summaryrefslogtreecommitdiff
path: root/libc/sysdeps/ieee754/dbl-64
diff options
context:
space:
mode:
Diffstat (limited to 'libc/sysdeps/ieee754/dbl-64')
-rw-r--r--libc/sysdeps/ieee754/dbl-64/e_gamma_r.c140
-rw-r--r--libc/sysdeps/ieee754/dbl-64/e_remainder.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/gamma_product.c75
-rw-r--r--libc/sysdeps/ieee754/dbl-64/gamma_productf.c46
-rw-r--r--libc/sysdeps/ieee754/dbl-64/s_sin.c2116
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/math_private.h1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c1
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c2
-rw-r--r--libc/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c2
14 files changed, 1478 insertions, 911 deletions
diff --git a/libc/sysdeps/ieee754/dbl-64/e_gamma_r.c b/libc/sysdeps/ieee754/dbl-64/e_gamma_r.c
index 987355175..5b17f7b5a 100644
--- a/libc/sysdeps/ieee754/dbl-64/e_gamma_r.c
+++ b/libc/sysdeps/ieee754/dbl-64/e_gamma_r.c
@@ -19,14 +19,104 @@
#include <math.h>
#include <math_private.h>
+#include <float.h>
+/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
+ approximation to gamma function. */
+
+static const double gamma_coeff[] =
+ {
+ 0x1.5555555555555p-4,
+ -0xb.60b60b60b60b8p-12,
+ 0x3.4034034034034p-12,
+ -0x2.7027027027028p-12,
+ 0x3.72a3c5631fe46p-12,
+ -0x7.daac36664f1f4p-12,
+ };
+
+#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
+
+/* Return gamma (X), for positive X less than 184, in the form R *
+ 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
+ avoid overflow or underflow in intermediate calculations. */
+
+static double
+gamma_positive (double x, int *exp2_adj)
+{
+ int local_signgam;
+ if (x < 0.5)
+ {
+ *exp2_adj = 0;
+ return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
+ }
+ else if (x <= 1.5)
+ {
+ *exp2_adj = 0;
+ return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
+ }
+ else if (x < 6.5)
+ {
+ /* Adjust into the range for using exp (lgamma). */
+ *exp2_adj = 0;
+ double n = __ceil (x - 1.5);
+ double x_adj = x - n;
+ double eps;
+ double prod = __gamma_product (x_adj, 0, n, &eps);
+ return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
+ * prod * (1.0 + eps));
+ }
+ else
+ {
+ double eps = 0;
+ double x_eps = 0;
+ double x_adj = x;
+ double prod = 1;
+ if (x < 12.0)
+ {
+ /* Adjust into the range for applying Stirling's
+ approximation. */
+ double n = __ceil (12.0 - x);
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ double x_tmp = x + n;
+ x_adj = x_tmp;
+ x_eps = (x - (x_adj - n));
+ prod = __gamma_product (x_adj - n, x_eps, n, &eps);
+ }
+ /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
+ Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
+ starting by computing pow (X_ADJ, X_ADJ) with a power of 2
+ factored out. */
+ double exp_adj = -eps;
+ double x_adj_int = __round (x_adj);
+ double x_adj_frac = x_adj - x_adj_int;
+ int x_adj_log2;
+ double x_adj_mant = __frexp (x_adj, &x_adj_log2);
+ if (x_adj_mant < M_SQRT1_2)
+ {
+ x_adj_log2--;
+ x_adj_mant *= 2.0;
+ }
+ *exp2_adj = x_adj_log2 * (int) x_adj_int;
+ double ret = (__ieee754_pow (x_adj_mant, x_adj)
+ * __ieee754_exp2 (x_adj_log2 * x_adj_frac)
+ * __ieee754_exp (-x_adj)
+ * __ieee754_sqrt (2 * M_PI / x_adj)
+ / prod);
+ exp_adj += x_eps * __ieee754_log (x);
+ double bsum = gamma_coeff[NCOEFF - 1];
+ double x_adj2 = x_adj * x_adj;
+ for (size_t i = 1; i <= NCOEFF - 1; i++)
+ bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
+ exp_adj += bsum / x_adj;
+ return ret + ret * __expm1 (exp_adj);
+ }
+}
double
__ieee754_gamma_r (double x, int *signgamp)
{
