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  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) */
  95.