1*1e651e1eSRoland Levillain 2*1e651e1eSRoland Levillain /* @(#)s_cbrt.c 1.3 95/01/18 */ 3*1e651e1eSRoland Levillain /* 4*1e651e1eSRoland Levillain * ==================================================== 5*1e651e1eSRoland Levillain * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6*1e651e1eSRoland Levillain * 7*1e651e1eSRoland Levillain * Developed at SunSoft, a Sun Microsystems, Inc. business. 8*1e651e1eSRoland Levillain * Permission to use, copy, modify, and distribute this 9*1e651e1eSRoland Levillain * software is freely granted, provided that this notice 10*1e651e1eSRoland Levillain * is preserved. 11*1e651e1eSRoland Levillain * ==================================================== 12*1e651e1eSRoland Levillain * 13*1e651e1eSRoland Levillain */ 14*1e651e1eSRoland Levillain 15*1e651e1eSRoland Levillain #include "fdlibm.h" 16*1e651e1eSRoland Levillain 17*1e651e1eSRoland Levillain /* ieee_cbrt(x) 18*1e651e1eSRoland Levillain * Return cube root of x 19*1e651e1eSRoland Levillain */ 20*1e651e1eSRoland Levillain #ifdef __STDC__ 21*1e651e1eSRoland Levillain static const unsigned 22*1e651e1eSRoland Levillain #else 23*1e651e1eSRoland Levillain static unsigned 24*1e651e1eSRoland Levillain #endif 25*1e651e1eSRoland Levillain B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 26*1e651e1eSRoland Levillain B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 27*1e651e1eSRoland Levillain 28*1e651e1eSRoland Levillain #ifdef __STDC__ 29*1e651e1eSRoland Levillain static const double 30*1e651e1eSRoland Levillain #else 31*1e651e1eSRoland Levillain static double 32*1e651e1eSRoland Levillain #endif 33*1e651e1eSRoland Levillain C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 34*1e651e1eSRoland Levillain D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 35*1e651e1eSRoland Levillain E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 36*1e651e1eSRoland Levillain F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 37*1e651e1eSRoland Levillain G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 38*1e651e1eSRoland Levillain 39*1e651e1eSRoland Levillain #ifdef __STDC__ ieee_cbrt(double x)40*1e651e1eSRoland Levillain double ieee_cbrt(double x) 41*1e651e1eSRoland Levillain #else 42*1e651e1eSRoland Levillain double ieee_cbrt(x) 43*1e651e1eSRoland Levillain double x; 44*1e651e1eSRoland Levillain #endif 45*1e651e1eSRoland Levillain { 46*1e651e1eSRoland Levillain int hx; 47*1e651e1eSRoland Levillain double r,s,t=0.0,w; 48*1e651e1eSRoland Levillain unsigned sign; 49*1e651e1eSRoland Levillain 50*1e651e1eSRoland Levillain 51*1e651e1eSRoland Levillain hx = __HI(x); /* high word of x */ 52*1e651e1eSRoland Levillain sign=hx&0x80000000; /* sign= sign(x) */ 53*1e651e1eSRoland Levillain hx ^=sign; 54*1e651e1eSRoland Levillain if(hx>=0x7ff00000) return(x+x); /* ieee_cbrt(NaN,INF) is itself */ 55*1e651e1eSRoland Levillain if((hx|__LO(x))==0) 56*1e651e1eSRoland Levillain return(x); /* ieee_cbrt(0) is itself */ 57*1e651e1eSRoland Levillain 58*1e651e1eSRoland Levillain __HI(x) = hx; /* x <- |x| */ 59*1e651e1eSRoland Levillain /* rough cbrt to 5 bits */ 60*1e651e1eSRoland Levillain if(hx<0x00100000) /* subnormal number */ 61*1e651e1eSRoland Levillain {__HI(t)=0x43500000; /* set t= 2**54 */ 62*1e651e1eSRoland Levillain t*=x; __HI(t)=__HI(t)/3+B2; 63*1e651e1eSRoland Levillain } 64*1e651e1eSRoland Levillain else 65*1e651e1eSRoland Levillain __HI(t)=hx/3+B1; 66*1e651e1eSRoland Levillain 67*1e651e1eSRoland Levillain 68*1e651e1eSRoland Levillain /* new cbrt to 23 bits, may be implemented in single precision */ 69*1e651e1eSRoland Levillain r=t*t/x; 70*1e651e1eSRoland Levillain s=C+r*t; 71*1e651e1eSRoland Levillain t*=G+F/(s+E+D/s); 72*1e651e1eSRoland Levillain 73*1e651e1eSRoland Levillain /* chopped to 20 bits and make it larger than ieee_cbrt(x) */ 74*1e651e1eSRoland Levillain __LO(t)=0; __HI(t)+=0x00000001; 75*1e651e1eSRoland Levillain 76*1e651e1eSRoland Levillain 77*1e651e1eSRoland Levillain /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 78*1e651e1eSRoland Levillain s=t*t; /* t*t is exact */ 79*1e651e1eSRoland Levillain r=x/s; 80*1e651e1eSRoland Levillain w=t+t; 81*1e651e1eSRoland Levillain r=(r-t)/(w+r); /* r-s is exact */ 82*1e651e1eSRoland Levillain t=t+t*r; 83*1e651e1eSRoland Levillain 84*1e651e1eSRoland Levillain /* retore the sign bit */ 85*1e651e1eSRoland Levillain __HI(t) |= sign; 86*1e651e1eSRoland Levillain return(t); 87*1e651e1eSRoland Levillain } 88