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x86-64: Vectorize sincosf_poly and update s_sincosf-fma.c
Add <sincosf_poly.h> and include it in s_sincosf.h to allow vectorized
sincosf_poly. Add x86 sincosf_poly.h to vectorize sincosf_poly. On
Broadwell, bench-sincosf shows:
Before After Improvement
max 160.273 114.198 40%
min 6.25 5.625 11%
mean 13.0325 10.6462 22%
Vectorized sincosf_poly shows
Before After Improvement
max 138.653 114.198 21%
min 5.004 5.625 -11%
mean 11.5934 10.6462 9%
Tested on x86-64 and i686 as well as with build-many-glibcs.py.
* sysdeps/ieee754/flt-32/s_sincosf.h: Include <sincosf_poly.h>.
(sincos_t, sincosf_poly, sinf_poly): Moved to ...
* sysdeps/ieee754/flt-32/sincosf_poly.h: Here. New file.
* sysdeps/x86/fpu/s_sincosf_data.c: New file.
* sysdeps/x86/fpu/sincosf_poly.h: Likewise.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include
<sysdeps/ieee754/flt-32/s_sincosf.c>.
This commit is contained in:
H.J. Lu
parent
57b3ff8e1a
commit
8700a7851b
10
ChangeLog
10
ChangeLog
@ -1,3 +1,13 @@
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2018-12-26 H.J. Lu <hongjiu.lu@intel.com>
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* sysdeps/ieee754/flt-32/s_sincosf.h: Include <sincosf_poly.h>.
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(sincos_t, sincosf_poly, sinf_poly): Moved to ...
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* sysdeps/ieee754/flt-32/sincosf_poly.h: Here. New file.
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* sysdeps/x86/fpu/s_sincosf_data.c: New file.
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* sysdeps/x86/fpu/sincosf_poly.h: Likewise.
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* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include
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<sysdeps/ieee754/flt-32/s_sincosf.c>.
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2018-12-21 Joseph Myers <joseph@codesourcery.com>
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[BZ #24023]
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@ -19,22 +19,13 @@
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#include <stdint.h>
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#include <math.h>
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#include "math_config.h"
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#include <sincosf_poly.h>
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/* 2PI * 2^-64. */
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static const double pi63 = 0x1.921FB54442D18p-62;
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/* PI / 4. */
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static const double pio4 = 0x1.921FB54442D18p-1;
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/* The constants and polynomials for sine and cosine. */
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typedef struct
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{
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double sign[4]; /* Sign of sine in quadrants 0..3. */
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double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
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double hpi; /* PI / 2. */
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double c0, c1, c2, c3, c4; /* Cosine polynomial. */
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double s1, s2, s3; /* Sine polynomial. */
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} sincos_t;
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/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
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extern const sincos_t __sincosf_table[2] attribute_hidden;
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@ -48,66 +39,6 @@ abstop12 (float x)
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return (asuint (x) >> 20) & 0x7ff;
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}
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/* Compute the sine and cosine of inputs X and X2 (X squared), using the
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polynomial P and store the results in SINP and COSP. N is the quadrant,
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if odd the cosine and sine polynomials are swapped. */
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static inline void
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sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
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float *cosp)
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{
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double x3, x4, x5, x6, s, c, c1, c2, s1;
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x4 = x2 * x2;
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x3 = x2 * x;
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c2 = p->c3 + x2 * p->c4;
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s1 = p->s2 + x2 * p->s3;
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/* Swap sin/cos result based on quadrant. */
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float *tmp = (n & 1 ? cosp : sinp);
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cosp = (n & 1 ? sinp : cosp);
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sinp = tmp;
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c1 = p->c0 + x2 * p->c1;
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x5 = x3 * x2;
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x6 = x4 * x2;
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s = x + x3 * p->s1;
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c = c1 + x4 * p->c2;
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*sinp = s + x5 * s1;
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*cosp = c + x6 * c2;
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}
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/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
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N is the quadrant, and if odd the cosine polynomial is used. */
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static inline float
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sinf_poly (double x, double x2, const sincos_t *p, int n)
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{
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double x3, x4, x6, x7, s, c, c1, c2, s1;
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if ((n & 1) == 0)
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{
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x3 = x * x2;
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s1 = p->s2 + x2 * p->s3;
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x7 = x3 * x2;
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s = x + x3 * p->s1;
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return s + x7 * s1;
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}
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else
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{
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x4 = x2 * x2;
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c2 = p->c3 + x2 * p->c4;
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c1 = p->c0 + x2 * p->c1;
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x6 = x4 * x2;
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c = c1 + x4 * p->c2;
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return c + x6 * c2;
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}
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}
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/* Fast range reduction using single multiply-subtract. Return the modulo of
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X as a value between -PI/4 and PI/4 and store the quadrant in NP.