- /* We don't have a real gamma implementation now. We'll use lgamma
- and the exp function. But due to the required boundary
- conditions we must check some values separately. */
int32_t hx;
u_int32_t lx;
@@ -51,8 +141,48 @@ __ieee754_gamma_r (double x, int *signgamp)
*signgamp = 0;
return x - x;
}
+ if (__builtin_expect ((hx & 0x7ff00000) == 0x7ff00000, 0))
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ *signgamp = 0;
+ return x + x;
+ }
- /* XXX FIXME. */
- return __ieee754_exp (__ieee754_lgamma_r (x, signgamp));
+ if (x >= 172.0)
+ {
+ /* Overflow. */
+ *signgamp = 0;
+ return DBL_MAX * DBL_MAX;
+ }
+ else if (x > 0.0)
+ {
+ *signgamp = 0;
+ int exp2_adj;
+ double ret = gamma_positive (x, &exp2_adj);
+ return __scalbn (ret, exp2_adj);
+ }
+ else if (x >= -DBL_EPSILON / 4.0)
+ {
+ *signgamp = 0;
+ return 1.0 / x;
+ }
+ else
+ {
+ double tx = __trunc (x);
+ *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
+ if (x <= -184.0)
+ /* Underflow. */
+ return DBL_MIN * DBL_MIN;
+ double frac = tx - x;
+ if (frac > 0.5)
+ frac = 1.0 - frac;
+ double sinpix = (frac <= 0.25
+ ? __sin (M_PI * frac)
+ : __cos (M_PI * (0.5 - frac)));
+ int exp2_adj;
+ double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj));
+ return __scalbn (ret, -exp2_adj);
+ }
}
strong_alias (__ieee754_gamma_r, __gamma_r_finite)
diff --git a/libc/sysdeps/ieee754/dbl-64/e_remainder.c b/libc/sysdeps/ieee754/dbl-64/e_remainder.c
index 39ca0c2d0..2d20bb1df 100644
--- a/libc/sysdeps/ieee754/dbl-64/e_remainder.c
+++ b/libc/sysdeps/ieee754/dbl-64/e_remainder.c
@@ -51,6 +51,7 @@ double __ieee754_remainder(double x, double y)
ky=t.i[HIGH_HALF];
/*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/
if (kx<0x7fe00000 && ky<0x7ff00000 && ky>=0x03500000) {
+ SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
if (kx+0x00100000<ky) return x;
if ((kx-0x01500000)<ky) {
z=x/t.x;
diff --git a/libc/sysdeps/ieee754/dbl-64/gamma_product.c b/libc/sysdeps/ieee754/dbl-64/gamma_product.c
new file mode 100644
index 000000000..2a3fc1aff
--- /dev/null
+++ b/libc/sysdeps/ieee754/dbl-64/gamma_product.c
@@ -0,0 +1,75 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Calculate X * Y exactly and store the result in *HI + *LO. It is
+ given that the values are small enough that no overflow occurs and
+ large enough (or zero) that no underflow occurs. */
+
+static void
+mul_split (double *hi, double *lo, double x, double y)
+{
+#ifdef __FP_FAST_FMA
+ /* Fast built-in fused multiply-add. */
+ *hi = x * y;
+ *lo = __builtin_fma (x, y, -*hi);
+#elif defined FP_FAST_FMA
+ /* Fast library fused multiply-add, compiler before GCC 4.6. */
+ *hi = x * y;
+ *lo = __fma (x, y, -*hi);
+#else
+ /* Apply Dekker's algorithm. */
+ *hi = x * y;
+# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+ double x1 = x * C;
+ double y1 = y * C;
+# undef C
+ x1 = (x - x1) + x1;
+ y1 = (y - y1) + y1;
+ double x2 = x - x1;
+ double y2 = y - y1;
+ *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
+#endif
+}
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+double
+__gamma_product (double x, double x_eps, int n, double *eps)
+{
+ SET_RESTORE_ROUND (FE_TONEAREST);
+ double ret = x;
+ *eps = x_eps / x;
+ for (int i = 1; i < n; i++)
+ {
+ *eps += x_eps / (x + i);
+ double lo;
+ mul_split (&ret, &lo, ret, x + i);
+ *eps += lo / ret;
+ }
+ return ret;
+}
diff --git a/libc/sysdeps/ieee754/dbl-64/gamma_productf.c b/libc/sysdeps/ieee754/dbl-64/gamma_productf.c
new file mode 100644
index 000000000..46072f16e
--- /dev/null
+++ b/libc/sysdeps/ieee754/dbl-64/gamma_productf.c
@@ -0,0 +1,46 @@
+/* Compute a product of X, X+1, ..., with an error estimate.
