75 lines
1.9 KiB
C
75 lines
1.9 KiB
C
/* s_cbrtf.c -- float version of s_cbrt.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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* Debugged and optimized by Bruce D. Evans.
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*/
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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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#include "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.18 2008/02/22 02:30:35 das Exp $");
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#include <openlibm_math.h>
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#include "math_private.h"
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/* cbrtf(x)
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* Return cube root of x
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*/
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static const unsigned
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B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
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B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
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OLM_DLLEXPORT float
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cbrtf(float x)
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{
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double r,T;
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float t;
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int32_t hx;
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u_int32_t sign;
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u_int32_t high;
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GET_FLOAT_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>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
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/* rough cbrt to 5 bits */
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if(hx<0x00800000) { /* zero or subnormal? */
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if(hx==0)
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return(x); /* cbrt(+-0) is itself */
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SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
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t*=x;
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GET_FLOAT_WORD(high,t);
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SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
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} else
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SET_FLOAT_WORD(t,sign|(hx/3+B1));
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/*
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* First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
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* double precision so that its terms can be arranged for efficiency
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* without causing overflow or underflow.
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*/
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T=t;
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r=T*T*T;
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T=T*((double)x+x+r)/(x+r+r);
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/*
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* Second step Newton iteration to 47 bits. In double precision for
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* efficiency and accuracy.
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*/
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r=T*T*T;
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T=T*((double)x+x+r)/(x+r+r);
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/* rounding to 24 bits is perfect in round-to-nearest mode */
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return(T);
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}
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