), 1.0f);
+ float w = p / q;
+ return mad(x, w, x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_asin(float x) {
+ uint ix;
+ union { uint i; float f; } u;
+ u.f = x;
+ ix = u.i & 0x7fffffff;
+ if(ix == 0x3f800000) {
+ return x * M_PI_2_F; /* asin(|1|)=+-pi/2 with inexact */
+ }
+ if(ix > 0x3f800000) { /* |x|>= 1 */
+ return NAN; /* asin(|x|>1) is NaN */
+ }
+
+ if(ix < 0x32000000) { /* if |x| < 2**-27 */
+ if(HUGE_VALF + x > FLT_ONE) return x; /* return x with inexact if x!=0*/
+ }
+
+ if(x < -0.5) {
+ return 2 * __gen_ocl_asin_util(native_sqrt((1+x) / 2)) - M_PI_2_F;
+ } else if(x > 0.5) {
+ return M_PI_2_F - 2 * __gen_ocl_asin_util(native_sqrt((1-x) / 2));
+ } else {
+ return __gen_ocl_asin_util(x);
+ }
+}
+OVERLOADABLE float __gen_ocl_internal_asinpi(float x) {
+ return __gen_ocl_internal_asin(x) / M_PI_F;
+}
+OVERLOADABLE float __gen_ocl_internal_acos(float x) {
+ if(x > 0.5)
+ return 2 * __gen_ocl_asin_util(native_sqrt((1-x)/2));
+ else
+ return M_PI_2_F - __gen_ocl_internal_asin(x);
+}
+OVERLOADABLE float __gen_ocl_internal_acospi(float x) {
+ return __gen_ocl_internal_acos(x) / M_PI_F;
+}
+__constant float atanhi[4] = {
+ 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
+ 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
+ 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
+ 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
+};
+__constant float atanlo[4] = {
+ 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
+ 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
+ 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
+ 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
+};
+
+OVERLOADABLE float __gen_ocl_internal_atan(float x) {
+ /* copied from fdlibm */
+ float aT[11];
+ aT[0] = 3.3333334327e-01; /* 0x3eaaaaaa */
+ aT[1] = -2.0000000298e-01; /* 0xbe4ccccd */
+ aT[2] = 1.4285714924e-01; /* 0x3e124925 */
+ aT[3] = -1.1111110449e-01; /* 0xbde38e38 */
+ aT[4] = 9.0908870101e-02; /* 0x3dba2e6e */
+ aT[5] = -7.6918758452e-02; /* 0xbd9d8795 */
+ aT[6] = 6.6610731184e-02; /* 0x3d886b35 */
+ const float one = 1.0, huge = 1.0e30;
+
+ float w,s1,s2,z;
+ int ix,hx,id;
+
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x50800000) { /* if |x| >= 2^34 */
+ if(ix>0x7f800000)
+ return x+x; /* NaN */
+ if(hx>0) return atanhi[3]+atanlo[3];
+ else return -atanhi[3]-atanlo[3];
+ } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
+ if (ix < 0x31000000) { /* |x| < 2^-29 */
+ if(huge+x>one) return x; /* raise inexact */
+ }
+ id = -1;
+ } else {
+ x = __gen_ocl_fabs(x);
+ if (ix < 0x3f980000) { /* |x| < 1.1875 */
+ if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
+ id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
+ } else { /* 11/16<=|x|< 19/16 */
+ id = 1; x = (x-one)/(x+one);
+ }
+ } else {
+ if (ix < 0x401c0000) { /* |x| < 2.4375 */
+ id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
+ } else { /* 2.4375 <= |x| < 2^66 */
+ id = 3; x = -(float)1.0/x;
+ }
+ }}
+ /* end of argument reduction */
+ z = x*x;
+ w = z*z;
+ /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+ s1 = z * mad(w, mad(w, mad(w, aT[6], aT[4]), aT[2]), aT[0]);
+ s2 = w * mad(w, mad(w, aT[5], aT[3]), aT[1]);
+ if (id<0) return x - x*(s1+s2);
+ else {
+ z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+ return (hx<0)? -z:z;
+ }
+
+}
+OVERLOADABLE float __gen_ocl_internal_atanpi(float x) {
+ return __gen_ocl_internal_atan(x) / M_PI_F;
+}
+
+// XXX work-around PTX profile
+OVERLOADABLE float sqrt(float x) { return native_sqrt(x); }
+OVERLOADABLE float rsqrt(float x) { return native_rsqrt(x); }
+
+/*
+ * Copyright (c) 2014 Advanced Micro Devices, Inc.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+OVERLOADABLE float __gen_ocl_internal_atan2(float y, float x) {
+ const float pi = 0x1.921fb6p+1f;
+ const float piby2 = 0x1.921fb6p+0f;
+ const float piby4 = 0x1.921fb6p-1f;
+ const float threepiby4 = 0x1.2d97c8p+1f;
+
+ float ax = fabs(x);
+ float ay = fabs(y);
+ float v = min(ax, ay);
+ float u = max(ax, ay);
+
+ // Scale since u could be large, as in "regular" divide
+ float s = u > 0x1.0p+96f ? 0x1.0p-32f : 1.0f;
+ float vbyu = s * v/ (s*u);
+
+ float vbyu2 = vbyu * vbyu;
+
+ float p = mad(vbyu2, mad(vbyu2, -0x1.7e1f78p-9f, -0x1.7d1b98p-3f), -0x1.5554d0p-2f) * vbyu2 * vbyu;
+ float q = mad(vbyu2, mad(vbyu2, 0x1.1a714cp-2f, 0x1.287c56p+0f), 1.0f);
+
+ // Octant 0 result
+ float a = mad(p, 1.0f/q, vbyu);
+
+ // Fix up 3 other octants
+ float at = piby2 - a;
+ a = ay > ax ? at : a;
+ at = pi - a;
+ a = x < 0.0F ? at : a;
+
+ // y == 0 => 0 for x >= 0, pi for x < 0
+ int hx = as_int(x);
+ at = (hx < 0) ? pi : 0.0f;
+ a = y == 0.0f ? at : a;
+
+ at = x > 0.0f ? piby4 : threepiby4;
+ a = ax == INFINITY & ay == INFINITY ? at : a;
+
+ // x or y is NaN
+ a = isnan(x) | isnan(y) ? NAN : a;
+
+ // Fixup sign and return
+ return copysign(a, y);
+}
+
+OVERLOADABLE float __gen_ocl_internal_atan2pi(float y, float x) {
+ return __gen_ocl_internal_atan2(y, x) / M_PI_F;
+}
+OVERLOADABLE float __gen_ocl_internal_fabs(float x) { return __gen_ocl_fabs(x); }
+OVERLOADABLE float __gen_ocl_internal_trunc(float x) { return __gen_ocl_rndz(x); }
+OVERLOADABLE float __gen_ocl_internal_round(float x) {
+ float y = __gen_ocl_rndz(x);
+ if (__gen_ocl_fabs(x - y) >= 0.5f)
+ y += __gen_ocl_internal_copysign(1.f, x);
+ return y;
+}
+OVERLOADABLE float __gen_ocl_internal_ceil(float x) { return __gen_ocl_rndu(x); }
+OVERLOADABLE float __gen_ocl_internal_rint(float x) {
+ return __gen_ocl_rnde(x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_exp(float x) {
+ float o_threshold = 8.8721679688e+01, /* 0x42b17180 */
+ u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
+ twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
+ ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ one = 1.0,
+ huge = 1.0e+30,
+ P1 = 1.6666667163e-01, /* 0x3e2aaaab */
+ P2 = -2.7777778450e-03; /* 0xbb360b61 */
+ float y,hi=0.0,lo=0.0,c,t;
+ int k=0,xsb;
+ unsigned hx;
+ float ln2HI_0 = 6.9313812256e-01; /* 0x3f317180 */
+ float ln2HI_1 = -6.9313812256e-01; /* 0xbf317180 */
+ float ln2LO_0 = 9.0580006145e-06; /* 0x3717f7d1 */
+ float ln2LO_1 = -9.0580006145e-06; /* 0xb717f7d1 */
+ float half_0 = 0.5;
+ float half_1 = -0.5;
+
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ xsb = (hx>>31)&1; /* sign bit of x */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out non-finite argument */
+ if(hx >= 0x42b17218) { /* if |x|>=88.721... */
+ if(hx>0x7f800000)
+ return x+x; /* NaN */
+ if(hx==0x7f800000)
+ return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
+ if(x > o_threshold) return huge*huge; /* overflow */
+ if(x < u_threshold) return twom100*twom100; /* underflow */
+ }
+ /* argument reduction */
+ if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
+ hi = x-(xsb ==1 ? ln2HI_1 : ln2HI_0); lo= xsb == 1? ln2LO_1 : ln2LO_0; k = 1-xsb-xsb;
+ } else {
+ float tmp = xsb == 1 ? half_1 : half_0;
+ k = ivln2*x+tmp;
+ t = k;
+ hi = x - t*ln2HI_0; /* t*ln2HI is exact here */
+ lo = t*ln2LO_0;
+ }
+ x = hi - lo;
+ }
+ else if(hx < 0x31800000) { /* when |x|<2**-28 */
+ if(huge+x>one) return one+x;/* trigger inexact */
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ t = x*x;
+ c = x - t*(P1+t*P2);
+ if(k==0)
+ return one-((x*c)/(c-(float)2.0)-x);
+ else
+ y = one-((lo-(x*c)/((float)2.0-c))-hi);
+ if(k >= -125) {
+ unsigned hy;
+ GEN_OCL_GET_FLOAT_WORD(hy,y);
+ GEN_OCL_SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
+ return y;
+ } else {
+ unsigned hy;
+ GEN_OCL_GET_FLOAT_WORD(hy,y);
+ GEN_OCL_SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
+ return y*twom100;
+ }
+}
+
+/* erf,erfc from glibc s_erff.c -- float version of s_erf.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+INLINE_OVERLOADABLE float __gen_ocl_internal_erf(float x) {
+/*...*/
+const float
+tiny = 1.0e-30,
+half_val= 5.0000000000e-01, /* 0x3F000000 */
+one = 1.0000000000e+00, /* 0x3F800000 */
+two = 2.0000000000e+00, /* 0x40000000 */
+ /* c = (subfloat)0.84506291151 */
+erx = 8.4506291151e-01, /* 0x3f58560b */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+efx = 1.2837916613e-01, /* 0x3e0375d4 */
+efx8= 1.0270333290e+00, /* 0x3f8375d4 */
+pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
+pp1 = -3.2504209876e-01, /* 0xbea66beb */
+pp2 = -2.8481749818e-02, /* 0xbce9528f */
+pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
+pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
+qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
+qq2 = 6.5022252500e-02, /* 0x3d852a63 */
+qq3 = 5.0813062117e-03, /* 0x3ba68116 */
+qq4 = 1.3249473704e-04, /* 0x390aee49 */
+qq5 = -3.9602282413e-06, /* 0xb684e21a */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
+pa1 = 4.1485610604e-01, /* 0x3ed46805 */