+ Copyright (C) 2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+
+float
+__gamma_productf (float x, float x_eps, int n, float *eps)
+{
+ double x_full = (double) x + (double) x_eps;
+ double ret = x_full;
+ for (int i = 1; i < n; i++)
+ ret *= x_full + i;
+
+#if FLT_EVAL_METHOD != 0
+ volatile
+#endif
+ float fret = ret;
+ *eps = (ret - fret) / fret;
+
+ return fret;
+}
diff --git a/libc/sysdeps/ieee754/dbl-64/s_sin.c b/libc/sysdeps/ieee754/dbl-64/s_sin.c
index 5038b7261..5c388c8b9 100644
--- a/libc/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/libc/sysdeps/ieee754/dbl-64/s_sin.c
@@ -66,299 +66,359 @@ extern const union
} __sincostab attribute_hidden;
static const double
- sn3 = -1.66666666666664880952546298448555E-01,
- sn5 = 8.33333214285722277379541354343671E-03,
- cs2 = 4.99999999999999999999950396842453E-01,
- cs4 = -4.16666666666664434524222570944589E-02,
- cs6 = 1.38888874007937613028114285595617E-03;
-
-void __dubsin(double x, double dx, double w[]);
-void __docos(double x, double dx, double w[]);
-double __mpsin(double x, double dx);
-double __mpcos(double x, double dx);
-double __mpsin1(double x);
-double __mpcos1(double x);
-static double slow(double x);
-static double slow1(double x);
-static double slow2(double x);
-static double sloww(double x, double dx, double orig);
-static double sloww1(double x, double dx, double orig);
-static double sloww2(double x, double dx, double orig, int n);
-static double bsloww(double x, double dx, double orig, int n);
-static double bsloww1(double x, double dx, double orig, int n);
-static double bsloww2(double x, double dx, double orig, int n);
-int __branred(double x, double *a, double *aa);
-static double cslow2(double x);
-static double csloww(double x, double dx, double orig);
-static double csloww1(double x, double dx, double orig);
-static double csloww2(double x, double dx, double orig, int n);
+ sn3 = -1.66666666666664880952546298448555E-01,
+ sn5 = 8.33333214285722277379541354343671E-03,
+ cs2 = 4.99999999999999999999950396842453E-01,
+ cs4 = -4.16666666666664434524222570944589E-02,
+ cs6 = 1.38888874007937613028114285595617E-03;
+
+void __dubsin (double x, double dx, double w[]);
+void __docos (double x, double dx, double w[]);
+double __mpsin (double x, double dx);
+double __mpcos (double x, double dx);
+double __mpsin1 (double x);
+double __mpcos1 (double x);
+static double slow (double x);
+static double slow1 (double x);
+static double slow2 (double x);
+static double sloww (double x, double dx, double orig);
+static double sloww1 (double x, double dx, double orig);
+static double sloww2 (double x, double dx, double orig, int n);
+static double bsloww (double x, double dx, double orig, int n);
+static double bsloww1 (double x, double dx, double orig, int n);
+static double bsloww2 (double x, double dx, double orig, int n);
+int __branred (double x, double *a, double *aa);
+static double cslow2 (double x);
+static double csloww (double x, double dx, double orig);
+static double csloww1 (double x, double dx, double orig);
+static double csloww2 (double x, double dx, double orig, int n);
+
/*******************************************************************/
/* An ultimate sin routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of sin(x) */
/*******************************************************************/
double
SECTION
-__sin(double x){
- double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
- mynumber u,v;
- int4 k,m,n;
- double retval = 0;
-
- SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
-
- u.x = x;
- m = u.i[HIGH_HALF];
- k = 0x7fffffff&m; /* no sign */
- if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
- { retval = x; goto ret; }
+__sin (double x)
+{
+ double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+ xn2;
+ mynumber u, v;
+ int4 k, m, n;
+ double retval = 0;
+
+ SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
+
+ u.x = x;
+ m = u.i[HIGH_HALF];
+ k = 0x7fffffff & m; /* no sign */
+ if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
+ {
+ retval = x;
+ goto ret;
+ }
/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
- else if (k < 0x3fd00000){
- xx = x*x;
- /*Taylor series */
- t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x);
- res = x+t;
- cor = (x-res)+t;
- retval = (res == res + 1.07*cor)? res : slow(x);
- goto ret;
- } /* else if (k < 0x3fd00000) */
+ else if (k < 0x3fd00000)
+ {
+ xx = x * x;
+ /*Taylor series. */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+ * (xx * x));
+ res = x + t;
+ cor = (x - res) + t;
+ retval = (res == res + 1.07 * cor) ? res : slow (x);
+ goto ret;
+ } /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
- else if (k < 0x3feb6000) {
- u.x=(m>0)?big.x+x:big.x-x;
- y=(m>0)?x-(u.x-big.x):x+(u.x-big.x);
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=(m>0)?__sincostab.x[k]:-__sincostab.x[k];
