/* Optimized with sse2 version of cosf
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: 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) = 1 not raising inexact,
* cos(subnormal) raises inexact,
* cos(min_normalized) raises inexact,
* cos(normalized) raises inexact,
* cos(Inf) = NaN, raises invalid, sets errno to EDOM,
* 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)
#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)
#endif
.text
ENTRY(__cosf_sse2)
/* Input: single precision x on stack at address ARG_X */
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) */
cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */
addl $1, %eax /* k+1 */
movl $0x0e, %edx
andl %eax, %edx /* j = (k+1)&0x0e */
addl $2, %eax /* n */
subsd MO2(PIO4J,%edx,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 MO1(DP_C4), %xmm4 /* C4 */
mulsd %xmm0, %xmm4 /* z*C4 */
movsd MO1(DP_C3), %xmm3 /* C3 */
mulsd %xmm0, %xmm3 /* z*C3 */
addsd MO1(DP_C2), %xmm4 /* C2+z*C4 */
mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */
lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */
addsd MO1(DP_C1), %xmm3 /* C1+z*C3 */
mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */
addsd MO1(DP_C0), %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 MO1(DP_ONES), %xmm3
mulsd MO2(DP_ONES,%eax,8), %xmm3 /* DP result */
movsd %xmm3, 0(%esp) /* Move result from sse... */
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
RETURN
.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 MO1(DP_S4), %xmm2 /* S4 */
mulsd %xmm0, %xmm2 /* z*S4 */
movsd MO1(DP_S3), %xmm3 /* S3 */
mulsd %xmm0, %xmm3 /* z*S3 */
lea -8(%esp), %esp /* Borrow 4 bytes of stack frame */
addsd MO1(DP_S2), %xmm2 /* S2+z*S4 */
mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */
addsd MO1(DP_S1), %xmm3 /* S1+z*S3 */
mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */
addsd MO1(DP_S0), %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 MO2(DP_ONES,%eax,8), %xmm4
addsd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
/* 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
movsd %xmm3, 0(%esp) /* Move result from sse... */
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
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 */
movsd MO1(DP_PIO4HI), %xmm2 /* -PIO4HI = high part of -Pi/4 */
mulsd %xmm4, %xmm2 /* -j*PIO4HI */
movsd MO1(DP_PIO4LO), %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 */
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 */
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 */
addsd %xmm3, %xmm0 /* t += tmp0 */
addl $3, %eax /* n=k+3 */
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|