From d4d26acd8a65fe6b641dbd448b734ad23b3242ad Mon Sep 17 00:00:00 2001 From: Wilco Dijkstra Date: Tue, 3 Apr 2018 16:41:36 +0100 Subject: [PATCH 4/7] sin/cos slow paths: remove slow paths from huge range reduction For huge inputs use the improved do_sincos function as well. Now no cases use the correction factor returned by do_sin, do_cos and TAYLOR_SIN, so remove it. * sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SIN): Remove cor parameter. (do_cos): Remove corp parameter and calculations. (do_sin): Likewise. (do_sincos): Remove cor variable. (__sin): Use do_sincos for huge inputs. (__cos): Likewise. * sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Likewise. (reduce_and_compute_sincos): Remove unused function. --- sysdeps/ieee754/dbl-64/s_sin.c | 60 +++++++++++++++++++-------------------- sysdeps/ieee754/dbl-64/s_sincos.c | 38 ++++--------------------- 2 files changed, 34 insertions(+), 64 deletions(-) diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index b8c366a6f0..7d0f375ca1 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -66,12 +66,11 @@ a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2 The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so - on. The result is returned to LHS and correction in COR. */ -#define TAYLOR_SIN(xx, a, da, cor) \ + on. The result is returned to LHS. */ +#define TAYLOR_SIN(xx, a, da) \ ({ \ double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \ double res = (a) + t; \ - (cor) = ((a) - res) + t; \ res; \ }) @@ -145,10 +144,10 @@ static double cslow2 (double x); /* Given a number partitioned into X and DX, this function computes the cosine of the number by combining the sin and cos of X (as computed by a variation of the Taylor series) with the values looked up from the sin/cos table to - get the result in RES and a correction value in COR. */ + get the result. */ static inline double __always_inline -do_cos (double x, double dx, double *corp) +do_cos (double x, double dx) { mynumber u; @@ -158,16 +157,13 @@ do_cos (double x, double dx, double *corp) u.x = big + fabs (x); x = fabs (x) - (u.x - big) + dx; - double xx, s, sn, ssn, c, cs, ccs, res, cor; + double xx, s, sn, ssn, c, cs, ccs, cor; xx = x * x; s = x + x * xx * (sn3 + xx * sn5); c = xx * (cs2 + xx * (cs4 + xx * cs6)); SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); cor = (ccs - s * ssn - cs * c) - sn * s; - res = cs + cor; - cor = (cs - res) + cor; - *corp = cor; - return res; + return cs + cor; } /* A more precise variant of DO_COS. EPS is the adjustment to the correction @@ -207,10 +203,10 @@ do_cos_slow (double x, double dx, double eps, double *corp) /* Given a number partitioned into X and DX, this function computes the sine of the number by combining the sin and cos of X (as computed by a variation of the Taylor series) with the values looked up from the sin/cos table to get - the result in RES and a correction value in COR. */ + the result. */ static inline double __always_inline -do_sin (double x, double dx, double *corp) +do_sin (double x, double dx) { mynumber u; @@ -219,16 +215,13 @@ do_sin (double x, double dx, double *corp) u.x = big + fabs (x); x = fabs (x) - (u.x - big); - double xx, s, sn, ssn, c, cs, ccs, cor, res; + double xx, s, sn, ssn, c, cs, ccs, cor; xx = x * x; s = x + (dx + x * xx * (sn3 + xx * sn5)); c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); cor = (ssn + s * ccs - sn * c) + cs * s; - res = sn + cor; - cor = (sn - res) + cor; - *corp = cor; - return res; + return sn + cor; } /* A more precise variant of DO_SIN. EPS is the adjustment to the correction @@ -330,19 +323,19 @@ static double __always_inline do_sincos (double a, double da, int4 n) { - double retval, cor; + double retval; if (n & 1) /* Max ULP is 0.513. */ - retval = do_cos (a, da, &cor); + retval = do_cos (a, da); else { double xx = a * a; /* Max ULP is 0.501 if xx < 0.01588, otherwise ULP is 0.518. */ if (xx < 0.01588) - retval = TAYLOR_SIN (xx, a, da, cor); + retval = TAYLOR_SIN (xx, a, da); else - retval = __copysign (do_sin (a, da, &cor), a); + retval = __copysign (do_sin (a, da), a); } return (n & 2) ? -retval : retval; @@ -362,7 +355,7 @@ SECTION __sin (double x) { #ifndef IN_SINCOS - double xx, t, a, da, cor; + double xx, t, a, da; mynumber u; int4 k, m, n; double retval = 0; @@ -396,7 +389,7 @@ __sin (double x) else if (k < 0x3feb6000) { /* Max ULP is 0.548. */ - retval = __copysign (do_sin (x, 0, &cor), x); + retval = __copysign (do_sin (x, 0), x); } /* else if (k < 0x3feb6000) */ /*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ @@ -404,7 +397,7 @@ __sin (double x) { t = hp0 - fabs (x); /* Max ULP is 0.51. */ - retval = __copysign (do_cos (t, hp1, &cor), x); + retval = __copysign (do_cos (t, hp1), x); } /* else if (k < 0x400368fd) */ #ifndef IN_SINCOS @@ -417,8 +410,10 @@ __sin (double x) /* --------------------105414350 <|x| <2^1024------------------------------*/ else if (k < 0x7ff00000) - retval = reduce_and_compute (x, false); - + { + n = __branred (x, &a, &da); + retval = do_sincos (a, da, n); + } /*--------------------- |x| > 2^1024 ----------------------------------*/ else { @@ -445,7 +440,7 @@ SECTION #endif __cos (double x) { - double y, xx, cor, a, da; + double y, xx, a, da; mynumber u; #ifndef IN_SINCOS int4 k, m, n; @@ -470,7 +465,7 @@ __cos (double x) else if (k < 0x3feb6000) { /* 2^-27 < |x| < 0.855469 */ /* Max ULP is 0.51. */ - retval = do_cos (x, 0, &cor); + retval = do_cos (x, 0); } /* else if (k < 0x3feb6000) */ else if (k < 0x400368fd) @@ -482,9 +477,9 @@ __cos (double x) /* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise. Range reduction uses 106 bits here which is sufficient. */ if (xx < 0.01588) - retval = TAYLOR_SIN (xx, a, da, cor); + retval = TAYLOR_SIN (xx, a, da); else - retval = __copysign (do_sin (a, da, &cor), a); + retval = __copysign (do_sin (a, da), a); } /* else if (k < 0x400368fd) */ @@ -497,7 +492,10 @@ __cos (double x) /* 105414350 <|x| <2^1024 */ else if (k < 0x7ff00000) - retval = reduce_and_compute (x, true); + { + n = __branred (x, &a, &da); + retval = do_sincos (a, da, n + 1); + } else { diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c index 4f032d2e42..4335ecbba3 100644 --- a/sysdeps/ieee754/dbl-64/s_sincos.c +++ b/sysdeps/ieee754/dbl-64/s_sincos.c @@ -28,37 +28,6 @@ #define IN_SINCOS 1 #include "s_sin.c" -/* Consolidated version of reduce_and_compute in s_sin.c that does range - reduction only once and computes sin and cos together. */ -static inline void -__always_inline -reduce_and_compute_sincos (double x, double *sinx, double *cosx) -{ - double a, da; - unsigned int n = __branred (x, &a, &da); - - n = n & 3; - - if (n == 1 || n == 2) - { - a = -a; - da = -da; - } - - if (n & 1) - { - double *temp = cosx; - cosx = sinx; - sinx = temp; - } - - if (a * a < 0.01588) - *sinx = bsloww (a, da, x, n); - else - *sinx = bsloww1 (a, da, x, n); - *cosx = bsloww2 (a, da, x, n); -} - void __sincos (double x, double *sinx, double *cosx) { @@ -88,8 +57,11 @@ __sincos (double x, double *sinx, double *cosx) } if (k < 0x7ff00000) { - reduce_and_compute_sincos (x, sinx, cosx); - return; + double a, da; + int4 n = __branred (x, &a, &da); + + *sinx = do_sincos (a, da, n); + *cosx = do_sincos (a, da, n + 1); } if (isinf (x)) -- cgit v1.2.1