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;/* File: "atan_wmt.asm". */;//;// INTEL CORPORATION PROPRIETARY INFORMATION;// This software is supplied under the terms of a license agreement or;// nondisclosure agreement with Intel Corporation and may not be copied;// or disclosed except in accordance with the terms of that agreement.;// Copyright (c) 2000 Intel Corporation. All Rights Reserved.;//;//;// Contents: atan.;//;// Purpose: Libm ;//
.686P .387 .XMM .MODEL FLAT,C
EXTRN C __libm_error_support : NEAR
CONST SEGMENT PARA PUBLIC USE32 'CONST' ALIGN 16
EXTRN C _atan_table:QWORD
_atn TEXTEQU <_atan_table>
;/*;// FUNCTION: double atan(double x);//;// DESCRIPTION:;//;// 1. For |x| < 2^(-27), where atan(x) ~= x, return x.;// 2. For |x| >= 0.1633123935319536975596774e+17, where atan(x) ~= +-Pi/2, return +-Pi/2.;// 3. In interval [0.0,0.03125] polynomial approximation of atan(x)=x-x*P(x^2).;// 4. In interval [0.03125,0.375] polynomial approximation of atan(x)=x-x*D(x^2).;// 5. In interval [0.375,8.0] we compute ind and eps such, that x=0.03125*ind+eps and 0.0<eps<0.03125.;// Let s=0.03125*ind, then atan(x)=atan(s)+atan(t), where t=((x-s)/(1+x*s)). For lo and hi part of;// atan(s) we have table (see file atan_table.c): atn[ind]+atn[ind+1]=atan(s).;// atan(t) is approximated atan(t)=t-t*P(t^2).;// 6. In interval [8.0,0.1633123935319536975596774e+17] atan(x)=Pi/2+atan(-1/x).;// atan(-1/x) is approximated atan(t)=t-t*P(t^2), where t=-1/x.;// 7. For x < 0.0 atan(x) = -atan(|x|).;// 8. Special cases:;// atan(+0) = +0;;// atan(-0) = -0;;// atan(+INF) = +Pi/2;;// atan(-INF) = -Pi/2;;// atan(NaN) = NaN.;//;// KEYS OF COMPILER: -c -w -Zl -Di386 /QIfdiv-;*/
_mexp DQ 07ff0000000000000H, 07ff0000000000000H_mabs DQ 07fffffffffffffffH, 07fffffffffffffffH_pi_2d DQ 03ff921fb54442d18H, 0bff921fb54442d18H_cntshf DQ 00000000000040201H, 00000000000040201H_d1400 DQ 03fd5555555555552H, 00000000000000000H_d1213 DQ 03fc249249246aa76H, 0bfc99999999992acH_d1011 DQ 03fb745d15933de8aH, 0bfbc71c71b835923H_d89 DQ 03fb110f5eeb76ecaH, 0bfb3b1390a3b9899H_d67 DQ 03faae4492fe3a600H, 0bfae1c1704144b68H_d45 DQ 03fa51fa164891abeH, 0bfa8171d55d53138H_d23 DQ 03f974721481ca2a2H, 0bfa124ce2388f2cbH_d01 DQ 03f66107c30e0b8a5H, 0bf866e5652b14bbdH_p60 DQ 03fd55555555554ebH, 00000000000000000H_p45 DQ 03fc249249014497eH, 0bfc9999999976718H_p23 DQ 03fb7453ba342480fH, 0bfbc71c4eebfb10eH_p01 DQ 03fae9be97b0f8d08H, 0bfb39ad683f878c6H_zero DQ 00000000000000000H, 00000000000000000H_onen DQ 0bff0000000000000H, 0bff0000000000000H_one DQ 03ff0000000000000H, 03ff0000000000000H_cnst8 DQ 04020000000000000H, 04020000000000000H_in3 DQ 04020000000000000H, 04020000000000000H_in2 DQ 03fd8000000000000H, 03fd8000000000000H_in1 DQ 03fa0000000000000H, 03fa0000000000000H_in0 DQ 03e40000000000000H, 03e40000000000000H_in DQ 0434d02967c31cdb5H, 0434d02967c31cdb5H_minval DQ 00010000000000000H, 00010000000000000Hlibm_small DQ 00200000000000000H CONST ENDS
