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[/] [openrisc/] [trunk/] [gnu-old/] [newlib-1.17.0/] [newlib/] [libm/] [common/] [s_cbrt.c] - Blame information for rev 158

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1 148 jeremybenn
 
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/* @(#)s_cbrt.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 *
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 */
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/*
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FUNCTION
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        <<cbrt>>, <<cbrtf>>---cube root
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INDEX
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        cbrt
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INDEX
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        cbrtf
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ANSI_SYNOPSIS
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        #include <math.h>
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        double cbrt(double <[x]>);
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        float  cbrtf(float <[x]>);
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TRAD_SYNOPSIS
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        #include <math.h>
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        double cbrt(<[x]>);
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        float  cbrtf(<[x]>);
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DESCRIPTION
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        <<cbrt>> computes the cube root of the argument.
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RETURNS
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        The cube root is returned.
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PORTABILITY
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        <<cbrt>> is in System V release 4.  <<cbrtf>> is an extension.
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*/
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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/* cbrt(x)
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 * Return cube root of x
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 */
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#ifdef __STDC__
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static const __uint32_t
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#else
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static __uint32_t
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#endif
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        B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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        B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
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D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
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F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
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G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
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#ifdef __STDC__
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        double cbrt(double x)
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#else
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        double cbrt(x)
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        double x;
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#endif
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{
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        __int32_t       hx;
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        double r,s,t=0.0,w;
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        __uint32_t sign;
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        __uint32_t high,low;
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        GET_HIGH_WORD(hx,x);
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        sign=hx&0x80000000;             /* sign= sign(x) */
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        hx  ^=sign;
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        if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
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        GET_LOW_WORD(low,x);
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        if((hx|low)==0)
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            return(x);          /* cbrt(0) is itself */
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        SET_HIGH_WORD(x,hx);    /* x <- |x| */
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    /* rough cbrt to 5 bits */
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        if(hx<0x00100000)               /* subnormal number */
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          {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
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           t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
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          }
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        else
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          SET_HIGH_WORD(t,hx/3+B1);
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    /* new cbrt to 23 bits, may be implemented in single precision */
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        r=t*t/x;
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        s=C+r*t;
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        t*=G+F/(s+E+D/s);
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    /* chopped to 20 bits and make it larger than cbrt(x) */
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        GET_HIGH_WORD(high,t);
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        INSERT_WORDS(t,high+0x00000001,0);
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    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
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        s=t*t;          /* t*t is exact */
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        r=x/s;
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        w=t+t;
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        r=(r-t)/(w+r);  /* r-s is exact */
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        t=t+t*r;
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    /* retore the sign bit */
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        GET_HIGH_WORD(high,t);
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        SET_HIGH_WORD(t,high|sign);
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        return(t);
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}
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#endif /* _DOUBLE_IS_32BITS */

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