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The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
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87
sysdeps/ieee754/flt-32/sincosf_poly.h
Normal file
87
sysdeps/ieee754/flt-32/sincosf_poly.h
Normal file
@ -0,0 +1,87 @@
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/* Used by sinf, cosf and sincosf functions.
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Copyright (C) 2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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/* The constants and polynomials for sine and cosine. */
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typedef struct
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{
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double sign[4]; /* Sign of sine in quadrants 0..3. */
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double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
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double hpi; /* PI / 2. */
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double c0, c1, c2, c3, c4; /* Cosine polynomial. */
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double s1, s2, s3; /* Sine polynomial. */
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} sincos_t;
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/* Compute the sine and cosine of inputs X and X2 (X squared), using the
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polynomial P and store the results in SINP and COSP. N is the quadrant,
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if odd the cosine and sine polynomials are swapped. */
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static inline void
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sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
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float *cosp)
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{
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double x3, x4, x5, x6, s, c, c1, c2, s1;
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x4 = x2 * x2;
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x3 = x2 * x;
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c2 = p->c3 + x2 * p->c4;
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s1 = p->s2 + x2 * p->s3;
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/* Swap sin/cos result based on quadrant. */
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float *tmp = (n & 1 ? cosp : sinp);
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cosp = (n & 1 ? sinp : cosp);
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sinp = tmp;
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c1 = p->c0 + x2 * p->c1;
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x5 = x3 * x2;
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x6 = x4 * x2;
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s = x + x3 * p->s1;
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c = c1 + x4 * p->c2;
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*sinp = s + x5 * s1;
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*cosp = c + x6 * c2;
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}
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/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
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N is the quadrant, and if odd the cosine polynomial is used. */
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static inline float
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sinf_poly (double x, double x2, const sincos_t *p, int n)
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{
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double x3, x4, x6, x7, s, c, c1, c2, s1;
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if ((n & 1) == 0)
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{
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x3 = x * x2;
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s1 = p->s2 + x2 * p->s3;
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x7 = x3 * x2;
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s = x + x3 * p->s1;
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return s + x7 * s1;
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}
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else
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{
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x4 = x2 * x2;
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c2 = p->c3 + x2 * p->c4;
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c1 = p->c0 + x2 * p->c1;
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x6 = x4 * x2;
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c = c1 + x4 * p->c2;
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return c + x6 * c2;
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}
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}
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68
sysdeps/x86/fpu/s_sincosf_data.c
Normal file
68
sysdeps/x86/fpu/s_sincosf_data.c
Normal file
@ -0,0 +1,68 @@
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/* Compute sine and cosine of argument.
