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annotate libquadmath/math/atan2q.c @ 145:1830386684a0

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gcc-9.2.0
author anatofuz
date Thu, 13 Feb 2020 11:34:05 +0900
parents 04ced10e8804
children
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145
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diff changeset
1 /* e_atan2l.c -- long double version of e_atan2.c.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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3 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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4
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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5 /*
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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6 * ====================================================
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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8 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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9 * Developed at SunPro, a Sun Microsystems, Inc. business.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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10 * Permission to use, copy, modify, and distribute this
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11 * software is freely granted, provided that this notice
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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12 * is preserved.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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13 * ====================================================
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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14 */
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15
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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16 /* atan2q(y,x)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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17 * Method :
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18 * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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19 * 2. Reduce x to positive by (if x and y are unexceptional):
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20 * ARG (x+iy) = arctan(y/x) ... if x > 0,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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21 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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22 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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23 * Special cases:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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24 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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25 * ATAN2((anything), NaN ) is NaN;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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26 * ATAN2(NAN , (anything) ) is NaN;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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27 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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28 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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29 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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30 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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31 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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32 * ATAN2(+-INF,+INF ) is +-pi/4 ;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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33 * ATAN2(+-INF,-INF ) is +-3pi/4;
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34 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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35 *
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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36 * Constants:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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37 * The hexadecimal values are the intended ones for the following
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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38 * constants. The decimal values may be used, provided that the
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39 * compiler will convert from decimal to binary accurately enough
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40 * to produce the hexadecimal values shown.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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41 */
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42
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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43 #include "quadmath-imp.h"
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44
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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45 static const __float128
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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46 tiny = 1.0e-4900Q,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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47 zero = 0.0,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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48 pi_o_4 = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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49 pi_o_2 = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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50 pi = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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51 pi_lo = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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52
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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53 __float128
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54 atan2q(__float128 y, __float128 x)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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55 {
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56 __float128 z;
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57 int64_t k,m,hx,hy,ix,iy;
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58 uint64_t lx,ly;
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59
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60 GET_FLT128_WORDS64(hx,lx,x);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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61 ix = hx&0x7fffffffffffffffLL;
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62 GET_FLT128_WORDS64(hy,ly,y);
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63 iy = hy&0x7fffffffffffffffLL;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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64 if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
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65 ((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */
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66 return x+y;
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67 if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y); /* x=1.0L */
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68 m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
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69
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70 /* when y = 0 */
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71 if((iy|ly)==0) {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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72 switch(m) {
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73 case 0:
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74 case 1: return y; /* atan(+-0,+anything)=+-0 */
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75 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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76 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
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77 }
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78 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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79 /* when x = 0 */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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80 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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81
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82 /* when x is INF */
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83 if(ix==0x7fff000000000000LL) {
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84 if(iy==0x7fff000000000000LL) {
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85 switch(m) {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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86 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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87 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
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88 case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/
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89 case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
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90 }
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91 } else {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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92 switch(m) {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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93 case 0: return zero ; /* atan(+...,+INF) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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94 case 1: return -zero ; /* atan(-...,+INF) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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95 case 2: return pi+tiny ; /* atan(+...,-INF) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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96 case 3: return -pi-tiny ; /* atan(-...,-INF) */
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97 }
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98 }
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99 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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100 /* when y is INF */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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101 if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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102
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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103 /* compute y/x */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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104 k = (iy-ix)>>48;
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105 if(k > 120) z=pi_o_2+0.5Q*pi_lo; /* |y/x| > 2**120 */
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106 else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */
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107 else z=atanq(fabsq(y/x)); /* safe to do y/x */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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108 switch (m) {
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109 case 0: return z ; /* atan(+,+) */
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parents:
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110 case 1: {
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111 uint64_t zh;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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112 GET_FLT128_MSW64(zh,z);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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113 SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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114 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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115 return z ; /* atan(-,+) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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116 case 2: return pi-(z-pi_lo);/* atan(+,-) */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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117 default: /* case 3 */
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118 return (z-pi_lo)-pi;/* atan(-,-) */
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119 }
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120 }