From 4ffffbd272264f083f35783ed81339304025f855 Mon Sep 17 00:00:00 2001 From: Liubov Dmitrieva Date: Mon, 3 Sep 2012 15:32:13 +0200 Subject: [PATCH] Add optimized sinf and cosf routines for x86 and x86-64 * sysdeps/i386/i686/fpu/multiarch/Makefile (sysdep_routines): Add s_sinf-sse2, s_conf-sse2. * sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S: New file. * sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S: New file. * sysdeps/i386/i686/fpu/multiarch/s_sinf.c: New file. * sysdeps/i386/i686/fpu/multiarch/s_cosf.c: New file. * sysdeps/ieee754/flt-32/s_sinf.c (SINF, SINF_FUNC): Add macros for using routine as __sinf_ia32. Use macro for function declaration and weak_alias. * sysdeps/ieee754/flt-32/s_cosf.c (COSF, COSF_FUNC): Add macros for using routine as __cosf_ia32. Use macro for function declaration and weak_alias. * sysdeps/i386/i686/fpu/multiarch/e_expf-sse2.S: Fix Copyright. * sysdeps/i386/i686/fpu/multiarch/e_expf.c: Fix Copyright. * sysdeps/x86_64/fpu/s_sinf.S: New file. * sysdeps/x86_64/fpu/s_cosf.S: New file. * sysdeps/x86_64/fpu/libm-test-ulps: Update. * math/libm-test.inc (cos_test): Add more test cases. (sin_test): Likewise. (sincos_test): Likewise. --- ChangeLog | 28 + math/libm-test.inc | 21 + sysdeps/i386/i686/fpu/multiarch/Makefile | 2 +- sysdeps/i386/i686/fpu/multiarch/e_expf.c | 18 + sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S | 559 +++++++++++++++++ sysdeps/i386/i686/fpu/multiarch/s_cosf.c | 29 + sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S | 575 ++++++++++++++++++ sysdeps/i386/i686/fpu/multiarch/s_sinf.c | 28 + sysdeps/ieee754/flt-32/s_cosf.c | 11 +- sysdeps/ieee754/flt-32/s_sinf.c | 11 +- sysdeps/x86_64/fpu/libm-test-ulps | 35 +- sysdeps/x86_64/fpu/s_cosf.S | 535 ++++++++++++++++ sysdeps/x86_64/fpu/s_sinf.S | 558 +++++++++++++++++ 13 files changed, 2403 insertions(+), 7 deletions(-) create mode 100644 sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S create mode 100644 sysdeps/i386/i686/fpu/multiarch/s_cosf.c create mode 100644 sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S create mode 100644 sysdeps/i386/i686/fpu/multiarch/s_sinf.c create mode 100644 sysdeps/x86_64/fpu/s_cosf.S create mode 100644 sysdeps/x86_64/fpu/s_sinf.S diff --git a/ChangeLog b/ChangeLog index ef7477d920..dd40cb8342 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,31 @@ +2012-09-03 Liubov Dmitrieva + + * sysdeps/i386/i686/fpu/multiarch/Makefile (sysdep_routines): + Add s_sinf-sse2, s_conf-sse2. + + * sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S: New file. + * sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S: New file. + * sysdeps/i386/i686/fpu/multiarch/s_sinf.c: New file. + * sysdeps/i386/i686/fpu/multiarch/s_cosf.c: New file. + + * sysdeps/ieee754/flt-32/s_sinf.c (SINF, SINF_FUNC): Add macros + for using routine as __sinf_ia32. + Use macro for function declaration and weak_alias. + * sysdeps/ieee754/flt-32/s_cosf.c (COSF, COSF_FUNC): Add macros + for using routine as __cosf_ia32. + Use macro for function declaration and weak_alias. + + * sysdeps/i386/i686/fpu/multiarch/e_expf-sse2.S: Fix Copyright. + * sysdeps/i386/i686/fpu/multiarch/e_expf.c: Fix Copyright. + + * sysdeps/x86_64/fpu/s_sinf.S: New file. + * sysdeps/x86_64/fpu/s_cosf.S: New file. + * sysdeps/x86_64/fpu/libm-test-ulps: Update. + + * math/libm-test.inc (cos_test): Add more test cases. + (sin_test): Likewise. + (sincos_test): Likewise. + 2012-09-03 Andreas Krebbel * sysdeps/s390/s390-32/multiarch/ifunc-resolve.c diff --git a/math/libm-test.inc b/math/libm-test.inc index 0f64ea4971..fa781fc592 100644 --- a/math/libm-test.inc +++ b/math/libm-test.inc @@ -2752,6 +2752,13 @@ cos_test (void) TEST_f_f (cos, 0x1p16383L, 0.9210843909921906206874509522505756251609L); #endif + TEST_f_f (cos, 0x1p+120, -9.25879022854837867303861764107414946730833e-01L); + TEST_f_f (cos, 0x1p+127, 7.81914638714960072263910298466369236613162e-01L); + TEST_f_f (cos, 0x1.fffff8p+127, 9.98819362551949040703862043664101081064641e-01L); + TEST_f_f (cos, 0x1.fffffep+127, 8.53021039830304158051791467692161107353094e-01L); + TEST_f_f (cos, 0x1p+50, 8.68095904660550604334592502063501320395739e-01L); + TEST_f_f (cos, 0x1p+28, -1.65568979490578758865468278195361551113358e-01L); + END (cos); } @@ -8179,6 +8186,13 @@ sin_test (void) TEST_f_f (sin, 0x1p16383L, 0.3893629985894208126948115852610595405563L); #endif + TEST_f_f (sin, 0x1p+120, 3.77820109360752022655548470056922991960587e-01L); + TEST_f_f (sin, 0x1p+127, 6.23385512955870240370428801097126489001833e-01L); + TEST_f_f (sin, 0x1.fffff8p+127, 4.85786063130487339701113680434728152037092e-02L); + TEST_f_f (sin, 0x1.fffffep+127, -5.21876523333658540551505357019806722935726e-01L); + TEST_f_f (sin, 0x1p+50, 4.96396515208940840876821859865411368093356e-01L); + TEST_f_f (sin, 0x1p+28, -9.86198211836975655703110310527108292055548e-01L); + END (sin); } @@ -8362,6 +8376,13 @@ sincos_test (void) TEST_extra (sincos, 0x1p16383L, 0.3893629985894208126948115852610595405563L, 0.9210843909921906206874509522505756251609L); #endif + TEST_extra (sincos, 0x1p+120, 3.77820109360752022655548470056922991960587e-01L, -9.25879022854837867303861764107414946730833e-01L); + TEST_extra (sincos, 0x1p+127, 6.23385512955870240370428801097126489001833e-01L, 7.81914638714960072263910298466369236613162e-01L); + TEST_extra (sincos, 0x1.fffff8p+127, 4.85786063130487339701113680434728152037092e-02L, 