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Copyright (C) 2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <stdint.h>
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#include <math.h>
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#include <sysdeps/ieee754/flt-32/math_config.h>
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#include <s_sincosf.h>
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/* The constants and polynomials for sine and cosine. The 2nd entry
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computes -cos (x) rather than cos (x) to get negation for free. */
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const sincos_t __sincosf_table[2] =
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{
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{
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{ 1.0, -1.0, -1.0, 1.0 },
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#if TOINT_INTRINSICS
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0x1.45F306DC9C883p-1,
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#else
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0x1.45F306DC9C883p+23,
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#endif
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0x1.921FB54442D18p0,
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0x1p0,
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-0x1.ffffffd0c621cp-2,
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{ -0x1.555545995a603p-3, 0x1.55553e1068f19p-5 },
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{ 0x1.1107605230bc4p-7, -0x1.6c087e89a359dp-10 },
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{ -0x1.994eb3774cf24p-13, 0x1.99343027bf8c3p-16 }
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},
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{
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{ 1.0, -1.0, -1.0, 1.0 },
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#if TOINT_INTRINSICS
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0x1.45F306DC9C883p-1,
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#else
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0x1.45F306DC9C883p+23,
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#endif
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0x1.921FB54442D18p0,
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-0x1p0,
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0x1.ffffffd0c621cp-2,
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{ -0x1.555545995a603p-3, -0x1.55553e1068f19p-5 },
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{ 0x1.1107605230bc4p-7, 0x1.6c087e89a359dp-10 },
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{ -0x1.994eb3774cf24p-13, -0x1.99343027bf8c3p-16 }
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}
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};
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/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
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only 8 new bits are added per entry, making the table 4 times larger. */
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const uint32_t __inv_pio4[24] =
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{
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0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
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0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
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0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
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0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
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0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
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0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
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};
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111
sysdeps/x86/fpu/sincosf_poly.h
Normal file
111
sysdeps/x86/fpu/sincosf_poly.h
Normal file
@ -0,0 +1,111 @@
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/* Used by sinf, cosf and sincosf functions. X86-64 version.
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Copyright (C) 2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
|
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License as published by the Free Software Foundation; either
|
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version 2.1 of the License, or (at your option) any later version.
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|
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
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Lesser General Public License for more details.
|
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|
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double))));
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#ifdef __SSE2_MATH__
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typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float))));
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static inline void
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v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
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{
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v4sf_t v4sf = __builtin_ia32_cvtpd2ps (v2df);
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*f0p = v4sf[0];
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*f1p = v4sf[1];
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}
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#else
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static inline void
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v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
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{
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*f0p = (float) v2df[0];
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*f1p = (float) v2df[1];
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}
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#endif
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/* The constants and polynomials for sine and cosine. */
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typedef struct
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{
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double sign[4]; /* Sign of sine in quadrants 0..3. */
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double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
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double hpi; /* PI / 2. */
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/* Cosine polynomial: c0, c1, c2, c3, c4.
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Sine polynomial: s1, s2, s3. */
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double c0, c1;
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v2df_t s1c2, s2c3, s3c4;
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} sincos_t;
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/* Compute the sine and cosine of inputs X and X2 (X squared), using the
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polynomial P and store the results in SINP and COSP. N is the quadrant,
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if odd the cosine and sine polynomials are swapped. */
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static inline void
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sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
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float *cosp)
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{
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v2df_t vx2x2 = { x2, x2 };
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v2df_t vxx2 = { x, x2 };
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v2df_t vx3x4, vs1c2;
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vx3x4 = vx2x2 * vxx2;
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vs1c2 = p->s2c3 + vx2x2 * p->s3c4;
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/* Swap sin/cos result based on quadrant. */
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if (n & 1)
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{
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float *tmp = cosp;
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cosp = sinp;
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sinp = tmp;
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}
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double c1 = p->c0 + x2 * p->c1;
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v2df_t vxc1 = { x, c1 };
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v2df_t vx5x6 = vx3x4 * vx2x2;
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v2df_t vsincos = vxc1 + vx3x4 * p->s1c2;
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vsincos = vsincos + vx5x6 * vs1c2;
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v2df_to_sf (vsincos, sinp, cosp);
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}
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/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
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N is the quadrant, and if odd the cosine polynomial is used. */
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static inline float
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sinf_poly (double x, double x2, const sincos_t *p, int n)
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{
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double x3, x4, x6, x7, s, c, c1, c2, s1;
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if ((n & 1) == 0)
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{
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x3 = x * x2;
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s1 = p->s2c3[0] + x2 * p->s3c4[0];
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x7 = x3 * x2;
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s = x + x3 * p->s1c2[0];
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return s + x7 * s1;
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}
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else
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{
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x4 = x2 * x2;
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c2 = p->s2c3[1] + x2 * p->s3c4[1];
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c1 = p->c0 + x2 * p->c1;
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x6 = x4 * x2;
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c = c1 + x4 * p->s1c2[1];
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return c + x6 * c2;
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}
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}
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@ -1,271 +1,2 @@
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/* Compute sine and cosine of argument optimized with vector.
