/* Optimized with sse2 version of sincosf
Copyright (C) 2012-2014 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.
*/
#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 */
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|