From patchwork Tue Dec 4 19:47:06 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: 30541 Received: (qmail 29489 invoked by alias); 4 Dec 2018 19:47:52 -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 29330 invoked by uid 89); 4 Dec 2018 19:47:51 -0000 Authentication-Results: sourceware.org; auth=none X-Spam-SWARE-Status: No, score=-26.9 required=5.0 tests=BAYES_00, FREEMAIL_FROM, GIT_PATCH_0, GIT_PATCH_1, GIT_PATCH_2, GIT_PATCH_3, KAM_SHORT, RCVD_IN_DNSWL_NONE, SPF_PASS autolearn=ham version=3.3.2 spammy=271, 03 X-HELO: mail-oi1-f195.google.com DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=Z4XKvZNNkFHki3AbHZirNBmQGbg3Mn6dyo1t7Uvtsbs=; b=qiBCdMaS3FWDbY76wrKftKOGCfgP/VFFzip9kWp6YswuUPHv35Rdc1MB7Pz9+CWBQy e366WpkJ5tOKncRhWx2PUfQjcc41NwKM01a6xV23WV/EEZy0HQOEvrXOQJN5Jk6EPd6/ guD9tao4mjw1kea84h/4eQ/2+SxFcpULbuaI2l4W0jU5ps5VHzKzso5IiU5mzxQT6l0y Emat9C32O4KP87GLUkvIIN8na8Fa8a4/F/shSXlLG2VOea7FyEtxDhz6T0if+svZXlkG wcn8Xi8HnV7WsFmifuBAizMbYkXle3gg0TFVm0umfbPZZLjA6M/cj6F2mz/tk0EG9RcF nacg== MIME-Version: 1.0 References: In-Reply-To: From: "H.J. Lu" Date: Tue, 4 Dec 2018 11:47:06 -0800 Message-ID: Subject: Re: [PATCH] Use generic vector computations in s_sincosf.h To: Wilco Dijkstra Cc: Adhemerval Zanella , "szabolcs.nagy" , GNU C Library , nd On Mon, Dec 3, 2018 at 1:22 PM H.J. Lu wrote: > > On Mon, Dec 3, 2018 at 12:22 PM H.J. Lu wrote: > > > > On Mon, Dec 3, 2018 at 10:44 AM Wilco Dijkstra wrote: > > > > > > Hi, > > > > > > > H.J. Lu wrote: > > > > Only sincosf_poly is vectorized. Without changing the existing > > > > structure, I need > > > > to duplicate everything in sysdeps/ieee754/flt-32/s_sincosf.h. > > > > > > The only shared function which relies on the structure is reduce_fast. > > > To avoid any duplication it could just get the 2 values it needs as arguments. > > > > > > > My x86-64 vector version has x86-64 specific intrinsics: > > > > > > > > __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); > > > > > > Simple vector loads are supported, you don't need any intrinsics for these. > > > > I try to replace > > > > struct > > { > > double s1; > > double c2; > > } s1c2; > > > > with __v2df. > > > > > > __v4sf v4sf = _mm_cvtpd_ps (vsincos); > > > > > > This works fine too for me using v4sf = {(float)vsincos[0], (float)vsincos[1]}; > > > > > > > I got > > > > vcvtsd2ss %xmm1, %xmm2, %xmm0 > > vunpckhpd %xmm1, %xmm1, %xmm1 > > vmovss %xmm0, (%rdi) > > vcvtsd2ss %xmm1, %xmm2, %xmm2 > > vmovss %xmm2, (%rsi) > > ret > > > > instead of > > > > vcvtpd2psx %xmm2, %xmm2 > > vmovss %xmm2, (%rdi) > > vextractps $1, %xmm2, (%rsi) > > ret > > > > I prefer > > > > __v4sf v4sf = _mm_cvtpd_ps (vsincos); > > > > I am testing this patch to use generic vector computations in s_sincosf.h. > OK for master if build-many-glibcs.py passes? > Here is the updated patch. I added v2df_to_sf.h to use static inline void v2df_to_sf (v2df_t v2df, float *f0p, float *f1p); Tested on x86-64 and i686 as well as with build-many-glibcs.py. OK for master? From 1678be70260358c5919e90bfa2aef497ac227925 Mon Sep 17 00:00:00 2001 From: "H.J. Lu" Date: Mon, 22 Oct 2018 16:09:57 -0700 Subject: [PATCH] Use generic vector computations in s_sincosf.h Use generic vector computations in s_sincosf.h to support vectorized s_sincosf. Update __sincosf_table for vectorized s_sincosf. 