|
||||
Copyright (C) 2017 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 <errno.h>
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <x86intrin.h>
|
||||
#include <libm-alias-float.h>
|
||||
|
||||
#define SINCOSF __sincosf_fma
|
||||
|
||||
#ifndef SINCOSF
|
||||
# define SINCOSF_FUNC __sincosf
|
||||
#else
|
||||
# define SINCOSF_FUNC SINCOSF
|
||||
#endif
|
||||
|
||||
/* PI/2 with 98 bits of accuracy. */
|
||||
static const double PI_2_hi = 0x1.921fb544p+0;
|
||||
static const double PI_2_lo = 0x1.0b4611a626332p-34;
|
||||
|
||||
static const double SMALL = 0x1p-50; /* 2^-50. */
|
||||
static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
|
||||
|
||||
#define FLOAT_EXPONENT_SHIFT 23
|
||||
#define FLOAT_EXPONENT_BIAS 127
|
||||
|
||||
static const double pio2_table[] = {
|
||||
0 * M_PI_2,
|
||||
1 * M_PI_2,
|
||||
2 * M_PI_2,
|
||||
3 * M_PI_2,
|
||||
4 * M_PI_2,
|
||||
5 * M_PI_2
|
||||
};
|
||||
|
||||
static const double invpio4_table[] = {
|
||||
0x0p+0,
|
||||
0x1.45f306cp+0,
|
||||
0x1.c9c882ap-28,
|
||||
0x1.4fe13a8p-58,
|
||||
0x1.f47d4dp-85,
|
||||
0x1.bb81b6cp-112,
|
||||
0x1.4acc9ep-142,
|
||||
0x1.0e4107cp-169
|
||||
};
|
||||
|
||||
static const double ones[] = { 1.0, -1.0 };
|
||||
|
||||
/* Chebyshev constants for sin and cos, range -PI/4 - PI/4. */
|
||||
static const __v2df V0 = { -0x1.5555555551cd9p-3, -0x1.ffffffffe98aep-2};
|
||||
static const __v2df V1 = { 0x1.1111110c2688bp-7, 0x1.55555545c50c7p-5 };
|
||||
static const __v2df V2 = { -0x1.a019f8b4bd1f9p-13, -0x1.6c16b348b6874p-10 };
|
||||
static const __v2df V3 = { 0x1.71d7264e6b5b4p-19, 0x1.a00eb9ac43ccp-16 };
|
||||
static const __v2df V4 = { -0x1.a947e1674b58ap-26, -0x1.23c97dd8844d7p-22 };
|
||||
|
||||
/* Chebyshev constants for sin and cos, range 2^-27 - 2^-5. */
|
||||
static const __v2df VC0 = { -0x1.555555543d49dp-3, -0x1.fffffff5cc6fdp-2 };
|
||||
static const __v2df VC1 = { 0x1.110f475cec8c5p-7, 0x1.55514b178dac5p-5 };
|
||||
|
||||
static const __v2df v2ones = { 1.0, 1.0 };
|
||||
|
||||
/* Compute the sine and cosine values using Chebyshev polynomials where
|
||||
THETA is the range reduced absolute value of the input
|
||||
and it is less than Pi/4,
|
||||
N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
|
||||
whether a sine or cosine approximation is more accurate and
|
||||
SIGNBIT is used to add the correct sign after the Chebyshev
|
||||
polynomial is computed. */
|
||||
static void
|
||||
reduced_sincos (const double theta, const unsigned int n,
|
||||
const unsigned int signbit, float *sinx, float *cosx)
|
||||
{
|
||||
__v2df v2x, v2sx, v2cx;
|
||||
const __v2df v2theta = { theta, theta };
|
||||
const __v2df v2theta2 = v2theta * v2theta;
|
||||