- ssn=(m>0)?__sincostab.x[k+1]:-__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- retval = (res==res+1.096*cor)? res : slow1(x);
- goto ret;
- } /* else if (k < 0x3feb6000) */
+ else if (k < 0x3feb6000)
+ {
+ u.x = (m > 0) ? big.x + x : big.x - x;
+ y = (m > 0) ? x - (u.x - big.x) : x + (u.x - big.x);
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = (m > 0) ? __sincostab.x[k] : -__sincostab.x[k];
+ ssn = (m > 0) ? __sincostab.x[k + 1] : -__sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ retval = (res == res + 1.096 * cor) ? res : slow1 (x);
+ goto ret;
+ } /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
- else if (k < 0x400368fd ) {
-
- y = (m>0)? hp0.x-x:hp0.x+x;
- if (y>=0) {
- u.x = big.x+y;
- y = (y-(u.x-big.x))+hp1.x;
- }
- else {
- u.x = big.x-y;
- y = (-hp1.x) - (y+(u.x-big.x));
- }
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- retval = (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x);
- goto ret;
- } /* else if (k < 0x400368fd) */
+ else if (k < 0x400368fd)
+ {
+
+ y = (m > 0) ? hp0.x - x : hp0.x + x;
+ if (y >= 0)
+ {
+ u.x = big.x + y;
+ y = (y - (u.x - big.x)) + hp1.x;
+ }
+ else
+ {
+ u.x = big.x - y;
+ y = (-hp1.x) - (y + (u.x - big.x));
+ }
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
+ goto ret;
+ } /* else if (k < 0x400368fd) */
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
- else if (k < 0x419921FB ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (x - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*mp3.x;
- a=y-da;
- da = (y-a)-da;
- eps = ABS(x)*1.2e-30;
-
- switch (n) { /* quarter of unit circle */
- case 0:
- case 2:
- xx = a*a;
- if (n) {a=-a;da=-da;}
- if (xx < 0.01588) {
- /*Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : sloww(a,da,x);
+ else if (k < 0x419921FB)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (x - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * mp3.x;
+ a = y - da;
+ da = (y - a) - da;
+ eps = ABS (x) * 1.2e-30;
+
+ switch (n)
+ { /* quarter of unit circle */
+ case 0:
+ case 2:
+ xx = a * a;
+ if (n)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ /*Taylor series */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : sloww (a, da, x);
goto ret;
}
- else {
- if (a>0)
- {m=1;t=a;db=da;}
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
else
- {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x);
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : sloww1 (a, da, x));
goto ret;
}
- break;
-
- case 1:
- case 3:
- if (a<0)
- {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n);
- goto ret;
-
- break;
-
- }
-
- } /* else if (k < 0x419921FB ) */
+ break;
+
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : sloww2 (a, da, x, n));
+ goto ret;
+
+ break;
+ }
+
+ } /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
- else if (k < 0x42F00000 ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- xn1 = (xn+8.0e22)-8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
- n =v.i[LOW_HALF]&3;
- da = xn1*pp3.x;
- t=y-da;
- da = (y-t)-da;
- da = (da - xn2*pp3.x) -xn*pp4.x;
- a = t+da;
- da = (t-a)+da;
- eps = 1.0e-24;
-
- switch (n) {
- case 0:
- case 2:
- xx = a*a;
- if (n) {a=-a;da=-da;}
- if (xx < 0.01588) {
+ else if (k < 0x42F00000)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ xn1 = (xn + 8.0e22) - 8.0e22;
+ xn2 = xn - xn1;
+ y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+ n = v.i[LOW_HALF] & 3;
+ da = xn1 * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ da = (da - xn2 * pp3.x) - xn * pp4.x;
+ a = t + da;
+ da = (t - a) + da;
+ eps = 1.0e-24;
+
+ switch (n)
+ {
+ case 0:
+ case 2:
+ xx = a * a;
+ if (n)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
/* Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : bsloww(a,da,x,n);
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : bsloww (a, da, x, n);
goto ret;
}
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : bsloww1 (a, da, x, n));
goto ret;
- }
- break;
-
- case 1:
- case 3:
- if (a<0)
- {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n);
- goto ret;
-
- break;
-
- }
-
- } /* else if (k < 0x42F00000 ) */
+ }
+ break;
+
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : bsloww2 (a, da, x, n));
+ goto ret;
+
+ break;
+ }
+ } /* else if (k < 0x42F00000 ) */
/* -----------------281474976710656 <|x| <2^1024----------------------------*/
- else if (k < 0x7ff00000) {
-
- n = __branred(x,&a,&da);
- switch (n) {
- case 0:
- if (a*a < 0.01588) retval = bsloww(a,da,x,n);
- else retval = bsloww1(a,da,x,n);
- goto ret;
- break;
- case 2:
- if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
- else retval = bsloww1(-a,-da,x,n);
- goto ret;
- break;
-
- case 1:
- case 3:
- retval = bsloww2(a,da,x,n);
- goto ret;
- break;
- }
-
- } /* else if (k < 0x7ff00000 ) */
+ else if (k < 0x7ff00000)
+ {
+ n = __branred (x, &a, &da);
+ switch (n)
+ {
+ case 0:
+ if (a * a < 0.01588)
+ retval = bsloww (a, da, x, n);