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 (v2df_t): New. Include . (sincos_t): Use v2df_t for generic vector computations. (sincosf_poly): Use generic vector computations. (sinf_poly): Updated for generic vector computations. * sysdeps/ieee754/flt-32/s_sincosf_data.c (__sincosf_table): Rearranged for generic vector computations. * sysdeps/ieee754/flt-32/v2df_to_sf.h: New file. * sysdeps/x86/fpu/v2df_to_sf.h: Likewise. * sysdeps/powerpc/Makefile (CFLAGS-s_sincosf.c): New. * sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include . --- sysdeps/ieee754/flt-32/s_sincosf.h | 51 ++-- sysdeps/ieee754/flt-32/s_sincosf_data.c | 18 +- sysdeps/ieee754/flt-32/v2df_to_sf.h | 24 ++ sysdeps/powerpc/Makefile | 4 + sysdeps/x86/fpu/v2df_to_sf.h | 31 +++ sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c | 271 +------------------ 6 files changed, 95 insertions(+), 304 deletions(-) create mode 100644 sysdeps/ieee754/flt-32/v2df_to_sf.h create mode 100644 sysdeps/x86/fpu/v2df_to_sf.h diff --git a/sysdeps/ieee754/flt-32/s_sincosf.h b/sysdeps/ieee754/flt-32/s_sincosf.h index 1dcb04f235..3842b5ebf7 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.h +++ b/sysdeps/ieee754/flt-32/s_sincosf.h @@ -20,6 +20,10 @@ #include #include "math_config.h" +typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double)))); + +#include + /* 2PI * 2^-64. */ static const double pi63 = 0x1.921FB54442D18p-62; /* PI / 4. */ @@ -31,8 +35,10 @@ 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; + v2df_t s1c2, s2c3, s3c4; } sincos_t; /* Polynomial data (the cosine polynomial is negated in the 2nd entry). */ @@ -55,27 +61,28 @@ static inline void sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp, float *cosp) { - double x3, x4, x5, x6, s, c, c1, c2, s1; + v2df_t vx2x2 = { x2, x2 }; + v2df_t vxx2 = { x, x2 }; + v2df_t vx3x4, vs1c2; - x4 = x2 * x2; - x3 = x2 * x; - c2 = p->c3 + x2 * p->c4; - s1 = p->s2 + x2 * p->s3; + vx3x4 = vx2x2 * vxx2; + vs1c2 = p->s2c3 + vx2x2 * p->s3c4; /* Swap sin/cos result based on quadrant. */ - float *tmp = (n & 1 ? cosp : sinp); - cosp = (n & 1 ? sinp : cosp); - sinp = tmp; - - c1 = p->c0 + x2 * p->c1; - x5 = x3 * x2; - x6 = x4 * x2; + if (n & 1) + { + float *tmp = cosp; + cosp = sinp; + sinp = tmp; + } - s = x + x3 * p->s1; - c = c1 + x4 * p->c2; + double c1 = p->c0 + x2 * p->c1; + v2df_t vxc1 = { x, c1 }; + v2df_t vx5x6 = vx3x4 * vx2x2; - *sinp = s + x5 * s1; - *cosp = c + x6 * c2; + v2df_t vsincos = vxc1 + vx3x4 * p->s1c2; + vsincos = vsincos + vx5x6 * vs1c2; + v2df_to_sf (vsincos, sinp, cosp); } /* Return the sine of inputs X and X2 (X squared) using the polynomial P. @@ -88,21 +95,21 @@ 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[0] + x2 * p->s3c4[0]; x7 = x3 * x2; - s = x + x3 * p->s1; + s = x + x3 * p->s1c2[0]; return s + x7 * s1; } else { x4 = x2 * x2; - c2 = p->c3 + x2 * p->c4; + c2 = p->s2c3[1] + x2 * p->s3c4[1]; c1 = p->c0 + x2 * p->c1; x6 = x4 * x2; - c = c1 + x4 * p->c2; + c = c1 + x4 * p->s1c2[1]; 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/ieee754/flt-32/v2df_to_sf.h b/sysdeps/ieee754/flt-32/v2df_to_sf.h new file mode 100644 index 0000000000..f3fb7968da --- /dev/null +++ b/sysdeps/ieee754/flt-32/v2df_to_sf.h @@ -0,0 +1,24 @@ +/* Convert V2DF to SF. Generic version. + 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 + . */ + +static inline void +v2df_to_sf (v2df_t v2df, float *f0p, float *f1p) +{ + *f0p = (float) v2df[0]; + *f1p = (float) v2df[1]; +} diff --git a/sysdeps/powerpc/Makefile b/sysdeps/powerpc/Makefile index 6aa683b03f..25f14f3044 100644 --- a/sysdeps/powerpc/Makefile +++ b/sysdeps/powerpc/Makefile @@ -50,3 +50,7 @@ endif ifneq (,$(filter %le,$(config-machine))) abilist-pattern = %-le.abilist endif + +ifeq ($(subdir),math) +CFLAGS-s_sincosf.c += -Wno-psabi +endif diff --git a/sysdeps/x86/fpu/v2df_to_sf.h b/sysdeps/x86/fpu/v2df_to_sf.h new file mode 100644 index 0000000000..b0f99666fc --- /dev/null +++ b/sysdeps/x86/fpu/v2df_to_sf.h @@ -0,0 +1,31 @@ +/* Convert V2DF to SF. x86 version. + 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 + . */ + +#ifdef __SSE2_MATH__ +typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float)))); + +static inline void +v2df_to_sf (v2df_t v2df, float *f0p, float *f1p) +{ + v4sf_t v4sf = __builtin_ia32_cvtpd2ps (v2df); + *f0p = v4sf[0]; + *f1p = v4sf[1]; +} +#else +# include +#endif 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 -- 2.19.2