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Cider Isn't Darwin Emulation, Really
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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596/* @(#)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. * ==================================================== */
#if defined(LIBM_SCCS) && !defined(lint)static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $";#endif
#include "math.h"#include "math_private.h"#include "fp_private.h"
/* cbrt(x) * Return cube root of x */#ifdef __STDC__static const u_int32_t#elsestatic u_int32_t#endif B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
#ifdef __STDC__static const double#elsestatic double#endifC = 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; u_int32_t sign; u_int32_t high,low;
GET_HIGH_WORD(hx,x); sign=hx&0x80000000; /* sign= sign(x) */ hx ^=sign; if(unlikely(hx>=0x7ff00000)) return(x+x); /* cbrt(NaN,INF) is itself */ GET_LOW_WORD(low,x); if(unlikely((hx|low)==0)) return(x); /* cbrt(0) is itself */
SET_HIGH_WORD(x,hx); /* x <- |x| */ /* rough cbrt to 5 bits */ if(unlikely(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);}