+ else
+ retval = bsloww1 (a, da, x, n);
+ goto ret;
+ break;
+ case 2:
+ if (a * a < 0.01588)
+ retval = bsloww (-a, -da, x, n);
+ else
+ retval = bsloww1 (-a, -da, x, n);
+ goto ret;
+ break;
-/*--------------------- |x| > 2^1024 ----------------------------------*/
- else {
- if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
- __set_errno (EDOM);
- retval = x / x;
+ case 1:
+ case 3:
+ retval = bsloww2 (a, da, x, n);
goto ret;
+ break;
}
+ } /* else if (k < 0x7ff00000 ) */
+
+/*--------------------- |x| > 2^1024 ----------------------------------*/
+ else
+ {
+ if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+ __set_errno (EDOM);
+ retval = x / x;
+ goto ret;
+ }
- ret:
- return retval;
+ret:
+ return retval;
}
@@ -369,11 +429,12 @@ __sin(double x){
double
SECTION
-__cos(double x)
+__cos (double x)
{
- double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
- mynumber u,v;
- int4 k,m,n;
+ double y, xx, res, t, cor, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+ xn2;
+ mynumber u, v;
+ int4 k, m, n;
double retval = 0;
@@ -381,251 +442,318 @@ __cos(double x)
u.x = x;
m = u.i[HIGH_HALF];
- k = 0x7fffffff&m;
-
- if (k < 0x3e400000 ) { retval = 1.0; goto ret; } /* |x|<2^-27 => cos(x)=1 */
-
- else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */
- y=ABS(x);
- u.x = big.x+y;
- y = y-(u.x-big.x);
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- retval = (res==res+1.020*cor)? res : cslow2(x);
- goto ret;
-
-} /* else if (k < 0x3feb6000) */
-
- else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */;
- y=hp0.x-ABS(x);
- a=y+hp1.x;
- da=(y-a)+hp1.x;
- xx=a*a;
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31;
- retval = (res == res + cor)? res : csloww(a,da,x);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31;
- retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
- goto ret;
-}
+ k = 0x7fffffff & m;
-} /* else if (k < 0x400368fd) */
-
-
- else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (x - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*mp3.x;
- a=y-da;
- da = (y-a)-da;
- eps = ABS(x)*1.2e-30;
-
- switch (n) {
- case 1:
- case 3:
- xx = a*a;
- if (n == 1) {a=-a;da=-da;}
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : csloww(a,da,x);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
- goto ret;
- }
- break;
-
- case 0:
- case 2:
- if (a<0) {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n);
+ if (k < 0x3e400000)
+ {
+ retval = 1.0;
+ goto ret;
+ } /* |x|<2^-27 => cos(x)=1 */
+
+ else if (k < 0x3feb6000)
+ { /* 2^-27 < |x| < 0.855469 */
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
goto ret;
+ } /* else if (k < 0x3feb6000) */
+
+ else if (k < 0x400368fd)
+ { /* 0.855469 <|x|<2.426265 */ ;
+ y = hp0.x - ABS (x);
+ a = y + hp1.x;
+ da = (y - a) + hp1.x;
+ xx = a * a;
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+ * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
+ retval = (res == res + cor) ? res : csloww (a, da, x);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : csloww1 (a, da, x));
+ goto ret;
+ }
- break;
+ } /* else if (k < 0x400368fd) */
- }
- } /* else if (k < 0x419921FB ) */
-
-
- else if (k < 0x42F00000 ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- xn1 = (xn+8.0e22)-8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
- n =v.i[LOW_HALF]&3;
- da = xn1*pp3.x;
- t=y-da;
- da = (y-t)-da;
- da = (da - xn2*pp3.x) -xn*pp4.x;
- a = t+da;
- da = (t-a)+da;
- eps = 1.0e-24;
-
- switch (n) {
- case 1:
- case 3:
- xx = a*a;
- if (n==1) {a=-a;da=-da;}
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : bsloww(a,da,x,n);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
- goto ret;
- }
- break;
-
- case 0:
- case 2:
- if (a<0) {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n);
- goto ret;
- break;
+ else if (k < 0x419921FB)
+ { /* 2.426265<|x|< 105414350 */
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (x - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * mp3.x;
+ a = y - da;
+ da = (y - a) - da;
+ eps = ABS (x) * 1.2e-30;
+
+ switch (n)
+ {
+ case 1:
+ case 3:
+ xx = a * a;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : csloww (a, da, x);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : csloww1 (a, da, x));
+ goto ret;
+ }
+ break;
+
+ case 0:
+ case 2:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n) ? -res : res)
+ : csloww2 (a, da, x, n));
+ goto ret;
- }
+ break;
+ }
+ } /* else if (k < 0x419921FB ) */
- } /* else if (k < 0x42F00000 ) */
+ else if (k < 0x42F00000)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ xn1 = (xn + 8.0e22) - 8.0e22;
+ xn2 = xn - xn1;
+ y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+ n = v.i[LOW_HALF] & 3;
+ da = xn1 * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ da = (da - xn2 * pp3.x) - xn * pp4.x;
+ a = t + da;
+ da = (t - a) + da;
+ eps = 1.0e-24;
+
+ switch (n)
+ {
+ case 1:
+ case 3:
+ xx = a * a;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : bsloww1 (a, da, x, n));
+ goto ret;
+ }
+ break;
+
+ case 0:
+ case 2:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n) ? -res : res)
+ : bsloww2 (a, da, x, n));
+ goto ret;
+ break;
+ }
+ } /* else if (k < 0x42F00000 ) */
+
+ else if (k < 0x7ff00000)
+ { /* 281474976710656 <|x| <2^1024 */
+
+ n = __branred (x, &a, &da);
+ switch (n)
+ {
+ case 1:
+ if (a * a < 0.01588)
+ retval = bsloww (-a, -da, x, n);
+ else
+ retval = bsloww1 (-a, -da, x, n);
+ goto ret;
+ break;
+ case 3:
+ if (a * a < 0.01588)
+ retval = bsloww (a, da, x, n);
+ else
+ retval = bsloww1 (a, da, x, n);
+ goto ret;
+ break;
- else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */
+ case 0:
+ case 2:
+ retval = bsloww2 (a, da, x, n);
+ goto ret;
+ break;
+ }
+ } /* else if (k < 0x7ff00000 ) */
- n = __branred(x,&a,&da);
- switch (n) {
- case 1:
- if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
- else retval = bsloww1(-a,-da,x,n);
+ else
+ {
+ if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+ __set_errno (EDOM);
+ retval = x / x; /* |x| > 2^1024 */
goto ret;
- break;
- case 3:
- if (a*a < 0.01588) retval = bsloww(a,da,x,n);
- else retval = bsloww1(a,da,x,n);
- goto ret;
- break;
-
- case 0:
- case 2:
- retval = bsloww2(a,da,x,n);
- goto ret;
- break;
}
- } /* else if (k < 0x7ff00000 ) */
-
-
-
-
- else {
- if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
- __set_errno (EDOM);
- retval = x / x; /* |x| > 2^1024 */
- goto ret;
- }
-
- ret:
+ret:
return retval;
}
@@ -636,25 +764,32 @@ __cos(double x)
static double
SECTION
-slow(double x) {
-static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2];
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=x-x1;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- if (res == res + 1.0007*cor) return res;
- else {
- __dubsin(ABS(x),0,w);
- if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+slow (double x)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2];
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = x - x1;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ if (res == res + 1.0007 * cor)
+ return res;
+ else
+ {
+ __dubsin (ABS (x), 0, w);
+ if (w[0] == w[0] + 1.000000001 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/*******************************************************************************/
/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */
/* and if result still doesn't accurate enough by mpsin or dubsin */
@@ -662,88 +797,102 @@ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
static double
SECTION
-slow1(double x) {
+slow1 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k]; /* Data */
- ssn=__sincostab.x[k+1]; /* from */
- cs=__sincostab.x[k+2]; /* tables */
- ccs=__sincostab.x[k+3]; /* __sincostab.tbl */
- y1 = (y+t22)-t22;
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k]; /* Data */
+ ssn = __sincostab.x[k + 1]; /* from */
+ cs = __sincostab.x[k + 2]; /* tables */
+ ccs = __sincostab.x[k + 3]; /* __sincostab.tbl */
+ y1 = (y + t22) - t22;
y2 = y - y1;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),0,w);
- if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/**************************************************************************/
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */
/* and if result still doesn't accurate enough by mpsin or dubsin */
/**************************************************************************/
static double
SECTION
-slow2(double x) {
+slow2 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res, del;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- y = hp0.x-y;
- if (y>=0) {
- u.x = big.x+y;
- y = y-(u.x-big.x);
- del = hp1.x;
- }
- else {
- u.x = big.x-y;
- y = -(y+(u.x-big.x));
- del = -hp1.x;
- }
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+del;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor) return (x>0)?res:-res;
- else {
- y=ABS(x)-hp0.x;
- y1=y-hp1.x;
- y2=(y-y1)-hp1.x;
- __docos(y1,y2,w);
- if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+ y = ABS (x);
+ y = hp0.x - y;
+ if (y >= 0)
+ {
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ del = hp1.x;
+ }
+ else
+ {
+ u.x = big.x - y;
+ y = -(y + (u.x - big.x));
+ del = -hp1.x;
+ }
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * del + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + del;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ y = ABS (x) - hp0.x;
+ y1 = y - hp1.x;
+ y2 = (y - y1) - hp1.x;
+ __docos (y1, y2, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
/* to use Taylor series around zero and (x+dx) */
@@ -754,46 +903,74 @@ slow2(double x) {
static double
SECTION
-sloww(double x,double dx, double orig) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
- union {int4 i[2]; double x;} v;
+sloww (double x, double dx, double orig)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ union
