newlib/libm/common/sf_cbrt.c

   1 /* sf_cbrt.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
  17 #include "fdlibm.h"
  18
  19 /* cbrtf(x)
  20  * Return cube root of x
  21  */
  22 #ifdef __STDC__
  23 static const __uint32_t
  24 #else
  25 static __uint32_t
  26 #endif
  27         B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
  28         B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
  29
  30 #ifdef __STDC__
  31 static const float
  32 #else
  33 static float
  34 #endif
  35 C =  5.4285717010e-01, /* 19/35     = 0x3f0af8b0 */
  36 D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
  37 E =  1.4142856598e+00, /* 99/70     = 0x3fb50750 */
  38 F =  1.6071428061e+00, /* 45/28     = 0x3fcdb6db */
  39 G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */
  40
  41 #ifdef __STDC__
  42         float cbrtf(float x)
  43 #else
  44         float cbrtf(x)
  45         float x;
  46 #endif
  47 {
  48         __int32_t       hx;
  49         float r,s,t;
  50         __uint32_t sign;
  51         __uint32_t high;
  52
  53         GET_FLOAT_WORD(hx,x);
  54         sign=hx&0x80000000;             /* sign= sign(x) */
  55         hx  ^=sign;
  56         if(!FLT_UWORD_IS_FINITE(hx))
  57             return(x+x);                /* cbrt(NaN,INF) is itself */
  58         if(FLT_UWORD_IS_ZERO(hx))
  59             return(x);                  /* cbrt(0) is itself */
  60
  61         SET_FLOAT_WORD(x,hx);   /* x <- |x| */
  62     /* rough cbrt to 5 bits */
  63         if(FLT_UWORD_IS_SUBNORMAL(hx))          /* subnormal number */
  64           {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
  65            t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
  66           }
  67         else
  68           SET_FLOAT_WORD(t,hx/3+B1);
  69
  70
  71     /* new cbrt to 23 bits */
  72         r=t*t/x;
  73         s=C+r*t;
  74         t*=G+F/(s+E+D/s);
  75
  76     /* retore the sign bit */
  77         GET_FLOAT_WORD(high,t);
  78         SET_FLOAT_WORD(t,high|sign);
  79         return(t);
  80 }
  81
  82 #ifdef _DOUBLE_IS_32BITS
  83
  84 #ifdef __STDC__
  85         double cbrt(double x)
  86 #else
  87         double cbrt(x)
  88         double x;
  89 #endif
  90 {
  91         return (double) cbrtf((float) x);
  92 }
  93
  94 #endif /* defined(_DOUBLE_IS_32BITS) */