From patchwork Wed Nov 21 18:11:00 2018 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: "H.J. Lu" X-Patchwork-Id: 30247 Received: (qmail 54320 invoked by alias); 21 Nov 2018 18:11:11 -0000 Mailing-List: contact libc-alpha-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Unsubscribe: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: libc-alpha-owner@sourceware.org Delivered-To: mailing list libc-alpha@sourceware.org Received: (qmail 54018 invoked by uid 89); 21 Nov 2018 18:11:09 -0000 Authentication-Results: sourceware.org; auth=none X-Spam-SWARE-Status: No, score=-26.2 required=5.0 tests=BAYES_00, FREEMAIL_FROM, GIT_PATCH_0, GIT_PATCH_1, GIT_PATCH_2, GIT_PATCH_3, KAM_SHORT, SPF_SOFTFAIL autolearn=ham version=3.3.2 spammy=Sign, 03, NaN, v4sf X-HELO: mga18.intel.com From: "H.J. Lu" To: libc-alpha@sourceware.org Subject: [PATCH 1/3] Update s_sincosf.c and x86-64 s_sincosf-fma.c Date: Wed, 21 Nov 2018 10:11:00 -0800 Message-Id: <20181121181102.27119-2-hjl.tools@gmail.com> In-Reply-To: <20181121181102.27119-1-hjl.tools@gmail.com> References: <20181121181102.27119-1-hjl.tools@gmail.com> MIME-Version: 1.0 Include in s_sincosf.c, instead of "s_sincosf.h", to allow x86-64 s_sincosf.h with vectorized sincosf_poly. Update __sincosf_table to allow vectorized load in vectorized 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% * sysdeps/ieee754/flt-32/s_sincosf.c: Include instead of "s_sincosf.h". * sysdeps/ieee754/flt-32/s_sincosf.h (sincos_t): Rearranged to support vectorized load. (sincosf_poly): Don't define if HAVE_SINCOSF_POLY is defined. Updated for vectorized load. (sinf_poly): Updated for vectorized load. * sysdeps/ieee754/flt-32/s_sincosf_data.c (__sincosf_table): Rearranged to allow vectorized load. * sysdeps/x86_64/fpu/s_sincosf.h: New file. * sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include . --- sysdeps/ieee754/flt-32/s_sincosf.c | 2 +- sysdeps/ieee754/flt-32/s_sincosf.h | 38 ++- sysdeps/ieee754/flt-32/s_sincosf_data.c | 18 +- sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c | 271 +------------------ sysdeps/x86_64/fpu/s_sincosf.h | 57 ++++ 5 files changed, 93 insertions(+), 293 deletions(-) create mode 100644 sysdeps/x86_64/fpu/s_sincosf.h diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c index f7e3245097..28dd7530c5 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.c +++ b/sysdeps/ieee754/flt-32/s_sincosf.c @@ -22,7 +22,7 @@ #include #include #include "math_config.h" -#include "s_sincosf.h" +#include #ifndef SINCOSF # define SINCOSF_FUNC __sincosf diff --git a/sysdeps/ieee754/flt-32/s_sincosf.h b/sysdeps/ieee754/flt-32/s_sincosf.h index 1dcb04f235..a1d1639c17 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.h +++ b/sysdeps/ieee754/flt-32/s_sincosf.h @@ -31,8 +31,24 @@ typedef struct double sign[4]; /* Sign of sine in quadrants 0..3. */ double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */ double hpi; /* PI / 2. */ - double c0, c1, c2, c3, c4; /* Cosine polynomial. */ - double s1, s2, s3; /* Sine polynomial. */ + /* Cosine polynomial: c0, c1, c2, c3, c4. + Sine polynomial: s1, s2, s3. */ + double c0, c1; + struct + { + double s1; + double c2; + } s1c2; + struct + { + double s2; + double c3; + } s2c3; + struct + { + double s3; + double c4; + } s3c4; } sincos_t; /* Polynomial data (the cosine polynomial is negated in the 2nd entry). */ @@ -48,6 +64,7 @@ abstop12 (float x) return (asuint (x) >> 20) & 0x7ff; } +#ifndef HAVE_SINCOSF_POLY /* Compute the sine and cosine of inputs X and X2 (X squared), using the polynomial P and store the results in SINP and COSP. N is the quadrant, if odd the cosine and sine polynomials are swapped. */ @@ -59,8 +76,8 @@ sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp, x4 = x2 * x2; x3 = x2 * x; - c2 = p->c3 + x2 * p->c4; - s1 = p->s2 + x2 * p->s3; + c2 = p->s2c3.c3 + x2 * p->s3c4.c4; + s1 = p->s2c3.s2 + x2 * p->s3c4.s3; /* Swap sin/cos result based on quadrant. */ float *tmp = (n & 1 ? cosp : sinp); @@ -71,12 +88,13 @@ sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp, x5 = x3 * x2; x6 = x4 * x2; - s = x + x3 * p->s1; - c = c1 + x4 * p->c2; + s = x + x3 * p->s1c2.s1; + c = c1 + x4 * p->s1c2.c2; *sinp = s + x5 * s1; *cosp = c + x6 * c2; } +#endif /* Return the sine of inputs X and X2 (X squared) using the polynomial P. N is the quadrant, and if odd the cosine polynomial is used. */ @@ -88,21 +106,21 @@ sinf_poly (double x, double x2, const sincos_t *p, int n) if ((n & 1) == 0) { x3 = x * x2; - s1 = p->s2 + x2 * p->s3; + s1 = p->s2c3.s2 + x2 * p->s3c4.s3; x7 = x3 * x2; - s = x + x3 * p->s1; + s = x + x3 * p->s1c2.s1; return s + x7 * s1; } else { x4 = x2 * x2; - c2 = p->c3 + x2 * p->c4; + c2 = p->s2c3.c3 + x2 * p->s3c4.c4; c1 = p->c0 + x2 * p->c1; x6 = x4 * x2; - c = c1 + x4 * p->c2; + c = c1 + x4 * p->s1c2.c2; return c + x6 * c2; } diff --git a/sysdeps/ieee754/flt-32/s_sincosf_data.c b/sysdeps/ieee754/flt-32/s_sincosf_data.c index 21fc2b60f9..6d3ed77d4c 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf_data.c +++ b/sysdeps/ieee754/flt-32/s_sincosf_data.c @@ -35,12 +35,9 @@ const sincos_t __sincosf_table[2] = 0x1.921FB54442D18p0, 0x1p0, -0x1.ffffffd0c621cp-2, - 0x1.55553e1068f19p-5, - -0x1.6c087e89a359dp-10, - 0x1.99343027bf8c3p-16, - -0x1.555545995a603p-3, - 0x1.1107605230bc4p-7, - -0x1.994eb3774cf24p-13 + { -0x1.555545995a603p-3, 0x1.55553e1068f19p-5 }, + { 0x1.1107605230bc4p-7, -0x1.6c087e89a359dp-10 }, + { -0x1.994eb3774cf24p-13, 0x1.99343027bf8c3p-16 } }, { { 1.0, -1.0, -1.0, 1.0 }, @@ -52,12 +49,9 @@ const sincos_t __sincosf_table[2] = 0x1.921FB54442D18p0, -0x1p0, 0x1.ffffffd0c621cp-2, - -0x1.55553e1068f19p-5, - 0x1.6c087e89a359dp-10, - -0x1.99343027bf8c3p-16, - -0x1.555545995a603p-3, - 0x1.1107605230bc4p-7, - -0x1.994eb3774cf24p-13 + { -0x1.555545995a603p-3, -0x1.55553e1068f19p-5 }, + { 0x1.1107605230bc4p-7, 0x1.6c087e89a359dp-10 }, + { -0x1.994eb3774cf24p-13, -0x1.99343027bf8c3p-16 } } }; diff --git a/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c b/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c index 0b80c4fe0d..253dab15d8 100644 --- a/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c +++ b/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c @@ -1,271 +1,2 @@ -/* 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 - . */ - -#include -#include -#include -#include -#include - #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 diff --git a/sysdeps/x86_64/fpu/s_sincosf.h b/sysdeps/x86_64/fpu/s_sincosf.h new file mode 100644 index 0000000000..ecca29db12 --- /dev/null +++ b/sysdeps/x86_64/fpu/s_sincosf.h @@ -0,0 +1,57 @@ +/* x86-64 sincosf_poly for sincosf. + Copyright (C) 2018 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 + . */ + +#define HAVE_SINCOSF_POLY +#include_next +#include + +/* Compute the sine and cosine of inputs X and X2 (X squared), using the + polynomial P and store the results in SINP and COSP. N is the quadrant, + if odd the cosine and sine polynomials are swapped. */ +static inline void +sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp, + float *cosp) +{ + __v2df vx2x2 = { x2, x2 }; + __v2df vxx2 = { x, x2 }; + __v2df vps1c2 = (__v2df) _mm_loadu_pd (&p->s1c2.s1); + __v2df vps2c3 = (__v2df) _mm_loadu_pd (&p->s2c3.s2); + __v2df vps3c4 = (__v2df) _mm_loadu_pd (&p->s3c4.s3); + __v2df vx3x4, vs1c2; + + vx3x4 = vx2x2 * vxx2; + vs1c2 = vps2c3 + vx2x2 * vps3c4; + + /* Swap sin/cos result based on quadrant. */ + if (n & 1) + { + float *tmp = cosp; + cosp = sinp; + sinp = tmp; + } + + double c1 = p->c0 + x2 * p->c1; + __v2df vxc1 = { x, c1 }; + __v2df vx5x6 = vx3x4 * vx2x2; + + __v2df vsincos = vxc1 + vx3x4 * vps1c2; + vsincos = vsincos + vx5x6 * vs1c2; + __v4sf v4sf = _mm_cvtpd_ps (vsincos); + *sinp = v4sf[0]; + *cosp = v4sf[1]; +}