compiler/stdc/math/e_atan2l.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 #ifndef lint
  13 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_atan2l.c,v 1.3 2008/08/02 19:17:00 das Exp $";
  14 #endif
  15
  16 #include <float.h>
  17 #include "math.h"
  18
  19 #include "invtrig.h"
  20 #include "math_private.h"
  21
  22 static const volatile long double
  23 tiny  __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) = 1.0e-300;
  24 static const long double
  25 zero  = 0.0;
  26
  27 #ifdef __i386__
  28 /* XXX Work around the fact that gcc truncates long double constants on i386 */
  29 static const volatile double
  30 pi1 __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) =  3.14159265358979311600e+00,       /*  0x1.921fb54442d18p+1  */
  31 pi2 __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) =  1.22514845490862001043e-16;       /*  0x1.1a80000000000p-53 */
  32 #define pi      ((long double)pi1 + pi2)
  33 #else
  34 static const long double
  35 pi =  3.14159265358979323846264338327950280e+00L;
  36 #endif
  37
  38 long double
  39 atan2l(long double y, long double x)
  40 {
  41         union IEEEl2bits ux, uy;
  42         long double z;
  43         int32_t k,m;
  44         int16_t exptx, expsignx, expty, expsigny;
  45
  46         uy.e = y;
  47         expsigny = uy.xbits.expsign;
  48         expty = expsigny & 0x7fff;
  49         ux.e = x;
  50         expsignx = ux.xbits.expsign;
  51         exptx = expsignx & 0x7fff;
  52
  53         if ((exptx==BIAS+LDBL_MAX_EXP &&
  54              ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) ||    /* x is NaN */
  55             (expty==BIAS+LDBL_MAX_EXP &&
  56              ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))      /* y is NaN */
  57             return x+y;
  58         if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
  59             return atanl(y);                                    /* x=1.0 */
  60         m = ((expsigny>>15)&1)|((expsignx>>14)&2);      /* 2*sign(x)+sign(y) */
  61
  62     /* when y = 0 */
  63         if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
  64             switch(m) {
  65                 case 0:
  66                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  67                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  68                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  69             }
  70         }
  71     /* when x = 0 */
  72         if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
  73             return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
  74
  75     /* when x is INF */
  76         if(exptx==BIAS+LDBL_MAX_EXP) {
  77             if(expty==BIAS+LDBL_MAX_EXP) {
  78                 switch(m) {
  79                     case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
  80                     case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
  81                     case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
  82                     case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
  83                 }
  84             } else {
  85                 switch(m) {
  86                     case 0: return  zero  ;     /* atan(+...,+INF) */
  87                     case 1: return -zero  ;     /* atan(-...,+INF) */
  88                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
  89                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
  90                 }
  91             }
  92         }
  93     /* when y is INF */
  94         if(expty==BIAS+LDBL_MAX_EXP)
  95             return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
  96
  97     /* compute y/x */
  98         k = expty-exptx;
  99         if(k > LDBL_MANT_DIG+2) {                       /* |y/x| huge */
 100             z=pio2_hi+pio2_lo;
 101             m&=1;
 102         }
 103         else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0;  /* |y/x| tiny, x<0 */
 104         else z=atanl(fabsl(y/x));               /* safe to do y/x */
 105         switch (m) {
 106             case 0: return       z  ;   /* atan(+,+) */
 107             case 1: return      -z  ;   /* atan(-,+) */
 108             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 109             default: /* case 3 */
 110                     return  (z-pi_lo)-pi;/* atan(-,-) */
 111         }
 112 }