sysdeps/ieee754/ldbl-128/e_atan2l.c

   1 /* e_atan2l.c -- long double version of e_atan2.c.
   2  */
   3
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 /* __ieee754_atan2l(y,x)
  16  * Method :
  17  *      1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
  18  *      2. Reduce x to positive by (if x and y are unexceptional):
  19  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  20  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  21  *
  22  * Special cases:
  23  *
  24  *      ATAN2((anything), NaN ) is NaN;
  25  *      ATAN2(NAN , (anything) ) is NaN;
  26  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  27  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  28  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  29  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  30  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  31  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  32  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  33  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  34  *
  35  * Constants:
  36  * The hexadecimal values are the intended ones for the following
  37  * constants. The decimal values may be used, provided that the
  38  * compiler will convert from decimal to binary accurately enough
  39  * to produce the hexadecimal values shown.
  40  */
  41
  42 #include <math.h>
  43 #include <math_private.h>
  44 #include <libm-alias-finite.h>
  45
  46 static const _Float128
  47 tiny  = L(1.0e-4900),
  48 zero  = 0.0,
  49 pi_o_4  = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */
  50 pi_o_2  = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */
  51 pi      = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */
  52 pi_lo   = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */
  53
  54 _Float128
  55 __ieee754_atan2l(_Float128 y, _Float128 x)
  56 {
  57         _Float128 z;
  58         int64_t k,m,hx,hy,ix,iy;
  59         uint64_t lx,ly;
  60
  61         GET_LDOUBLE_WORDS64(hx,lx,x);
  62         ix = hx&0x7fffffffffffffffLL;
  63         GET_LDOUBLE_WORDS64(hy,ly,y);
  64         iy = hy&0x7fffffffffffffffLL;
  65         if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
  66            ((iy|((ly|-ly)>>63))>0x7fff000000000000LL))  /* x or y is NaN */
  67            return x+y;
  68         if(((hx-0x3fff000000000000LL)|lx)==0) return __atanl(y);   /* x=1.0L */
  69         m = ((hy>>63)&1)|((hx>>62)&2);  /* 2*sign(x)+sign(y) */
  70
  71     /* when y = 0 */
  72         if((iy|ly)==0) {
  73             switch(m) {
  74                 case 0:
  75                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  76                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  77                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  78             }
  79         }
  80     /* when x = 0 */
  81         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  82
  83     /* when x is INF */
  84         if(ix==0x7fff000000000000LL) {
  85             if(iy==0x7fff000000000000LL) {
  86                 switch(m) {
  87                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  88                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  89                     case 2: return  3*pi_o_4+tiny;/*atan(+INF,-INF)*/
  90                     case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
  91                 }
  92             } else {
  93                 switch(m) {
  94                     case 0: return  zero  ;     /* atan(+...,+INF) */
  95                     case 1: return -zero  ;     /* atan(-...,+INF) */
  96                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
  97                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
  98                 }
  99             }
 100         }
 101     /* when y is INF */
 102         if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 103
 104     /* compute y/x */
 105         k = (iy-ix)>>48;
 106         if(k > 120) z=pi_o_2+L(0.5)*pi_lo;      /* |y/x| >  2**120 */
 107         else if(hx<0&&k<-120) z=0;              /* |y|/x < -2**120 */
 108         else z=__atanl(fabsl(y/x));             /* safe to do y/x */
 109         switch (m) {
 110             case 0: return       z  ;   /* atan(+,+) */
 111             case 1: {
 112                       uint64_t zh;
 113                       GET_LDOUBLE_MSW64(zh,z);
 114                       SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL);
 115                     }
 116                     return       z  ;   /* atan(-,+) */
 117             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 118             default: /* case 3 */
 119                     return  (z-pi_lo)-pi;/* atan(-,-) */
 120         }
 121 }
 122 libm_alias_finite (__ieee754_atan2l, __atan2l)