+ {
+ int4 i[2];
+ double x;
+ } v;
int4 n;
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else {
- t = (orig*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (orig - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*pp3.x;
- t=y-da;
- da = (y-t)-da;
- y = xn*pp4.x;
- a = t - y;
- da = ((t-a)-y)+da;
- if (n&2) {a=-a; da=-da;}
- (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
- if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
- else return __mpsin1(orig);
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ cor =
+ (cor >
+ 0) ? 1.0005 * cor + ABS (orig) * 3.1e-30 : 1.0005 * cor -
+ ABS (orig) * 3.1e-30;
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ {
+ t = (orig * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (orig - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4.x;
+ a = t - y;
+ da = ((t - a) - y) + da;
+ if (n & 2)
+ {
+ a = -a;
+ da = -da;
+ }
+ (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+ if (w[0] == w[0] + cor)
+ return (a > 0) ? w[0] : -w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
- }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x in first or */
/* third quarter of unit circle.Routine receive also (right argument) the */
@@ -803,41 +980,58 @@ sloww(double x,double dx, double orig) {
static double
SECTION
-sloww1(double x, double dx, double orig) {
+sloww1 (double x, double dx, double orig)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return __mpsin1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
/* fourth quarter of unit circle.Routine receive also the original value */
@@ -847,42 +1041,59 @@ sloww1(double x, double dx, double orig) {
static double
SECTION
-sloww2(double x, double dx, double orig, int n) {
+sloww2 (double x, double dx, double orig, int n)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (n&2)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
- else return __mpsin1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (n & 2) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+ if (w[0] == w[0] + cor)
+ return (n & 2) ? -w[0] : w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
/* is small enough to use Taylor series around zero and (x+dx) */
@@ -893,26 +1104,36 @@ sloww2(double x, double dx, double orig, int n) {
static double
SECTION
-bsloww(double x,double dx, double orig,int n) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2];
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return (n&1)?__mpcos1(orig):__mpsin1(orig);
- }
+bsloww (double x, double dx, double orig, int n)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2];
+
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000001 * w[1] - 1.1e-24;
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+ }
}
/***************************************************************************/
@@ -924,40 +1145,51 @@ bsloww(double x,double dx, double orig,int n) {
static double
SECTION
-bsloww1(double x, double dx, double orig,int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return (n&1)?__mpcos1(orig):__mpsin1(orig);
- }
+bsloww1 (double x, double dx, double orig, int n)
+{
+ mynumber u;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ static const double t22 = 6291456.0;
+ int4 k;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000005 * w[1] - 1.1e-24;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+ }
}
/***************************************************************************/
@@ -969,41 +1201,52 @@ mynumber u;
static double
SECTION
-bsloww2(double x, double dx, double orig, int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (n&2)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24;
- if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
- else return (n&1)?__mpsin1(orig):__mpcos1(orig);
- }
+bsloww2 (double x, double dx, double orig, int n)
+{
+ mynumber u;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ static const double t22 = 6291456.0;
+ int4 k;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return (n & 2) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000005 * w[1] - 1.1e-24;
+
+ if (w[0] == w[0] + cor)
+ return (n & 2) ? -w[0] : w[0];
+ else
+ return (n & 1) ? __mpsin1 (orig) : __mpcos1 (orig);
+ }
}
/************************************************************************/
@@ -1013,39 +1256,44 @@ mynumber u;
static double
SECTION
-cslow2(double x) {
+cslow2 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x = big.x+y;
- y = y-(u.x-big.x);
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
y2 = y - y1;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor)
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
return res;
- else {
- y=ABS(x);
- __docos(y,0,w);
- if (w[0] == w[0]+1.000000005*w[1]) return w[0];
- else return __mpcos(x,0);
- }
+ else
+ {
+ y = ABS (x);
+ __docos (y, 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return w[0];
