| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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 | |
| 17 | #ifndef lint |
| 18 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.12 2005/12/13 20:17:23 bde 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 | 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 | static const float |
| 32 | C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */ |
| 33 | D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */ |
| 34 | E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */ |
| 35 | F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */ |
| 36 | G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */ |
| 37 | |
| 38 | float |
| 39 | cbrtf(float x) |
| 40 | { |
| 41 | float r,s,t,w; |
| 42 | int32_t hx; |
| 43 | u_int32_t sign; |
| 44 | u_int32_t high; |
| 45 | |
| 46 | GET_FLOAT_WORD(hx,x); |
| 47 | sign=hx&0x80000000; /* sign= sign(x) */ |
| 48 | hx ^=sign; |
| 49 | if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ |
| 50 | if(hx==0) |
| 51 | return(x); /* cbrt(0) is itself */ |
| 52 | |
| 53 | /* rough cbrt to 5 bits */ |
| 54 | if(hx<0x00800000) { /* subnormal number */ |
| 55 | SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ |
| 56 | t*=x; |
| 57 | GET_FLOAT_WORD(high,t); |
| 58 | SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2)); |
| 59 | } else |
| 60 | SET_FLOAT_WORD(t,sign|(hx/3+B1)); |
| 61 | |
| 62 | /* new cbrt to 23 bits */ |
| 63 | r=t*t/x; |
| 64 | s=C+r*t; |
| 65 | t*=G+F/(s+E+D/s); |
| 66 | |
| 67 | /* chop t to 12 bits and make it larger in magnitude than cbrt(x) */ |
| 68 | GET_FLOAT_WORD(high,t); |
| 69 | SET_FLOAT_WORD(t,(high&0xfffff000)+0x00001000); |
| 70 | |
| 71 | /* one step Newton iteration to 24 bits with error less than 0.667 ulps */ |
| 72 | s=t*t; /* t*t is exact */ |
| 73 | r=x/s; |
| 74 | w=t+t; |
| 75 | r=(r-t)/(w+r); /* r-t is exact */ |
| 76 | t=t+t*r; |
| 77 | |
| 78 | return(t); |
| 79 | } |