9.98819362551949040703862043664101081064641e-01L); + TEST_extra (sincos, 0x1.fffffep+127, -5.21876523333658540551505357019806722935726e-01L, 8.53021039830304158051791467692161107353094e-01L); + TEST_extra (sincos, 0x1p+50, 4.96396515208940840876821859865411368093356e-01L, 8.68095904660550604334592502063501320395739e-01L); + TEST_extra (sincos, 0x1p+28, -9.86198211836975655703110310527108292055548e-01L, -1.65568979490578758865468278195361551113358e-01L); + END (sincos); } diff --git a/sysdeps/i386/i686/fpu/multiarch/Makefile b/sysdeps/i386/i686/fpu/multiarch/Makefile index 1de37fe4aa..aa28f72841 100644 --- a/sysdeps/i386/i686/fpu/multiarch/Makefile +++ b/sysdeps/i386/i686/fpu/multiarch/Makefile @@ -1,3 +1,3 @@ ifeq ($(subdir),math) -libm-sysdep_routines += e_expf-sse2 e_expf-ia32 +libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2 endif diff --git a/sysdeps/i386/i686/fpu/multiarch/e_expf.c b/sysdeps/i386/i686/fpu/multiarch/e_expf.c index 65858a3113..1966400d1b 100644 --- a/sysdeps/i386/i686/fpu/multiarch/e_expf.c +++ b/sysdeps/i386/i686/fpu/multiarch/e_expf.c @@ -1,3 +1,21 @@ +/* Multiple versions of expf + Copyright (C) 2012 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 extern double __ieee754_expf_sse2 (double); diff --git a/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S b/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S new file mode 100644 index 0000000000..2b5a2a5ae2 --- /dev/null +++ b/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S @@ -0,0 +1,559 @@ +/* Optimized with sse2 version of cosf + Copyright (C) 2012 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 +#define __need_Emath +#include + +/* Short algorithm description: + * + * 1) if |x| == 0: return 1.0-|x|. + * 2) if |x| < 2^-27: return 1.0-|x|. + * 3) if |x| < 2^-5 : return 1.0+x^2*DP_COS2_0+x^5*DP_COS2_1. + * 4) if |x| < Pi/4: return 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). + * 5) if |x| < 9*Pi/4: + * 5.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+3, + * t=|x|-j*Pi/4. + * 5.2) Reconstruction: + * s = (-1.0)^((n>>2)&1) + * if(n&2 != 0) { + * using cos(t) polynomial for |t|= 2^23, very large args: + * 7.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+3, + * t=|x|-j*Pi/4. + * 7.2) Reconstruction same as (5.2). + * 8) if x is Inf, return x-x, and set errno=EDOM. + * 9) if x is NaN, return x-x. + * + * Special cases: + * cos(+-0)==+-0 not raising inexact/underflow, + * cos(subnormal) raises inexact/underflow + * cos(min_normalized) raises inexact/underflow + * cos(normalized) raises inexact + * cos(Inf) = NaN, raises invalid, sets errno to EDOM + * cos(NaN) = NaN + */ + +#ifdef PIC +# define MO1(symbol) L(symbol)##@GOTOFF(%ebx) +# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale) +# define SAVE_BX pushl %ebx +# define RESTORE_BX popl %ebx +# define ARG_X 8(%esp) +#else +# define MO1(symbol) L(symbol) +# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale) +# define SAVE_BX +# define RESTORE_BX +# define ARG_X 4(%esp) +#endif + + .text +ENTRY(__cosf_sse2) + /* Input: single precision x on stack at address ARG_X */ + +#ifdef PIC + SAVE_BX + LOAD_PIC_REG(bx) +#endif + + movl ARG_X, %eax /* Bits of x */ + cvtss2sd ARG_X, %xmm0 /* DP x */ + andl $0x7fffffff, %eax /* |x| */ + + cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */ + movd %eax, %xmm3 /* SP |x| */ + andpd MO1(DP_ABS_MASK),%xmm0 /* DP |x| */ + movss MO1(SP_INVPIO4), %xmm2 /* SP 1/(Pi/4) */ + + cmpl $0x40e231d6, %eax /* |x|<9*Pi/4? */ + jae L(large_args) + + /* Here if Pi/4<=|x|<9*Pi/4 */ + mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */ + cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ + addl $1, %eax /* k+1 */ + movl $0x0e, %edx + andl %eax, %edx /* j = (k+1)&0x0e */ + addl $2, %eax /* n */ + subsd MO2(PIO4J,%edx,8), %xmm0 /* t = |x| - j * Pi/4 */ + +L(reconstruction): + /* Input: %eax=n, %xmm0=t */ + testl $2, %eax /* n&2 != 0? */ + jz L(sin_poly) + +/*L(cos_poly):*/ + /* Here if cos(x) calculated using cos(t) polynomial for |t|>2)&1) + * result = s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))) + */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd MO1(DP_C4), %xmm4 /* C4 */ + mulsd %xmm0, %xmm4 /* z*C4 */ + movsd MO1(DP_C3), %xmm3 /* C3 */ + mulsd %xmm0, %xmm3 /* z*C3 */ + addsd MO1(DP_C2), %xmm4 /* C2+z*C4 */ + mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */ + lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */ + addsd MO1(DP_C1), %xmm3 /* C1+z*C3 */ + mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */ + addsd MO1(DP_C0), %xmm4 /* C0+z*(C2+z*C4) */ + mulsd %xmm1, %xmm4 /* y*(C0+z*(C2+z*C4)) */ + + addsd %xmm4, %xmm3 /* y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + /* 1.0+y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + addsd MO1(DP_ONES), %xmm3 + + mulsd MO2(DP_ONES,%eax,8), %xmm3 /* DP result */ + movsd %xmm3, 0(%esp) /* Move result from sse... */ + fldl 0(%esp) /* ...to FPU. */ + /* Return back 4 bytes of stack frame */ + lea 8(%esp), %esp + RESTORE_BX + ret + + .p2align 4 +L(sin_poly): + /* Here if cos(x) calculated using sin(t) polynomial for |t|>2)&1) + * result = s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))) + */ + + movaps %xmm0, %xmm4 /* t */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd MO1(DP_S4), %xmm2 /* S4 */ + mulsd %xmm0, %xmm2 /* z*S4 */ + movsd MO1(DP_S3), %xmm3 /* S3 */ + mulsd %xmm0, %xmm3 /* z*S3 */ + lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */ + addsd MO1(DP_S2), %xmm2 /* S2+z*S4 */ + mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */ + addsd MO1(DP_S1), %xmm3 /* S1+z*S3 */ + mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */ + addsd MO1(DP_S0), %xmm2 /* S0+z*(S2+z*S4) */ + mulsd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ + /* t*s, where s = sign(x) * (-1.0)^((n>>2)&1) */ + mulsd MO2(DP_ONES,%eax,8), %xmm4 + addsd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + /* t*s*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + mulsd %xmm4, %xmm3 + /* t*s*(1.0+y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm4, %xmm3 + movsd %xmm3, 0(%esp) /* Move result from sse... */ + fldl 0(%esp) /* ...to FPU. */ + /* Return back 4 bytes of stack frame */ + lea 8(%esp), %esp + RESTORE_BX + ret + + + .p2align 4 +L(large_args): + /* Here if |x|>=9*Pi/4 */ + cmpl $0x7f800000, %eax /* x is Inf or NaN? */ + jae L(arg_inf_or_nan) + + /* Here if finite |x|>=9*Pi/4 */ + cmpl $0x4b000000, %eax /* |x|<2^23? */ + jae L(very_large_args) + + /* Here if 9*Pi/4<=|x|<2^23 */ + movsd MO1(DP_INVPIO4), %xmm1 /* 1/(Pi/4) */ + mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */ + cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */ + addl $1, %eax /* k+1 */ + movl %eax, %edx + andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */ + cvtsi2sdl %edx, %xmm4 /* DP j */ + movsd MO1(DP_PIO4HI), %xmm2 /* -PIO4HI = high part of -Pi/4 */ + mulsd %xmm4, %xmm2 /* -j*PIO4HI */ + movsd MO1(DP_PIO4LO), %xmm3 /* -PIO4LO = low part of -Pi/4 */ + addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */ + addl $2, %eax /* n */ + mulsd %xmm3, %xmm4 /* j*PIO4LO */ + addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */ + jmp L(reconstruction) + + .p2align 4 +L(very_large_args): + /* Here if finite |x|>=2^23 */ + + /* bitpos = (ix>>23) - BIAS_32 + 59; */ + shrl $23, %eax /* eb = biased exponent of x */ + /* bitpos = eb - 0x7f + 59, where 0x7f is exponent bias */ + subl $68, %eax + movl $28, %ecx /* %cl=28 */ + movl %eax, %edx /* bitpos copy */ + + /* j = bitpos/28; */ + div %cl /* j in register %al=%ax/%cl */ + movapd %xmm0, %xmm3 /* |x| */ + /* clear unneeded remainder from %ah */ + andl $0xff, %eax + + imull $28, %eax, %ecx /* j*28 */ + movsd MO1(DP_HI_MASK), %xmm4 /* DP_HI_MASK */ + movapd %xmm0, %xmm5 /* |x| */ + mulsd -2*8+MO2(_FPI,%eax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ + movapd %xmm0, %xmm1 /* |x| */ + mulsd -1*8+MO2(_FPI,%eax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ + mulsd 0*8+MO2(_FPI,%eax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ + addl $19, %ecx /* j*28+19 */ + mulsd 1*8+MO2(_FPI,%eax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */ + cmpl %ecx, %edx /* bitpos>=j*28+19? */ + jl L(very_large_skip1) + + /* Here if bitpos>=j*28+19 */ + andpd %xmm3, %xmm4 /* HI(tmp3) */ + subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */ +L(very_large_skip1): + + movsd MO1(DP_2POW52), %xmm6 + movapd %xmm5, %xmm2 /* tmp2 copy */ + addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */ + movl $1, %edx + addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */ + movsd 8+MO1(DP_2POW52), %xmm4 + movd %xmm6, %eax /* k = I64_LO(tmp6); */ + addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */ + comisd %xmm5, %xmm4 /* tmp4 > tmp5? */ + jbe L(very_large_skip2) + + /* Here if tmp4 > tmp5 */ + subl $1, %eax /* k-- */ + addsd 8+MO1(DP_ONES), %xmm4 /* tmp4 -= 1.0 */ +L(very_large_skip2): + + andl %eax, %edx /* k&1 */ + subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ + addsd MO2(DP_ZERONE,%edx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ + addsd %xmm2, %xmm3 /* t += tmp2 */ + addsd %xmm3, %xmm0 /* t += tmp0 */ + addl $3, %eax /* n=k+3 */ + addsd %xmm1, %xmm0 /* t += tmp1 */ + mulsd MO1(DP_PIO4), %xmm0 /* t *= PI04 */ + + jmp L(reconstruction) /* end of very_large_args peth */ + + + .p2align 4 +L(arg_less_pio4): + /* Here if |x|. */ + +#include + +extern float __cosf_sse2 (float); +extern float __cosf_ia32 (float); +float __cosf (float); + +libm_ifunc (__cosf, HAS_SSE2 ? __cosf_sse2 : __cosf_ia32); +weak_alias (__cosf, cosf); + +#define COSF __cosf_ia32 +#include diff --git a/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S b/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S new file mode 100644 index 0000000000..cda175094a --- /dev/null +++ b/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S @@ -0,0 +1,575 @@ +/* Optimized with sse2 version of sinf + Copyright (C) 2012 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 +#define __need_Emath +#include + +/* Short algorithm description: + * + * 1) if |x| == 0: return x. + * 2) if |x| < 2^-27: return x-x*DP_SMALL, raise underflow only when needed. + * 3) if |x| < 2^-5 : return x+x^3*DP_SIN2_0+x^5*DP_SIN2_1. + * 4) if |x| < Pi/4: return x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). + * 5) if |x| < 9*Pi/4: + * 5.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, + * t=|x|-j*Pi/4. + * 5.2) Reconstruction: + * s = sign(x) * (-1.0)^((n>>2)&1) + * if(n&2 != 0) { + * using cos(t) polynomial for |t|= 2^23, very large args: + * 7.