+ else
+ return __mpcos (x, 0);
+ }
}
/***************************************************************************/
@@ -1058,46 +1306,78 @@ cslow2(double x) {
static double
SECTION
-csloww(double x,double dx, double orig) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
- union {int4 i[2]; double x;} v;
+csloww (double x, double dx, double orig)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ union
+ {
+ int4 i[2];
+ double x;
+ } v;
int4 n;
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- /* Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else {
- t = (orig*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (orig - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*pp3.x;
- t=y-da;
- da = (y-t)-da;
- y = xn*pp4.x;
- a = t - y;
- da = ((t-a)-y)+da;
- if (n==1) {a=-a; da=-da;}
- (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
- if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
- else return __mpcos1(orig);
+
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ /* Taylor series */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
+ else
+ cor = 1.0005 * cor - ABS (orig) * 3.1e-30;
+
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ {
+ t = (orig * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (orig - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4.x;
+ a = t - y;
+ da = ((t - a) - y) + da;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+ if (w[0] == w[0] + cor)
+ return (a > 0) ? w[0] : -w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
- }
}
/***************************************************************************/
@@ -1109,40 +1389,54 @@ csloww(double x,double dx, double orig) {
static double
SECTION
-csloww1(double x, double dx, double orig) {
+csloww1 (double x, double dx, double orig)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return __mpcos1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
@@ -1155,41 +1449,55 @@ csloww1(double x, double dx, double orig) {
static double
SECTION
-csloww2(double x, double dx, double orig, int n) {
+csloww2 (double x, double dx, double orig, int n)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (n)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (n)?-w[0]:w[0];
- else return __mpcos1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (n) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ if (w[0] == w[0] + cor)
+ return (n) ? -w[0] : w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
#ifndef __cos
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c
index a630d10fe..f686bb670 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
static const double one = 1.0, Zero[] = {0.0, -0.0,};
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
index 488a0efae..dcb7b58a1 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c
@@ -45,6 +45,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */
static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/math_private.h b/libc/sysdeps/ieee754/dbl-64/wordsize-64/math_private.h
index b66085eb1..4f9219934 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/math_private.h
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/math_private.h
@@ -1,6 +1,7 @@
#ifndef _MATH_PRIVATE_H_
#include_next <math_private.h>
+#include <stdint.h>
#ifndef __isnan
extern __always_inline int
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c
index f25ede8f9..fcf2e6d5b 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c
@@ -16,6 +16,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
#undef __finite
int
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c
index 5beccb0ac..914a3c823 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c
@@ -32,6 +32,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
/*
* floor(x)
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c
index 70a620cf6..e80b84ca0 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c
@@ -17,6 +17,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
#undef __isnan
int __isnan(double x)
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c
index 89743168c..c309e5627 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c
@@ -22,6 +22,7 @@
#include <math.h>
#include <math_private.h>
+#include <stdint.h>
static const double one = 1.0;
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c
index e9ae82bdb..29e62874b 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c
@@ -20,7 +20,7 @@
#include <math.h>
#include <math_private.h>
-
+#include <stdint.h>
static const double zero = 0.0;
diff --git a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c
index df674670e..bea796083 100644
--- a/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c
+++ b/libc/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c
@@ -20,7 +20,7 @@
#include <math.h>
#include <math_private.h>
-
+#include <stdint.h>
static const double huge = 1.0e300;
View Lorry Controller Status