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[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.
This commit is contained in:
Wilco Dijkstra
Fangrui Song
parent
76f9784421
commit
d4d26acd8a
@ -66,12 +66,11 @@
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a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2
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The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
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on. The result is returned to LHS and correction in COR. */
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#define TAYLOR_SIN(xx, a, da, cor) \
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on. The result is returned to LHS. */
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#define TAYLOR_SIN(xx, a, da) \
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({ \
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double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \
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double res = (a) + t; \
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(cor) = ((a) - res) + t; \
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res; \
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})
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@ -145,10 +144,10 @@ static double cslow2 (double x);
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/* Given a number partitioned into X and DX, this function computes the cosine
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of the number by combining the sin and cos of X (as computed by a variation
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of the Taylor series) with the values looked up from the sin/cos table to
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get the result in RES and a correction value in COR. */
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get the result. */
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static inline double
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__always_inline
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do_cos (double x, double dx, double *corp)
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do_cos (double x, double dx)
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{
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mynumber u;
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@ -158,16 +157,13 @@ do_cos (double x, double dx, double *corp)
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big) + dx;
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double xx, s, sn, ssn, c, cs, ccs, res, cor;
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double xx, s, sn, ssn, c, cs, ccs, cor;
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xx = x * x;
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s = x + x * xx * (sn3 + xx * sn5);
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c = xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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cor = (ccs - s * ssn - cs * c) - sn * s;
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res = cs + cor;
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cor = (cs - res) + cor;
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*corp = cor;
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return res;
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return cs + cor;
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}
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/* A more precise variant of DO_COS. EPS is the adjustment to the correction
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@ -207,10 +203,10 @@ do_cos_slow (double x, double dx, double eps, double *corp)
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/* Given a number partitioned into X and DX, this function computes the sine of
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the number by combining the sin and cos of X (as computed by a variation of
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the Taylor series) with the values looked up from the sin/cos table to get
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the result in RES and a correction value in COR. */
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the result. */
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static inline double
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__always_inline
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do_sin (double x, double dx, double *corp)
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do_sin (double x, double dx)
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{
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mynumber u;
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@ -219,16 +215,13 @@ do_sin (double x, double dx, double *corp)
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big);
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double xx, s, sn, ssn, c, cs, ccs, cor, res;
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double xx, s, sn, ssn, c, cs, ccs, cor;
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xx = x * x;
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s = x + (dx + x * xx * (sn3 + xx * sn5));
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c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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cor = (ssn + s * ccs - sn * c) + cs * s;
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res = sn + cor;
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cor = (sn - res) + cor;
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*corp = cor;
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return res;
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return sn + cor;
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}
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/* A more precise variant of DO_SIN. EPS is the adjustment to the correction
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@ -330,19 +323,19 @@ static double
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__always_inline
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do_sincos (double a, double da, int4 n)
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{
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double retval, cor;
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double retval;
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if (n & 1)
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/* Max ULP is 0.513. */
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retval = do_cos (a, da, &cor);
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retval = do_cos (a, da);
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else
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{
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double xx = a * a;
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/* Max ULP is 0.501 if xx < 0.01588, otherwise ULP is 0.518. */
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if (xx < 0.01588)
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retval = TAYLOR_SIN (xx, a, da, cor);
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retval = TAYLOR_SIN (xx, a, da);
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else
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retval = __copysign (do_sin (a, da, &cor), a);
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retval = __copysign (do_sin (a, da), a);
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}
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return (n & 2) ? -retval : retval;
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@ -362,7 +355,7 @@ SECTION
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__sin (double x)
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{
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#ifndef IN_SINCOS
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double xx, t, a, da, cor;
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double xx, t, a, da;
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mynumber u;
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int4 k, m, n;
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double retval = 0;
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@ -396,7 +389,7 @@ __sin (double x)
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else if (k < 0x3feb6000)
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{
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/* Max ULP is 0.548. */
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retval = __copysign (do_sin (x, 0, &cor), x);
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retval = __copysign (do_sin (x, 0), x);
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} /* else if (k < 0x3feb6000) */
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/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
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@ -404,7 +397,7 @@ __sin (double x)
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{
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t = hp0 - fabs (x);
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/* Max ULP is 0.51. */
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retval = __copysign (do_cos (t, hp1, &cor), x);
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retval = __copysign (do_cos (t, hp1), x);
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} /* else if (k < 0x400368fd) */
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#ifndef IN_SINCOS
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@ -417,8 +410,10 @@ __sin (double x)
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/* --------------------105414350 <|x| <2^1024------------------------------*/
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else if (k < 0x7ff00000)
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retval = reduce_and_compute (x, false);
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{
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n = __branred (x, &a, &da);
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retval = do_sincos (a, da, n);
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}
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/*--------------------- |x| > 2^1024 ----------------------------------*/
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else
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{
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@ -445,7 +440,7 @@ SECTION
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#endif
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__cos (double x)
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{
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double y, xx, cor, a, da;
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double y, xx, a, da;
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mynumber u;
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#ifndef IN_SINCOS
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int4 k, m, n;
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@ -470,7 +465,7 @@ __cos (double x)
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else if (k < 0x3feb6000)
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{ /* 2^-27 < |x| < 0.855469 */
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/* Max ULP is 0.51. */
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retval = do_cos (x, 0, &cor);
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retval = do_cos (x, 0);
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} /* else if (k < 0x3feb6000) */
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else if (k < 0x400368fd)
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@ -482,9 +477,9 @@ __cos (double x)
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/* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise.
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Range reduction uses 106 bits here which is sufficient. */
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if (xx < 0.01588)
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retval = TAYLOR_SIN (xx, a, da, cor);
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retval = TAYLOR_SIN (xx, a, da);
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else
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retval = __copysign (do_sin (a, da, &cor), a);
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retval = __copysign (do_sin (a, da), a);
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} /* else if (k < 0x400368fd) */
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@ -497,7 +492,10 @@ __cos (double x)
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/* 105414350 <|x| <2^1024 */
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else if (k < 0x7ff00000)
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retval = reduce_and_compute (x, true);
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{
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n = __branred (x, &a, &da);
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retval = do_sincos (a, da, n + 1);
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}
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else
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{
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@ -28,37 +28,6 @@
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#define IN_SINCOS 1
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#include "s_sin.c"
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/* Consolidated version of reduce_and_compute in s_sin.c that does range
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reduction only once and computes sin and cos together. */
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static inline void
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__always_inline
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reduce_and_compute_sincos (double x, double *sinx, double *cosx)
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{
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double a, da;
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unsigned int n = __branred (x, &a, &da);
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n = n & 3;
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if (n == 1 || n == 2)
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{
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a = -a;
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da = -da;
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}
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if (n & 1)
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{
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double *temp = cosx;
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cosx = sinx;
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sinx = temp;
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}
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if (a * a < 0.01588)
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*sinx = bsloww (a, da, x, n);
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else
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*sinx = bsloww1 (a, da, x, n);
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*cosx = bsloww2 (a, da, x, n);
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}
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void
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__sincos (double x, double *sinx, double *cosx)
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{
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@ -88,8 +57,11 @@ __sincos (double x, double *sinx, double *cosx)
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}
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if (k < 0x7ff00000)
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{
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reduce_and_compute_sincos (x, sinx, cosx);
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return;
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double a, da;
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int4 n = __branred (x, &a, &da);
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*sinx = do_sincos (a, da, n);
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*cosx = do_sincos (a, da, n + 1);
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}
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if (isinf (x))
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