2006-01-28 00:15:15 +00:00
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/* e_atan2l.c -- long double version of e_atan2.c.
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* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
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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 atan2l(y,x)=-atan2l(-y,x).
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* 2. Reduce x to positive by (if x and y are unexceptional):
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2011-10-12 15:27:51 +00:00
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* ARG (x+iy) = arctan(y/x) ... if x > 0,
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2006-01-28 00:15:15 +00:00
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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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2012-03-09 19:29:16 +00:00
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#include <math.h>
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#include <math_private.h>
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2019-07-16 15:17:22 +00:00
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#include <libm-alias-finite.h>
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2006-01-28 00:15:15 +00:00
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static const long double
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tiny = 1.0e-300L,
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zero = 0.0,
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pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */
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pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */
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pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */
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pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */
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2011-10-12 15:27:51 +00:00
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long double
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__ieee754_atan2l(long double y, long double x)
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2006-01-28 00:15:15 +00:00
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{
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long double z;
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int64_t k,m,hx,hy,ix,iy;
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2013-08-17 08:54:58 +00:00
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uint64_t lx;
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double xhi, xlo, yhi;
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2006-01-28 00:15:15 +00:00
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2013-08-17 08:54:58 +00:00
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ldbl_unpack (x, &xhi, &xlo);
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EXTRACT_WORDS64 (hx, xhi);
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EXTRACT_WORDS64 (lx, xlo);
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2006-01-28 00:15:15 +00:00
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ix = hx&0x7fffffffffffffffLL;
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2013-08-17 08:54:58 +00:00
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yhi = ldbl_high (y);
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EXTRACT_WORDS64 (hy, yhi);
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2006-01-28 00:15:15 +00:00
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iy = hy&0x7fffffffffffffffLL;
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if(((ix)>0x7ff0000000000000LL)||
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((iy)>0x7ff0000000000000LL)) /* x or y is NaN */
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return x+y;
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2012-10-31 20:44:59 +00:00
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if(((hx-0x3ff0000000000000LL))==0
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&& (lx&0x7fffffffffffffff)==0) return __atanl(y); /* x=1.0L */
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2006-01-28 00:15:15 +00:00
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m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
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/* when y = 0 */
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2013-08-17 08:54:58 +00:00
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if(iy==0) {
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2006-01-28 00:15:15 +00:00
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switch(m) {
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case 0:
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2011-10-12 15:27:51 +00:00
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case 1: return y; /* atan(+-0,+anything)=+-0 */
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2006-01-28 00:15:15 +00:00
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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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2013-08-17 08:54:58 +00:00
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if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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2006-01-28 00:15:15 +00:00
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/* when x is INF */
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if(ix==0x7ff0000000000000LL) {
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if(iy==0x7ff0000000000000LL) {
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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 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/
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case 3: return -3.0L*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==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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/* compute y/x */
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k = (iy-ix)>>52;
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2011-10-12 15:27:51 +00:00
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if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */
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else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */
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2006-01-28 00:15:15 +00:00
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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: 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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2011-10-12 15:27:51 +00:00
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return (z-pi_lo)-pi;/* atan(-,-) */
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2006-01-28 00:15:15 +00:00
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}
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}
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2019-07-16 15:17:22 +00:00
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libm_alias_finite (__ieee754_atan2l, __atan2l)
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