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Add optimized sincosf for SSE2 for x86 and x86-64

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Liubov Dmitrieva 2012-09-25 20:44:46 +02:00 committed by Andreas Jaeger
parent 6d3bf19931
commit 22bf5c1793
8 changed files with 1241 additions and 34 deletions
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14
ChangeLog
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@ -1,6 +1,18 @@
2012-09-25 Liubov Dmitrieva <liubov.dmitrieva@gmail.com>
* math/s_ccoshf.c (__ccoshf): Fix wrong using of sincosf for
* sysdeps/i386/i686/fpu/multiarch/Makefile (sysdep_routines):
Add s_sincosf-sse2.
* sysdeps/i386/i686/fpu/multiarch/s_sincosf.c: New file.
* sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S: New file.
* sysdeps/ieee754/flt-32/s_sincosf.c (SINCOSF, SINCOSF_FUNC): Add
macros for using routine as __sincosf_ia32.
Use macro for function declaration and weak_alias.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/s_sincosf.S: New file.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
* math/s_ccoshf.c (__ccoshf): Fix wrong usage of sincos for
subnormal argument.
* math/s_cexpf.c (__cexpf): Likewise.
* math/s_csinf.c (__csinf): Likewise.

33
sysdeps/i386/fpu/libm-test-ulps
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@ -1490,9 +1490,9 @@ float: 1
ifloat: 1
Test "Real part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
double: 2
float: 3
float: 4
idouble: 2
ifloat: 3
ifloat: 4
ildouble: 3
ldouble: 3
Test "Imaginary part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
@ -1704,6 +1704,8 @@ ldouble: 1
# ctan
Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
float: 1
ifloat: 1
double: 1
idouble: 1
ildouble: 1
@ -1797,6 +1799,8 @@ Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) ==
ildouble: 1
ldouble: 1
Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
@ -1827,9 +1831,9 @@ ildouble: 2
ldouble: 2
Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
double: 1
float: 1
float: 2
idouble: 1
ifloat: 1
ifloat: 2
ildouble: 1
ldouble: 1
@ -1940,6 +1944,8 @@ ifloat: 3
ildouble: 4
ldouble: 4
Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
@ -1954,9 +1960,9 @@ ildouble: 1
ldouble: 1
Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
double: 1
float: 1
float: 2
idouble: 1
ifloat: 1
ifloat: 2
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
@ -2564,9 +2570,6 @@ Test "sincos (0x1.fffff8p+127, &sin_res, &cos_res) puts 4.8578606313048733970111
float: 1
Test "sincos (0x1p+127, &sin_res, &cos_res) puts 6.23385512955870240370428801097126489001833e-01 in sin_res":
float: 1
Test "sincos (0x1p+50, &sin_res, &cos_res) puts 8.68095904660550604334592502063501320395739e-01 in cos_res":
float: 1
ifloat: 1
Test "sincos (0x1p65, &sin_res, &cos_res) puts -0.047183876212354673805106149805700013943218 in sin_res":
float: 1
ifloat: 1
@ -3442,6 +3445,8 @@ ildouble: 1
ldouble: 1
Function: Real part of "ctan_towardzero":
float: 1
ifloat: 1
double: 1
idouble: 1
ildouble: 1
@ -3461,9 +3466,9 @@ ldouble: 2
Function: Imaginary part of "ctan_upward":
double: 1
float: 1
float: 2
idouble: 1
ifloat: 1
ifloat: 2
ildouble: 4
ldouble: 4
@ -3514,6 +3519,8 @@ ildouble: 4
ldouble: 4
Function: Imaginary part of "ctanh_towardzero":
float: 1
ifloat: 1
double: 1
idouble: 1
ildouble: 1
@ -3521,9 +3528,9 @@ ldouble: 1
Function: Real part of "ctanh_upward":
double: 1
float: 1
float: 2
idouble: 1
ifloat: 1
ifloat: 2
ildouble: 4
ldouble: 4

3
sysdeps/i386/i686/fpu/multiarch/Makefile
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@ -1,3 +1,4 @@
ifeq ($(subdir),math)
libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2
libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2 \
s_sincosf-sse2
endif

586
sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S Normal file
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@ -0,0 +1,586 @@
/* Optimized with sse2 version of sincosf
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
<http://www.gnu.org/licenses/>. */
#include <sysdep.h>
#define __need_Emath
#include <bits/errno.h>
/* 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|<Pi/4, results are
* cos(x) = poly_sin * sign_cos
* sin(x) = poly_cos * sign_sin
* } else {
* sin(x) = poly_sin * sign_sin
* cos(x) = poly_cos * sign_cos
* }
* 6) if |x| < 2^23, large args:
* 6.1) Range reduction:
* k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4
* 6.2) Reconstruction same as (5.2).
