From 22bf5c179315edd33b8399102ea3cfbf92b4807f Mon Sep 17 00:00:00 2001 From: Liubov Dmitrieva Date: Tue, 25 Sep 2012 20:44:46 +0200 Subject: Add optimized sincosf for SSE2 for x86 and x86-64 --- sysdeps/x86_64/fpu/libm-test-ulps | 42 +-- sysdeps/x86_64/fpu/s_sincosf.S | 558 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 582 insertions(+), 18 deletions(-) create mode 100644 sysdeps/x86_64/fpu/s_sincosf.S (limited to 'sysdeps/x86_64/fpu') diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index b02b9e6baf..d79578ce41 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -1579,6 +1579,9 @@ ildouble: 1 ldouble: 1 # ctan +Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i": +float: 1 +ifloat: 1 Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i": double: 1 float: 1 @@ -1612,6 +1615,8 @@ Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.225462792499754505792678258 ildouble: 1 ldouble: 1 Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i": +float: 2 +ifloat: 2 double: 1 idouble: 1 Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i": @@ -1757,6 +1762,8 @@ idouble: 1 ildouble: 1 ldouble: 1 Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i": +float: 2 +ifloat: 2 double: 1 idouble: 1 Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i": @@ -1765,6 +1772,9 @@ ldouble: 1 Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i": ildouble: 2 ldouble: 2 +Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i": +float: 1 +ifloat: 1 # ctanh_downward Test "Real part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": @@ -2399,8 +2409,8 @@ ifloat: 2 ildouble: 1 ldouble: 1 Test "sin_upward (3) == 0.1411200080598672221007448028081102798469": -float: 1 -ifloat: 1 +float: 2 +ifloat: 2 ildouble: 1 ldouble: 1 Test "sin_upward (4) == -0.7568024953079282513726390945118290941359": @@ -2430,12 +2440,6 @@ ifloat: 1 Test "sincos (0.80190127184058835, &sin_res, &cos_res) puts 0.69534156199418473 in cos_res": double: 1 idouble: 1 -Test "sincos (0x1p+120, &sin_res, &cos_res) puts -9.25879022854837867303861764107414946730833e-01 in cos_res": -float: 1 -ifloat: 1 -Test "sincos (0x1p+127, &sin_res, &cos_res) puts 7.81914638714960072263910298466369236613162e-01 in cos_res": -float: 1 -ifloat: 1 Test "sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.5 in cos_res": double: 1 float: 1 @@ -2705,6 +2709,8 @@ Test "y1 (0x1.001000001p+593) == 3.927269966354206207832593635798954916263e-90": ildouble: 2 ldouble: 2 Test "y1 (0x1.27e204p+99) == -8.881610148467797208469612080785210013461e-16": +float: 1 +ifloat: 1 double: 1 idouble: 1 ildouble: 1 @@ -3085,8 +3091,8 @@ ildouble: 1 ldouble: 1 Function: "cos_upward": -float: 1 -ifloat: 1 +float: 2 +ifloat: 2 ildouble: 1 ldouble: 1 @@ -3174,17 +3180,17 @@ ldouble: 1 Function: Real part of "ctan": double: 1 -float: 1 +float: 2 idouble: 1 -ifloat: 1 +ifloat: 2 ildouble: 2 ldouble: 2 Function: Imaginary part of "ctan": double: 1 -float: 1 +float: 2 idouble: 1 -ifloat: 1 +ifloat: 2 ildouble: 1 ldouble: 1 @@ -3242,9 +3248,9 @@ ldouble: 4 Function: Real part of "ctanh": double: 1 -float: 1 +float: 2 idouble: 1 -ifloat: 1 +ifloat: 2 ildouble: 1 ldouble: 1 @@ -3445,8 +3451,8 @@ ildouble: 1 ldouble: 1 Function: "sin_upward": -float: 1 -ifloat: 1 +float: 2 +ifloat: 2 ildouble: 1 ldouble: 1 diff --git a/sysdeps/x86_64/fpu/s_sincosf.S b/sysdeps/x86_64/fpu/s_sincosf.S new file mode 100644 index 0000000000..3334a3a78f --- /dev/null +++ b/sysdeps/x86_64/fpu/s_sincosf.S @@ -0,0 +1,558 @@ +/* Optimized sincosf 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: sin(x)=x, + * cos(x)=1. + * 2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed, + * cos(x)=1-|x|. + * 3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1, + * cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1 + * 4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))), + * cos(x)=1+1*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+1, t=|x|-j*Pi/4. + * 5.2) Reconstruction: + * sign_sin = sign(x) * (-1.0)^(( n >>2)&1) + * sign_cos = (-1.0)^(((n+2)>>2)&1) + * poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t + * poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s + * if(n&2 != 0) { + * using cos(t) and sin(t) polynomials 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/cos(+-0) = +-0/1 not raising inexact/underflow, + * sin/cos(subnormal) raises