compiler/stdc/math/e_rem_pio2f.c

   1 /* e_rem_pio2f.c -- float version of e_rem_pio2.c
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  * Debugged and optimized by Bruce D. Evans.
   4  */
   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
  17 #ifndef lint
  18 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_rem_pio2f.c,v 1.19 2005/11/23 03:03:09 bde Exp $";
  19 #endif
  20
  21 /* __ieee754_rem_pio2f(x,y)
  22  *
  23  * return the remainder of x rem pi/2 in y[0]+y[1]
  24  * use double precision internally
  25  * use __kernel_rem_pio2() for large x
  26  */
  27
  28 #include "math.h"
  29 #include "math_private.h"
  30
  31 /*
  32  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  33  */
  34 static const int32_t two_over_pi[] = {
  35 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
  36 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
  37 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
  38 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
  39 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
  40 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
  41 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
  42 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
  43 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
  44 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
  45 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
  46 };
  47
  48 /*
  49  * invpio2:  53 bits of 2/pi
  50  * pio2_1:   first  33 bit of pi/2
  51  * pio2_1t:  pi/2 - pio2_1
  52  */
  53
  54 static const double
  55 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  56 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  57 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  58 invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  59 pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  60 pio2_1t =  6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
  61
  62 #ifdef INLINE_REM_PIO2F
  63 static __inline
  64 #endif
  65 int32_t __ieee754_rem_pio2f(float x, float *y)
  66 {
  67         double w,t,r,fn;
  68         double tx[1],ty[2];
  69         float z;
  70         int32_t e0,n,ix,hx;
  71
  72         GET_FLOAT_WORD(hx,x);
  73         ix = hx&0x7fffffff;
  74     /* 33+53 bit pi is good enough for medium size */
  75         if(ix<=0x49490f80) {            /* |x| ~<= 2^19*(pi/2), medium size */
  76             t  = fabsf(x);
  77             n  = (int32_t) (t*invpio2+half);
  78             fn = (double)n;
  79             r  = t-fn*pio2_1;
  80             w  = fn*pio2_1t;
  81                     y[0] = r-w;
  82             y[1] = (r-y[0])-w;
  83             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  84             else         return n;
  85         }
  86     /*
  87      * all other (large) arguments
  88      */
  89         if(ix>=0x7f800000) {            /* x is inf or NaN */
  90             y[0]=y[1]=x-x; return 0;
  91         }
  92     /* set z = scalbn(|x|,ilogb(|x|)-23) */
  93         e0 = (ix>>23)-150;              /* e0 = ilogb(|x|)-23; */
  94         SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
  95         tx[0] = z;
  96         n  =  __kernel_rem_pio2(tx,ty,e0,1,1,two_over_pi);
  97         y[0] = ty[0];
  98         y[1] = ty[0] - y[0];
  99         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 100         return n;
 101 }