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Diffstat (limited to 'libm/src/s_cbrt.c')
-rw-r--r-- | libm/src/s_cbrt.c | 92 |
1 files changed, 92 insertions, 0 deletions
diff --git a/libm/src/s_cbrt.c b/libm/src/s_cbrt.c new file mode 100644 index 0000000..b600677 --- /dev/null +++ b/libm/src/s_cbrt.c @@ -0,0 +1,92 @@ +/* @(#)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); +} |