1 /* @(#)s_cbrt.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <float.h> 14 #include <math.h> 15 16 #include "math_private.h" 17 18 /* cbrt(x) 19 * Return cube root of x 20 */ 21 static const u_int32_t 22 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 23 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 24 25 static const double 26 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 27 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 28 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 29 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 30 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 31 32 double 33 cbrt(double x) 34 { 35 int32_t hx; 36 double r,s,t=0.0,w; 37 u_int32_t sign; 38 u_int32_t high,low; 39 40 GET_HIGH_WORD(hx,x); 41 sign=hx&0x80000000; /* sign= sign(x) */ 42 hx ^=sign; 43 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 44 GET_LOW_WORD(low,x); 45 if((hx|low)==0) 46 return(x); /* cbrt(0) is itself */ 47 48 SET_HIGH_WORD(x,hx); /* x <- |x| */ 49 /* rough cbrt to 5 bits */ 50 if(hx<0x00100000) /* subnormal number */ 51 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ 52 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); 53 } 54 else 55 SET_HIGH_WORD(t,hx/3+B1); 56 57 58 /* new cbrt to 23 bits, may be implemented in single precision */ 59 r=t*t/x; 60 s=C+r*t; 61 t*=G+F/(s+E+D/s); 62 63 /* chopped to 20 bits and make it larger than cbrt(x) */ 64 GET_HIGH_WORD(high,t); 65 INSERT_WORDS(t,high+0x00000001,0); 66 67 68 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 69 s=t*t; /* t*t is exact */ 70 r=x/s; 71 w=t+t; 72 r=(r-t)/(w+r); /* r-s is exact */ 73 t=t+t*r; 74 75 /* retore the sign bit */ 76 GET_HIGH_WORD(high,t); 77 SET_HIGH_WORD(t,high|sign); 78 return(t); 79 } 80 81 #if LDBL_MANT_DIG == DBL_MANT_DIG 82 __strong_alias(cbrtl, cbrt); 83 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 84