* 7) if |x| >= 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.
*/
#ifdef PIC
# define MO1(symbol) L(symbol)##@GOTOFF(%ebx)
# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale)
# define CFI_PUSH(REG) cfi_adjust_cfa_offset(4); cfi_rel_offset(REG,0)
# define CFI_POP(REG) cfi_adjust_cfa_offset(-4); cfi_restore(REG)
# define PUSH(REG) pushl REG; CFI_PUSH(REG)
# define POP(REG) popl REG; CFI_POP(REG)
# define ENTRANCE PUSH(%ebx); LOAD_PIC_REG(bx)
# define RETURN POP(%ebx); ret; CFI_PUSH(%ebx)
# define ARG_X 8(%esp)
# define ARG_SIN_PTR 12(%esp)
# define ARG_COS_PTR 16(%esp)
#else
# define MO1(symbol) L(symbol)
# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale)
# define ENTRANCE
# define RETURN ret
# define ARG_X 4(%esp)
# define ARG_SIN_PTR 8(%esp)
# define ARG_COS_PTR 12(%esp)
#endif
.text
ENTRY(__sincosf_sse2)
/* Input: single precision x on stack at address ARG_X */
/* pointer to sin result on stack at address ARG_SIN_PTR */
/* pointer to cos result on stack at address ARG_COS_PTR */
ENTRANCE
movl ARG_X, %eax /* Bits of x */
cvtss2sd ARG_X, %xmm0 /* DP x */
andl $0x7fffffff, %eax /* |x| */
cmpl $0x3f490fdb, %eax /* |x|<Pi/4 ? */
jb L(arg_less_pio4)
/* Here if |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 $29, %ecx /* (sign of x) << 2 */
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) */
movaps %xmm0, %xmm4 /* t */
movhpd MO1(DP_ONES), %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 MO1(DP_SC4), %xmm2 /* S4 */
mulpd %xmm0, %xmm2 /* z*S4 */
movaps MO1(DP_SC3), %xmm3 /* S3 */
mulpd %xmm0, %xmm3 /* z*S3 */
xorl %eax, %ecx /* (sign_x ^ (k>>2))<<2 */
addpd MO1(DP_SC2), %xmm2 /* S2+z*S4 */
mulpd %xmm0, %xmm2 /* z*(S2+z*S4) */
shrl $2, %edx /* (k+2)>>2 */
addpd MO1(DP_SC1), %xmm3 /* S1+z*S3 */
mulpd %xmm0, %xmm3 /* z*(S1+z*S3) */
shrl $2, %ecx /* sign_x ^ k>>2 */
addpd MO1(DP_SC0), %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)))) */
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 MO2(DP_ONES,%ecx,8), %xmm4/* 0|sign_sin */
movhpd MO2(DP_ONES,%edx,8), %xmm4/* sign_cos|sign_sin */
mulpd %xmm4, %xmm3 /* result_cos|result_sin */
movl ARG_SIN_PTR, %eax
cvtpd2ps %xmm3, %xmm0 /* SP results */
movl ARG_COS_PTR, %ecx
movss %xmm0, (%eax) /* store sin(x) from xmm0[0] */
shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
movss %xmm0, (%ecx) /* store cos(x) */
RETURN
.p2align 4
L(sin_result_sin_poly):
/*
* Here if
* sin(x) = poly_sin * sign_sin
* cos(x) = poly_cos * sign_cos
*/
movsd MO2(DP_ONES,%edx,8), %xmm4/* 0|sign_cos */
movhpd MO2(DP_ONES,%ecx,8), %xmm4/* sign_sin|sign_cos */
mulpd %xmm4, %xmm3 /* result_sin|result_cos */
movl ARG_SIN_PTR, %eax
cvtpd2ps %xmm3, %xmm0 /* SP results */
movl ARG_COS_PTR, %ecx
movss %xmm0, (%ecx) /* store cos(x) from xmm0[0] */
shufps $1, %xmm0, %xmm0 /* move sin(x) to xmm0[0] */
movss %xmm0, (%eax) /* store sin(x) */
RETURN
.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 $29, %ecx /* (sign of x) << 2 */
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 */
