contrib/openbsd_libm/src/s_cbrtf.c

   1 /* s_cbrtf.c -- float version of s_cbrt.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   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 #include "math.h"
  17 #include "math_private.h"
  18
  19 /* cbrtf(x)
  20  * Return cube root of x
  21  */
  22 static const unsigned
  23 B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
  24 B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
  25
  26 static const float
  27 C =  5.4285717010e-01, /* 19/35     = 0x3f0af8b0 */
  28 D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
  29 E =  1.4142856598e+00, /* 99/70     = 0x3fb50750 */
  30 F =  1.6071428061e+00, /* 45/28     = 0x3fcdb6db */
  31 G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */
  32
  33 float
  34 cbrtf(float x)
  35 {
  36         float r,s,t;
  37         int32_t hx;
  38         u_int32_t sign;
  39         u_int32_t high;
  40
  41         GET_FLOAT_WORD(hx,x);
  42         sign=hx&0x80000000;             /* sign= sign(x) */
  43         hx  ^=sign;
  44         if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
  45         if(hx==0)
  46             return(x);          /* cbrt(0) is itself */
  47
  48         SET_FLOAT_WORD(x,hx);   /* x <- |x| */
  49     /* rough cbrt to 5 bits */
  50         if(hx<0x00800000)               /* subnormal number */
  51           {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
  52            t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
  53           }
  54         else
  55           SET_FLOAT_WORD(t,hx/3+B1);
  56
  57
  58     /* new cbrt to 23 bits */
  59         r=t*t/x;
  60         s=C+r*t;
  61         t*=G+F/(s+E+D/s);
  62
  63     /* retore the sign bit */
  64         GET_FLOAT_WORD(high,t);
  65         SET_FLOAT_WORD(t,high|sign);
  66         return(t);
  67 }