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  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  2. /* s_cbrtf.c -- float version of s_cbrt.c.
  3.  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
  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. #if defined(LIBM_SCCS) && !defined(lint)
  18. static char rcsid[] = "$Id: s_cbrtf.c,v 1.2 1994/08/18 23:06:27 jtc Exp $";
  19. #endif
  20.  
  21. #include "math.h"
  22. #include "math_private.h"
  23.  
  24. /* cbrtf(x)
  25.  * Return cube root of x
  26.  */
  27. #ifdef __STDC__
  28. static const unsigned
  29. #else
  30. static unsigned
  31. #endif
  32.         B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
  33.         B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
  34.  
  35. #ifdef __STDC__
  36. static const float
  37. #else
  38. static float
  39. #endif
  40. C =  5.4285717010e-01, /* 19/35     = 0x3f0af8b0 */
  41. D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
  42. E =  1.4142856598e+00, /* 99/70     = 0x3fb50750 */
  43. F =  1.6071428061e+00, /* 45/28     = 0x3fcdb6db */
  44. G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */
  45.  
  46. #ifdef __STDC__
  47.         float cbrtf(float x)
  48. #else
  49.         float cbrtf(x)
  50.         float x;
  51. #endif
  52. {
  53.         float r,s,t;
  54.         int32_t hx;
  55.         u_int32_t sign;
  56.         u_int32_t high;
  57.  
  58.         GET_FLOAT_WORD(hx,x);
  59.         sign=hx&0x80000000;             /* sign= sign(x) */
  60.         hx  ^=sign;
  61.         if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
  62.         if(hx==0)
  63.             return(x);          /* cbrt(0) is itself */
  64.  
  65.         SET_FLOAT_WORD(x,hx);   /* x <- |x| */
  66.     /* rough cbrt to 5 bits */
  67.         if(hx<0x00800000)               /* subnormal number */
  68.           {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
  69.            t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
  70.           }
  71.         else
  72.           SET_FLOAT_WORD(t,hx/3+B1);
  73.  
  74.  
  75.     /* new cbrt to 23 bits */
  76.         r=t*t/x;
  77.         s=C+r*t;
  78.         t*=G+F/(s+E+D/s);      
  79.  
  80.     /* retore the sign bit */
  81.         GET_FLOAT_WORD(high,t);
  82.         SET_FLOAT_WORD(t,high|sign);
  83.         return(t);
  84. }
  85.