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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [common/] [s_cbrt.c] - Rev 207
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/* @(#)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. * ==================================================== * */ /* FUNCTION <<cbrt>>, <<cbrtf>>---cube root INDEX cbrt INDEX cbrtf ANSI_SYNOPSIS #include <math.h> double cbrt(double <[x]>); float cbrtf(float <[x]>); TRAD_SYNOPSIS #include <math.h> double cbrt(<[x]>); float cbrtf(<[x]>); DESCRIPTION <<cbrt>> computes the cube root of the argument. RETURNS The cube root is returned. PORTABILITY <<cbrt>> is in System V release 4. <<cbrtf>> is an extension. */ #include "fdlibm.h" #ifndef _DOUBLE_IS_32BITS /* cbrt(x) * Return cube root of x */ #ifdef __STDC__ static const __uint32_t #else static __uint32_t #endif B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ #ifdef __STDC__ static const double #else static double #endif 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 */ #ifdef __STDC__ double cbrt(double x) #else double cbrt(x) double x; #endif { __int32_t hx; double r,s,t=0.0,w; __uint32_t sign; __uint32_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 */ SET_HIGH_WORD(x,hx); /* x <- |x| */ /* rough cbrt to 5 bits */ 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,high/3+B2); } else SET_HIGH_WORD(t,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); /* chopped to 20 bits and make it larger 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-s is exact */ t=t+t*r; /* retore the sign bit */ GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high|sign); return(t); } #endif /* _DOUBLE_IS_32BITS */