lib/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  * 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  * $FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.17 2007/05/29 07:13:07 bde Exp $
  17  * $NetBSD: s_cbrtf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $
  18  * $DragonFly: src/lib/libm/src/s_cbrtf.c,v 1.2 2007/07/03 04:54:07 pavalos Exp $
  19  */
  20
  21 #include <math.h>
  22 #include "math_private.h"
  23
  24 /* cbrtf(x)
  25  * Return cube root of x
  26  */
  27 static const unsigned
  28         B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
  29         B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
  30
  31 float
  32 cbrtf(float x)
  33 {
  34         double r,T;
  35         float t;
  36         int32_t hx;
  37         u_int32_t sign;
  38         u_int32_t high;
  39
  40         GET_FLOAT_WORD(hx,x);
  41         sign=hx&0x80000000;             /* sign= sign(x) */
  42         hx  ^=sign;
  43         if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
  44
  45     /* rough cbrt to 5 bits */
  46         if(hx<0x00800000) {             /* zero or subnormal? */
  47             if(hx==0)
  48                 return(x);              /* cbrt(+-0) is itself */
  49             SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
  50             t*=x;
  51             GET_FLOAT_WORD(high,t);
  52             SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
  53         } else
  54             SET_FLOAT_WORD(t,sign|(hx/3+B1));
  55
  56     /*
  57      * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
  58      * double precision so that its terms can be arranged for efficiency
  59      * without causing overflow or underflow.
  60      */
  61         T=t;
  62         r=T*T*T;
  63         T=T*((double)x+x+r)/(x+r+r);
  64
  65     /*
  66      * Second step Newton iteration to 47 bits.  In double precision for
  67      * efficiency and accuracy.
  68      */
  69         r=T*T*T;
  70         T=T*((double)x+x+r)/(x+r+r);
  71
  72     /* rounding to 24 bits is perfect in round-to-nearest mode */
  73         return(T);
  74 }