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, + * t=|x|-j*Pi/4. + * 7.2) Reconstruction same as (5.2). + * 8) if x is Inf, return x-x, and set errno=EDOM. + * 9) if x is NaN, return x-x. + * + * Special cases: + * sin(+-0)==+-0 not raising inexact/underflow, + * sin(subnormal) raises inexact/underflow + * sin(min_normalized) raises inexact/underflow + * sin(normalized) raises inexact + * sin(Inf) = NaN, raises invalid, sets errno to EDOM + * sin(NaN) = NaN + */ + +#ifdef PIC +# define MO1(symbol) L(symbol)##@GOTOFF(%ebx) +# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale) +# define SAVE_BX pushl %ebx +# define RESTORE_BX popl %ebx +# define ARG_X 8(%esp) +#else +# define MO1(symbol) L(symbol) +# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale) +# define SAVE_BX +# define RESTORE_BX +# define ARG_X 4(%esp) +#endif + + .text +ENTRY(__sinf_sse2) + /* Input: single precision x on stack at address ARG_X */ + +#ifdef PIC + SAVE_BX + LOAD_PIC_REG(bx) +#endif + + movl ARG_X, %eax /* Bits of x */ + cvtss2sd ARG_X, %xmm0 /* DP x */ + andl $0x7fffffff, %eax /* |x| */ + + cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */ + movd %eax, %xmm3 /* SP |x| */ + andpd MO1(DP_ABS_MASK),%xmm0 /* DP |x| */ + movss MO1(SP_INVPIO4), %xmm2 /* SP 1/(Pi/4) */ + + cmpl $0x40e231d6, %eax /* |x|<9*Pi/4? */ + jae L(large_args) + + /* Here if Pi/4<=|x|<9*Pi/4 */ + mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */ + movl ARG_X, %ecx /* Load x */ + cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ + shrl $31, %ecx /* sign of x */ + addl $1, %eax /* k+1 */ + movl $0x0e, %edx + andl %eax, %edx /* j = (k+1)&0x0e */ + subsd MO2(PIO4J,%edx,8), %xmm0 /* t = |x| - j * Pi/4 */ + +L(reconstruction): + /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */ + testl $2, %eax /* n&2 != 0? */ + jz L(sin_poly) + +/*L(cos_poly):*/ + /* Here if sin(x) calculated using cos(t) polynomial for |t|>2)&1) + * result = s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))) + */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd MO1(DP_C4), %xmm4 /* C4 */ + mulsd %xmm0, %xmm4 /* z*C4 */ + xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ + movsd MO1(DP_C3), %xmm3 /* C3 */ + mulsd %xmm0, %xmm3 /* z*C3 */ + addsd MO1(DP_C2), %xmm4 /* C2+z*C4 */ + mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */ + lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */ + addsd MO1(DP_C1), %xmm3 /* C1+z*C3 */ + mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */ + addsd MO1(DP_C0), %xmm4 /* C0+z*(C2+z*C4) */ + mulsd %xmm1, %xmm4 /* y*(C0+z*(C2+z*C4)) */ + + addsd %xmm4, %xmm3 /* y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + /* 1.0+y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + addsd MO1(DP_ONES), %xmm3 + + mulsd MO2(DP_ONES,%ecx,8), %xmm3 /* DP result */ + movsd %xmm3, 0(%esp) /* Move result from sse... */ + fldl 0(%esp) /* ...to FPU. */ + /* Return back 4 bytes of stack frame */ + lea 8(%esp), %esp + RESTORE_BX + ret + + .p2align 4 +L(sin_poly): + /* Here if sin(x) calculated using sin(t) polynomial for |t|>2)&1) + * result = s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))) + */ + + movaps %xmm0, %xmm4 /* t */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd MO1(DP_S4), %xmm2 /* S4 */ + mulsd %xmm0, %xmm2 /* z*S4 */ + movsd MO1(DP_S3), %xmm3 /* S3 */ + mulsd %xmm0, %xmm3 /* z*S3 */ + lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */ + addsd MO1(DP_S2), %xmm2 /* S2+z*S4 */ + mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */ + addsd MO1(DP_S1), %xmm3 /* S1+z*S3 */ + mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */ + addsd MO1(DP_S0), %xmm2 /* S0+z*(S2+z*S4) */ + mulsd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ + /* t*s, where s = sign(x) * (-1.0)^((n>>2)&1) */ + mulsd MO2(DP_ONES,%ecx,8), %xmm4 + addsd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + /* t*s*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + mulsd %xmm4, %xmm3 + /* t*s*(1.0+y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm4, %xmm3 + movsd %xmm3, 0(%esp) /* Move result from sse... */ + fldl 0(%esp) /* ...to FPU. */ + /* Return back 4 bytes of stack frame */ + lea 8(%esp), %esp + RESTORE_BX + ret + + + .p2align 4 +L(large_args): + /* Here if |x|>=9*Pi/4 */ + cmpl $0x7f800000, %eax /* x is Inf or NaN? */ + jae L(arg_inf_or_nan) + + /* Here if finite |x|>=9*Pi/4 */ + cmpl $0x4b000000, %eax /* |x|<2^23? */ + jae L(very_large_args) + + /* Here if 9*Pi/4<=|x|<2^23 */ + movsd MO1(DP_INVPIO4), %xmm1 /* 1/(Pi/4) */ + mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */ + cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */ + addl $1, %eax /* k+1 */ + movl %eax, %edx + andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */ + cvtsi2sdl %edx, %xmm4 /* DP j */ + movl ARG_X, %ecx /* Load x */ + movsd MO1(DP_PIO4HI), %xmm2 /* -PIO4HI = high part of -Pi/4 */ + shrl $31, %ecx /* sign bit of x */ + mulsd %xmm4, %xmm2 /* -j*PIO4HI */ + movsd MO1(DP_PIO4LO), %xmm3 /* -PIO4LO = low part of -Pi/4 */ + addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */ + mulsd %xmm3, %xmm4 /* j*PIO4LO */ + addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */ + jmp L(reconstruction) + + .p2align 4 +L(very_large_args): + /* Here if finite |x|>=2^23 */ + + /* bitpos = (ix>>23) - BIAS_32 + 59; */ + shrl $23, %eax /* eb = biased exponent of x */ + /* bitpos = eb - 0x7f + 59, where 0x7f is exponent bias */ + subl $68, %eax + movl $28, %ecx /* %cl=28 */ + movl %eax, %edx /* bitpos copy */ + + /* j = bitpos/28; */ + div %cl /* j in register %al=%ax/%cl */ + movapd %xmm0, %xmm3 /* |x| */ + /* clear unneeded remainder from %ah */ + andl $0xff, %eax + + imull $28, %eax, %ecx /* j*28 */ + movsd MO1(DP_HI_MASK), %xmm4 /* DP_HI_MASK */ + movapd %xmm0, %xmm5 /* |x| */ + mulsd -2*8+MO2(_FPI,%eax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ + movapd %xmm0, %xmm1 /* |x| */ + mulsd -1*8+MO2(_FPI,%eax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ + mulsd 0*8+MO2(_FPI,%eax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ + addl $19, %ecx /* j*28+19 */ + mulsd 1*8+MO2(_FPI,%eax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */ + cmpl %ecx, %edx /* bitpos>=j*28+19? */ + jl L(very_large_skip1) + + /* Here if bitpos>=j*28+19 */ + andpd %xmm3, %xmm4 /* HI(tmp3) */ + subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */ +L(very_large_skip1): + + movsd MO1(DP_2POW52), %xmm6 + movapd %xmm5, %xmm2 /* tmp2 copy */ + addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */ + movl $1, %edx + addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */ + movsd 8+MO1(DP_2POW52), %xmm4 + movd %xmm6, %eax /* k = I64_LO(tmp6); */ + addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */ + movl ARG_X, %ecx /* Load x */ + comisd %xmm5, %xmm4 /* tmp4 > tmp5? */ + jbe L(very_large_skip2) + + /* Here if tmp4 > tmp5 */ + subl $1, %eax /* k-- */ + addsd 8+MO1(DP_ONES), %xmm4 /* tmp4 -= 1.0 */ +L(very_large_skip2): + + andl %eax, %edx /* k&1 */ + subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ + addsd MO2(DP_ZERONE,%edx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ + addsd %xmm2, %xmm3 /* t += tmp2 */ + shrl $31, %ecx /* sign of x */ + addsd %xmm3, %xmm0 /* t += tmp0 */ + addl $1, %eax /* n=k+1 */ + addsd %xmm1, %xmm0 /* t += tmp1 */ + mulsd MO1(DP_PIO4), %xmm0 /* t *= PI04 */ + + jmp L(reconstruction) /* end of very_large_args peth */ + + + + + + .p2align 4 +L(arg_less_pio4): + /* Here if |x|. */ + +#include + +extern float __sinf_sse2 (float); +extern float __sinf_ia32 (float); +float __sinf (float); + +libm_ifunc (__sinf, HAS_SSE2 ? __sinf_sse2 : __sinf_ia32); +weak_alias (__sinf, sinf); +#define SINF __sinf_ia32 +#include diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c index f4bd81904b..864ab27a4f 100644 --- a/sysdeps/ieee754/flt-32/s_cosf.c +++ b/sysdeps/ieee754/flt-32/s_cosf.c @@ -23,7 +23,13 @@ static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $"; static const float one=1.0; -float __cosf(float x) +#ifndef COSF +# define COSF_FUNC __cosf +#else +# define COSF_FUNC COSF +#endif + +float COSF_FUNC(float x) { float y[2],z=0.0; int32_t n,ix; @@ -53,4 +59,7 @@ float __cosf(float x) } } } + +#ifndef COSF weak_alias (__cosf, cosf) +#endif diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c index 02fa29f23b..916e345571 100644 --- a/sysdeps/ieee754/flt-32/s_sinf.c +++ b/sysdeps/ieee754/flt-32/s_sinf.c @@ -21,7 +21,13 @@ static char rcsid[] = "$NetBSD: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $"; #include #include -float __sinf(float x) +#ifndef SINF +# define SINF_FUNC __sinf +#else +# define SINF_FUNC SINF +#endif + +float SINF_FUNC(float x) { float y[2],z=0.0; int32_t n, ix; @@ -51,4 +57,7 @@ float __sinf(float x) } } } + +#ifndef SINF weak_alias (__sinf, sinf) +#endif diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index 8a38221133..eb02222d23 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -1208,6 +1208,8 @@ ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_downward (10) == -0.8390715290764524522588639478240648345199": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_downward (2) == -0.4161468365471423869975682295007621897660": @@ -1239,6 +1241,8 @@ ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_downward (9) == -0.9111302618846769883682947111811653112463": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 @@ -1285,15 +1289,22 @@ ildouble: 1 ldouble: 1 # cos_upward +Test "cos_upward (1) == 0.5403023058681397174009366074429766037323": +float: 1 +ifloat: 1 Test "cos_upward (10) == -0.8390715290764524522588639478240648345199": float: 1 ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_upward (2) == -0.4161468365471423869975682295007621897660": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_upward (3) == -0.9899924966004454572715727947312613023937": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_upward (4) == -0.6536436208636119146391681830977503814241": @@ -1311,6 +1322,8 @@ Test "cos_upward (7) == 0.7539022543433046381411975217191820122183": float: 1 ifloat: 1 Test "cos_upward (8) == -0.1455000338086135258688413818311946826093": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "cos_upward (9) == -0.9111302618846769883682947111811653112463": @@ -2319,6 +2332,8 @@ Test "sin_downward (8) == 0.9893582466233817778081235982452886721164": ildouble: 1 ldouble: 1 Test "sin_downward (9) == 0.4121184852417565697562725663524351793439": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 @@ -2374,6 +2389,8 @@ Test "sin_upward (1) == 0.8414709848078965066525023216302989996226": float: 1 ifloat: 1 Test "sin_upward (10) == -0.5440211108893698134047476618513772816836": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "sin_upward (2) == 0.9092974268256816953960198659117448427023": @@ -2382,6 +2399,8 @@ ifloat: 2 ildouble: 1 ldouble: 1 Test "sin_upward (3) == 0.1411200080598672221007448028081102798469": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "sin_upward (4) == -0.7568024953079282513726390945118290941359": @@ -2390,11 +2409,19 @@ ifloat: 1 ildouble: 1 ldouble: 1 Test "sin_upward (5) == -0.9589242746631384688931544061559939733525": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 Test "sin_upward (6) == -0.2794154981989258728115554466118947596280": ildouble: 1 ldouble: 1 +Test "sin_upward (7) == 0.6569865987187890903969990915936351779369": +float: 1 +ifloat: 1 +Test "sin_upward (8) == 0.9893582466233817778081235982452886721164": +float: 1 +ifloat: 1 Test "sin_upward (9) == 0.4121184852417565697562725663524351793439": float: 1 ifloat: 1 @@ -3052,8 +3079,8 @@ ildouble: 1 ldouble: 1 Function: "cos_upward": -float: 2 -ifloat: 2 +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 @@ -3412,8 +3439,8 @@ ildouble: 1 ldouble: 1 Function: "sin_upward": -float: 2 -ifloat: 2 +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 diff --git a/sysdeps/x86_64/fpu/s_cosf.S b/sysdeps/x86_64/fpu/s_cosf.S new file mode 100644 index 0000000000..7eeefe8f30 --- /dev/null +++ b/sysdeps/x86_64/fpu/s_cosf.S @@ -0,0 +1,535 @@ +/* Optimized cosf function. + Copyright (C) 2012 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 +#define __need_Emath +#include + +/* Short algorithm description: + * + * 1) if |x| == 0: return 1.0-|x|. + * 2) if |x| < 2^-27: return 1.0-|x|. + * 3) if |x| < 2^-5 : return 1.0+x^2*DP_COS2_0+x^5*DP_COS2_1. + * 4) if |x| < Pi/4: return 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). + * 5) if |x| < 9*Pi/4: + * 5.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+3, + * t=|x|-j*Pi/4. + * 5.2) Reconstruction: + * s = (-1.0)^((n>>2)&1) + * if(n&2 != 0) { + * using cos(t) polynomial for |t|= 2^23, very large args: + * 7.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+3, + * t=|x|-j*Pi/4. + * 7.2) Reconstruction same as (5.2). + * 8) if x is Inf, return x-x, and set errno=EDOM. + * 9) if x is NaN, return x-x. + * + * Special cases: + * cos(+-0)==+-0 not raising inexact/underflow, + * cos(subnormal) raises inexact/underflow + * cos(min_normalized) raises inexact/underflow + * cos(normalized) raises inexact + * cos(Inf) = NaN, raises invalid, sets errno to EDOM + * cos(NaN) = NaN + */ + + .text +ENTRY(__cosf) + /* Input: single precision x in %xmm0 */ + + movd %xmm0, %eax /* Bits of x */ + movaps %xmm0, %xmm7 /* Copy of x */ + cvtss2sd %xmm0, %xmm0 /* DP x */ + movss L(SP_ABS_MASK)(%rip), %xmm3 + andl $0x7fffffff, %eax /* |x| */ + + cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */ + andps %xmm7, %xmm3 /* SP |x| */ + andpd L(DP_ABS_MASK)(%rip), %xmm0 /* DP |x| */ + movss L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */ + + cmpl $0x40e231d6, %eax /* |x|<9*Pi/4? */ + jae L(large_args) + + /* Here if Pi/4<=|x|<9*Pi/4 */ + mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */ + cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ + lea L(PIO4J)(%rip), %rsi + addl $1, %eax /* k+1 */ + movl $0x0e, %edx + andl %eax, %edx /* j = (k+1)&0x0e */ + addl $2, %eax /* n */ + subsd (%rsi,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */ + +L(reconstruction): + /* Input: %eax=n, %xmm0=t */ + testl $2, %eax /* n&2 != 0? */ + jz L(sin_poly) + +/*L(cos_poly):*/ + /* Here if cos(x) calculated using cos(t) polynomial for |t|>2)&1) + * result = s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))) + */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd L(DP_C4)(%rip), %xmm4 /* C4 */ + mulsd %xmm0, %xmm4 /* z*C4 */ + movsd L(DP_C3)(%rip), %xmm3 /* C3 */ + mulsd %xmm0, %xmm3 /* z*C3 */ + lea L(DP_ONES)(%rip), %rsi + addsd L(DP_C2)(%rip), %xmm4 /* C2+z*C4 */ + mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */ + addsd L(DP_C1)(%rip), %xmm3 /* C1+z*C3 */ + mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */ + addsd L(DP_C0)(%rip), %xmm4 /* C0+z*(C2+z*C4) */ + mulsd %xmm1, %xmm4 /* y*(C0+z*(C2+z*C4)) */ + + addsd %xmm4, %xmm3 /* y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + /* 1.0+y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + addsd L(DP_ONES)(%rip), %xmm3 + + mulsd (%rsi,%rax,8), %xmm3 /* DP result */ + cvtsd2ss %xmm3, %xmm0 /* SP result */ + ret + + .p2align 4 +L(sin_poly): + /* Here if cos(x) calculated using sin(t) polynomial for |t|>2)&1) + * result = s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))) + */ + + movaps %xmm0, %xmm4 /* t */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd L(DP_S4)(%rip), %xmm2 /* S4 */ + mulsd %xmm0, %xmm2 /* z*S4 */ + movsd L(DP_S3)(%rip), %xmm3 /* S3 */ + mulsd %xmm0, %xmm3 /* z*S3 */ + lea L(DP_ONES)(%rip), %rsi + addsd L(DP_S2)(%rip), %xmm2 /* S2+z*S4 */ + mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */ + addsd L(DP_S1)(%rip), %xmm3 /* S1+z*S3 */ + mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */ + addsd L(DP_S0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */ + mulsd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ + /* t*s, where s = sign(x) * (-1.0)^((n>>2)&1) */ + mulsd (%rsi,%rax,8), %xmm4 + /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm2, %xmm3 + /* t*s*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + mulsd %xmm4, %xmm3 + /* t*s*(1.0+y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm4, %xmm3 + cvtsd2ss %xmm3, %xmm0 /* SP result */ + ret + + + + + + .p2align 4 +L(large_args): + /* Here if |x|>=9*Pi/4 */ + cmpl $0x7f800000, %eax /* x is Inf or NaN? */ + jae L(arg_inf_or_nan) + + /* Here if finite |x|>=9*Pi/4 */ + cmpl $0x4b000000, %eax /* |x|<2^23? */ + jae L(very_large_args) + + /* Here if 9*Pi/4<=|x|<2^23 */ + movsd L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */ + mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */ + cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */ + addl $1, %eax /* k+1 */ + movl %eax, %edx + andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */ + cvtsi2sdl %edx, %xmm4 /* DP j */ + movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */ + mulsd %xmm4, %xmm2 /* -j*PIO4HI */ + movsd L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */ + addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */ + addl $2, %eax /* n */ + mulsd %xmm3, %xmm4 /* j*PIO4LO */ + addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */ + jmp L(reconstruction) + + .p2align 4 +L(very_large_args): + /* Here if finite |x|>=2^23 */ + + /* bitpos = (ix>>23) - BIAS_32 + 59; */ + shrl $23, %eax /* eb = biased exponent of x */ + /* bitpos = eb - 0x7f + 59, where 0x7f is exponent bias */ + subl $68, %eax + movl $28, %ecx /* %cl=28 */ + movl %eax, %edx /* bitpos copy */ + + /* j = bitpos/28; */ + div %cl /* j in register %al=%ax/%cl */ + movapd %xmm0, %xmm3 /* |x| */ + /* clear unneeded remainder from %ah */ + andl $0xff, %eax + + imull $28, %eax, %ecx /* j*28 */ + lea L(_FPI)(%rip), %rsi + movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */ + movapd %xmm0, %xmm5 /* |x| */ + mulsd -16(%rsi,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ + movapd %xmm0, %xmm1 /* |x| */ + mulsd -8(%rsi,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ + mulsd (%rsi,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ + addl $19, %ecx /* j*28+19 */ + mulsd 8(%rsi,%rax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */ + cmpl %ecx, %edx /* bitpos>=j*28+19? */ + jl L(very_large_skip1) + + /* Here if bitpos>=j*28+19 */ + andpd %xmm3, %xmm4 /* HI(tmp3) */ + subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */ +L(very_large_skip1): + + movsd L(DP_2POW52)(%rip), %xmm6 + movapd %xmm5, %xmm2 /* tmp2 copy */ + addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */ + movl $1, %edx + addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */ + movsd 8+L(DP_2POW52)(%rip), %xmm4 + movd %xmm6, %eax /* k = I64_LO(tmp6); */ + addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */ + comisd %xmm5, %xmm4 /* tmp4 > tmp5? */ + jbe L(very_large_skip2) + + /* Here if tmp4 > tmp5 */ + subl $1, %eax /* k-- */ + addsd 8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */ +L(very_large_skip2): + + andl %eax, %edx /* k&1 */ + lea L(DP_ZERONE)(%rip), %rsi + subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ + addsd (%rsi,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ + addsd %xmm2, %xmm3 /* t += tmp2 */ + addsd %xmm3, %xmm0 /* t += tmp0 */ + addl $3, %eax /* n=k+3 */ + addsd %xmm1, %xmm0 /* t += tmp1 */ + mulsd L(DP_PIO4)(%rip), %xmm0 /* t *= PI04 */ + + jmp L(reconstruction) /* end of very_large_args peth */ + + + .p2align 4 +L(arg_less_pio4): + /* Here if |x|. */ + +#include +#define __need_Emath +#include + +/* Short algorithm description: + * + * 1) if |x| == 0: return x. + * 2) if |x| < 2^-27: return x-x*DP_SMALL, raise underflow only when needed. + * 3) if |x| < 2^-5 : return x+x^3*DP_SIN2_0+x^5*DP_SIN2_1. + * 4) if |x| < Pi/4: return x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). + * 5) if |x| < 9*Pi/4: + * 5.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, + * t=|x|-j*Pi/4. + * 5.2) Reconstruction: + * s = sign(x) * (-1.0)^((n>>2)&1) + * if(n&2 != 0) { + * using cos(t) polynomial for |t|= 2^23, very large args: + * 7.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, + * t=|x|-j*Pi/4. + * 7.2) Reconstruction same as (5.2). + * 8) if x is Inf, return x-x, and set errno=EDOM. + * 9) if x is NaN, return x-x. + * + * Special cases: + * sin(+-0)==+-0 not raising inexact/underflow, + * sin(subnormal) raises inexact/underflow + * sin(min_normalized) raises inexact/underflow + * sin(normalized) raises inexact + * sin(Inf) = NaN, raises invalid, sets errno to EDOM + * sin(NaN) = NaN + */ + + .text +ENTRY(__sinf) + /* Input: single precision x in %xmm0 */ + + movd %xmm0, %eax /* Bits of x */ + movaps %xmm0, %xmm7 /* Copy of x */ + cvtss2sd %xmm0, %xmm0 /* DP x */ + movss L(SP_ABS_MASK)(%rip), %xmm3 + movl %eax, %edi /* Copy of x bits */ + andl $0x7fffffff, %eax /* |x| */ + + cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */ + andps %xmm7, %xmm3 /* SP |x| */ + andpd L(DP_ABS_MASK)(%rip),%xmm0 /* DP |x| */ + movss L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */ + + cmpl $0x40e231d6, %eax /* |x|<9*Pi/4? */ + jae L(large_args) + + /* Here if Pi/4<=|x|<9*Pi/4 */ + mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */ + movl %edi, %ecx /* Load x */ + cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ + lea L(PIO4J)(%rip), %rsi + shrl $31, %ecx /* sign of x */ + addl $1, %eax /* k+1 */ + movl $0x0e, %edx + andl %eax, %edx /* j = (k+1)&0x0e */ + subsd (%rsi,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */ + +L(reconstruction): + /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */ + testl $2, %eax /* n&2 != 0? */ + jz L(sin_poly) + +/*L(cos_poly):*/ + /* Here if sin(x) calculated using cos(t) polynomial for |t|>2)&1) + * result = s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))) + */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd L(DP_C4)(%rip), %xmm4 /* C4 */ + mulsd %xmm0, %xmm4 /* z*C4 */ + xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ + movsd L(DP_C3)(%rip), %xmm3 /* C3 */ + mulsd %xmm0, %xmm3 /* z*C3 */ + lea L(DP_ONES)(%rip), %rsi + addsd L(DP_C2)(%rip), %xmm4 /* C2+z*C4 */ + mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */ + addsd L(DP_C1)(%rip), %xmm3 /* C1+z*C3 */ + mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */ + addsd L(DP_C0)(%rip), %xmm4 /* C0+z*(C2+z*C4) */ + mulsd %xmm1, %xmm4 /* y*(C0+z*(C2+z*C4)) */ + + /* y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + addsd %xmm4, %xmm3 + /* 1.0+y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ + addsd L(DP_ONES)(%rip), %xmm3 + + mulsd (%rsi,%rcx,8), %xmm3 /* DP result */ + cvtsd2ss %xmm3, %xmm0 /* SP result */ + ret + + .p2align 4 +L(sin_poly): + /* Here if sin(x) calculated using sin(t) polynomial for |t|>2)&1) + * result = s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))) + */ + + movaps %xmm0, %xmm4 /* t */ + shrl $2, %eax /* n>>2 */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + andl $1, %eax /* (n>>2)&1 */ + movaps %xmm0, %xmm1 /* y */ + xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ + mulsd %xmm0, %xmm0 /* z=t^4 */ + + movsd L(DP_S4)(%rip), %xmm2 /* S4 */ + mulsd %xmm0, %xmm2 /* z*S4 */ + movsd L(DP_S3)(%rip), %xmm3 /* S3 */ + mulsd %xmm0, %xmm3 /* z*S3 */ + lea L(DP_ONES)(%rip), %rsi + addsd L(DP_S2)(%rip), %xmm2 /* S2+z*S4 */ + mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */ + addsd L(DP_S1)(%rip), %xmm3 /* S1+z*S3 */ + mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */ + addsd L(DP_S0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */ + mulsd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ + /* t*s, where s = sign(x) * (-1.0)^((n>>2)&1) */ + mulsd (%rsi,%rcx,8), %xmm4 + /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm2, %xmm3 + /* t*s*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + mulsd %xmm4, %xmm3 + /* t*s*(1.0+y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + addsd %xmm4, %xmm3 + cvtsd2ss %xmm3, %xmm0 /* SP result */ + ret + + + .p2align 4 +L(large_args): + /* Here if |x|>=9*Pi/4 */ + cmpl $0x7f800000, %eax /* x is Inf or NaN? */ + jae L(arg_inf_or_nan) + + /* Here if finite |x|>=9*Pi/4 */ + cmpl $0x4b000000, %eax /* |x|<2^23? */ + jae L(very_large_args) + + /* Here if 9*Pi/4<=|x|<2^23 */ + movsd L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */ + mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */ + cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */ + addl $1, %eax /* k+1 */ + movl %eax, %edx + andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */ + cvtsi2sdl %edx, %xmm4 /* DP j */ + movl %edi, %ecx /* Load x */ + movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */ + shrl $31, %ecx /* sign bit of x */ + mulsd %xmm4, %xmm2 /* -j*PIO4HI */ + movsd L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */ + addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */ + mulsd %xmm3, %xmm4 /* j*PIO4LO */ + addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */ + jmp L(reconstruction) + + .p2align 4 +L(very_large_args): + /* Here if finite |x|>=2^23 */ + + /* bitpos = (ix>>23) - BIAS_32 + 59; */ + shrl $23, %eax /* eb = biased exponent of x */ + /* bitpos = eb - 0x7f + 59, where 0x7f is exponent bias */ + subl $68, %eax + movl $28, %ecx /* %cl=28 */ + movl %eax, %edx /* bitpos copy */ + + /* j = bitpos/28; */ + div %cl /* j in register %al=%ax/%cl */ + movapd %xmm0, %xmm3 /* |x| */ + /* clear unneeded remainder from %ah */ + andl $0xff, %eax + + imull $28, %eax, %ecx /* j*28 */ + lea L(_FPI)(%rip), %rsi + movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */ + movapd %xmm0, %xmm5 /* |x| */ + mulsd -16(%rsi,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ + movapd %xmm0, %xmm1 /* |x| */ + mulsd -8(%rsi,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ + mulsd (%rsi,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ + addl $19, %ecx /* j*28+19 */ + mulsd 8(%rsi,%rax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */ + cmpl %ecx, %edx /* bitpos>=j*28+19? */ + jl L(very_large_skip1) + + /* Here if bitpos>=j*28+19 */ + andpd %xmm3, %xmm4 /* HI(tmp3) */ + subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */ +L(very_large_skip1): + + movsd L(DP_2POW52)(%rip), %xmm6 + movapd %xmm5, %xmm2 /* tmp2 copy */ + addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */ + movl $1, %edx + addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */ + movsd 8+L(DP_2POW52)(%rip), %xmm4 + movd %xmm6, %eax /* k = I64_LO(tmp6); */ + addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */ + movl %edi, %ecx /* Load x */ + comisd %xmm5, %xmm4 /* tmp4 > tmp5? */ + jbe L(very_large_skip2) + + /* Here if tmp4 > tmp5 */ + subl $1, %eax /* k-- */ + addsd 8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */ +L(very_large_skip2): + + andl %eax, %edx /* k&1 */ + lea L(DP_ZERONE)(%rip), %rsi + subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ + addsd (%rsi,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ + addsd %xmm2, %xmm3 /* t += tmp2 */ + shrl $31, %ecx /* sign of x */ + addsd %xmm3, %xmm0 /* t += tmp0 */ + addl $1, %eax /* n=k+1 */ + addsd %xmm1, %xmm0 /* t += tmp1 */ + mulsd L(DP_PIO4)(%rip), %xmm0 /* t *= PI04 */ + + jmp L(reconstruction) /* end of very_large_args peth */ + + + .p2align 4 +L(arg_less_pio4): + /* Here if |x|