inexact/underflow, + * sin/cos(min_normalized) raises inexact/underflow, + * sin/cos(normalized) raises inexact, + * sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM, + * sin/cos(NaN) = NaN. + */ + +# define ARG_SIN_PTR %rdi +# define ARG_COS_PTR %rsi + + .text +ENTRY(__sincosf) + /* Input: %xmm0 contains single precision argument x */ + /* %rdi points to sin result */ + /* %rsi points to cos result */ + + 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, %r8d /* 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 %r8d, %ecx /* Load x */ + cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ + lea L(PIO4J)(%rip), %r9 + shrl $29, %ecx /* (sign of x) << 2 */ + addl $1, %eax /* k+1 */ + movl $0x0e, %edx + andl %eax, %edx /* j = (k+1)&0x0e */ + subsd (%r9,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */ + +L(reconstruction): + /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */ + + movaps %xmm0, %xmm4 /* t */ + movhpd L(DP_ONES)(%rip), %xmm4 /* 1|t */ + mulsd %xmm0, %xmm0 /* y=t^2 */ + movl $2, %edx + unpcklpd %xmm0, %xmm0 /* y|y */ + addl %eax, %edx /* k+2 */ + movaps %xmm0, %xmm1 /* y|y */ + mulpd %xmm0, %xmm0 /* z=t^4|z=t^4 */ + + movaps L(DP_SC4)(%rip), %xmm2 /* S4 */ + mulpd %xmm0, %xmm2 /* z*S4 */ + movaps L(DP_SC3)(%rip), %xmm3 /* S3 */ + mulpd %xmm0, %xmm3 /* z*S3 */ + xorl %eax, %ecx /* (sign_x ^ (k>>2))<<2 */ + addpd L(DP_SC2)(%rip), %xmm2 /* S2+z*S4 */ + mulpd %xmm0, %xmm2 /* z*(S2+z*S4) */ + shrl $2, %edx /* (k+2)>>2 */ + addpd L(DP_SC1)(%rip), %xmm3 /* S1+z*S3 */ + mulpd %xmm0, %xmm3 /* z*(S1+z*S3) */ + shrl $2, %ecx /* sign_x ^ k>>2 */ + addpd L(DP_SC0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */ + andl $1, %edx /* sign_cos = ((k+2)>>2)&1 */ + mulpd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ + andl $1, %ecx /* sign_sin = sign_x ^ ((k>>2)&1) */ + addpd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ + lea L(DP_ONES)(%rip), %r9 + mulpd %xmm4, %xmm3 /*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/ + testl $2, %eax /* n&2 != 0 ? */ + addpd %xmm4, %xmm3 /*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/ + jnz L(sin_result_sin_poly) + +/*L(sin_result_cos_poly):*/ + /* + * Here if + * cos(x) = poly_sin * sign_cos + * sin(x) = poly_cos * sign_sin + */ + movsd (%r9,%rcx,8), %xmm4 /* 0|sign_sin */ + movhpd (%r9,%rdx,8), %xmm4 /* sign_cos|sign_sin */ + mulpd %xmm4, %xmm3 /* result_cos|result_sin */ + cvtpd2ps %xmm3, %xmm0 /* SP results */ + movss %xmm0, (ARG_SIN_PTR) /* store sin(x) from xmm0[0] */ + shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */ + movss %xmm0, (ARG_COS_PTR) /* store cos(x) */ + ret + + .p2align 4 +L(sin_result_sin_poly): + /* + * Here if + * sin(x) = poly_sin * sign_sin + * cos(x) = poly_cos * sign_cos + */ + movsd (%r9,%rdx,8), %xmm4 /* 0|sign_cos */ + movhpd (%r9,%rcx,8), %xmm4 /* sign_sin|sign_cos */ + mulpd %xmm4, %xmm3 /* result_sin|result_cos */ + cvtpd2ps %xmm3, %xmm0 /* SP results */ + movss %xmm0, (ARG_COS_PTR) /* store cos(x) from xmm0[0] */ + shufps $1, %xmm0, %xmm0 /* move sin(x) to xmm0[0] */ + movss %xmm0, (ARG_SIN_PTR) /* store sin(x) */ + 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 %r8d, %ecx /* Load x */ + movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */ + shrl $29, %ecx /* (sign of x) << 2 */ + 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 */ + subl $68, %eax /* bitpos=eb-0x7f+59, where 0x7f */ + /*is exponent bias */ + 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| */ + andl $0xff, %eax /* clear unneeded remainder from %ah*/ + + imull $28, %eax, %ecx /* j*28 */ + lea L(_FPI)(%rip), %r9 + movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */ + movapd %xmm0, %xmm5 /* |x| */ + mulsd -16(%r9,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ + movapd %xmm0, %xmm1 /* |x| */ + mulsd -8(%r9,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ + mulsd (%r9,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ + addl $19, %ecx /* j*28+19 */ + mulsd 8(%r9,%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 %r8d, %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), %r9 + subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ + addsd (%r9,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ + addsd %xmm2, %xmm3 /* t += tmp2 */ + shrl $29, %ecx /* (sign of x) << 2 */ + 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|