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 */
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 $29, %ecx /* (sign of x) << 2 */
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|<Pi/4 */
cmpl $0x3d000000, %eax /* |x|<2^-5 ? */
jl L(arg_less_2pn5)
/* Here if 2^-5<=|x|<Pi/4 */
movaps %xmm0, %xmm3 /* DP x */
movhpd MO1(DP_ONES), %xmm3 /* DP 1|x */
mulsd %xmm0, %xmm0 /* DP y=x^2 */
unpcklpd %xmm0, %xmm0 /* DP y|y */
movaps %xmm0, %xmm1 /* y|y */
mulpd %xmm0, %xmm0 /* z=x^4|z=x^4 */
movapd MO1(DP_SC4), %xmm4 /* S4 */
mulpd %xmm0, %xmm4 /* z*S4 */
movapd MO1(DP_SC3), %xmm5 /* S3 */
mulpd %xmm0, %xmm5 /* z*S3 */
addpd MO1(DP_SC2), %xmm4 /* S2+z*S4 */
mulpd %xmm0, %xmm4 /* z*(S2+z*S4) */
addpd MO1(DP_SC1), %xmm5 /* S1+z*S3 */
mulpd %xmm0, %xmm5 /* z*(S1+z*S3) */
addpd MO1(DP_SC0), %xmm4 /* S0+z*(S2+z*S4) */
mulpd %xmm1, %xmm4 /* y*(S0+z*(S2+z*S4)) */
mulpd %xmm3, %xmm5 /* x*z*(S1+z*S3) */
mulpd %xmm3, %xmm4 /* x*y*(S0+z*(S2+z*S4)) */
addpd %xmm5, %xmm4 /*x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
movl ARG_SIN_PTR, %eax
addpd %xmm4, %xmm3 /*x+x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
movl ARG_COS_PTR, %ecx
cvtpd2ps %xmm3, %xmm0 /* SP results */
movss %xmm0, (%eax) /* store sin(x) from xmm0[0] */
shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
movss %xmm0, (%ecx) /* store cos(x) */
RETURN
.p2align 4
L(arg_less_2pn5):
/* Here if |x|<2^-5 */
cmpl $0x32000000, %eax /* |x|<2^-27 ? */
jl L(arg_less_2pn27)
/* Here if 2^-27<=|x|<2^-5 */
movaps %xmm0, %xmm1 /* DP x */
movhpd MO1(DP_ONES), %xmm1 /* DP 1|x */
mulsd %xmm0, %xmm0 /* DP x^2 */
unpcklpd %xmm0, %xmm0 /* DP x^2|x^2 */
movaps MO1(DP_SINCOS2_1), %xmm3/* DP DP_SIN2_1 */
mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_1 */
addpd MO1(DP_SINCOS2_0), %xmm3/* DP DP_SIN2_0+x^2*DP_SIN2_1 */
mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */
mulpd %xmm1, %xmm3 /* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
addpd %xmm1, %xmm3 /* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
movl ARG_SIN_PTR, %eax
cvtpd2ps %xmm3, %xmm0 /* SP results */
movl ARG_COS_PTR, %ecx
movss %xmm0, (%eax) /* store sin(x) from xmm0[0] */
shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
movss %xmm0, (%ecx) /* store cos(x) */
RETURN
.p2align 4
L(arg_less_2pn27):
movss ARG_X, %xmm7 /* SP x */
cmpl $0, %eax /* x=0 ? */
je L(arg_zero) /* in case x=0 return sin(+-0)==+-0 */
/* Here if |x|<2^-27 */
/*
* Special cases here:
* sin(subnormal) raises inexact/underflow
* sin(min_normalized) raises inexact/underflow
* sin(normalized) raises inexact
* cos(here)=1-|x| (raising inexact)
*/
movaps %xmm0, %xmm3 /* DP x */
mulsd MO1(DP_SMALL), %xmm0 /* DP x*DP_SMALL */
subsd %xmm0, %xmm3 /* DP sin result is x-x*DP_SMALL */
andps MO1(SP_ABS_MASK), %xmm7 /* SP |x| */
cvtsd2ss %xmm3, %xmm0 /* sin(x) */
movl ARG_SIN_PTR, %eax
movss MO1(SP_ONE), %xmm1 /* SP 1.0 */
movss %xmm0, (%eax) /* sin(x) store */
movl ARG_COS_PTR, %ecx
subss %xmm7, %xmm1 /* cos(x) */
