libquadmath/math/atan2q.c

   1 /* atan2q.c -- __float128 version of e_atan2.c.
   2  * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 /* atan2q(y,x)
  17  * Method :
  18  *      1. Reduce y to positive by atan2q(y,x)=-atan2q(-y,x).
  19  *      2. Reduce x to positive by (if x and y are unexceptional):
  20  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  21  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  22  *
  23  * Special cases:
  24  *
  25  *      ATAN2((anything), NaN ) is NaN;
  26  *      ATAN2(NAN , (anything) ) is NaN;
  27  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  28  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  29  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  30  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  31  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  32  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  33  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  34  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  35  *
  36  * Constants:
  37  * The hexadecimal values are the intended ones for the following
  38  * constants. The decimal values may be used, provided that the
  39  * compiler will convert from decimal to binary accurately enough
  40  * to produce the hexadecimal values shown.
  41  */
  42
  43 #include "quadmath-imp.h"
  44
  45 static const __float128
  46 tiny  = 1.0e-4900Q,
  47 zero  = 0.0,
  48 pi_o_4  = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */
  49 pi_o_2  = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */
  50 pi      = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */
  51 pi_lo   = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
  52
  53 __float128
  54 atan2q (__float128 y, __float128 x)
  55 {
  56         __float128 z;
  57         int64_t k,m,hx,hy,ix,iy;
  58         uint64_t lx,ly;
  59
  60         GET_FLT128_WORDS64(hx,lx,x);
  61         ix = hx&0x7fffffffffffffffLL;
  62         GET_FLT128_WORDS64(hy,ly,y);
  63         iy = hy&0x7fffffffffffffffLL;
  64         if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
  65            ((iy|((ly|-ly)>>63))>0x7fff000000000000LL))  /* x or y is NaN */
  66            return x+y;
  67         if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y);   /* x=1.0Q */
  68         m = ((hy>>63)&1)|((hx>>62)&2);  /* 2*sign(x)+sign(y) */
  69
  70     /* when y = 0 */
  71         if((iy|ly)==0) {
  72             switch(m) {
  73                 case 0:
  74                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  75                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  76                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  77             }
  78         }
  79     /* when x = 0 */
  80         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  81
  82     /* when x is INF */
  83         if(ix==0x7fff000000000000LL) {
  84             if(iy==0x7fff000000000000LL) {
  85                 switch(m) {
  86                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  87                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  88                     case 2: return  3.0Q*pi_o_4+tiny;/*atan(+INF,-INF)*/
  89                     case 3: return -3.0Q*pi_o_4-tiny;/*atan(-INF,-INF)*/
  90                 }
  91             } else {
  92                 switch(m) {
  93                     case 0: return  zero  ;     /* atan(+...,+INF) */
  94                     case 1: return -zero  ;     /* atan(-...,+INF) */
  95                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
  96                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
  97                 }
  98             }
  99         }
 100     /* when y is INF */
 101         if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 102
 103     /* compute y/x */
 104         k = (iy-ix)>>48;
 105         if(k > 120) z=pi_o_2+0.5Q*pi_lo;        /* |y/x| >  2**120 */
 106         else if(hx<0&&k<-120) z=0.0Q;           /* |y|/x < -2**120 */
 107         else z=atanq(fabsq(y/x));               /* safe to do y/x */
 108         switch (m) {
 109             case 0: return       z  ;   /* atan(+,+) */
 110             case 1: {
 111                       uint64_t zh;
 112                       GET_FLT128_MSW64(zh,z);
 113                       SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL);
 114                     }
 115                     return       z  ;   /* atan(-,+) */
 116             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 117             default: /* case 3 */
 118                     return  (z-pi_lo)-pi;/* atan(-,-) */
 119         }
 120 }