/* Here sinf() and cosf() are calculated using sin Chebyshev polynomial:
|
||||
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
|
||||
v2x = V3 + v2theta2 * V4; /* S3+x^2*S4. */
|
||||
v2x = V2 + v2theta2 * v2x; /* S2+x^2*(S3+x^2*S4). */
|
||||
v2x = V1 + v2theta2 * v2x; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
|
||||
v2x = V0 + v2theta2 * v2x; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
|
||||
v2x = v2theta2 * v2x;
|
||||
v2cx = v2ones + v2x;
|
||||
v2sx = v2theta + v2theta * v2x;
|
||||
/* We are operating on |x|, so we need to add back the original
|
||||
signbit for sinf. */
|
||||
/* Determine positive or negative primary interval. */
|
||||
/* Are we in the primary interval of sin or cos? */
|
||||
if ((n & 2) == 0)
|
||||
{
|
||||
const __v2df v2sign =
|
||||
{
|
||||
ones[((n >> 2) & 1) ^ signbit],
|
||||
ones[((n + 2) >> 2) & 1]
|
||||
};
|
||||
v2cx[0] = v2sx[0];
|
||||
v2cx *= v2sign;
|
||||
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
|
||||
*sinx = v4sx[0];
|
||||
*cosx = v4sx[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
const __v2df v2sign =
|
||||
{
|
||||
ones[((n + 2) >> 2) & 1],
|
||||
ones[((n >> 2) & 1) ^ signbit]
|
||||
};
|
||||
v2cx[0] = v2sx[0];
|
||||
v2cx *= v2sign;
|
||||
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
|
||||
*sinx = v4sx[1];
|
||||
*cosx = v4sx[0];
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
SINCOSF_FUNC (float x, float *sinx, float *cosx)
|
||||
{
|
||||
double theta = x;
|
||||
double abstheta = fabs (theta);
|
||||
uint32_t ix, xi;
|
||||
GET_FLOAT_WORD (xi, x);
|
||||
/* |x| */
|
||||
ix = xi & 0x7fffffff;
|
||||
/* If |x|< Pi/4. */
|
||||
if (ix < 0x3f490fdb)
|
||||
{
|
||||
if (ix >= 0x3d000000) /* |x| >= 2^-5. */
|
||||
{
|
||||
__v2df v2x, v2sx, v2cx;
|
||||
const __v2df v2theta = { theta, theta };
|
||||
const __v2df v2theta2 = v2theta * v2theta;
|
||||
/* Chebyshev polynomial of the form for sin and cos. */
|
||||
v2x = V3 + v2theta2 * V4;
|
||||
v2x = V2 + v2theta2 * v2x;
|
||||
v2x = V1 + v2theta2 * v2x;
|
||||
v2x = V0 + v2theta2 * v2x;
|
||||
v2x = v2theta2 * v2x;
|
||||
v2cx = v2ones + v2x;
|
||||
v2sx = v2theta + v2theta * v2x;
|
||||
v2cx[0] = v2sx[0];
|
||||
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
|
||||
*sinx = v4sx[0];
|
||||
*cosx = v4sx[1];
|
||||
}
|
||||
else if (ix >= 0x32000000) /* |x| >= 2^-27. */
|
||||
{
|
||||
/* A simpler Chebyshev approximation is close enough for this range:
|
||||
for sin: x+x^3*(SS0+x^2*SS1)
|
||||
for cos: 1.0+x^2*(CC0+x^3*CC1). */
|
||||
__v2df v2x, v2sx, v2cx;
|
||||
const __v2df v2theta = { theta, theta };
|
||||
const __v2df v2theta2 = v2theta * v2theta;
|
||||
v2x = VC0 + v2theta * v2theta2 * VC1;