movss %xmm1, (%ecx) /* cos(x) store */
RETURN
.p2align 4
L(arg_zero):
movss MO1(SP_ONE), %xmm0 /* 1.0 */
movl ARG_SIN_PTR, %eax
movl ARG_COS_PTR, %ecx
movss %xmm7, (%eax) /* sin(+-0)==x */
movss %xmm0, (%ecx) /* cos(+-0)==1 */
RETURN
.p2align 4
L(arg_inf_or_nan):
movss ARG_X, %xmm7 /* SP x */
/* Here if |x| is Inf or NAN */
jne L(skip_errno_setting) /* in case of x is NaN */
/* Here if x is Inf. Set errno to EDOM. */
call JUMPTARGET(__errno_location)
movl $EDOM, (%eax)
.p2align 4
L(skip_errno_setting):
/* Here if |x| is Inf or NAN. Continued. */
subss %xmm7, %xmm7 /* x-x, result is NaN */
movl ARG_SIN_PTR, %eax
movl ARG_COS_PTR, %ecx
movss %xmm7, (%eax)
movss %xmm7, (%ecx)
RETURN
END(__sincosf_sse2)
.section .rodata, "a"
.p2align 3
L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */
.long 0x00000000,0x00000000
.long 0x54442d18,0x3fe921fb
.long 0x54442d18,0x3ff921fb
.long 0x7f3321d2,0x4002d97c
.long 0x54442d18,0x400921fb
.long 0x2955385e,0x400f6a7a
.long 0x7f3321d2,0x4012d97c
.long 0xe9bba775,0x4015fdbb
.long 0x54442d18,0x401921fb
.long 0xbeccb2bb,0x401c463a
.long 0x2955385e,0x401f6a7a
.type L(PIO4J), @object
ASM_SIZE_DIRECTIVE(L(PIO4J))
.p2align 3
L(_FPI): /* 4/Pi broken into sum of positive DP values */
.long 0x00000000,0x00000000
.long 0x6c000000,0x3ff45f30
.long 0x2a000000,0x3e3c9c88
.long 0xa8000000,0x3c54fe13
.long 0xd0000000,0x3aaf47d4
.long 0x6c000000,0x38fbb81b
.long 0xe0000000,0x3714acc9
.long 0x7c000000,0x3560e410
.long 0x56000000,0x33bca2c7
.long 0xac000000,0x31fbd778
.long 0xe0000000,0x300b7246
.long 0xe8000000,0x2e5d2126
.long 0x48000000,0x2c970032
.long 0xe8000000,0x2ad77504
.long 0xe0000000,0x290921cf
.long 0xb0000000,0x274deb1c
.long 0xe0000000,0x25829a73
.long 0xbe000000,0x23fd1046
.long 0x10000000,0x2224baed
.long 0x8e000000,0x20709d33
.long 0x80000000,0x1e535a2f
.long 0x64000000,0x1cef904e
.long 0x30000000,0x1b0d6398
.long 0x24000000,0x1964ce7d
.long 0x16000000,0x17b908bf
.type L(_FPI), @object
ASM_SIZE_DIRECTIVE(L(_FPI))
/* Coefficients of polynomials for */
/* sin(x)~=x+x*x^2*(DP_SIN2_0+x^2*DP_SIN2_1) in low DP part, */
/* cos(x)~=1+1*x^2*(DP_COS2_0+x^2*DP_COS2_1) in high DP part, */
/* for |x|<2^-5. */
.p2align 4
L(DP_SINCOS2_0):
.long 0x5543d49d,0xbfc55555
.long 0xff5cc6fd,0xbfdfffff
.type L(DP_SINCOS2_0), @object
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_0))
.p2align 4
L(DP_SINCOS2_1):
.long 0x75cec8c5,0x3f8110f4
.long 0xb178dac5,0x3fa55514
.type L(DP_SINCOS2_1), @object
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_1))
.p2align 3
L(DP_ZERONE):
.long 0x00000000,0x00000000 /* 0.0 */
.long 0x00000000,0xbff00000 /* 1.0 */
.type L(DP_ZERONE), @object
ASM_SIZE_DIRECTIVE(L(DP_ZERONE))
.p2align 3
L(DP_ONES):
.long 0x00000000,0x3ff00000 /* +1.0 */
.long 0x00000000,0xbff00000 /* -1.0 */
.type L(DP_ONES), @object
ASM_SIZE_DIRECTIVE(L(DP_ONES))
/* Coefficients of polynomials for */
/* sin(t)~=t+t*t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))) in low DP part, */
