278 lines
8.9 KiB
C
278 lines
8.9 KiB
C
/* pow.c - math routines */
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/* Copyright 1992-1993 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01e,05feb93,jdi doc changes based on kdl review.
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01d,02dec92,jdi doc tweaks.
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01c,28oct92,jdi documentation cleanup.
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01b,20sep92,smb documentation additions
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01a,08jul92,smb documentation.
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*/
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/*
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DESCRIPTION
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#include "private/mathP.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#include <errno.h>
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extern double infnan();
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
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/* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */
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/* invln2 = 1.4426950408889634148E0 , Hex 2^ 1 * .B8AA3B295C17F1 */
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/* sqrt2 = 1.4142135623730950622E0 ; Hex 2^ 1 * .B504F333F9DE65 */
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static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
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static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
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static long invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
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static long sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#define invln2 (*(double*)invln2x)
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#define sqrt2 (*(double*)sqrt2x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
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ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */
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invln2 = 1.4426950408889633870E0 , /*Hex 2^ 0 * 1.71547652B82FE */
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sqrt2 = 1.4142135623730951455E0 ; /*Hex 2^ 0 * 1.6A09E667F3BCD */
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#endif /* defined(vax)||defined(tahoe) */
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static double zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;
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/*******************************************************************************
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*
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* pow - compute the value of a number raised to a specified power (ANSI)
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*
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* This routine returns <x> to the power of <y> in
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* double precision (IEEE double, 53 bits).
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*
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* A domain error occurs if <x> is negative and <y> is not an integral value.
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* A domain error occurs if the result cannot be represented when <x> is zero
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* and <y> is less than or equal to zero. A range error may occur.
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*
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* INTERNAL:
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* Method:
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* (1) Compute and return log(x) in three pieces:
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*
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* log(x) = n*ln2 + hi + lo
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*
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* where <n> is an integer.
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*
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* (2) Perform y*log(x) by simulating multi-precision arithmetic and
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* return the answer in three pieces:
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*
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* y*log(x) = m*ln2 + hi + lo
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*
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* where <m> is an integer.
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*
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* (3) Return:
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*
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* x**y = exp(y*log(x)) = 2^m * ( exp(hi+lo) )
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*
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* INCLUDE FILES: math.h
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*
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* RETURNS: The double-precision value of <x> to the power of <y>.
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*
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* Special cases:
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* .TS
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* tab(|);
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* l0 c0 l.
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* (anything) ** 0 | is | 1
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* (anything) ** 1 | is | itself
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* (anything) ** NaN | is | NaN
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* NaN ** (anything except 0) | is | NaN
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* +-(anything > 1) ** +INF | is | +INF
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* +-(anything > 1) ** -INF | is | +0
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* +-(anything < 1) ** +INF | is | +0
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* +-(anything < 1) ** -INF | is | +INF
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* +-1 ** +-INF | is | NaN, signal INVALID
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* +0 ** +(anything non-0, NaN) | is | +0
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* -0 ** +(anything non-0, NaN, odd int) | is | +0
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* +0 ** -(anything non-0, NaN) | is | +INF, signal DIV-BY-ZERO
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* -0 ** -(anything non-0, NaN, odd int) | is | +INF with signal
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* -0 ** (odd integer) | = | -(+0 ** (odd integer))
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* +INF ** +(anything except 0, NaN) | is | +INF
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* +INF ** -(anything except 0, NaN) | is | +0
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* -INF ** (odd integer) | = | -(+INF ** (odd integer))
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* -INF ** (even integer) | = | (+INF ** (even integer))
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* -INF ** -(any non-integer, NaN) | is | NaN with signal
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* -(x=anything) ** (k=integer) | is | (-1)**k * (x ** k)
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* -(anything except 0) ** (non-integer) | is | NaN with signal
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* .TE
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*
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* SEE ALSO: mathALib
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*
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* INTERNAL:
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* Coded in C by K.C. Ng, 1/8/85;
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* Revised by K.C. Ng on 7/10/85.
