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Annotation of src/lib/libm/src/s_cbrt.c, Revision 1.2

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