_x TEXTEQU <esp+4>XMMWORD TEXTEQU <OWORD>
_TEXT SEGMENT PARA PUBLIC USE32 'CODE' ALIGN 4
PUBLIC C _atan_pentium4, _CIatan_pentium4_CIatan_pentium4 PROC NEAR push ebp mov ebp, esp sub esp, 8 ; for argument DBLSIZE and esp, 0fffffff0h fstp qword ptr [esp] movq xmm7, qword ptr [esp] call start leave ret_atan_pentium4 label proc movq xmm7, QWORD PTR [_x] ; xstart: unpcklpd xmm7, xmm7 movapd xmm2, xmm7 andpd xmm2, XMMWORD PTR _mabs ; |x| comisd xmm2, XMMWORD PTR _in ; |x| < 0.1633123935319536975596774e+17 ? jp x_nan jae bigx comisd xmm2, XMMWORD PTR _in1 ; |x| < 0.03125 ? jae xge0_03125 comisd xmm2, XMMWORD PTR _in0 ; |x| < 2^(-27) ? jb retx ; atan(x) ~= x
; 2^(-27) < |x| < 0.03125, atan(x)=x-x*P(x^2)
movapd xmm1, xmm2 mulpd xmm1, xmm2 ; |x|^2 movapd xmm3, xmm1 mulpd xmm3, xmm1 ; |x|^4 movapd xmm5, XMMWORD PTR _p01 ; calculate P(x^2) mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p23 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p45 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p60 mulsd xmm5, xmm1 movapd xmm3, xmm5 shufpd xmm3, xmm3, 1 addsd xmm5, xmm3 ; P(x^2) mulsd xmm5, xmm7 ; x * P(x^2) subsd xmm7, xmm5 ; x - x * P(x^2) movq QWORD PTR [_x], xmm7 fld QWORD PTR [_x] ret
xge0_03125: ; |x| >= 0.03125 comisd xmm2, XMMWORD PTR _in2 ; |x| < 0.375 ? jae xge0_375
; 0.03125 < |x| < 0.375, atan(x)=x-x*D(x^2)
movapd xmm1, xmm2 mulpd xmm1, xmm2 ; |x|^2 movapd xmm3, xmm1 mulpd xmm3, xmm1 ; |x|^4 movapd xmm5, XMMWORD PTR _d01 ; calculate D(x^2) mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d23 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d45 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d67 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d89 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d1011 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d1213 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _d1400 mulsd xmm5, xmm1 movapd xmm3, xmm5 shufpd xmm3, xmm3, 1 addsd xmm5, xmm3 ; D(x^2) mulsd xmm5, xmm7 ; x * D(x^2) subsd xmm7, xmm5 ; x - x * D(x^2) movq QWORD PTR [_x], xmm7 fld QWORD PTR [_x] ret
xge0_375: ; |x| >= 0.375 movq xmm6, xmm7 ; x xorpd xmm6, xmm2 ; sign x comisd xmm2, XMMWORD PTR _in3 ; |x| < 8.0 ? jae xge8_0
; 0.375 < |x| < 8.0:; atan(|x|)=atan(s)+atan(t), s=ind*0.03125, t=(|x|-s)/(1+|x|*s)
