projects / unix-history / blame
| Commit | Line | Data |
|---|---|---|
| 4acf9396 GCI |
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 | #ifndef lint | |
| 14 | static char rcsid[] = "$Id: s_cbrt.c,v 1.4 1994/03/03 17:04:28 jtc Exp $"; | |
| 15 | #endif | |
| 16 | ||
| 17 | #include "math.h" | |
| 18 | #include <machine/endian.h> | |
| 19 | ||
| 20 | #if BYTE_ORDER == LITTLE_ENDIAN | |
| 21 | #define n0 1 | |
| 22 | #else | |
| 23 | #define n0 0 | |
| 24 | #endif | |
| 25 | ||
| 26 | /* cbrt(x) | |
| 27 | * Return cube root of x | |
| 28 | */ | |
| 29 | #ifdef __STDC__ | |
| 30 | static const unsigned | |
| 31 | #else | |
| 32 | static unsigned | |
| 33 | #endif | |
| 34 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ | |
| 35 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ | |
| 36 | ||
| 37 | #ifdef __STDC__ | |
| 38 | static const double | |
| 39 | #else | |
| 40 | static double | |
| 41 | #endif | |
| 42 | C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ | |
| 43 | D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ | |
| 44 | E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ | |
| 45 | F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ | |
| 46 | G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ | |
| 47 | ||
| 48 | #ifdef __STDC__ | |
| 49 | double cbrt(double x) | |
| 50 | #else | |
| 51 | double cbrt(x) | |
| 52 | double x; | |
| 53 | #endif | |
| 54 | { | |
| 55 | int hx; | |
| 56 | double r,s,t=0.0,w; | |
| 57 | unsigned *pt = (unsigned *) &t, sign; | |
| 58 | ||
| 59 | hx = *( n0 + (int*)&x); /* high word of x */ | |
| 60 | sign=hx&0x80000000; /* sign= sign(x) */ | |
| 61 | hx ^=sign; | |
| 62 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ | |
| 63 | if((hx|*(1-n0+(int*)&x))==0) | |
| 64 | return(x); /* cbrt(0) is itself */ | |
| 65 | ||
| 66 | *(n0+(int*)&x) = hx; /* x <- |x| */ | |
| 67 | /* rough cbrt to 5 bits */ | |
| 68 | if(hx<0x00100000) /* subnormal number */ | |
| 69 | {pt[n0]=0x43500000; /* set t= 2**54 */ | |
| 70 | t*=x; pt[n0]=pt[n0]/3+B2; | |
| 71 | } | |
| 72 | else | |
| 73 | pt[n0]=hx/3+B1; | |
| 74 | ||
| 75 | ||
| 76 | /* new cbrt to 23 bits, may be implemented in single precision */ | |
| 77 | r=t*t/x; | |
| 78 | s=C+r*t; | |
| 79 | t*=G+F/(s+E+D/s); | |
| 80 | ||
| 81 | /* chopped to 20 bits and make it larger than cbrt(x) */ | |
| 82 | pt[1-n0]=0; pt[n0]+=0x00000001; | |
| 83 | ||
| 84 | ||
| 85 | /* one step newton iteration to 53 bits with error less than 0.667 ulps */ | |
| 86 | s=t*t; /* t*t is exact */ | |
| 87 | r=x/s; | |
| 88 | w=t+t; | |
| 89 | r=(r-t)/(w+r); /* r-s is exact */ | |
| 90 | t=t+t*r; | |
| 91 | ||
| 92 | /* retore the sign bit */ | |
| 93 | pt[n0] |= sign; | |
| 94 | return(t); | |
| 95 | } |