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| 2 | /* @(#)s_cbrt.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | * |
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| 13 | */ |
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| 14 | |
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| 15 | #include <libm/fdlibm.h> |
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| 16 | |
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| 17 | /* cbrt(x) |
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| 18 | * Return cube root of x |
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| 19 | */ |
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| 20 | #ifdef __STDC__ |
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| 21 | static const unsigned |
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| 22 | #else |
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| 23 | static unsigned |
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| 24 | #endif |
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| 25 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
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| 26 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
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| 27 | |
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| 28 | #ifdef __STDC__ |
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| 29 | static const double |
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| 30 | #else |
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| 31 | static double |
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| 32 | #endif |
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| 33 | C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ |
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| 34 | D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ |
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| 35 | E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ |
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| 36 | F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ |
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| 37 | G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ |
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| 38 | |
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| 39 | #ifdef __STDC__ |
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| 40 | double cbrt(double x) |
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| 41 | #else |
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| 42 | double cbrt(x) |
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| 43 | double x; |
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| 44 | #endif |
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| 45 | { |
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| 46 | double one = 1.0; |
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| 47 | int n0,hx; |
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| 48 | double r,s,t=0.0,w; |
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| 49 | unsigned *pt = (unsigned *) &t, sign; |
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| 50 | |
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| 51 | |
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| 52 | n0 = ((*(int*)&one)>>29)^1; /* index of high word */ |
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| 53 | hx = *( n0 + (int*)&x); /* high word of x */ |
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| 54 | sign=hx&0x80000000; /* sign= sign(x) */ |
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| 55 | hx ^=sign; |
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| 56 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
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| 57 | if((hx|*(1-n0+(int*)&x))==0) |
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| 58 | return(x); /* cbrt(0) is itself */ |
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| 59 | |
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| 60 | *(n0+(int*)&x) = hx; /* x <- |x| */ |
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| 61 | /* rough cbrt to 5 bits */ |
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| 62 | if(hx<0x00100000) /* subnormal number */ |
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| 63 | {pt[n0]=0x43500000; /* set t= 2**54 */ |
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| 64 | t*=x; pt[n0]=pt[n0]/3+B2; |
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| 65 | } |
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| 66 | else |
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| 67 | pt[n0]=hx/3+B1; |
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| 68 | |
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| 69 | |
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| 70 | /* new cbrt to 23 bits, may be implemented in single precision */ |
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| 71 | r=t*t/x; |
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| 72 | s=C+r*t; |
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| 73 | t*=G+F/(s+E+D/s); |
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| 74 | |
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| 75 | /* chopped to 20 bits and make it larger than cbrt(x) */ |
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| 76 | pt[1-n0]=0; pt[n0]+=0x00000001; |
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| 77 | |
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| 78 | |
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| 79 | /* one step newton iteration to 53 bits with error less than 0.667 ulps */ |
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| 80 | s=t*t; /* t*t is exact */ |
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| 81 | r=x/s; |
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| 82 | w=t+t; |
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| 83 | r=(r-t)/(w+r); /* r-s is exact */ |
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| 84 | t=t+t*r; |
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| 85 | |
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| 86 | /* retore the sign bit */ |
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| 87 | pt[n0] |= sign; |
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| 88 | return(t); |
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| 89 | } |
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