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http://sourceware.org/ml/libc-alpha/2013-08/msg00083.html Further replacement of ieee854 macros and unions. These files also have some optimisations for comparison against 0.0L, infinity and nan. Since the ABI specifies that the high double of an IBM long double pair is the value rounded to double, a high double of 0.0 means the low double must also be 0.0. The ABI also says that infinity and nan are encoded in the high double, with the low double unspecified. This means that tests for 0.0L, +/-Infinity and +/-NaN need only check the high double. * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c (__ieee754_atan2l): Rewrite all uses of ieee854 long double macros and unions. Simplify tests for long doubles that are fully specified by the high double. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c (__ieee754_ilogbl): Likewise. Remove dead code too. * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise. (__ieee754_ynl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_logl.c (__ieee754_logl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise. Remove dead code too. * sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_isinf_nsl.c (__isinf_nsl): Likewise. Simplify. * sysdeps/ieee754/ldbl-128ibm/s_isinfl.c (___isinfl): Likewise. Simplify. * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_modfl.c (__modfl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl): Likewise. Comment on variable precision. * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c (__nexttoward): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c (__scalblnl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c (__scalbnl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise. * sysdeps/powerpc/fpu/libm-test-ulps: Adjust tan_towardzero ulps.
123 lines
4.0 KiB
C
123 lines
4.0 KiB
C
/* 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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* 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-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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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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int64_t k,m,hx,hy,ix,iy;
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uint64_t lx;
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double xhi, xlo, yhi;
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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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ix = hx&0x7fffffffffffffffLL;
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yhi = ldbl_high (y);
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EXTRACT_WORDS64 (hy, yhi);
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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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if(((hx-0x3ff0000000000000LL))==0
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&& (lx&0x7fffffffffffffff)==0) return __atanl(y); /* x=1.0L */
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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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if(iy==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==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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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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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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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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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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