/* cos(t)~=1+1*t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))) in high DP part, */
/* for |t|<Pi/4. */
.p2align 4
L(DP_SC4):
.long 0x1674b58a,0xbe5a947e
.long 0xdd8844d7,0xbe923c97
.type L(DP_SC4), @object
ASM_SIZE_DIRECTIVE(L(DP_SC4))
.p2align 4
L(DP_SC3):
.long 0x64e6b5b4,0x3ec71d72
.long 0x9ac43cc0,0x3efa00eb
.type L(DP_SC3), @object
ASM_SIZE_DIRECTIVE(L(DP_SC3))
.p2align 4
L(DP_SC2):
.long 0x8b4bd1f9,0xbf2a019f
.long 0x348b6874,0xbf56c16b
.type L(DP_SC2), @object
ASM_SIZE_DIRECTIVE(L(DP_SC2))
.p2align 4
L(DP_SC1):
.long 0x10c2688b,0x3f811111
.long 0x545c50c7,0x3fa55555
.type L(DP_SC1), @object
ASM_SIZE_DIRECTIVE(L(DP_SC1))
.p2align 4
L(DP_SC0):
.long 0x55551cd9,0xbfc55555
.long 0xfffe98ae,0xbfdfffff
.type L(DP_SC0), @object
ASM_SIZE_DIRECTIVE(L(DP_SC0))
.p2align 3
L(DP_SMALL):
.long 0x00000000,0x3cd00000 /* 2^(-50) */
.type L(DP_SMALL), @object
ASM_SIZE_DIRECTIVE(L(DP_SMALL))
.p2align 3
L(DP_PIO4):
.long 0x54442d18,0x3fe921fb /* Pi/4 */
.type L(DP_PIO4), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4))
.p2align 3
L(DP_2POW52):
.long 0x00000000,0x43300000 /* +2^52 */
.long 0x00000000,0xc3300000 /* -2^52 */
.type L(DP_2POW52), @object
ASM_SIZE_DIRECTIVE(L(DP_2POW52))
.p2align 3
L(DP_INVPIO4):
.long 0x6dc9c883,0x3ff45f30 /* 4/Pi */
.type L(DP_INVPIO4), @object
ASM_SIZE_DIRECTIVE(L(DP_INVPIO4))
.p2align 3
L(DP_PIO4HI):
.long 0x54000000,0xbfe921fb /* High part of Pi/4 */
.type L(DP_PIO4HI), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4HI))
.p2align 3
L(DP_PIO4LO):
.long 0x11A62633,0xbe010b46 /* Low part of Pi/4 */
.type L(DP_PIO4LO), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4LO))
.p2align 2
L(SP_INVPIO4):
.long 0x3fa2f983 /* 4/Pi */
.type L(SP_INVPIO4), @object
ASM_SIZE_DIRECTIVE(L(SP_INVPIO4))
.p2align 4
L(DP_ABS_MASK): /* Mask for getting DP absolute value */
.long 0xffffffff,0x7fffffff
.long 0xffffffff,0x7fffffff
.type L(DP_ABS_MASK), @object
ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK))
.p2align 3
L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */
.long 0x00000000,0xffffffff
.type L(DP_HI_MASK), @object
ASM_SIZE_DIRECTIVE(L(DP_HI_MASK))
.p2align 4
L(SP_ABS_MASK): /* Mask for getting SP absolute value */
.long 0x7fffffff,0x7fffffff
.long 0x7fffffff,0x7fffffff
.type L(SP_ABS_MASK), @object
ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK))
.p2align 2
L(SP_ONE):
.long 0x3f800000 /* 1.0 */
.type L(SP_ONE), @object
ASM_SIZE_DIRECTIVE(L(SP_ONE))
weak_alias(__sincosf, sincosf)

29
sysdeps/i386/i686/fpu/multiarch/s_sincosf.c Normal file
View File

@ -0,0 +1,29 @@
/* Multiple versions of sincosf
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
<http://www.gnu.org/licenses/>. */
#include <init-arch.h>
extern void __sincosf_sse2 (float, float *, float *);
extern void __sincosf_ia32 (float, float *, float *);
void __sincosf (float, float *, float *);
libm_ifunc (__sincosf, HAS_SSE2 ? __sincosf_sse2 : __sincosf_ia32);
weak_alias (__sincosf, sincosf);
#define SINCOSF __sincosf_ia32
#include <sysdeps/ieee754/flt-32/s_sincosf.c>