+pa2 = -3.7220788002e-01, /* 0xbebe9208 */
+pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
+pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
+pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
+pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
+qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
+qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
+qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
+qa4 = 1.2617121637e-01, /* 0x3e013307 */
+qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
+qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
+ /*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
+ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
+ra2 = -1.0558626175e+01, /* 0xc128f022 */
+ra3 = -6.2375331879e+01, /* 0xc2798057 */
+ra4 = -1.6239666748e+02, /* 0xc322658c */
+ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
+ra6 = -8.1287437439e+01, /* 0xc2a2932b */
+ra7 = -9.8143291473e+00, /* 0xc11d077e */
+sa1 = 1.9651271820e+01, /* 0x419d35ce */
+sa2 = 1.3765776062e+02, /* 0x4309a863 */
+sa3 = 4.3456588745e+02, /* 0x43d9486f */
+sa4 = 6.4538726807e+02, /* 0x442158c9 */
+sa5 = 4.2900814819e+02, /* 0x43d6810b */
+sa6 = 1.0863500214e+02, /* 0x42d9451f */
+sa7 = 6.5702495575e+00, /* 0x40d23f7c */
+sa8 = -6.0424413532e-02, /* 0xbd777f97 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+rb0 = -9.8649431020e-03, /* 0xbc21a092 */
+rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
+rb2 = -1.7757955551e+01, /* 0xc18e104b */
+rb3 = -1.6063638306e+02, /* 0xc320a2ea */
+rb4 = -6.3756646729e+02, /* 0xc41f6441 */
+rb5 = -1.0250950928e+03, /* 0xc480230b */
+rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
+sb1 = 3.0338060379e+01, /* 0x41f2b459 */
+sb2 = 3.2579251099e+02, /* 0x43a2e571 */
+sb3 = 1.5367296143e+03, /* 0x44c01759 */
+sb4 = 3.1998581543e+03, /* 0x4547fdbb */
+sb5 = 2.5530502930e+03, /* 0x451f90ce */
+sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
+sb7 = -2.2440952301e+01; /* 0xc1b38712 */
+
+ int hx,ix,i;
+ float R,S,P,Q,s,y,z,r;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7f800000) { /* erf(nan)=nan */
+ i = ((unsigned int)hx>>31)<<1;
+ return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
+ }
+
+ if(ix < 0x3f580000) { /* |x|<0.84375 */
+ if(ix < 0x31800000) { /* |x|<2**-28 */
+ if (ix < 0x04000000)
+ /*avoid underflow */
+ return (float)0.125*((float)8.0*x+efx8*x);
+ return x + efx*x;
+ }
+ z = x*x;
+ r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
+ s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5,qq4), qq3), qq2), qq1), one);
+ y = r / s;
+ return mad(x, y, x);
+ }
+ if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
+ s = __gen_ocl_internal_fabs(x)-one;
+ P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
+ Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
+ if(hx>=0) return erx + P/Q; else return -erx - P/Q;
+ }
+ if (ix >= 0x40c00000) { /* inf>|x|>=6 */
+ if(hx>=0) return one-tiny; else return tiny-one;
+ }
+ x = __gen_ocl_internal_fabs(x);
+ s = one/(x*x);
+ if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
+ R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
+ S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
+ } else { /* |x| >= 1/0.35 */
+ R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ rb6, rb5), rb4), rb3), rb2), rb1), rb0);
+ S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
+ }
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ GEN_OCL_SET_FLOAT_WORD(z,ix&0xfffff000);
+ r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*__gen_ocl_internal_exp((z-x)*(z+x)+R/S);
+ if(hx>=0) return one-r/x; else return r/x-one;
+}
+INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
+/*...*/
+const float
+tiny = 1.0e-30,
+half_val= 5.0000000000e-01, /* 0x3F000000 */
+one = 1.0000000000e+00, /* 0x3F800000 */
+two = 2.0000000000e+00, /* 0x40000000 */
+ /* c = (subfloat)0.84506291151 */
+erx = 8.4506291151e-01, /* 0x3f58560b */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+efx = 1.2837916613e-01, /* 0x3e0375d4 */
+efx8= 1.0270333290e+00, /* 0x3f8375d4 */
+pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
+pp1 = -3.2504209876e-01, /* 0xbea66beb */
+pp2 = -2.8481749818e-02, /* 0xbce9528f */
+pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
+pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
+qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
+qq2 = 6.5022252500e-02, /* 0x3d852a63 */
+qq3 = 5.0813062117e-03, /* 0x3ba68116 */
+qq4 = 1.3249473704e-04, /* 0x390aee49 */
+qq5 = -3.9602282413e-06, /* 0xb684e21a */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
+pa1 = 4.1485610604e-01, /* 0x3ed46805 */
+pa2 = -3.7220788002e-01, /* 0xbebe9208 */
+pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
+pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
+pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
+pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
+qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
+qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
+qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
+qa4 = 1.2617121637e-01, /* 0x3e013307 */
+qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
+qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
+ /*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
+ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
+ra2 = -1.0558626175e+01, /* 0xc128f022 */
+ra3 = -6.2375331879e+01, /* 0xc2798057 */
+ra4 = -1.6239666748e+02, /* 0xc322658c */
+ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
+ra6 = -8.1287437439e+01, /* 0xc2a2932b */
+ra7 = -9.8143291473e+00, /* 0xc11d077e */
+sa1 = 1.9651271820e+01, /* 0x419d35ce */
+sa2 = 1.3765776062e+02, /* 0x4309a863 */
+sa3 = 4.3456588745e+02, /* 0x43d9486f */
+sa4 = 6.4538726807e+02, /* 0x442158c9 */
+sa5 = 4.2900814819e+02, /* 0x43d6810b */
+sa6 = 1.0863500214e+02, /* 0x42d9451f */
+sa7 = 6.5702495575e+00, /* 0x40d23f7c */
+sa8 = -6.0424413532e-02, /* 0xbd777f97 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+rb0 = -9.8649431020e-03, /* 0xbc21a092 */
+rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
+rb2 = -1.7757955551e+01, /* 0xc18e104b */
+rb3 = -1.6063638306e+02, /* 0xc320a2ea */
+rb4 = -6.3756646729e+02, /* 0xc41f6441 */
+rb5 = -1.0250950928e+03, /* 0xc480230b */
+rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
+sb1 = 3.0338060379e+01, /* 0x41f2b459 */
+sb2 = 3.2579251099e+02, /* 0x43a2e571 */
+sb3 = 1.5367296143e+03, /* 0x44c01759 */
+sb4 = 3.1998581543e+03, /* 0x4547fdbb */
+sb5 = 2.5530502930e+03, /* 0x451f90ce */
+sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
+sb7 = -2.2440952301e+01; /* 0xc1b38712 */
+ int hx,ix;
+ float R,S,P,Q,s,y,z,r;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x7f800000) { /* erfc(nan)=nan */
+ /* erfc(+-inf)=0,2 */
+ return (float)(((unsigned int)hx>>31)<<1)+one/x;
+ }
+
+ if(ix < 0x3f580000) { /* |x|<0.84375 */
+ if(ix < 0x23800000) /* |x|<2**-56 */
+ return one-x;
+ z = x*x;
+ r = mad(z, mad(z, mad(z, mad(z, pp4, pp3), pp2), pp1), pp0);
+ s = mad(z, mad(z, mad(z, mad(z, mad(z, qq5, qq4), qq3), qq2), qq1), one);
+ y = r/s;
+ if(hx < 0x3e800000) { /* x<1/4 */
+ return one-(x+x*y);
+ } else {
+ r = x*y;
+ r += (x-half_val);
+ return half_val - r ;
+ }
+ }
+ if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
+ s = __gen_ocl_internal_fabs(x)-one;
+ P = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, pa6, pa5), pa4), pa3), pa2), pa1), pa0);
+ Q = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, qa6, qa5), qa4), qa3), qa2), qa1), one);
+ if(hx>=0) {
+ z = one-erx; return z - P/Q;
+ } else {
+ z = erx+P/Q; return one+z;
+ }
+ }
+ if (ix < 0x41e00000) { /* |x|<28 */
+ x = __gen_ocl_internal_fabs(x);
+ s = one/(x*x);
+ if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
+ R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0);
+ S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1), one);
+ } else { /* |x| >= 1/.35 ~ 2.857143 */
+ if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
+ R = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ rb6, rb5), rb4), rb3), rb2), rb1), rb0);
+ S = mad(s, mad(s, mad(s, mad(s, mad(s, mad(s, mad(s,
+ sb7, sb6), sb5), sb4), sb3), sb2), sb1), one);
+ }
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ GEN_OCL_SET_FLOAT_WORD(z,ix&0xffffe000);
+ r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*
+ __gen_ocl_internal_exp((z-x)*(z+x)+R/S);
+ if(hx>0) {
+ float ret = r/x;
+ return ret;
+ } else
+ return two-r/x;
+ } else {
+ if(hx>0) {
+ return tiny*tiny;
+ } else
+ return two-tiny;
+ }
+}
+
+OVERLOADABLE float __gen_ocl_internal_fmod (float x, float y) {
+ //return x-y*__gen_ocl_rndz(x/y);
+ float one = 1.0;
+ float Zero[2];