|
||||
v2x = v2theta2 * v2x;
|
||||
v2cx = v2ones + v2x;
|
||||
v2sx = v2theta + v2theta * v2x;
|
||||
v2cx[0] = v2sx[0];
|
||||
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
|
||||
*sinx = v4sx[0];
|
||||
*cosx = v4sx[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
/* Handle some special cases. */
|
||||
if (ix)
|
||||
*sinx = theta - (theta * SMALL);
|
||||
else
|
||||
*sinx = theta;
|
||||
*cosx = 1.0 - abstheta;
|
||||
}
|
||||
}
|
||||
else /* |x| >= Pi/4. */
|
||||
{
|
||||
unsigned int signbit = xi >> 31;
|
||||
if (ix < 0x40e231d6) /* |x| < 9*Pi/4. */
|
||||
{
|
||||
/* There are cases where FE_UPWARD rounding mode can
|
||||
produce a result of abstheta * inv_PI_4 == 9,
|
||||
where abstheta < 9pi/4, so the domain for
|
||||
pio2_table must go to 5 (9 / 2 + 1). */
|
||||
unsigned int n = (abstheta * inv_PI_4) + 1;
|
||||
theta = abstheta - pio2_table[n / 2];
|
||||
reduced_sincos (theta, n, signbit, sinx, cosx);
|
||||
}
|
||||
else if (ix < 0x7f800000)
|
||||
{
|
||||
if (ix < 0x4b000000) /* |x| < 2^23. */
|
||||
{
|
||||
unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
|
||||
double x = n / 2;
|
||||
theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
|
||||
/* Argument reduction needed. */
|
||||
reduced_sincos (theta, n, signbit, sinx, cosx);
|
||||
}
|
||||
else /* |x| >= 2^23. */
|
||||
{
|
||||
x = fabsf (x);
|
||||
int exponent
|
||||
= (ix >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
|
||||
exponent += 3;
|
||||
exponent /= 28;
|
||||
double a = invpio4_table[exponent] * x;
|
||||
double b = invpio4_table[exponent + 1] * x;
|
||||
double c = invpio4_table[exponent + 2] * x;
|
||||
double d = invpio4_table[exponent + 3] * x;
|
||||
uint64_t l = a;
|
||||
l &= ~0x7;
|
||||
a -= l;
|
||||
double e = a + b;
|
||||
l = e;
|
||||
e = a - l;
|
||||
if (l & 1)
|
||||
{
|
||||
e -= 1.0;
|
||||
e += b;
|
||||
e += c;
|
||||
e += d;
|
||||
e *= M_PI_4;
|
||||
reduced_sincos (e, l + 1, signbit, sinx, cosx);
|
||||
}
|
||||
else
|
||||
{
|
||||
e += b;
|
||||
e += c;
|
||||
e += d;
|
||||
if (e <= 1.0)
|
||||
{
|
||||
e *= M_PI_4;
|
||||
reduced_sincos (e, l + 1, signbit, sinx, cosx);
|
||||
}
|
||||
else
|
||||
{
|
||||
l++;
|
||||
e -= 2.0;
|
||||
e *= M_PI_4;
|
||||
reduced_sincos (e, l + 1, signbit, sinx, cosx);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
if (ix == 0x7f800000)
|
||||
__set_errno (EDOM);
|
||||
/* sin/cos(Inf or NaN) is NaN. */
|
||||
*sinx = *cosx = x - x;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#ifndef SINCOSF
|
||||
libm_alias_float (__sincos, sincos)
|
||||
#endif
|
||||
#include <sysdeps/ieee754/flt-32/s_sincosf.c>
|
||||
|
||||
Loading…
Reference in New Issue
Block a user