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0ac5ae2335
libm is now somewhat integrated with gcc's -ffinite-math-only option and lots of the wrapper functions have been optimized.
126 lines
3.9 KiB
C
126 lines
3.9 KiB
C
/* e_atan2l.c -- long double version of e_atan2.c.
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* Conversion to long double by Ulrich Drepper,
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* Cygnus Support, drepper@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_atan2l(y,x)
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* Method :
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* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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* 2. Reduce x to positive by (if x and y are unexceptional):
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* ARG (x+iy) = arctan(y/x) ... if x > 0,
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* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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*
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* Special cases:
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*
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* ATAN2((anything), NaN ) is NaN;
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* ATAN2(NAN , (anything) ) is NaN;
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* ATAN2(+-0, +(anything but NaN)) is +-0 ;
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* ATAN2(+-0, -(anything but NaN)) is +-pi ;
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* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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* ATAN2(+-INF,+INF ) is +-pi/4 ;
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* ATAN2(+-INF,-INF ) is +-3pi/4;
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* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#include "math.h"
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#include "math_private.h"
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static const long double
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tiny = 1.0e-4900L,
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zero = 0.0,
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pi_o_4 = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */
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pi_o_2 = 1.5707963267948966192564E+00L, /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */
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pi = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */
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pi_lo = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */
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long double
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__ieee754_atan2l (long double y, long double x)
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{
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long double z;
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int32_t k,m,hx,hy,ix,iy;
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u_int32_t sx,sy,lx,ly;
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GET_LDOUBLE_WORDS(sx,hx,lx,x);
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ix = sx&0x7fff;
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lx |= hx & 0x7fffffff;
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GET_LDOUBLE_WORDS(sy,hy,ly,y);
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iy = sy&0x7fff;
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ly |= hy & 0x7fffffff;
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if(((2*ix|((lx|-lx)>>31))>0xfffe)||
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((2*iy|((ly|-ly)>>31))>0xfffe)) /* x or y is NaN */
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return x+y;
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if(((sx-0x3fff)|lx)==0) return __atanl(y); /* x=1.0 */
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m = ((sy>>15)&1)|((sx>>14)&2); /* 2*sign(x)+sign(y) */
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/* when y = 0 */
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if((iy|ly)==0) {
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switch(m) {
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case 0:
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case 1: return y; /* atan(+-0,+anything)=+-0 */
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case 2: return pi+tiny;/* atan(+0,-anything) = pi */
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case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
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}
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}
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/* when x = 0 */
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if((ix|lx)==0) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
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/* when x is INF */
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if(ix==0x7fff) {
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if(iy==0x7fff) {
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switch(m) {
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case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
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case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
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case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
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case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
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}
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} else {
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switch(m) {
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case 0: return zero ; /* atan(+...,+INF) */
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case 1: return -zero ; /* atan(-...,+INF) */
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case 2: return pi+tiny ; /* atan(+...,-INF) */
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case 3: return -pi-tiny ; /* atan(-...,-INF) */
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}
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}
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}
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/* when y is INF */
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if(iy==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
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/* compute y/x */
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k = sy-sx;
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if(k > 70) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**70 */
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else if(sx>=0x8000&&k<-70) z=0.0; /* |y|/x < -2**70 */
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else z=__atanl(fabsl(y/x)); /* safe to do y/x */
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switch (m) {
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case 0: return z ; /* atan(+,+) */
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case 1: {
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u_int32_t sz;
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GET_LDOUBLE_EXP(sz,z);
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SET_LDOUBLE_EXP(z,sz ^ 0x8000);
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}
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return z ; /* atan(-,+) */
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case 2: return pi-(z-pi_lo);/* atan(+,-) */
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default: /* case 3 */
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return (z-pi_lo)-pi;/* atan(-,-) */
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}
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}
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strong_alias (__ieee754_atan2l, __atan2l_finite)
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