+ int n,hx,hy,hz,ix,iy,sx,i;
+ Zero[0] = 0.0;
+ Zero[1] = -0.0;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ GEN_OCL_GET_FLOAT_WORD(hy,y);
+ sx = hx&0x80000000; /* sign of x */
+ hx ^=sx; /* |x| */
+ hy &= 0x7fffffff; /* |y| */
+ /* purge off exception values */
+ if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
+ (hy>0x7f800000)) /* or y is NaN */
+ return (x*y)/(x*y);
+ if(hx<hy) return x; /* |x|<|y| return x */
+ if(hx==hy)
+ return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
+
+ /* determine ix = ilogb(x) */
+ if(hx<0x00800000) { /* subnormal x */
+ for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
+ } else ix = (hx>>23)-127;
+
+ /* determine iy = ilogb(y) */
+ if(hy<0x00800000) { /* subnormal y */
+ for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
+ } else iy = (hy>>23)-127;
+
+ /* set up {hx,lx}, {hy,ly} and align y to x */
+ if(ix >= -126)
+ hx = 0x00800000|(0x007fffff&hx);
+ else { /* subnormal x, shift x to normal */
+ n = -126-ix;
+ hx = hx<<n;
+ }
+ if(iy >= -126)
+ hy = 0x00800000|(0x007fffff&hy);
+ else { /* subnormal y, shift y to normal */
+ n = -126-iy;
+ hy = hy<<n;
+ }
+ /* fix point fmod */
+ n = ix - iy;
+ while(n--) {
+ hz=hx-hy;
+ if(hz<0){hx = hx+hx;}
+ else {
+ if(hz==0) /* return sign(x)*0 */
+ return Zero[(unsigned)sx>>31];
+ hx = hz+hz;
+ }
+ }
+ hz=hx-hy;
+ if(hz>=0) {hx=hz;}
+
+ /* convert back to floating value and restore the sign */
+ if(hx==0) /* return sign(x)*0 */
+ return Zero[(unsigned)sx>>31];
+ while(hx<0x00800000) { /* normalize x */
+ hx = hx+hx;
+ iy -= 1;
+ }
+ if(iy>= -126) { /* normalize output */
+ hx = ((hx-0x00800000)|((iy+127)<<23));
+ GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
+ } else { /* subnormal output */
+ n = -126 - iy;
+ hx >>= n;
+ GEN_OCL_SET_FLOAT_WORD(x,hx|sx);
+ x *= one; /* create necessary signal */
+ }
+ return x; /* exact output */
+}
+
+OVERLOADABLE float __gen_ocl_internal_expm1(float x) {
+ //return __gen_ocl_pow(M_E_F, x) - 1;
+ float Q1 = -3.3333335072e-02, /* 0xbd088889 */
+ ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
+ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
+ Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
+ huge = 1.0e30,
+ tiny = 1.0e-30,
+ ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ one = 1.0,
+ o_threshold= 8.8721679688e+01; /* 0x42b17180 */
+ float y,hi,lo,c,t,e,hxs,hfx,r1;
+ int k,xsb;
+ int hx;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ xsb = hx&0x80000000;
+ /* sign bit of x */
+ //if(xsb==0)
+ //y=x;
+ //else
+ //y= -x; /* y = |x| */
+ y = __gen_ocl_internal_fabs(x);
+ hx &= 0x7fffffff; /* high word of |x| */
+ /* filter out huge and non-finite argument */
+ if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
+ if(hx >= 0x42b17218) { /* if |x|>=88.721... */
+ if(hx>0x7f800000)
+ return x+x; /* NaN */
+ if(hx==0x7f800000)
+ return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+ if(x > o_threshold)
+ return huge*huge; /* overflow */
+ }
+ if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
+ if(x+tiny<(float)0.0) /* raise inexact */
+ return tiny-one; /* return -1 */
+ }
+ }
+ /* argument reduction */
+ if(hx > 0x3eb17218) {/* if |x| > 0.5 ln2 */
+ if(hx < 0x3F851592) {/* and |x| < 1.5 ln2 */
+ if(xsb==0){
+ hi = x - ln2_hi; lo = ln2_lo; k = 1;
+ } else {
+ hi = x + ln2_hi; lo = -ln2_lo; k = -1;
+ }
+ } else {
+ k = ivln2*x+((xsb==0)?(float)0.5:(float)-0.5);
+ t = k;
+ hi = x - t*ln2_hi;/* t*ln2_hi is exact here */
+ lo = t*ln2_lo;
+ }
+ x = hi - lo;
+ c = (hi-x)-lo;
+ } else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
+ //t = huge+x; /* return x with inexact flags when x!=0 */
+ //return x - (t-(huge+x));
+ return x;
+ } else k = 0;
+ /* x is now in primary range */
+ hfx = (float)0.5*x;
+ hxs = x*hfx;
+ r1 = one+hxs*(Q1+hxs*Q2);
+ t = (float)3.0-r1*hfx;
+ e = hxs*((r1-t)/((float)6.0 - x*t));
+ if(k==0)
+ return x - (x*e-hxs); /* c is 0 */
+ else{
+ e = (x*(e-c)-c);
+ e -= hxs;
+ if(k== -1)return (float)0.5*(x-e)-(float)0.5;
+ if(k==1){
+ if(x < (float)-0.25)
+ return -(float)2.0*(e-(x+(float)0.5));
+ else
+ return (one+(float)2.0*(x-e));
+ }
+ if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
+ int i;
+ y = one-(e-x);
+ GEN_OCL_GET_FLOAT_WORD(i,y);
+ GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
+ return y-one;
+ }
+ t = one;
+ if(k<23) {
+ int i;
+ GEN_OCL_SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
+ y = t-(e-x);
+ GEN_OCL_GET_FLOAT_WORD(i,y);
+ GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
+ } else {
+ int i;
+ GEN_OCL_SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
+ y = x-(e+t);
+ y += one;
+ GEN_OCL_GET_FLOAT_WORD(i,y);
+ GEN_OCL_SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
+ }
+ }
+ return y;
+}
+
+OVERLOADABLE float __gen_ocl_internal_acosh(float x) {
+ //return native_log(x + native_sqrt(x + 1) * native_sqrt(x - 1));
+ float one = 1.0,
+ ln2 = 6.9314718246e-01;/* 0x3f317218 */
+ float t;
+ int hx;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ if(hx<0x3f800000) { /* x < 1 */
+ return (x-x)/(x-x);
+ } else if(hx >=0x4d800000) { /* x > 2**28 */
+ if(hx >=0x7f800000) {/* x is inf of NaN */
+ return x+x;
+ } else
+ return __gen_ocl_internal_log(x)+ln2;/* acosh(huge)=log(2x) */
+ } else if (hx==0x3f800000) {
+ return 0.0; /* acosh(1) = 0 */
+ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
+ t=x*x;
+ return __gen_ocl_internal_log((float)2.0*x-one/(x+__gen_ocl_sqrt(t-one)));
+ } else { /* 1<x<2 */
+ t = x-one;
+ return log1p(t+__gen_ocl_sqrt((float)2.0*t+t*t));
+ }
+}
+
+OVERLOADABLE float __gen_ocl_internal_asinh(float x){
+ //return native_log(x + native_sqrt(x * x + 1));
+ float one = 1.0000000000e+00, /* 0x3F800000 */
+ ln2 = 6.9314718246e-01, /* 0x3f317218 */
+ huge= 1.0000000000e+30;
+ float w;
+ int hx,ix;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix< 0x38000000) { /* |x|<2**-14 */
+ if(huge+x>one) return x; /* return x inexact except 0 */
+ }
+ if(ix>0x47000000) {/* |x| > 2**14 */
+ if(ix>=0x7f800000) return x+x;/* x is inf or NaN */
+ w = __gen_ocl_internal_log(__gen_ocl_internal_fabs(x))+ln2;
+ } else {
+ float xa = __gen_ocl_internal_fabs(x);
+ if (ix>0x40000000) {/* 2**14 > |x| > 2.0 */
+ w = __gen_ocl_internal_log(mad(xa, 2.0f, one / (__gen_ocl_sqrt(mad(xa, xa, one)) + xa)));
+ } else { /* 2.0 > |x| > 2**-14 */
+ float t = xa*xa;
+ w =log1p(xa+t/(one+__gen_ocl_sqrt(one+t)));
+ }
+ }
+ return __gen_ocl_internal_copysign(w, x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_sinh(float x){
+ //return (1 - native_exp(-2 * x)) / (2 * native_exp(-x));
+ float one = 1.0,
+ shuge = 1.0e37;
+ float t,w,h;
+ int ix,jx;
+ GEN_OCL_GET_FLOAT_WORD(jx,x);
+ ix = jx&0x7fffffff;
+ /* x is INF or NaN */
+ if(ix>=0x7f800000) return x+x;
+ h = 0.5;
+ if (jx<0) h = -h;
+ /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+ if (ix < 0x41b00000) { /* |x|<22 */
+ if (ix<0x31800000) /* |x|<2**-28 */
+ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+ t = __gen_ocl_internal_expm1(__gen_ocl_internal_fabs(x));
+ if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
+ return h*(t+t/(t+one));
+ }
+ /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+ if (ix < 0x42b17180) return h*__gen_ocl_internal_exp(__gen_ocl_internal_fabs(x));
+ /* |x| in [log(maxdouble), overflowthresold] */
+ if (ix<=0x42b2d4fc) {
+ w = __gen_ocl_internal_exp((float)0.5*__gen_ocl_internal_fabs(x));
+ t = h*w;
+ return t*w;
+ }
+ /* |x| > overflowthresold, sinh(x) overflow */
+ return x*shuge;
+}
+
+OVERLOADABLE float __gen_ocl_internal_tanh(float x) {
+ //float y = native_exp(-2 * x);
+ //return (1 - y) / (1 + y);
+ float one=1.0, two=2.0, tiny = 1.0e-30;
+ float t,z;
+ int jx,ix;
+ GEN_OCL_GET_FLOAT_WORD(jx,x);
+ ix = jx&0x7fffffff;
+ /* x is INF or NaN */
+ if(ix>=0x7f800000) {
+ if (jx>=0)
+ return one/x+one; /* tanh(+-inf)=+-1 */
+ else
+ return one/x-one; /* tanh(NaN) = NaN */
+ }
+
+ if (ix < 0x41b00000) { /* |x|<22 */
+ if (ix == 0)
+ return x; /* x == +-0 */
+ if (ix<0x24000000) /* |x|<2**-55 */
+ return x*(one+x); /* tanh(small) = small */
+ if (ix>=0x3f800000) { /* |x|>=1 */
+ t = __gen_ocl_internal_expm1(two*__gen_ocl_internal_fabs(x));
+ z = one - two/(t+two);
+ } else {
+ t = __gen_ocl_internal_expm1(-two*__gen_ocl_internal_fabs(x));
+ z= -t/(t+two);
+ }
+ } else { /* |x| > 22, return +-1 */
+ z = one - tiny; /* raised inexact flag */
+ }
+ return (jx>=0)? z: -z;
+}
+
+OVERLOADABLE float __gen_ocl_internal_cosh(float x) {
+ //return (1 + native_exp(-2 * x)) / (2 * native_exp(-x));
+ float halF = 0.5,
+ huge = 1.0e+30,
+ tiny = 1.0e-30,
+ one = 1.0;
+ float t,w;
+ int ix;
+ GEN_OCL_GET_FLOAT_WORD(ix,x);
+ ix &= 0x7fffffff;
+ /* |x| in [0,22] */
+ if (ix < 0x41b00000) {
