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glibc/sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S

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Add optimized sincosf for SSE2 for x86 and x86-64
2012-09-25 18:44:46 +00:00
/* Optimized with sse2 version of sincosf
Update copyright dates with scripts/update-copyrights.
2017-01-01 00:14:16 +00:00
Copyright (C) 2012-2017 Free Software Foundation, Inc.
Add optimized sincosf for SSE2 for x86 and x86-64
2012-09-25 18:44:46 +00:00
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>
Remove __need macros from errno.h (__need_Emath, __need_error_t). This is fairly complicated, not because the users of __need_Emath and __need_error_t have complicated requirements, but because the core changes had a lot of fallout. __need_error_t exists for gnulib compatibility in argz.h and argp.h. error_t itself is a Hurdism, an enum containing all the E-constants, so you can do 'p (error_t) errno' in gdb and get a symbolic value. argz.h and argp.h use it for function return values, and they want to fall back to 'int' when that's not available. There is no reason why these nonstandard headers cannot just go ahead and include all of errno.h; so we do that. __need_Emath is defined only by .S files; what they _really_ need is for errno.h to avoid declaring anything other than the E-constants (e.g. 'extern int __errno_location(void);' is a syntax error in assembly language). This is replaced with a check for __ASSEMBLER__ in errno.h, plus a carefully documented requirement for bits/errno.h not to define anything other than macros. That in turn has the consequence that bits/errno.h must not define errno - fortunately, all live ports use the same definition of errno, so I've moved it to errno.h. The Hurd bits/errno.h must also take care not to define error_t when __ASSEMBLER__ is defined, which involves repeating all of the definitions twice, but it's a generated file so that's okay. * stdlib/errno.h: Remove __need_Emath and __need_error_t logic. Reorganize file. Declare errno here. When __ASSEMBLER__ is defined, don't declare anything other than the E-constants. * include/errno.h: Change conditional for exposing internal declarations to (not _ISOMAC and not __ASSEMBLER__). * bits/errno.h: Remove logic for __need_Emath. Document requirements for a port-specific bits/errno.h. * sysdeps/unix/sysv/linux/bits/errno.h * sysdeps/unix/sysv/linux/alpha/bits/errno.h * sysdeps/unix/sysv/linux/hppa/bits/errno.h * sysdeps/unix/sysv/linux/mips/bits/errno.h * sysdeps/unix/sysv/linux/sparc/bits/errno.h: Add multiple-include guard and check against improper inclusion. Remove __need_Emath logic. Don't declare errno here. Ensure all constants are defined as simple integer literals. Consistent formatting. * sysdeps/mach/hurd/errnos.awk: Likewise. Only define error_t and enum __error_t_codes if __ASSEMBLER__ is not defined. * sysdeps/mach/hurd/bits/errno.h: Regenerate. * argp/argp.h, string/argz.h: Don't define __need_error_t before including errno.h. * sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S * sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S * sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S * sysdeps/x86_64/fpu/s_cosf.S * sysdeps/x86_64/fpu/s_sincosf.S * sysdeps/x86_64/fpu/s_sinf.S: Just include errno.h; don't define __need_Emath or include bits/errno.h directly.
2017-03-21 20:30:53 +00:00
#include <errno.h>
Add optimized sincosf for SSE2 for x86 and x86-64
2012-09-25 18:44:46 +00:00
/* 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)
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