/* Optimized sincosf function. Copyright (C) 2012-2015 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|