| lh | 9ed821d | 2023-04-07 01:36:19 -0700 | [diff] [blame] | 1 | /* |
| 2 | * ==================================================== |
| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 4 | * |
| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 6 | * Permission to use, copy, modify, and distribute this |
| 7 | * software is freely granted, provided that this notice |
| 8 | * is preserved. |
| 9 | * ==================================================== |
| 10 | */ |
| 11 | |
| 12 | #include "math.h" |
| 13 | #include "math_private.h" |
| 14 | |
| 15 | /* cbrt(x) |
| 16 | * Return cube root of x |
| 17 | */ |
| 18 | static const u_int32_t |
| 19 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
| 20 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
| 21 | |
| 22 | static const double |
| 23 | C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ |
| 24 | D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ |
| 25 | E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ |
| 26 | F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ |
| 27 | G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ |
| 28 | |
| 29 | double cbrt(double x) |
| 30 | { |
| 31 | int32_t hx; |
| 32 | double r,s,t=0.0,w; |
| 33 | u_int32_t sign; |
| 34 | u_int32_t high,low; |
| 35 | |
| 36 | GET_HIGH_WORD(hx,x); |
| 37 | sign=hx&0x80000000; /* sign= sign(x) */ |
| 38 | hx ^=sign; |
| 39 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
| 40 | GET_LOW_WORD(low,x); |
| 41 | if((hx|low)==0) |
| 42 | return(x); /* cbrt(0) is itself */ |
| 43 | |
| 44 | SET_HIGH_WORD(x,hx); /* x <- |x| */ |
| 45 | /* rough cbrt to 5 bits */ |
| 46 | if(hx<0x00100000) /* subnormal number */ |
| 47 | {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ |
| 48 | t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); |
| 49 | } |
| 50 | else |
| 51 | SET_HIGH_WORD(t,hx/3+B1); |
| 52 | |
| 53 | |
| 54 | /* new cbrt to 23 bits, may be implemented in single precision */ |
| 55 | r=t*t/x; |
| 56 | s=C+r*t; |
| 57 | t*=G+F/(s+E+D/s); |
| 58 | |
| 59 | /* chopped to 20 bits and make it larger than cbrt(x) */ |
| 60 | GET_HIGH_WORD(high,t); |
| 61 | INSERT_WORDS(t,high+0x00000001,0); |
| 62 | |
| 63 | |
| 64 | /* one step newton iteration to 53 bits with error less than 0.667 ulps */ |
| 65 | s=t*t; /* t*t is exact */ |
| 66 | r=x/s; |
| 67 | w=t+t; |
| 68 | r=(r-t)/(w+r); /* r-s is exact */ |
| 69 | t=t+t*r; |
| 70 | |
| 71 | /* retore the sign bit */ |
| 72 | GET_HIGH_WORD(high,t); |
| 73 | SET_HIGH_WORD(t,high|sign); |
| 74 | return(t); |
| 75 | } |
| 76 | libm_hidden_def(cbrt) |