+ /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+ if(ix<0x3eb17218) {
+ t = __gen_ocl_internal_expm1(__gen_ocl_fabs(x));
+ w = one+t;
+ if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
+ return one+(t*t)/(w+w);
+ }
+ /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+ t = __gen_ocl_internal_exp(__gen_ocl_fabs(x));
+ return halF*t+halF/t;
+ }
+ /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+ if (ix < 0x42b17180) return halF*__gen_ocl_internal_exp(__gen_ocl_fabs(x));
+ /* |x| in [log(maxdouble), overflowthresold] */
+ if (ix<=0x42b2d4fc) {
+ w = __gen_ocl_internal_exp(halF*__gen_ocl_fabs(x));
+ t = halF*w;
+ return t*w;
+ }
+ /* x is INF or NaN */
+ if(ix>=0x7f800000) return x*x;
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge*huge;
+}
+
+OVERLOADABLE float __gen_ocl_internal_remainder(float x, float p){
+ //return x-y*__gen_ocl_rnde(x/y);
+ float zero = 0.0;
+ int hx,hp;
+ unsigned sx;
+ float p_half;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ GEN_OCL_GET_FLOAT_WORD(hp,p);
+ sx = hx&0x80000000;
+ hp &= 0x7fffffff;
+ hx &= 0x7fffffff;
+ /* purge off exception values */
+ if(hp==0) return (x*p)/(x*p); /* p = 0 */
+ if((hx>=0x7f800000)|| /* x not finite */
+ ((hp>0x7f800000))) /* p is NaN */
+ return (x*p)/(x*p);
+ if (hp<=0x7effffff) x = __gen_ocl_internal_fmod(x,p+p); /* now x < 2p */
+ if ((hx-hp)==0) return zero*x;
+ x = __gen_ocl_fabs(x);
+ p = __gen_ocl_fabs(p);
+ if (hp<0x01000000) {
+ if(x+x>p) {
+ x-=p;
+ if(x+x>=p) x -= p;
+ }
+ } else {
+ p_half = (float)0.5*p;
+ if(x>p_half) {
+ x-=p;
+ if(x>=p_half) x -= p;
+ }
+ }
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ GEN_OCL_SET_FLOAT_WORD(x,hx^sx);
+ return x;
+}
+
+OVERLOADABLE float __gen_ocl_internal_ldexp(float x, int n) {
+ x = __gen_ocl_scalbnf(x,n);
+ return x;
+}
+
+OVERLOADABLE float __gen_ocl_internal_atanh(float x) {
+ //return 0.5f * native_sqrt((1 + x) / (1 - x));
+ float xa = __gen_ocl_fabs (x);
+ float t;
+ if (isless (xa, 0.5f)){
+ if (xa < 0x1.0p-28f) return x;
+ t = xa + xa;
+ t = 0.5f * log1p (t + t * xa / (1.0f - xa));
+ } else if (isless (xa, 1.0f)){
+ t = 0.5f * log1p ((xa + xa) / (1.0f - xa));
+ } else{
+ if (isgreater (xa, 1.0f)) return (x - x) / (x - x);
+ return x / 0.0f;
+ }
+ return __gen_ocl_internal_copysign(t, x);
+}
+
+OVERLOADABLE float __gen_ocl_internal_exp10(float x){
+ float px, qx,ans;
+ short n;
+ int i;
+ float*p;
+ float MAXL10 = 38.230809449325611792;
+ float LOG210 = 3.32192809488736234787e0;
+ float LG102A = 3.00781250000000000000E-1;
+ float LG102B = 2.48745663981195213739E-4;
+ float P[6];
+ P[0] = 2.063216740311022E-001;
+ P[1] = 5.420251702225484E-001;
+ P[2] = 1.171292686296281E+000;
+ P[3] = 2.034649854009453E+000;
+ P[4] = 2.650948748208892E+000;
+ P[5] = 2.302585167056758E+000;
+
+ if( x < -MAXL10 ) return 0.0;
+
+ if( isinf(x)) return INFINITY;
+ /* The following is necessary because range reduction blows up: */
+ if( x == 0 )return 1.0;
+
+ /* Express 10**x = 10**g 2**n
+ * = 10**g 10**( n log10(2) )
+ * = 10**( g + n log10(2) )
+ */
+ px = x * LOG210;
+ qx = __gen_ocl_internal_floor( px + 0.5 );
+ n = qx;
+ x -= qx * LG102A;
+ x -= qx * LG102B;
+
+ /* rational approximation for exponential
+ * of the fractional part:
+ * 10**x - 1 = 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+ p = P;
+ ans = *p++;
+ i = 5;
+ do{
+ ans = ans * x + *p++;
+ }
+ while( --i );
+ px = 1.0 + x * ans;
+
+ /* multiply by power of 2 */
+ x = __gen_ocl_internal_ldexp( px, n );
+ return x;
+}
+
+OVERLOADABLE float cospi(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_cospi(x);
+
+ return __gen_ocl_internal_cospi(x);
+}
+
+OVERLOADABLE float cosh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_cosh(x);
+
+ return __gen_ocl_internal_cosh(x);
+}
+
+OVERLOADABLE float acos(float x) {
+ return __gen_ocl_internal_acos(x);
+}
+
+OVERLOADABLE float acospi(float x) {
+ return __gen_ocl_internal_acospi(x);
+}
+
+OVERLOADABLE float acosh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_acosh(x);
+
+ return __gen_ocl_internal_acosh(x);
+}
+
+OVERLOADABLE float sinpi(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_sinpi(x);
+
+ return __gen_ocl_internal_sinpi(x);
+}
+
+OVERLOADABLE float sinh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_sinh(x);
+
+ return __gen_ocl_internal_sinh(x);
+}
+
+OVERLOADABLE float asin(float x) {
+ return __gen_ocl_internal_asin(x);
+}
+
+OVERLOADABLE float asinpi(float x) {
+ return __gen_ocl_internal_asinpi(x);
+}
+
+OVERLOADABLE float asinh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_asinh(x);
+
+ return __gen_ocl_internal_asinh(x);
+}
+
+OVERLOADABLE float tanpi(float x) {
+ return __gen_ocl_internal_tanpi(x);
+}
+
+OVERLOADABLE float tanh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_tanh(x);
+
+ return __gen_ocl_internal_tanh(x);
+}
+
+OVERLOADABLE float atan(float x) {
+ return __gen_ocl_internal_atan(x);
+}
+
+OVERLOADABLE float atan2(float y, float x) {
+ return __gen_ocl_internal_atan2(y, x);
+}
+
+OVERLOADABLE float atan2pi(float y, float x) {
+ return __gen_ocl_internal_atan2pi(y, x);
+}
+
+OVERLOADABLE float atanpi(float x) {
+ return __gen_ocl_internal_atanpi(x);
+}
+
+OVERLOADABLE float atanh(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_atanh(x);
+
+ return __gen_ocl_internal_atanh(x);
+}
+
+OVERLOADABLE float cbrt(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_cbrt(x);
+
+ return __gen_ocl_internal_cbrt(x);
+}
+
+OVERLOADABLE float rint(float x) {
+ return __gen_ocl_internal_rint(x);
+}
+
+OVERLOADABLE float copysign(float x, float y) {
+ return __gen_ocl_internal_copysign(x, y);
+}
+
+OVERLOADABLE float erf(float x) {
+ return __gen_ocl_internal_erf(x);
+}
+
+OVERLOADABLE float erfc(float x) {
+ return __gen_ocl_internal_erfc(x);
+}
+
+OVERLOADABLE float fmod (float x, float y) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_fmod(x, y);
+
+ return __gen_ocl_internal_fmod(x, y);
+}
+
+OVERLOADABLE float remainder(float x, float p) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_remainder(x, p);
+
+ return __gen_ocl_internal_remainder(x, p);
+}
+
+OVERLOADABLE float ldexp(float x, int n) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_ldexp(x, n);
+
+ if (x == (float)0.0f) x = 0.0f;
+ return __gen_ocl_internal_ldexp(x, n);
+}
+
+CONST OVERLOADABLE float __gen_ocl_mad(float a, float b, float c) __asm("llvm.fma" ".f32");
+CONST OVERLOADABLE half __gen_ocl_mad(half a, half b, half c) __asm("llvm.fma" ".f16");
+PURE CONST float __gen_ocl_fmax(float a, float b);
+PURE CONST float __gen_ocl_fmin(float a, float b);
+
+OVERLOADABLE float mad(float a, float b, float c) {
+ return __gen_ocl_mad(a, b, c);
+}
+
+OVERLOADABLE float __gen_ocl_internal_fmax(float a, float b) { return max(a,b); }
+OVERLOADABLE float __gen_ocl_internal_fmin(float a, float b) { return min(a,b); }
+OVERLOADABLE float __gen_ocl_internal_fmax(half a, half b) { return max(a,b); }
+OVERLOADABLE float __gen_ocl_internal_fmin(half a, half b) { return min(a,b); }
+OVERLOADABLE float __gen_ocl_internal_maxmag(float x, float y) {
+ float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
+ return a > b ? x : b > a ? y : max(x, y);
+}
+OVERLOADABLE float __gen_ocl_internal_minmag(float x, float y) {
+ float a = __gen_ocl_fabs(x), b = __gen_ocl_fabs(y);
+ return a < b ? x : b < a ? y : min(x, y);
+}
+OVERLOADABLE float __gen_ocl_internal_fdim(float x, float y) {
+ if(isnan(x))
+ return x;
+ if(isnan(y))
+ return y;
+ return x > y ? (x - y) : +0.f;
+}
+/*
+ * the pow/pown high precision implementation are copied from msun library.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+OVERLOADABLE float __gen_ocl_internal_pow(float x, float y) {
+ float z,ax,z_h,z_l,p_h,p_l;
+ float y1,t1,t2,r,s,sn,t,u,v,w;
+ int i,j,k,yisint,n;
+ int hx,hy,ix,iy,is;
+ float bp[2],dp_h[2],dp_l[2],
+ zero = 0.0,
+ one = 1.0,
+ two = 2.0,
+ two24 = 16777216.0, /* 0x4b800000 */
+ huge = 1.0e30,
+ tiny = 1.0e-30,
+ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+ L1 = 6.0000002384e-01, /* 0x3f19999a */
+ L2 = 4.2857143283e-01, /* 0x3edb6db7 */
+ P1 = 1.6666667163e-01, /* 0x3e2aaaab */
+ P2 = -2.7777778450e-03, /* 0xbb360b61 */
+ lg2 = 6.9314718246e-01, /* 0x3f317218 */
+ lg2_h = 6.93145752e-01, /* 0x3f317200 */
+ lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
+ ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
+ cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
+ cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
+ cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
+ ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
+ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
+ bp[0] = 1.0,bp[1] = 1.5,
+ dp_h[0] = 0.0,dp_h[1] = 5.84960938e-01,
