| /* s_cbrtf.c -- float version of s_cbrt.c. |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| * Debugged and optimized by Bruce D. Evans. |
| */ |
| |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #ifndef lint |
| static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.12 2005/12/13 20:17:23 bde Exp $"; |
| #endif |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| /* cbrtf(x) |
| * Return cube root of x |
| */ |
| static const unsigned |
| B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ |
| B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ |
| |
| static const float |
| C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */ |
| D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */ |
| E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */ |
| F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */ |
| G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */ |
| |
| float |
| cbrtf(float x) |
| { |
| float r,s,t,w; |
| int32_t hx; |
| u_int32_t sign; |
| u_int32_t high; |
| |
| GET_FLOAT_WORD(hx,x); |
| sign=hx&0x80000000; /* sign= sign(x) */ |
| hx ^=sign; |
| if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ |
| if(hx==0) |
| return(x); /* cbrt(0) is itself */ |
| |
| /* rough cbrt to 5 bits */ |
| if(hx<0x00800000) { /* subnormal number */ |
| SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ |
| t*=x; |
| GET_FLOAT_WORD(high,t); |
| SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2)); |
| } else |
| SET_FLOAT_WORD(t,sign|(hx/3+B1)); |
| |
| /* new cbrt to 23 bits */ |
| r=t*t/x; |
| s=C+r*t; |
| t*=G+F/(s+E+D/s); |
| |
| /* chop t to 12 bits and make it larger in magnitude than cbrt(x) */ |
| GET_FLOAT_WORD(high,t); |
| SET_FLOAT_WORD(t,(high&0xfffff000)+0x00001000); |
| |
| /* one step Newton iteration to 24 bits with error less than 0.667 ulps */ |
| s=t*t; /* t*t is exact */ |
| r=x/s; |
| w=t+t; |
| r=(r-t)/(w+r); /* r-t is exact */ |
| t=t+t*r; |
| |
| return(t); |
| } |