10
sysdeps/ieee754/flt-32/s_sincosf.c
View File

@ -21,9 +21,14 @@
#include <math_private.h>
#ifndef SINCOSF
# define SINCOSF_FUNC __sincosf
#else
# define SINCOSF_FUNC SINCOSF
#endif
void
__sincosf (float x, float *sinx, float *cosx)
SINCOSF_FUNC (float x, float *sinx, float *cosx)
{
int32_t ix;
@ -70,4 +75,7 @@ __sincosf (float x, float *sinx, float *cosx)
}
}
}
#ifndef SINCOSF
weak_alias (__sincosf, sincosf)
#endif

42
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -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

558
sysdeps/x86_64/fpu/s_sincosf.S Normal file
View File

@ -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
<http://www.gnu.org/licenses/>. */
#include <sysdep.h>
#define __need_Emath
#include <bits/errno.h>
/* 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|<Pi/4, results are
* cos(x) = poly_sin * sign_cos
* sin(x) = poly_cos * sign_sin
* } else {
* sin(x) = poly_sin * sign_sin
* cos(x) = poly_cos * sign_cos
* }
* 6) if |x| < 2^23, large args:
* 6.1) Range reduction:
* k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4
* 6.2) Reconstruction same as (5.2).
* 7) if |x| >= 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 ? */
jb L(arg_less_pio4)
/* Here if |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|<Pi/4 */
cmpl $0x3d000000, %eax /* |x|<2^-5 ? */
jl L(arg_less_2pn5)
/* Here if 2^-5<=|x|<Pi/4 */
movaps %xmm0, %xmm3 /* DP x */
movhpd L(DP_ONES)(%rip), %xmm3 /* DP 1|x */
mulsd %xmm0, %xmm0 /* DP y=x^2 */
unpcklpd %xmm0, %xmm0 /* DP y|y */
movaps %xmm0, %xmm1 /* y|y */
mulpd %xmm0, %xmm0 /* z=x^4|z=x^4 */
movapd L(DP_SC4)(%rip), %xmm4 /* S4 */
mulpd %xmm0, %xmm4 /* z*S4 */
movapd L(DP_SC3)(%rip), %xmm5 /* S3 */
mulpd %xmm0, %xmm5 /* z*S3 */
addpd L(DP_SC2)(%rip), %xmm4 /* S2+z*S4 */
mulpd %xmm0, %xmm4 /* z*(S2+z*S4) */
addpd L(DP_SC1)(%rip), %xmm5 /* S1+z*S3 */
mulpd %xmm0, %xmm5 /* z*(S1+z*S3) */
addpd L(DP_SC0)(%rip), %xmm4 /* S0+z*(S2+z*S4) */
mulpd %xmm1, %xmm4 /* y*(S0+z*(S2+z*S4)) */
mulpd %xmm3, %xmm5 /* x*z*(S1+z*S3) */
mulpd %xmm3, %xmm4 /* x*y*(S0+z*(S2+z*S4)) */
addpd %xmm5, %xmm4 /*x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
addpd %xmm4, %xmm3 /*x+x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
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(arg_less_2pn5):
/* Here if |x|<2^-5 */
cmpl $0x32000000, %eax /* |x|<2^-27 ? */
jl L(arg_less_2pn27)
/* Here if 2^-27<=|x|<2^-5 */
movaps %xmm0, %xmm1 /* DP x */
movhpd L(DP_ONES)(%rip), %xmm1 /* DP 1|x */
mulsd %xmm0, %xmm0 /* DP x^2 */
unpcklpd %xmm0, %xmm0 /* DP x^2|x^2 */
movaps L(DP_SINCOS2_1)(%rip), %xmm3 /* DP DP_SIN2_1 */
mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_1 */
addpd L(DP_SINCOS2_0)(%rip), %xmm3 /* DP DP_SIN2_0+x^2*DP_SIN2_1 */
mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */
mulpd %xmm1, %xmm3 /* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
addpd %xmm1, %xmm3 /* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
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(arg_less_2pn27):
