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| Rev | Author | Line No. | Line |
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| 3362 | Serge | 1 | |
| 2 | /* |
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| 3 | * ==================================================== |
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 5 | * |
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 7 | * Permission to use, copy, modify, and distribute this |
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| 8 | * software is freely granted, provided that this notice |
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| 9 | * is preserved. |
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| 10 | * ==================================================== |
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| 11 | * |
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| 12 | */ |
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| 13 | |||
| 14 | |||
| 15 | FUNCTION |
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| 16 | < |
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| 17 | |||
| 18 | |||
| 19 | cbrt |
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| 20 | INDEX |
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| 21 | cbrtf |
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| 22 | |||
| 23 | |||
| 24 | #include |
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| 25 | double cbrt(double <[x]>); |
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| 26 | float cbrtf(float <[x]>); |
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| 27 | |||
| 28 | |||
| 29 | #include |
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| 30 | double cbrt(<[x]>); |
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| 31 | float cbrtf(<[x]>); |
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| 32 | |||
| 33 | |||
| 34 | < |
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| 35 | |||
| 36 | |||
| 37 | The cube root is returned. |
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| 38 | |||
| 39 | |||
| 40 | < |
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| 41 | */ |
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| 42 | |||
| 43 | |||
| 44 | |||
| 45 | |||
| 46 | |||
| 47 | |||
| 48 | * Return cube root of x |
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| 49 | */ |
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| 50 | #ifdef __STDC__ |
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| 51 | static const __uint32_t |
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| 52 | #else |
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| 53 | static __uint32_t |
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| 54 | #endif |
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| 55 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
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| 56 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
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| 57 | |||
| 58 | |||
| 59 | static const double |
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| 60 | #else |
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| 61 | static double |
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| 62 | #endif |
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| 63 | C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ |
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| 64 | D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ |
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| 65 | E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ |
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| 66 | F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ |
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| 67 | G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ |
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| 68 | |||
| 69 | |||
| 70 | double cbrt(double x) |
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| 71 | #else |
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| 72 | double cbrt(x) |
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| 73 | double x; |
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| 74 | #endif |
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| 75 | { |
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| 76 | __int32_t hx; |
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| 77 | double r,s,t=0.0,w; |
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| 78 | __uint32_t sign; |
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| 79 | __uint32_t high,low; |
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| 80 | |||
| 81 | |||
| 82 | sign=hx&0x80000000; /* sign= sign(x) */ |
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| 83 | hx ^=sign; |
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| 84 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
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| 85 | GET_LOW_WORD(low,x); |
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| 86 | if((hx|low)==0) |
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| 87 | return(x); /* cbrt(0) is itself */ |
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| 88 | |||
| 89 | |||
| 90 | /* rough cbrt to 5 bits */ |
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| 91 | if(hx<0x00100000) /* subnormal number */ |
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| 92 | {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ |
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| 93 | t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); |
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| 94 | } |
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| 95 | else |
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| 96 | SET_HIGH_WORD(t,hx/3+B1); |
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| 97 | |||
| 98 | |||
| 99 | |||
| 100 | r=t*t/x; |
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| 101 | s=C+r*t; |
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| 102 | t*=G+F/(s+E+D/s); |
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| 103 | |||
| 104 | |||
| 105 | GET_HIGH_WORD(high,t); |
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| 106 | INSERT_WORDS(t,high+0x00000001,0); |
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| 107 | |||
| 108 | |||
| 109 | |||
| 110 | s=t*t; /* t*t is exact */ |
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| 111 | r=x/s; |
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| 112 | w=t+t; |
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| 113 | r=(r-t)/(w+r); /* r-s is exact */ |
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| 114 | t=t+t*r; |
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| 115 | |||
| 116 | |||
| 117 | GET_HIGH_WORD(high,t); |
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| 118 | SET_HIGH_WORD(t,high|sign); |
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| 119 | return(t); |
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| 120 | } |
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| 121 | |||
| 122 | |||
| 123 |