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Diffstat (limited to 'libm/src/s_cbrt.c')
-rw-r--r-- | libm/src/s_cbrt.c | 92 |
1 files changed, 0 insertions, 92 deletions
diff --git a/libm/src/s_cbrt.c b/libm/src/s_cbrt.c deleted file mode 100644 index b600677..0000000 --- a/libm/src/s_cbrt.c +++ /dev/null @@ -1,92 +0,0 @@ -/* @(#)s_cbrt.c 5.1 93/09/24 */ -/* - * ==================================================== - * 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. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ - -#ifndef lint -static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.10 2005/12/13 20:17:23 bde Exp $"; -#endif - -#include "math.h" -#include "math_private.h" - -/* cbrt(x) - * Return cube root of x - */ -static const u_int32_t - B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ - B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ - -static const double -C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ -D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ -E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ -F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ -G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ - -double -cbrt(double x) -{ - int32_t hx; - double r,s,t=0.0,w; - u_int32_t sign; - u_int32_t high,low; - - GET_HIGH_WORD(hx,x); - sign=hx&0x80000000; /* sign= sign(x) */ - hx ^=sign; - if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ - GET_LOW_WORD(low,x); - if((hx|low)==0) - return(x); /* cbrt(0) is itself */ - - /* - * Rough cbrt to 5 bits: - * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) - * where e is integral and >= 0, m is real and in [0, 1), and "/" and - * "%" are integer division and modulus with rounding towards minus - * infinity. The RHS is always >= the LHS and has a maximum relative - * error of about 1 in 16. Adding a bias of -0.03306235651 to the - * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE - * floating point representation, for finite positive normal values, - * ordinary integer divison of the value in bits magically gives - * almost exactly the RHS of the above provided we first subtract the - * exponent bias (1023 for doubles) and later add it back. We do the - * subtraction virtually to keep e >= 0 so that ordinary integer - * division rounds towards minus infinity; this is also efficient. - */ - if(hx<0x00100000) { /* subnormal number */ - SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ - t*=x; - GET_HIGH_WORD(high,t); - SET_HIGH_WORD(t,sign|((high&0x7fffffff)/3+B2)); - } else - SET_HIGH_WORD(t,sign|(hx/3+B1)); - - /* new cbrt to 23 bits; may be implemented in single precision */ - r=t*t/x; - s=C+r*t; - t*=G+F/(s+E+D/s); - - /* chop t to 20 bits and make it larger in magnitude than cbrt(x) */ - GET_HIGH_WORD(high,t); - INSERT_WORDS(t,high+0x00000001,0); - - /* one step Newton iteration to 53 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); -} |