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*/
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double pow
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(
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double x, /* operand */
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double y /* exponent */
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)
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{
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double drem(),pow_p(),copysign(),t;
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int finite();
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if (y==zero) return(one);
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else if(y==one
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#if !defined(vax)&&!defined(tahoe)
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||x!=x
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#endif /* !defined(vax)&&!defined(tahoe) */
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) return( x ); /* if x is NaN or y=1 */
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#if !defined(vax)&&!defined(tahoe)
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else if(y!=y) return( y ); /* if y is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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else if(!finite(y)) /* if y is INF */
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if((t=copysign(x,one))==one) return(zero/zero);
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else if(t>one) return((y>zero)?y:zero);
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else return((y<zero)?-y:zero);
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else if(y==two) return(x*x);
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else if(y==negone) return(one/x);
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/* sign(x) = 1 */
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else if(copysign(one,x)==one) return(pow_p(x,y));
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/* sign(x)= -1 */
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/* if y is an even integer */
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else if ( (t=drem(y,two)) == zero) return( pow_p(-x,y) );
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/* if y is an odd integer */
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else if (copysign(t,one) == one) return( -pow_p(-x,y) );
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/* Henceforth y is not an integer */
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else if(x==zero) /* x is -0 */
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return((y>zero)?-x:one/(-x));
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else { /* return NaN */
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#if defined(vax)||defined(tahoe)
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return (infnan(EDOM)); /* NaN */
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#else /* defined(vax)||defined(tahoe) */
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return(zero/zero);
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#endif /* defined(vax)||defined(tahoe) */
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}
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}
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/****************************************************************************
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*
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* pow_p -
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*
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* pow_p(x,y) return x**y for x with sign=1 and finite y *
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*
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* RETURN:
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* NOMANUAL
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*/
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double pow_p(x,y)
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double x,y;
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{
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double logb(),scalb(),copysign(),log__L(),exp__E();
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double c,s,t,z,tx,ty;
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#ifdef tahoe
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double tahoe_tmp;
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#endif /* tahoe */
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float sx,sy;
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long k=0;
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int n,m;
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if(x==zero||!finite(x)) { /* if x is +INF or +0 */
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#if defined(vax)||defined(tahoe)
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return((y>zero)?x:infnan(ERANGE)); /* if y<zero, return +INF */
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#else /* defined(vax)||defined(tahoe) */
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return((y>zero)?x:one/x);
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#endif /* defined(vax)||defined(tahoe) */
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}
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if(x==1.0) return(x); /* if x=1.0, return 1 since y is finite */
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/* reduce x to z in [sqrt(1/2)-1, sqrt(2)-1] */
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z=scalb(x,-(n=logb(x)));
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#if !defined(vax)&&!defined(tahoe) /* IEEE double; subnormal number */
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if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);}
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#endif /* !defined(vax)&&!defined(tahoe) */
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if(z >= sqrt2 ) {n += 1; z *= half;} z -= one ;
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/* log(x) = nlog2+log(1+z) ~ nlog2 + t + tx */
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s=z/(two+z); c=z*z*half; tx=s*(c+log__L(s*s));
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t= z-(c-tx); tx += (z-t)-c;
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/* if y*log(x) is neither too big nor too small */
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if((s=logb(y)+logb(n+t)) < 12.0)
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if(s>-60.0) {
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/* compute y*log(x) ~ mlog2 + t + c */
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s=y*(n+invln2*t);
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m=s+copysign(half,s); /* m := nint(y*log(x)) */
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k=y;
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if((double)k==y) { /* if y is an integer */
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k = m-k*n;
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sx=t; tx+=(t-sx); }
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else { /* if y is not an integer */
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k =m;
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tx+=n*ln2lo;
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sx=(c=n*ln2hi)+t; tx+=(c-sx)+t; }
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/* end of checking whether k==y */
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sy=y; ty=y-sy; /* y ~ sy + ty */
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#ifdef tahoe
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s = (tahoe_tmp = sx)*sy-k*ln2hi;
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#else /* tahoe */
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s=(double)sx*sy-k*ln2hi; /* (sy+ty)*(sx+tx)-kln2 */
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#endif /* tahoe */
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z=(tx*ty-k*ln2lo);
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tx=tx*sy; ty=sx*ty;
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t=ty+z; t+=tx; t+=s;
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c= -((((t-s)-tx)-ty)-z);
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/* return exp(y*log(x)) */
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t += exp__E(t,c); return(scalb(one+t,m));
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}
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/* end of if log(y*log(x)) > -60.0 */
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else
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/* exp(+- tiny) = 1 with inexact flag */
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{ln2hi+ln2lo; return(one);}
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else if(copysign(one,y)*(n+invln2*t) <zero)
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/* exp(-(big#)) underflows to zero */
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return(scalb(one,-5000));
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else
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/* exp(+(big#)) overflows to INF */
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return(scalb(one, 5000));
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}
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