movq xmm0, XMMWORD PTR _cnst8 movq xmm5, XMMWORD PTR _cntshf movq xmm3, xmm2 ; calculate ind addsd xmm3, xmm0 psrlq xmm3, 44 psubd xmm3, xmm5 movd eax, xmm3 ; ind lea eax, DWORD PTR [eax+eax*2] ; ind*3 movq xmm5, QWORD PTR _atn[eax*8+16] ; s movq xmm3, xmm2 ; |x| subsd xmm2, xmm5 ; |x|-s mulsd xmm3, xmm5 ; |x|*s addsd xmm3, XMMWORD PTR _one ; 1+|x|*s divsd xmm2, xmm3 ; (|x|-s)/(1+|x|*s) unpcklpd xmm2, xmm2 jmp clcpol
xge8_0: ; |x| > 8.0
; 8.0 < |x| < 0.1633123935319536975596774e+17:; atan(|x|)=Pi/2+atan(-1/|x|)
mov eax, 768 ; ind*3 - entry point in table, where lo and hi part of Pi/2 movq xmm0, xmm2 ; |x| movq xmm2, XMMWORD PTR _onen divsd xmm2, xmm0 ;-1/|x| unpcklpd xmm2, xmm2
clcpol: movq xmm0, QWORD PTR _atn[0+eax*8] ; atn[ind+0] - hi part of atan(s) or Pi/2 movq xmm4, QWORD PTR _atn[8+eax*8] ; atn[ind+1] - lo part of atan(s) or Pi/2 movapd xmm1, xmm2 mulpd xmm1, xmm2 ; |x|^2 movapd xmm3, xmm1 mulpd xmm3, xmm1 ; |x|^4 movapd xmm5, XMMWORD PTR _p01 ; calculate P(x^2) mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p23 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p45 mulpd xmm5, xmm3 addpd xmm5, XMMWORD PTR _p60 mulsd xmm5, xmm1 movapd xmm3, xmm5 shufpd xmm3, xmm3, 1 addsd xmm5, xmm3 ; P(x^2)
; atan(|x|) = atn[ind+0]-((|x|*P(x^2)-atn[ind+1])-|x|)
mulsd xmm5, xmm2 ; |x|*P(x^2) subsd xmm5, xmm4 ; |x|*P(x^2)-atn[ind+1] subsd xmm5, xmm2 ; (|x|*P(x^2)-atn[ind+1])-|x| subsd xmm0, xmm5 ; atn[ind+0]-((|x|*P(x^2)-atn[ind+1])-|x|) orpd xmm0, xmm6 ; sign x movq QWORD PTR [_x], xmm0 fld QWORD PTR [_x] ret
retx: ; |x| < 2^(-27): atan(x) ~= x comisd xmm2, XMMWORD PTR _zero ; x == 0 ? jne notzero fld QWORD PTR [_x] ; x == +0.0 or -0.0 ret
notzero: comisd xmm2, XMMWORD PTR _minval ; x < minval ? jae ge_minval fld QWORD PTR libm_small fmul QWORD PTR libm_small sub esp, 8 fstp QWORD PTR [esp] ; should be flag UNDERFLOW fld QWORD PTR [esp] add esp, 8 fadd QWORD PTR [_x] ; should be inexact result ret
ge_minval: ; minval < x < 2^(-27) fld QWORD PTR libm_small fmul QWORD PTR libm_small fadd QWORD PTR [_x] ; should be inexact result ret
bigx: ; |x| > 0.1633123935319536975596774e+17 movq xmm0, xmm2 ; |x| movq xmm3, QWORD PTR _mexp andpd xmm0, xmm3 ucomisd xmm0, xmm3 jp x_nan
mov eax, DWORD PTR [_x+4] ; x shr eax, 31 ; sign x fld QWORD PTR libm_small fadd QWORD PTR _pi_2d[eax*8] ; should be inexact result ret ; return +-Pi/2
x_nan: mov edx, 1003 ;call libm_error_support(void *arg1,void *arg2,void *retval,error_types input_tag) sub esp, 16 mov DWORD PTR [esp+12],edx mov edx, esp add edx, 16+4 mov DWORD PTR [esp+8],edx mov DWORD PTR [esp+4],edx mov DWORD PTR [esp],edx call NEAR PTR __libm_error_support add esp, 16
fld QWORD PTR [_x] ret ; return same nan
ALIGN 4
_CIatan_pentium4 ENDP
_TEXT ENDS
END
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