src/math/__rem_pio2f.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   4  * Debugged and optimized by Bruce D. Evans.
   5  */
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16 /* __rem_pio2f(x,y)
  17  *
  18  * return the remainder of x rem pi/2 in *y
  19  * use double precision for everything except passing x
  20  * use __rem_pio2_large() for large x
  21  */
  22
  23 #include "libm.h"
  24
  25 #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
  26 #define EPS DBL_EPSILON
  27 #elif FLT_EVAL_METHOD==2
  28 #define EPS LDBL_EPSILON
  29 #endif
  30
  31 /*
  32  * invpio2:  53 bits of 2/pi
  33  * pio2_1:   first 25 bits of pi/2
  34  * pio2_1t:  pi/2 - pio2_1
  35  */
  36 static const double
  37 toint   = 1.5/EPS,
  38 pio4    = 0x1.921fb6p-1,
  39 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  40 pio2_1  = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
  41 pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
  42
  43 int __rem_pio2f(float x, double *y)
  44 {
  45         union {float f; uint32_t i;} u = {x};
  46         double tx[1],ty[1];
  47         double_t fn;
  48         uint32_t ix;
  49         int n, sign, e0;
  50
  51         ix = u.i & 0x7fffffff;
  52         /* 25+53 bit pi is good enough for medium size */
  53         if (ix < 0x4dc90fdb) {  /* |x| ~< 2^28*(pi/2), medium size */
  54                 /* Use a specialized rint() to get fn. */
  55                 fn = (double_t)x*invpio2 + toint - toint;
  56                 n  = (int32_t)fn;
  57                 *y = x - fn*pio2_1 - fn*pio2_1t;
  58                 /* Matters with directed rounding. */
  59                 if (predict_false(*y < -pio4)) {
  60                         n--;
  61                         fn--;
  62                         *y = x - fn*pio2_1 - fn*pio2_1t;
  63                 } else if (predict_false(*y > pio4)) {
  64                         n++;
  65                         fn++;
  66                         *y = x - fn*pio2_1 - fn*pio2_1t;
  67                 }
  68                 return n;
  69         }
  70         if(ix>=0x7f800000) {  /* x is inf or NaN */
  71                 *y = x-x;
  72                 return 0;
  73         }
  74         /* scale x into [2^23, 2^24-1] */
  75         sign = u.i>>31;
  76         e0 = (ix>>23) - (0x7f+23);  /* e0 = ilogb(|x|)-23, positive */
  77         u.i = ix - (e0<<23);
  78         tx[0] = u.f;
  79         n  =  __rem_pio2_large(tx,ty,e0,1,0);
  80         if (sign) {
  81                 *y = -ty[0];
  82                 return -n;
  83         }
  84         *y = ty[0];
  85         return n;
  86 }