+ dp_l[0] = 0.0,dp_l[1] = 1.56322085e-06;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ GEN_OCL_GET_FLOAT_WORD(hy,y);
+ ix = hx&0x7fffffff; iy = hy&0x7fffffff;
+ if (ix < 0x00800000) { /* x < 2**-126 */
+ ix = 0;/* Gen does not support subnormal number now */
+ }
+ if (iy < 0x00800000) { /* y < 2**-126 */
+ iy = 0;/* Gen does not support subnormal number now */
+ }
+ /* y==zero: x**0 = 1 */
+ if(iy==0) return one;
+ /* pow(+1, y) returns 1 for any y, even a NAN */
+ if(hx==0x3f800000) return one;
+ /* +-NaN return x+y */
+ if(ix > 0x7f800000 || iy > 0x7f800000)
+ return (x+0.0f)+y+(0.0f);
+ /* determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = 0;
+ if(hx<0) {
+ if(iy>=0x4b800000) yisint = 2; /* even integer y */
+ else if(iy>=0x3f800000) {
+ k = (iy>>23)-0x7f; /* exponent */
+ j = iy>>(23-k);
+ if((j<<(23-k))==iy) yisint = 2-(j&1);
+ }
+ }
+ /* special value of y */
+ if (iy==0x7f800000) { /* y is +-inf */
+ if (ix==0x3f800000)
+ //return y - y; /* inf**+-1 is NaN */
+ return one;
+ else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
+ return (hy>=0)? y: zero;
+ else /* (|x|<1)**-,+inf = inf,0 */
+ return (hy<0)?-y: zero;
+ }
+ if(iy==0x3f800000) { /* y is +-1 */
+ if(hy<0) return one/x; else return x;
+ }
+ if(hy==0x40000000) return x*x; /* y is 2 */
+ if(hy==0x3f000000) { /* y is 0.5 */
+ if(hx>=0)return __gen_ocl_sqrt(x);
+ }
+
+ ax = __gen_ocl_fabs(x);
+ /* special value of x */
+ if(ix==0x7f800000||ix==0||ix==0x3f800000){
+ z = ax; /*x is +-0,+-inf,+-1*/
+ if(hy<0) z = one/z; /* z = (1/|x|) */
+ if(hx<0) {
+ if(((ix-0x3f800000)|yisint)==0) {
+ z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+ } else if(yisint==1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return z;
+ }
+ n = ((uint)hx>>31)-1;
+
+ /* (x<0)**(non-int) is NaN */
+ if((n|yisint)==0) return (x-x)/(x-x);
+
+ sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+ if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
+
+ /* |y| is huge */
+ if(iy>0x4d000000) { /* if |y| > 2**27 */
+ /* over/underflow if x is not close to one */
+ if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
+ if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = ax-1; /* t has 20 trailing zeros */
+ w = (t*t)*((float)0.5-t*(0.333333333333f-t*0.25f));
+ u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
+ v = t*ivln2_l-w*ivln2;
+ t1 = u+v;
+ GEN_OCL_GET_FLOAT_WORD(is,t1);
+ GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
+ t2 = v-(t1-u);
+ } else {
+ float s2,s_h,s_l,t_h,t_l;
+ n = 0;
+ /* take care subnormal number */
+ //if(ix<0x00800000)
+ //{ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
+ n += ((ix)>>23)-0x7f;
+ j = ix&0x007fffff;
+ /* determine interval */
+ ix = j|0x3f800000; /* normalize ix */
+ if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
+ else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
+ else {k=0;n+=1;ix -= 0x00800000;}
+ GEN_OCL_SET_FLOAT_WORD(ax,ix);
+
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
+ v = one/(ax+bp[k]);
+ s = u*v;
+ s_h = s;
+ GEN_OCL_GET_FLOAT_WORD(is,s_h);
+ GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
+ /* t_h=ax+bp[k] High */
+ is = ((ix>>1)&0xfffff000)|0x20000000;
+ GEN_OCL_SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
+ t_l = ax - (t_h-bp[k]);
+ s_l = v*((u-s_h*t_h)-s_h*t_l);
+
+ /* compute log(ax) */
+ s2 = s*s;
+ r = s2*s2*(L1+s2*L2);
+ r += s_l*(s_h+s);
+ s2 = s_h*s_h;
+ t_h = 3.0f+s2+r;
+ GEN_OCL_GET_FLOAT_WORD(is,t_h);
+ GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
+ t_l = r-((t_h-3.0f)-s2);
+ /* u+v = s*(1+...) */
+ u = s_h*t_h;
+ v = s_l*t_h+t_l*s;
+ /* 2/(3log2)*(s+...) */
+ p_h = u+v;
+ GEN_OCL_GET_FLOAT_WORD(is,p_h);
+ GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
+ p_l = v-(p_h-u);
+ z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
+ z_l = cp_l*p_h+p_l*cp+dp_l[k];
+ /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ t = (float)n;
+ t1 = (((z_h+z_l)+dp_h[k])+t);
+ GEN_OCL_GET_FLOAT_WORD(is,t1);
+ GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ }
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ GEN_OCL_GET_FLOAT_WORD(is,y);
+ GEN_OCL_SET_FLOAT_WORD(y1,is&0xffffe000);
+ p_l = (y-y1)*t1+y*t2;
+ p_h = y1*t1;
+ z = p_l+p_h;
+ GEN_OCL_GET_FLOAT_WORD(j,z);
+ if (j>0x43000000) /* if z > 128 */
+ return sn*huge*huge; /* overflow */
+ else if (j==0x43000000) { /* if z == 128 */
+ if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
+ }
+ else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
+ return sn*tiny*tiny; /* underflow */
+ else if (j==0xc3160000){ /* z == -150 */
+ if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
+ }
+
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ i = j&0x7fffffff;
+ k = (i>>23)-0x7f;
+ n = 0;
+ if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
+ n = j+(0x00800000>>(k+1));
+ k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
+ GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
+ n = ((n&0x007fffff)|0x00800000)>>(23-k);
+ if(j<0) n = -n;
+ p_h -= t;
+ }
+ t = p_l+p_h;
+ GEN_OCL_GET_FLOAT_WORD(is,t);
+ GEN_OCL_SET_FLOAT_WORD(t,is&0xffff8000);
+ u = t*lg2_h;
+ v = (p_l-(t-p_h))*lg2+t*lg2_l;
+ z = u+v;
+ w = v-(z-u);
+ t = z*z;
+ t1 = z - t*(P1+t*P2);
+ r = (z*t1)/(t1-two)-(w+z*w);
+ z = one-(r-z);
+ GEN_OCL_GET_FLOAT_WORD(j,z);
+ j += (n<<23);
+ if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
+ else GEN_OCL_SET_FLOAT_WORD(z,j);
+ return sn*z;
+}
+
+#define BODY \
+ if (isnan(x_abs) || isinf(x_abs)) { \
+ x_log2 = 0; \
+ return x_abs; \
+ } \
+ uint u = as_uint(x_abs); \
+ uint a = u & 0x7FFFFFFFu; \
+ if (a == 0) { \
+ x_log2 = 0; \
+ return x_abs; \
+ } \
+ if (a >= 0x800000) { \
+ x_log2 = (a >> 23) - 126; \
+ return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
+ } \
+ int e = -126; \
+ while (a < 0x400000) { \
+ e --; \
+ a <<= 1; \
+ } \
+ a <<= 1; \
+ x_log2 = e; \
+ float x_mant = as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
+
+OVERLOADABLE float tgamma (float x)
+{
+ /* based on glibc __ieee754_gammaf_r by Ulrich Drepper <drepper@cygnus.com> */
+
+ unsigned int hx;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ if (hx == 0xff800000)
+ {
+ /* x == -Inf. According to ISO this is NaN. */
+ return NAN;
+ }
+ if ((hx & 0x7f800000) == 0x7f800000)
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ return x;
+ }
+ if (x < 0.0f && __gen_ocl_internal_floor (x) == x)
+ {
+ /* integer x < 0 */
+ return NAN;
+ }
+
+ if (x >= 36.0f)
+ {
+ /* Overflow. */
+ return INFINITY;
+ }
+ else if (x <= 0.0f && x >= -FLT_EPSILON / 4.0f)
+ {
+ return 1.0f / x;
+ }
+ else
+ {
+ float sinpix = __gen_ocl_internal_sinpi(x);
+ if (x <= -42.0f)
+ /* Underflow. */
+ {return 0.0f * sinpix /*for sign*/;}
+ int exp2_adj = 0;
+ float x_abs = __gen_ocl_fabs(x);
+ float gam0;
+
+ if (x_abs < 4.0f) {
+ /* gamma = exp(lgamma) is only accurate for small lgamma */
+ float prod,x_adj;
+ if (x_abs < 0.5f) {
+ prod = 1.0f / x_abs;
+ x_adj = x_abs + 1.0f;
+ } else if (x_abs <= 1.5f) {
+ prod = 1.0f;
+ x_adj = x_abs;
+ } else if (x_abs < 2.5f) {
+ x_adj = x_abs - 1.0f;
+ prod = x_adj;
+ } else {
+ x_adj = x_abs - 2.0f;
+ prod = x_adj * (x_abs - 1.0f);
+ }
+ gam0 = __gen_ocl_internal_exp (lgamma (x_adj)) * prod;
+ }
+ else {
+ /* Compute gamma (X) using Stirling's approximation,
+ starting by computing pow (X, X) with a power of 2
+ factored out to avoid intermediate overflow. */
+ float x_int = __gen_ocl_internal_round (x_abs);
+ float x_frac = x_abs - x_int;
+ int x_log2;
+
+ BODY
+
+ if (x_mant < M_SQRT1_2_F)
+ {
+ x_log2--;
+ x_mant *= 2.0f;
+ }
+ exp2_adj = x_log2 * (int) x_int;
+ float ret = (__gen_ocl_internal_pow(x_mant, x_abs)
+ * exp2 (x_log2 * x_frac)
+ * __gen_ocl_internal_exp (-x_abs)
+ * sqrt (2.0f * M_PI_F / x_abs) );
+
+ float x2 = x_abs * x_abs;
+ float bsum = (0x3.403404p-12f / x2 -0xb.60b61p-12f) / x2 + 0x1.555556p-4f;
+ gam0 = ret + ret * __gen_ocl_internal_expm1 (bsum / x_abs);
+ }
+ if (x > 0.0f) {return __gen_ocl_internal_ldexp (gam0, exp2_adj);}
+ float gam1 = M_PI_F / (-x * sinpix * gam0);
+ return __gen_ocl_internal_ldexp (gam1, -exp2_adj);
+ }
+}
+#undef BODY
+
+float __gen_ocl_internal_pown(float x, int y) {
+ const float
+ bp[] = {1.0, 1.5,},
+ dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
+ dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
+ zero = 0.0,
+ one = 1.0,
+ two = 2.0,
+ two24 = 16777216.0, /* 0x4b800000 */
+ huge = 1.0e30,
+ tiny = 1.0e-30,
+ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+ L1 = 6.0000002384e-01, /* 0x3f19999a */
+ L2 = 4.2857143283e-01, /* 0x3edb6db7 */
+ P1 = 1.6666667163e-01, /* 0x3e2aaaab */
+ P2 = -2.7777778450e-03, /* 0xbb360b61 */
+ lg2 = 6.9314718246e-01, /* 0x3f317218 */
+ lg2_h = 0x1.62ep-1,
+ lg2_l = 0x1.0bfbe8p-15,
+ ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
+ cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
+ cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
+ cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
+ ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
+ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
+
+ float z,ax,z_h,z_l,p_h,p_l;
+ float y1,t1,t2,r,s,t,u,v,w;
+ int i,j,k,yisint,n;
+ int hx,ix,iy,is;
+
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ iy = y > 0 ? y&0x7fffffff : (-y)&0x7fffffff;
+ /* y==zero: x**0 = 1 */
+ if(y==0) return one;
+
+ /* +-NaN return NAN */
+ if(ix > 0x7f800000)
+ return NAN;
+
+ /* determine if y is an odd int
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = y&1 ? 1 : 2;
+
+ if (y == 1) return x;
+ if (y == -1) return one/x;
+ if (y == 2) return x*x;
+
+ ax = __gen_ocl_fabs(x);
+
+ /* special value of x */
+ if(ix==0x7f800000||ix==0||ix==0x3f800000){
+ z = ax; /*x is +-0,+-inf,+-1*/
+ if(y<0) z = one/z; /* z = (1/|x|) */
+ if(hx<0) {
+ if(yisint==1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return z;
+ }
+
+ float sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+ if(((((unsigned)hx>>31)-1)|(yisint-1))==0)
+ sn = -one; /* (-ve)**(odd int) */
+
+ /* |y| is huge */
+ if(iy>0x08000000) { /* if |y| > 2**27 */
+ /* over/underflow if x is not close to one */
+ if(ix<0x3f7ffff8) return (y<0)? sn*huge*huge:tiny*tiny;
+ if(ix>0x3f800007) return (y>0)? sn*huge*huge:tiny*tiny;
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = ax-1; /* t has 20 trailing zeros */
+ w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
+ u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
+ v = t*ivln2_l-w*ivln2;
+ t1 = u+v;
+ GEN_OCL_GET_FLOAT_WORD(is,t1);
+ GEN_OCL_SET_FLOAT_WORD(t1,is&0xfffff000);
+ t2 = v-(t1-u);
+ } else {
+ float s2,s_h,s_l,t_h,t_l;
+ n = 0;
+ /* take care subnormal number */
+// if(ix<0x00800000)
+// {ax *= two24; n -= 24; GEN_OCL_GET_FLOAT_WORD(ix,ax); }
+ n += ((ix)>>23)-0x7f;
+ j = ix&0x007fffff;
+ /* determine interval */
+ ix = j|0x3f800000; /* normalize ix */
+ if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
+ else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
+ else {k=0;n+=1;ix -= 0x00800000;}
+ GEN_OCL_SET_FLOAT_WORD(ax,ix);
+
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
+ v = one/(ax+bp[k]);
+ s = u*v;
+ s_h = s;
+ GEN_OCL_GET_FLOAT_WORD(is,s_h);
+ GEN_OCL_SET_FLOAT_WORD(s_h,is&0xfffff000);
+
+ /* t_h=ax+bp[k] High */
+ GEN_OCL_SET_FLOAT_WORD(t_h, (((ix>>1)|0x20000000)+0x00400000+(k<<21)) &0xfffff000);
+ t_l = ax - (t_h-bp[k]);
+ s_l = v*((u-s_h*t_h)-s_h*t_l);
+
+
+ /* compute log(ax) */
+ s2 = s*s;
+ r = s2*s2*(L1+s2*L2);
+ r += s_l*(s_h+s);
+ s2 = s_h*s_h;
+ t_h = (float)3.0+s2+r;
+ GEN_OCL_GET_FLOAT_WORD(is,t_h);
+ GEN_OCL_SET_FLOAT_WORD(t_h,is&0xffffe000);
+ t_l = r-((t_h-(float)3.0)-s2);
+ /* u+v = s*(1+...) */
+ u = s_h*t_h;
+ v = s_l*t_h+t_l*s;
+ /* 2/(3log2)*(s+...) */
+ p_h = u+v;
+ GEN_OCL_GET_FLOAT_WORD(is,p_h);
+ GEN_OCL_SET_FLOAT_WORD(p_h,is&0xffffe000);
+ p_l = v-(p_h-u);
+ z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
+ z_l = cp_l*p_h+p_l*cp+dp_l[k];
+ /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ t = (float)n;
+ t1 = (((z_h+z_l)+dp_h[k])+t);
+ GEN_OCL_GET_FLOAT_WORD(is,t1);
+ GEN_OCL_SET_FLOAT_WORD(t1,is&0xffffe000);
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ }
+
+ /* split up y into y1+y2+y3 and compute (y1+y2+y3)*(t1+t2) */
+
+ float fy = (float)y;
+ float y3 = (float)(y-(int)fy);
+ GEN_OCL_GET_FLOAT_WORD(is,fy);
+ GEN_OCL_SET_FLOAT_WORD(y1,is&0xfffff000);
+
+ p_l = (fy-y1)*t1 + y3*t1 + fy*t2 + y3*t2;
+ p_h = y1*t1;
+ z = p_l+p_h;
+
+ GEN_OCL_GET_FLOAT_WORD(j,z);
+ if (j>0x43000000) /* if z > 128 */
+ return sn*huge*huge; /* overflow */
+ else if (j==0x43000000) { /* if z == 128 */
+ if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
+ }
+ else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
+ return sn*tiny*tiny; /* underflow */
+ else if (j==0xc3160000){ /* z == -150 */
+ if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
+ }
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ i = j&0x7fffffff;
+ k = (i>>23)-0x7f;
+ n = 0;
+ if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
+ n = j+(0x00800000>>(k+1));
+ k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
+ GEN_OCL_SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
+ n = ((n&0x007fffff)|0x00800000)>>(23-k);
+ if(j<0) n = -n;
+ p_h -= t;
+
+ z -= n;
+ }
+
+ t = z;
+ GEN_OCL_GET_FLOAT_WORD(is,t);
+ GEN_OCL_SET_FLOAT_WORD(t,is&0xfffff000);
+ u = t*lg2_h;
+ v = (p_l-(t-p_h))*lg2+t*lg2_l;
+ z = u+v;
+ w = v-(z-u);
+ t = z*z;
+ t1 = z - t*(P1+t*P2);
+ r = (z*t1)/(t1-two)-(w+z*w);
+ z = one-(r-z);
+ GEN_OCL_GET_FLOAT_WORD(j,z);
+ j += (n<<23);
+ if((j>>23)<=0) z = __gen_ocl_scalbnf(z,n); /* subnormal output */
+ else GEN_OCL_SET_FLOAT_WORD(z,j);
+ return sn*z;
+}
+
+#define BODY \
+ if (isnan(x) || isinf(x)) { \
+ *exp = 0; \
+ return x; \
+ } \
+ uint u = as_uint(x); \
+ uint a = u & 0x7FFFFFFFu; \
+ if (a == 0) { \
+ *exp = 0; \
+ return x; \
+ } \
+ if (a >= 0x800000) { \
+ *exp = (a >> 23) - 126; \
+ return as_float((u & (0x807FFFFFu)) | 0x3F000000); \
+ } \
+ int e = -126; \
+ while (a < 0x400000) { \
+ e --; \
+ a <<= 1; \
+ } \
+ a <<= 1; \
+ *exp = e; \
+ return as_float((a & (0x807FFFFFu)) | (u & 0x80000000u) | 0x3F000000);
+float __gen_ocl_internal_frexp(float x, int *exp) { BODY; }
+
+OVERLOADABLE float hypot(float x, float y) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_hypot(x, y);
+
+ //return __gen_ocl_sqrt(x*x + y*y);
+ float a,b,an,bn,cn;
+ int e;
+ if (isfinite (x) && isfinite (y)){ /* Determine absolute values. */
+ x = __gen_ocl_fabs (x);
+ y = __gen_ocl_fabs (y);
+ /* Find the bigger and the smaller one. */
+ a = max(x,y);
+ b = min(x,y);
+ /* Now 0 <= b <= a. */
+ /* Write a = an * 2^e, b = bn * 2^e with 0 <= bn <= an < 1. */
+ an = __gen_ocl_internal_frexp (a, &e);
+ bn = ldexp (b, - e);
+ /* Through the normalization, no unneeded overflow or underflow will occur here. */
+ cn = __gen_ocl_sqrt (an * an + bn * bn);
+ return ldexp (cn, e);
+ }else{
+ if (isinf (x) || isinf (y)) /* x or y is infinite. Return +Infinity. */
+ return INFINITY;
+ else /* x or y is NaN. Return NaN. */
+ return x + y;
+ }
+}
+
+OVERLOADABLE float powr(float x, float y) {
+ unsigned int hx, sx, hy, sy;
+
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_pow(x,y);
+ else {
+ if (isnan(x) || isnan(y)) return NAN;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ GEN_OCL_GET_FLOAT_WORD(hy,y);
+ sx = (hx & 0x80000000) >> 31;
+ sy = (hy & 0x80000000) >> 31;
+
+ if ((hx&0x7fffffff) < 0x00800000) { /* x < 2**-126 */
+ x = 0.0f;/* Gen does not support subnormal number now */
+ hx = hx &0x80000000;
+ }
+ if ((hy&0x7fffffff) < 0x00800000) { /* y < 2**-126 */
+ y = 0.0;/* Gen does not support subnormal number now */
+ hy = hy &0x80000000;
+ }
+
+ // (x < 0) ** y = NAN (y!=0)
+ if ((sx && (hx & 0x7fffffff))) return NAN;
+
+ // +/-0 ** +/-0 = NAN
+ if ( !(hx&0x7fffffff) && !(hy&0x7fffffff)) return NAN;
+
+ // +inf ** +/-0 = NAN
+ if ( ((hx & 0x7f800000) ==0x7f800000) && !(hy&0x7fffffff)) return NAN;
+
+ // others except nan/inf/0 ** 0 = 1.0
+ if (!(hy&0x7fffffff)) return 1.0f;
+
+ // +1 ** inf = NAN; +1 ** finite = 1;
+ if (hx == 0x3f800000) {
+ return isinf(y) ? NAN : 1.0f;
+ }
+
+ if ( !(hx & 0x7fffffff)) {
+ // +/-0 ** y<0 = +inf
+ // +/-0 ** y>0 = +0
+ return sy ? INFINITY : 0.0f;
+ }
+
+ return __gen_ocl_internal_pow(x,y);
+ }
+}
+
+OVERLOADABLE float pown(float x, int n) {
+ if (__ocl_math_fastpath_flag) {
+ if (x == 0.f && n == 0)
+ return 1.f;
+ if (x < 0.f && (n&1) )
+ return -powr(-x, n);
+ return powr(x, n);
+ } else {
+ int ix;
+ GEN_OCL_GET_FLOAT_WORD(ix, x);
+ float sign = ix < 0 ? -1.0f : 1.0f;
+ if (x == 0.0f) x = sign * 0.0f;
+
+ return __gen_ocl_internal_pown(x, n);
+ }
+}
+
+OVERLOADABLE float pow(float x, float y) {
+ if (!__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_pow(x,y);
+ else {
+ int n;
+ if (x == 0.f && y == 0.f)
+ return 1.f;
+ if (x >= 0.f)
+ return powr(x, y);
+ n = y;
+ if ((float)n == y)//is exact integer
+ return pown(x, n);
+ return NAN;
+ }
+}
+
+OVERLOADABLE float rootn(float x, int n) {
+ float ax,re;
+ int sign = 0;
+ int hx;
+ if( n == 0 )return NAN;
+
+ GEN_OCL_GET_FLOAT_WORD(hx, x);
+ // Gen does not support denorm, flush to zero
+ if ((hx & 0x7fffffff) < 0x00800000) {
+ x = hx < 0 ? -0.0f : 0.0f;
+ }
+
+ //rootn ( x, n ) returns a NaN for x < 0 and n is even.
+ if( x < 0 && 0 == (n&1) )
+ return NAN;
+ if( x == 0.0 ){
+ switch( n & 0x80000001 ){
+ //rootn ( +-0, n ) is +0 for even n > 0.
+ case 0:
+ return 0.0f;
+ //rootn ( +-0, n ) is +-0 for odd n > 0.
