| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #ifndef __vax__ |
| static const unsigned long |
| B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
| B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
| |
| static const double |
| C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ |
| D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ |
| E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ |
| F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ |
| G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ |
| |
| double |
| cbrtl (double x) |
| { |
| long hx; |
| double r,s,w; |
| double lt; |
| unsigned sign; |
| typedef unsigned unsigned32 __attribute__((mode(SI))); |
| union { |
| double t; |
| unsigned32 pt[2]; |
| } ut, ux; |
| int n0; |
| |
| ut.t = 1.0; |
| n0 = (ut.pt[0] == 0); |
| |
| ut.t = 0.0; |
| ux.t = x; |
| |
| hx = ux.pt[n0]; /* high word of x */ |
| sign=hx&0x80000000; /* sign= sign(x) */ |
| hx ^=sign; |
| if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
| if((hx| ux.pt[1-n0])==0) |
| return(ux.t); /* cbrt(0) is itself */ |
| |
| ux.pt[n0] = hx; |
| /* rough cbrt to 5 bits */ |
| if(hx<0x00100000) /* subnormal number */ |
| {ut.pt[n0]=0x43500000; /* set t= 2**54 */ |
| ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2; |
| } |
| else |
| ut.pt[n0]=hx/3+B1; |
| |
| /* new cbrt to 23 bits, may be implemented in single precision */ |
| r=ut.t*ut.t/ux.t; |
| s=C+r*ut.t; |
| ut.t*=G+F/(s+E+D/s); |
| |
| /* chopped to 20 bits and make it larger than cbrt(x) */ |
| ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001; |
| |
| /* one step newton iteration to 53 bits with error less than 0.667 ulps */ |
| s=ut.t*ut.t; /* t*t is exact */ |
| r=ux.t/s; |
| w=ut.t+ut.t; |
| r=(r-ut.t)/(w+r); /* r-s is exact */ |
| ut.t=ut.t+ut.t*r; |
| |
| /* restore the sign bit */ |
| ut.pt[n0] |= sign; |
| |
| lt = ut.t; |
| lt -= (lt - (x/(lt*lt))) * 0.333333333333333333333; |
| return lt; |
| } |
| |
| main () |
| { |
| if ((int) (cbrtl (27.0) + 0.5) != 3) |
| abort (); |
| |
| exit (0); |
| } |
| #else |
| main () { exit (0); } |
| #endif |