sysdeps/ieee754/ldbl-128ibm/e_atan2l.c

   1 /* e_atan2l.c -- long double 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 /* __ieee754_atan2l(y,x)
  17  * Method :
  18  *      1. Reduce y to positive by atan2l(y,x)=-atan2l(-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 "math.h"
  44 #include "math_private.h"
  45
  46 #ifdef __STDC__
  47 static const long double
  48 #else
  49 static long double
  50 #endif
  51 tiny  = 1.0e-300L,
  52 zero  = 0.0,
  53 pi_o_4  = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */
  54 pi_o_2  = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */
  55 pi      = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */
  56 pi_lo   = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */
  57
  58 #ifdef __STDC__
  59         long double __ieee754_atan2l(long double y, long double x)
  60 #else
  61         long double __ieee754_atan2l(y,x)
  62         long double  y,x;
  63 #endif
  64 {
  65         long double z;
  66         int64_t k,m,hx,hy,ix,iy;
  67         u_int64_t lx,ly;
  68
  69         GET_LDOUBLE_WORDS64(hx,lx,x);
  70         ix = hx&0x7fffffffffffffffLL;
  71         GET_LDOUBLE_WORDS64(hy,ly,y);
  72         iy = hy&0x7fffffffffffffffLL;
  73         if(((ix)>0x7ff0000000000000LL)||
  74            ((iy)>0x7ff0000000000000LL)) /* x or y is NaN */
  75            return x+y;
  76         if(((hx-0x3ff0000000000000LL))==0) return __atanl(y);   /* x=1.0L */
  77         m = ((hy>>63)&1)|((hx>>62)&2);  /* 2*sign(x)+sign(y) */
  78
  79     /* when y = 0 */
  80         if((iy|(ly&0x7fffffffffffffffLL))==0) {
  81             switch(m) {
  82                 case 0:
  83                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  84                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  85                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  86             }
  87         }
  88     /* when x = 0 */
  89         if((ix|(lx&0x7fffffffffffffff))==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  90
  91     /* when x is INF */
  92         if(ix==0x7ff0000000000000LL) {
  93             if(iy==0x7ff0000000000000LL) {
  94                 switch(m) {
  95                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  96                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  97                     case 2: return  3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/
  98                     case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/
  99                 }
 100             } else {
 101                 switch(m) {
 102                     case 0: return  zero  ;     /* atan(+...,+INF) */
 103                     case 1: return -zero  ;     /* atan(-...,+INF) */
 104                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 105                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 106                 }
 107             }
 108         }
 109     /* when y is INF */
 110         if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 111
 112     /* compute y/x */
 113         k = (iy-ix)>>52;
 114         if(k > 120) z=pi_o_2+0.5L*pi_lo;        /* |y/x| >  2**120 */
 115         else if(hx<0&&k<-120) z=0.0L;           /* |y|/x < -2**120 */
 116         else z=__atanl(fabsl(y/x));             /* safe to do y/x */
 117         switch (m) {
 118             case 0: return       z  ;   /* atan(+,+) */
 119             case 1: return      -z  ;   /* atan(-,+) */
 120             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 121             default: /* case 3 */
 122                     return  (z-pi_lo)-pi;/* atan(-,-) */
 123         }
 124 }