cmpl $0, %eax /* x=0 ? */
je L(arg_zero) /* in case x=0 return sin(+-0)==+-0 */
/* Here if |x|<2^-27 */
/*
* Special cases here:
* sin(subnormal) raises inexact/underflow
* sin(min_normalized) raises inexact/underflow
* sin(normalized) raises inexact
* cos(here)=1-|x| (raising inexact)
*/
movaps %xmm0, %xmm3 /* DP x */
mulsd L(DP_SMALL)(%rip), %xmm0/* DP x*DP_SMALL */
subsd %xmm0, %xmm3 /* DP sin result is x-x*DP_SMALL */
andps L(SP_ABS_MASK)(%rip), %xmm7/* SP |x| */
cvtsd2ss %xmm3, %xmm0 /* sin(x) */
movss L(SP_ONE)(%rip), %xmm1 /* SP 1.0 */
movss %xmm0, (ARG_SIN_PTR) /* sin(x) store */
subss %xmm7, %xmm1 /* cos(x) */
movss %xmm1, (ARG_COS_PTR) /* cos(x) store */
ret
.p2align 4
L(arg_zero):
movss L(SP_ONE)(%rip), %xmm0 /* 1.0 */
movss %xmm7, (ARG_SIN_PTR) /* sin(+-0)==x */
movss %xmm0, (ARG_COS_PTR) /* cos(+-0)==1 */
ret
.p2align 4
L(arg_inf_or_nan):
/* Here if |x| is Inf or NAN */
jne L(skip_errno_setting) /* in case of x is NaN */
/* Here if x is Inf. Set errno to EDOM. */
call JUMPTARGET(__errno_location)
movl $EDOM, (%rax)
.p2align 4
L(skip_errno_setting):
/* Here if |x| is Inf or NAN. Continued. */
subss %xmm7, %xmm7 /* x-x, result is NaN */
movss %xmm7, (ARG_SIN_PTR)
movss %xmm7, (ARG_COS_PTR)
ret
END(__sincosf)
.section .rodata, "a"
.p2align 3
L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */
.long 0x00000000,0x00000000
.long 0x54442d18,0x3fe921fb
.long 0x54442d18,0x3ff921fb
.long 0x7f3321d2,0x4002d97c
.long 0x54442d18,0x400921fb
.long 0x2955385e,0x400f6a7a
.long 0x7f3321d2,0x4012d97c
.long 0xe9bba775,0x4015fdbb
.long 0x54442d18,0x401921fb
.long 0xbeccb2bb,0x401c463a
.long 0x2955385e,0x401f6a7a
.type L(PIO4J), @object
ASM_SIZE_DIRECTIVE(L(PIO4J))
.p2align 3
L(_FPI): /* 4/Pi broken into sum of positive DP values */
.long 0x00000000,0x00000000
.long 0x6c000000,0x3ff45f30
.long 0x2a000000,0x3e3c9c88
.long 0xa8000000,0x3c54fe13
.long 0xd0000000,0x3aaf47d4
.long 0x6c000000,0x38fbb81b
.long 0xe0000000,0x3714acc9
.long 0x7c000000,0x3560e410
.long 0x56000000,0x33bca2c7
.long 0xac000000,0x31fbd778
.long 0xe0000000,0x300b7246
.long 0xe8000000,0x2e5d2126
.long 0x48000000,0x2c970032
.long 0xe8000000,0x2ad77504
.long 0xe0000000,0x290921cf
.long 0xb0000000,0x274deb1c
.long 0xe0000000,0x25829a73
.long 0xbe000000,0x23fd1046
.long 0x10000000,0x2224baed
.long 0x8e000000,0x20709d33
.long 0x80000000,0x1e535a2f
.long 0x64000000,0x1cef904e
.long 0x30000000,0x1b0d6398
.long 0x24000000,0x1964ce7d
.long 0x16000000,0x17b908bf
.type L(_FPI), @object
ASM_SIZE_DIRECTIVE(L(_FPI))
/* Coefficients of polynomials for */
/* sin(x)~=x+x*x^2*(DP_SIN2_0+x^2*DP_SIN2_1) in low DP part, */
/* cos(x)~=1+1*x^2*(DP_COS2_0+x^2*DP_COS2_1) in high DP part, */
/* for |x|<2^-5. */
.p2align 4
L(DP_SINCOS2_0):
.long 0x5543d49d,0xbfc55555
.long 0xff5cc6fd,0xbfdfffff
.type L(DP_SINCOS2_0), @object
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_0))
.p2align 4
L(DP_SINCOS2_1):
.long 0x75cec8c5,0x3f8110f4
.long 0xb178dac5,0x3fa55514