+ case 1:
+ return x;
+ //rootn ( +-0, n ) is +inf for even n < 0.
+ case 0x80000000:
+ return INFINITY;
+
+ //rootn ( +-0, n ) is +-inf for odd n < 0.
+ case 0x80000001:
+ return __gen_ocl_internal_copysign(INFINITY, x);
+ }
+ }
+ ax = __gen_ocl_fabs(x);
+ if(x <0.0f && (n&1))
+ sign = 1;
+ if (__ocl_math_fastpath_flag)
+ re = __gen_ocl_pow(ax, 1.f/n);
+ else
+ re = __gen_ocl_internal_pow(ax,1.f/n);
+ if(sign)
+ re = -re;
+ return re;
+}
+
+OVERLOADABLE float fabs(float x) {
+ return __gen_ocl_internal_fabs(x);
+}
+
+OVERLOADABLE float trunc(float x) {
+ return __gen_ocl_internal_trunc(x);
+}
+
+OVERLOADABLE float round(float x) {
+ return __gen_ocl_internal_round(x);
+}
+
+OVERLOADABLE float floor(float x) {
+ return __gen_ocl_internal_floor(x);
+}
+
+OVERLOADABLE float ceil(float x) {
+ return __gen_ocl_internal_ceil(x);
+}
+
+OVERLOADABLE float log(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_log(x);
+
+ /* Use native instruction when it has enough precision */
+ if((x > 0x1.1p0) || (x <= 0))
+ return __gen_ocl_internal_fastpath_log(x);
+
+ return __gen_ocl_internal_log(x);
+}
+
+OVERLOADABLE float log2(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_log2(x);
+
+ /* Use native instruction when it has enough precision */
+ if((x > 0x1.1p0) || (x <= 0))
+ return __gen_ocl_internal_fastpath_log2(x);
+
+ return __gen_ocl_internal_log2(x);
+}
+
+OVERLOADABLE float log10(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_log10(x);
+
+ /* Use native instruction when it has enough precision */
+ if((x > 0x1.1p0) || (x <= 0))
+ return __gen_ocl_internal_fastpath_log10(x);
+
+ return __gen_ocl_internal_log10(x);
+}
+
+OVERLOADABLE float exp(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_exp(x);
+
+ /* Use native instruction when it has enough precision */
+ if (x > -0x1.6p1 && x < 0x1.6p1)
+ return __gen_ocl_internal_fastpath_exp(x);
+
+ return __gen_ocl_internal_exp(x);
+}
+
+OVERLOADABLE float exp2(float x) {
+ /* Use native instruction when it has enough precision, exp2 always */
+ return native_exp2(x);
+}
+
+OVERLOADABLE float exp10(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_exp10(x);
+
+ return __gen_ocl_internal_exp10(x);
+}
+
+OVERLOADABLE float expm1(float x) {
+ if (__ocl_math_fastpath_flag)
+ return __gen_ocl_internal_fastpath_expm1(x);
+
+ return __gen_ocl_internal_expm1(x);
+}
+
+OVERLOADABLE float fmin(float a, float b) {
+ return __gen_ocl_internal_fmin(a, b);
+}
+
+OVERLOADABLE float fmax(float a, float b) {
+ return __gen_ocl_internal_fmax(a, b);
+}
+
+OVERLOADABLE float fma(float a, float b, float c) {
+ return mad(a, b, c);
+}
+
+OVERLOADABLE float fdim(float x, float y) {
+ return __gen_ocl_internal_fdim(x, y);
+}
+
+OVERLOADABLE float maxmag(float x, float y) {
+ return __gen_ocl_internal_maxmag(x, y);
+}
+
+OVERLOADABLE float minmag(float x, float y) {
+ return __gen_ocl_internal_minmag(x, y);
+}
+
+OVERLOADABLE float nextafter(float x, float y) {
+ int hx, hy, ix, iy;
+ hx = as_int(x);
+ hy = as_int(y);
+ ix = hx & 0x7fffffff;
+ iy = hy & 0x7fffffff;
+ if(ix == 0)
+ ix = hx & 0x7fffff;
+ if(iy == 0)
+ iy = hy & 0x7fffff;
+ if(ix>0x7f800000 || iy>0x7f800000)
+ return x+y;
+ if(hx == hy)
+ return y;
+ if(ix == 0) {
+ if(iy == 0)
+ return y;
+ else
+ return as_float((hy&0x80000000) | 1);
+ }
+ if(hx >= 0) {
+ if(hx > hy) {
+ hx -= 1;
+ } else {
+ hx += 1;
+ }
+ } else {
+ if(hy >= 0 || hx > hy){
+ hx -= 1;
+ } else {
+ hx += 1;
+ }
+ }
+ return as_float(hx);
+}
+
+/* So far, the HW do not support half float math function.
+ We just do the conversion and call the float version here. */
+OVERLOADABLE half cospi(half x) {
+ float _x = (float)x;
+ return (half)cospi(_x);
+}
+OVERLOADABLE half cosh(half x) {
+ float _x = (float)x;
+ return (half)cosh(_x);
+}
+OVERLOADABLE half acos(half x) {
+ float _x = (float)x;
+ return (half)acos(_x);
+}
+OVERLOADABLE float half_cos(float x) {
+ return (float)cos(x);
+}
+OVERLOADABLE float half_divide(float x, float y) {
+ return (float)native_divide(x, y);
+}
+OVERLOADABLE float half_exp(float x) {
+ return (float)native_exp(x);
+}
+OVERLOADABLE float half_exp2(float x){
+ return (float)native_exp2(x);
+}
+OVERLOADABLE float half_exp10(float x){
+ return (float)native_exp10(x);
+}
+OVERLOADABLE float half_log(float x){
+ return (float)native_log(x);
+}
+OVERLOADABLE float half_log2(float x){
+ return (float)native_log2(x);
+}
+OVERLOADABLE float half_log10(float x){
+ return (float)native_log10(x);
+}
+OVERLOADABLE float half_powr(float x, float y){
+ return (float)powr(x, y);
+}
+OVERLOADABLE float half_recip(float x){
+ return (float)native_recip(x);
+}
+OVERLOADABLE float half_rsqrt(float x){
+ return (float)native_rsqrt(x);
+}
+OVERLOADABLE float half_sin(float x){
+ return (float)sin(x);
+}
+OVERLOADABLE float half_sqrt(float x){
+ return (float)native_sqrt(x);
+}
+OVERLOADABLE float half_tan(float x){
+ return (float)tan(x);
+}
+OVERLOADABLE half acospi(half x) {
+ float _x = (float)x;
+ return (half)acospi(_x);
+}
+OVERLOADABLE half acosh(half x) {
+ float _x = (float)x;
+ return (half)acosh(_x);
+}
+OVERLOADABLE half sinpi(half x) {
+ float _x = (float)x;
+ return (half)sinpi(_x);
+}
+OVERLOADABLE half sinh(half x) {
+ float _x = (float)x;
+ return (half)sinh(_x);
+}
+OVERLOADABLE half asin(half x) {
+ float _x = (float)x;
+ return (half)asin(_x);
+}
+OVERLOADABLE half asinpi(half x) {
+ float _x = (float)x;
+ return (half)asinpi(_x);
+}
+OVERLOADABLE half asinh(half x) {
+ float _x = (float)x;
+ return (half)asinh(_x);
+}
+OVERLOADABLE half tanpi(half x) {
+ float _x = (float)x;
+ return (half)tanpi(_x);
+}
+OVERLOADABLE half tanh(half x) {
+ float _x = (float)x;
+ return (half)tanh(_x);
+}
+OVERLOADABLE half atan(half x) {
+ float _x = (float)x;
+ return (half)atan(_x);
+}
+OVERLOADABLE half atan2(half y, half x) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)atan2(_x, _y);
+}
+OVERLOADABLE half atan2pi(half y, half x) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)atan2pi(_x, _y);
+}
+OVERLOADABLE half atanpi(half x) {
+ float _x = (float)x;
+ return (half)atanpi(_x);
+}
+OVERLOADABLE half atanh(half x) {
+ float _x = (float)x;
+ return (half)atanh(_x);
+}
+OVERLOADABLE half cbrt(half x) {
+ float _x = (float)x;
+ return (half)cbrt(_x);
+}
+OVERLOADABLE half rint(half x) {
+ float _x = (float)x;
+ return (half)rint(_x);
+}
+OVERLOADABLE half copysign(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)copysign(_x, _y);
+}
+OVERLOADABLE half erf(half x) {
+ float _x = (float)x;
+ return (half)erf(_x);
+}
+OVERLOADABLE half erfc(half x) {
+ float _x = (float)x;
+ return (half)erfc(_x);
+}
+OVERLOADABLE half fmod(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)fmod(_x, _y);
+}
+OVERLOADABLE half remainder(half x, half p) {
+ float _x = (float)x;
+ float _p = (float)p;
+ return (half)remainder(_x, _p);
+}
+OVERLOADABLE half ldexp(half x, int n) {
+ float _x = (float)x;
+ return (half)ldexp(_x, n);
+}
+OVERLOADABLE half powr(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)powr(_x, _y);
+}
+OVERLOADABLE half pow(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)pow(_x, _y);
+}
+//no pow, we use powr instead
+OVERLOADABLE half fabs(half x) {
+ float _x = (float)x;
+ return (half)fabs(_x);
+}
+OVERLOADABLE half trunc(half x) {
+ float _x = (float)x;
+ return (half)trunc(_x);
+}
+OVERLOADABLE half round(half x) {
+ float _x = (float)x;
+ return (half)round(_x);
+}
+OVERLOADABLE half floor(half x) {
+ float _x = (float)x;
+ return (half)floor(_x);
+}
+OVERLOADABLE half ceil(half x) {
+ float _x = (float)x;
+ return (half)ceil(_x);
+}
+OVERLOADABLE half log(half x) {
+ float _x = (float)x;
+ return (half)log(_x);
+}
+OVERLOADABLE half log2(half x) {
+ float _x = (float)x;
+ return (half)log2(_x);
+}
+OVERLOADABLE half log10(half x) {
+ float _x = (float)x;
+ return (half)log10(_x);
+}
+OVERLOADABLE half exp(half x) {
+ float _x = (float)x;
+ return (half)exp(_x);
+}
+OVERLOADABLE half exp10(half x) {
+ float _x = (float)x;
+ return (half)exp10(_x);
+}
+OVERLOADABLE half expm1(half x) {
+ float _x = (float)x;
+ return (half)expm1(_x);
+}
+OVERLOADABLE half fmin(half a, half b) {
+ return __gen_ocl_internal_fmin(a, b);
+}
+OVERLOADABLE half fmax(half a, half b) {
+ return __gen_ocl_internal_fmax(a, b);
+}
+OVERLOADABLE half fma(half a, half b, half c) {
+ float _a = (float)a;
+ float _b = (float)b;
+ float _c = (float)c;
+ return (half)fma(_a, _b, _c);
+}
+OVERLOADABLE half fdim(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)fdim(_x, _y);
+}
+OVERLOADABLE half maxmag(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)maxmag(_x, _y);
+}
