From 4ffffbd272264f083f35783ed81339304025f855 Mon Sep 17 00:00:00 2001 From: Liubov Dmitrieva Date: Mon, 3 Sep 2012 15:32:13 +0200 Subject: 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. --- sysdeps/x86_64/fpu/s_cosf.S | 535 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 535 insertions(+) create mode 100644 sysdeps/x86_64/fpu/s_cosf.S (limited to 'sysdeps/x86_64/fpu/s_cosf.S') diff --git a/sysdeps/x86_64/fpu/s_cosf.S b/sysdeps/x86_64/fpu/s_cosf.S new file mode 100644 index 0000000..7eeefe8 --- /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|