.type L(DP_SINCOS2_1), @object
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_1))
.p2align 3
L(DP_ZERONE):
.long 0x00000000,0x00000000 /* 0.0 */
.long 0x00000000,0xbff00000 /* 1.0 */
.type L(DP_ZERONE), @object
ASM_SIZE_DIRECTIVE(L(DP_ZERONE))
.p2align 3
L(DP_ONES):
.long 0x00000000,0x3ff00000 /* +1.0 */
.long 0x00000000,0xbff00000 /* -1.0 */
.type L(DP_ONES), @object
ASM_SIZE_DIRECTIVE(L(DP_ONES))
/* Coefficients of polynomials for */
/* sin(t)~=t+t*t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))) in low DP part, */
/* cos(t)~=1+1*t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))) in high DP part, */
/* for |t|<Pi/4. */
.p2align 4
L(DP_SC4):
.long 0x1674b58a,0xbe5a947e
.long 0xdd8844d7,0xbe923c97
.type L(DP_SC4), @object
ASM_SIZE_DIRECTIVE(L(DP_SC4))
.p2align 4
L(DP_SC3):
.long 0x64e6b5b4,0x3ec71d72
.long 0x9ac43cc0,0x3efa00eb
.type L(DP_SC3), @object
ASM_SIZE_DIRECTIVE(L(DP_SC3))
.p2align 4
L(DP_SC2):
.long 0x8b4bd1f9,0xbf2a019f
.long 0x348b6874,0xbf56c16b
.type L(DP_SC2), @object
ASM_SIZE_DIRECTIVE(L(DP_SC2))
.p2align 4
L(DP_SC1):
.long 0x10c2688b,0x3f811111
.long 0x545c50c7,0x3fa55555
.type L(DP_SC1), @object
ASM_SIZE_DIRECTIVE(L(DP_SC1))
.p2align 4
L(DP_SC0):
.long 0x55551cd9,0xbfc55555
.long 0xfffe98ae,0xbfdfffff
.type L(DP_SC0), @object
ASM_SIZE_DIRECTIVE(L(DP_SC0))
.p2align 3
L(DP_SMALL):
.long 0x00000000,0x3cd00000 /* 2^(-50) */
.type L(DP_SMALL), @object
ASM_SIZE_DIRECTIVE(L(DP_SMALL))
.p2align 3
L(DP_PIO4):
.long 0x54442d18,0x3fe921fb /* Pi/4 */
.type L(DP_PIO4), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4))
.p2align 3
L(DP_2POW52):
.long 0x00000000,0x43300000 /* +2^52 */
.long 0x00000000,0xc3300000 /* -2^52 */
.type L(DP_2POW52), @object
ASM_SIZE_DIRECTIVE(L(DP_2POW52))
.p2align 3
L(DP_INVPIO4):
.long 0x6dc9c883,0x3ff45f30 /* 4/Pi */
.type L(DP_INVPIO4), @object
ASM_SIZE_DIRECTIVE(L(DP_INVPIO4))
.p2align 3
L(DP_PIO4HI):
.long 0x54000000,0xbfe921fb /* High part of Pi/4 */
.type L(DP_PIO4HI), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4HI))
.p2align 3
L(DP_PIO4LO):
.long 0x11A62633,0xbe010b46 /* Low part of Pi/4 */
.type L(DP_PIO4LO), @object
ASM_SIZE_DIRECTIVE(L(DP_PIO4LO))
.p2align 2
L(SP_INVPIO4):
.long 0x3fa2f983 /* 4/Pi */
.type L(SP_INVPIO4), @object
ASM_SIZE_DIRECTIVE(L(SP_INVPIO4))
.p2align 4
L(DP_ABS_MASK): /* Mask for getting DP absolute value */
.long 0xffffffff,0x7fffffff
.long 0xffffffff,0x7fffffff
.type L(DP_ABS_MASK), @object
ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK))
.p2align 3
L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */
.long 0x00000000,0xffffffff
.type L(DP_HI_MASK), @object
ASM_SIZE_DIRECTIVE(L(DP_HI_MASK))
.p2align 4
L(SP_ABS_MASK): /* Mask for getting SP absolute value */
.long 0x7fffffff,0x7fffffff
.long 0x7fffffff,0x7fffffff
.type L(SP_ABS_MASK), @object
ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK))
.p2align 2
L(SP_ONE):
.long 0x3f800000 /* 1.0 */
.type L(SP_ONE), @object
ASM_SIZE_DIRECTIVE(L(SP_ONE))
weak_alias(__sincosf, sincosf)