+OVERLOADABLE half minmag(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)minmag(_x, _y);
+}
+OVERLOADABLE half exp2(half x) {
+ float _x = (float)x;
+ return (half)exp2(_x);
+}
+OVERLOADABLE half mad(half a, half b, half c) {
+ return __gen_ocl_mad(a,b,c);
+}
+OVERLOADABLE half sin(half x) {
+ float _x = (float)x;
+ return (half)sin(_x);
+}
+OVERLOADABLE half cos(half x) {
+ float _x = (float)x;
+ return (half)cos(_x);
+}
+OVERLOADABLE half tan(half x) {
+ float _x = (float)x;
+ return (half)tan(_x);
+}
+OVERLOADABLE half tgamma(half x) {
+ float _x = (float)x;
+ return (half)tgamma(_x);
+}
+OVERLOADABLE half lgamma(half x) {
+ float _x = (float)x;
+ return (half)lgamma(_x);
+}
+
+OVERLOADABLE half log1p(half x) {
+ float _x = (float)x;
+ return (half)log1p(_x);
+}
+OVERLOADABLE half logb(half x) {
+ float _x = (float)x;
+ return (half)logb(_x);
+}
+OVERLOADABLE int ilogb(half x) {
+ float _x = (float)x;
+ return ilogb(_x);
+}
+OVERLOADABLE half nan(ushort code) {
+ return (half)NAN;
+}
+
+OVERLOADABLE half sqrt(half x) {
+ float _x = (float)x;
+ return (half)sqrt(_x);
+}
+OVERLOADABLE half rsqrt(half x) {
+ float _x = (float)x;
+ return (half)rsqrt(_x);
+}
+
+OVERLOADABLE half nextafter(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)nextafter(_x, _y);
+}
+
+OVERLOADABLE half hypot(half x, half y) {
+ float _x = (float)x;
+ float _y = (float)y;
+ return (half)hypot(_x, _y);
+}
+
+OVERLOADABLE half pown(half x, int n) {
+ float _x = (float)x;
+ return (half)pown(_x, n);
+}
+OVERLOADABLE half rootn(half x, int n) {
+ float _x = (float)x;
+ return (half)rootn(_x, n);
+}
+
INLINE int __HI(double x){
long x64 = as_long(x);
int high = convert_int((x64 >> 32) & 0xFFFFFFFF);
diff --git a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
index 3a9c5e6c..112b4384 100644
--- a/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
+++ b/backend/src/libocl/tmpl/ocl_math_common.tmpl.h
@@ -20,6 +20,185 @@
#include "ocl_types.h"
+OVERLOADABLE float cospi(float x);
+OVERLOADABLE float cosh(float x);
+OVERLOADABLE float acos(float x);
+OVERLOADABLE float acospi(float x);
+OVERLOADABLE float acosh(float x);
+OVERLOADABLE float sinpi(float x);
+OVERLOADABLE float sinh(float x);
+OVERLOADABLE float asin(float x);
+OVERLOADABLE float asinpi(float x);
+OVERLOADABLE float asinh(float x);
+OVERLOADABLE float tanpi(float x);
+OVERLOADABLE float tanh(float x);
+OVERLOADABLE float atan(float x);
+OVERLOADABLE float atan2(float y, float x);
+OVERLOADABLE float atan2pi(float y, float x);
+OVERLOADABLE float atanpi(float x);
+OVERLOADABLE float atanh(float x);
+OVERLOADABLE float cbrt(float x);
+OVERLOADABLE float rint(float x);
+OVERLOADABLE float copysign(float x, float y);
+OVERLOADABLE float erf(float x);
+OVERLOADABLE float erfc(float x);
+OVERLOADABLE float fmod (float x, float y);
+OVERLOADABLE float remainder(float x, float p);
+OVERLOADABLE float ldexp(float x, int n);
+OVERLOADABLE float powr(float x, float y);
+OVERLOADABLE float pow(float x, float y);
+//no pow, we use powr instead
+OVERLOADABLE float fabs(float x);
+OVERLOADABLE float trunc(float x);
+OVERLOADABLE float round(float x);
+OVERLOADABLE float floor(float x);
+OVERLOADABLE float ceil(float x);
+OVERLOADABLE float log(float x);
+OVERLOADABLE float log2(float x);
+OVERLOADABLE float log10(float x);
+OVERLOADABLE float exp(float x);
+OVERLOADABLE float exp10(float x);
+OVERLOADABLE float expm1(float x);
+OVERLOADABLE float fmin(float a, float b);
+OVERLOADABLE float fmax(float a, float b);
+OVERLOADABLE float fma(float a, float b, float c);
+OVERLOADABLE float fdim(float x, float y);
+OVERLOADABLE float maxmag(float x, float y);
+OVERLOADABLE float minmag(float x, float y);
+OVERLOADABLE float exp2(float x);
+OVERLOADABLE float mad(float a, float b, float c);
+OVERLOADABLE float sin(float x);
+OVERLOADABLE float cos(float x);
+OVERLOADABLE float tan(float x);
+OVERLOADABLE float tgamma(float x);
+OVERLOADABLE float lgamma(float x);
+
+OVERLOADABLE float log1p(float x);
+OVERLOADABLE float logb(float x);
+OVERLOADABLE int ilogb(float x);
+OVERLOADABLE float nan(uint code);
+OVERLOADABLE float sqrt(float x);
+OVERLOADABLE float rsqrt(float x);
+OVERLOADABLE float hypot(float x, float y);
+OVERLOADABLE float nextafter(float x, float y);
+OVERLOADABLE float pown(float x, int n);
+OVERLOADABLE float rootn(float x, int n);
+
+// native
+OVERLOADABLE float native_cos(float x);
+OVERLOADABLE float native_divide(float x, float y);
+OVERLOADABLE float native_exp(float x);
+OVERLOADABLE float native_exp2(float x);
+OVERLOADABLE float native_exp10(float x);
+OVERLOADABLE float native_log(float x);
+OVERLOADABLE float native_log2(float x);
+OVERLOADABLE float native_log10(float x);
+OVERLOADABLE float native_powr(float x, float y);
+OVERLOADABLE float native_recip(float x);
+OVERLOADABLE float native_rsqrt(float x);
+OVERLOADABLE float native_sin(float x);
+OVERLOADABLE float native_sqrt(float x);
+OVERLOADABLE float native_tan(float x);
+
+
+// Half float version.
+OVERLOADABLE half cospi(half x);
+OVERLOADABLE half cosh(half x);
+OVERLOADABLE half acos(half x);
+OVERLOADABLE half acospi(half x);
+OVERLOADABLE half acosh(half x);
+OVERLOADABLE half sinpi(half x);
+OVERLOADABLE half sinh(half x);
+OVERLOADABLE half asin(half x);
+OVERLOADABLE half asinpi(half x);
+OVERLOADABLE half asinh(half x);
+OVERLOADABLE half tanpi(half x);
+OVERLOADABLE half tanh(half x);
+OVERLOADABLE half atan(half x);
+OVERLOADABLE half atan2(half y, half x);
+OVERLOADABLE half atan2pi(half y, half x);
+OVERLOADABLE half atanpi(half x);
+OVERLOADABLE half atanh(half x);
+OVERLOADABLE half cbrt(half x);
+OVERLOADABLE half rint(half x);
+OVERLOADABLE half copysign(half x, half y);
+OVERLOADABLE half erf(half x);
+OVERLOADABLE half erfc(half x);
+OVERLOADABLE half fmod (half x, half y);
+OVERLOADABLE half remainder(half x, half p);
+OVERLOADABLE half ldexp(half x, int n);
+OVERLOADABLE half powr(half x, half y);
+OVERLOADABLE half pow(half x, half y);
+//no pow, we use powr instead
+OVERLOADABLE half fabs(half x);
+OVERLOADABLE half trunc(half x);
+OVERLOADABLE half round(half x);
+OVERLOADABLE half floor(half x);
+OVERLOADABLE half ceil(half x);
+OVERLOADABLE half log(half x);
+OVERLOADABLE half log2(half x);
+OVERLOADABLE half log10(half x);
+OVERLOADABLE half exp(half x);
+OVERLOADABLE half exp10(half x);
+OVERLOADABLE half expm1(half x);
+OVERLOADABLE half fmin(half a, half b);
+OVERLOADABLE half fmax(half a, half b);
+OVERLOADABLE half fma(half a, half b, half c);
+OVERLOADABLE half fdim(half x, half y);
+OVERLOADABLE half maxmag(half x, half y);
+OVERLOADABLE half minmag(half x, half y);
+OVERLOADABLE half exp2(half x);
+OVERLOADABLE half mad(half a, half b, half c);
+OVERLOADABLE half sin(half x);
+OVERLOADABLE half cos(half x);
+OVERLOADABLE half tan(half x);
+OVERLOADABLE half tgamma(half x);
+OVERLOADABLE half lgamma(half x);
+OVERLOADABLE half log1p(half x);
+OVERLOADABLE half logb(half x);
+OVERLOADABLE int ilogb(half x);
+OVERLOADABLE half nan(ushort code);
+OVERLOADABLE half pown(half x, int n);
+OVERLOADABLE half rootn(half x, int n);
+OVERLOADABLE half hypot(half x, half y);
+OVERLOADABLE half nextafter(half x, half y);
+OVERLOADABLE half sqrt(half x);
+OVERLOADABLE half rsqrt(half x);
+
+
+// native half
+OVERLOADABLE half native_cos(half x);
+OVERLOADABLE half native_divide(half x, half y);
+OVERLOADABLE half native_exp(half x);
+OVERLOADABLE half native_exp2(half x);
+OVERLOADABLE half native_exp10(half x);
+OVERLOADABLE half native_log(half x);
+OVERLOADABLE half native_log2(half x);
+OVERLOADABLE half native_log10(half x);
+OVERLOADABLE half native_powr(half x, half y);
+OVERLOADABLE half native_recip(half x);
+OVERLOADABLE half native_rsqrt(half x);
+OVERLOADABLE half native_sin(half x);
+OVERLOADABLE half native_sqrt(half x);
+OVERLOADABLE half native_tan(half x);
+
+// half accuracy
+OVERLOADABLE float half_cos(float x);
+OVERLOADABLE float half_divide(float x, float y);
+OVERLOADABLE float half_exp(float x);
+OVERLOADABLE float half_exp2(float x);
+OVERLOADABLE float half_exp10(float x);
+OVERLOADABLE float half_log(float x);
+OVERLOADABLE float half_log2(float x);
+OVERLOADABLE float half_log10(float x);
+OVERLOADABLE float half_powr(float x, float y);
+OVERLOADABLE float half_recip(float x);
+OVERLOADABLE float half_rsqrt(float x);
+OVERLOADABLE float half_sin(float x);
+OVERLOADABLE float half_sqrt(float x);
+OVERLOADABLE float half_tan(float x);
+
+
OVERLOADABLE double acos(double x);
OVERLOADABLE double acospi(double x);
OVERLOADABLE double acosh(double x);
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