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377 lines
10 KiB
377 lines
10 KiB
//-----------------------------------------------------------------------------
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// Package Title ratpak
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// File exp.c
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// Author Timothy David Corrie Jr. ([email protected])
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// Copyright (C) 1995-96 Microsoft
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// Date 01-16-95
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//
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//
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// Description
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//
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// Contains exp, and log functions for rationals
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//
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//
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//-----------------------------------------------------------------------------
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#include <stdio.h>
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#include <stdlib.h>
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#if defined( DOS )
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#include <dosstub.h>
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#else
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#include <windows.h>
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#endif
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#include <ratpak.h>
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: exprat
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//
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// ARGUMENTS: x PRAT representation of number to exponentiate
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//
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// RETURN: exp of x in PRAT form.
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//
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// EXPLANATION: This uses Taylor series
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//
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// n
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// ___
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// \ ] X
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// \ thisterm ; where thisterm = thisterm * ---------
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// / j j+1 j j+1
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// /__]
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// j=0
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//
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// thisterm = X ; and stop when thisterm < precision used.
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// 0 n
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//
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//-----------------------------------------------------------------------------
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void _exprat( PRAT *px )
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{
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CREATETAYLOR();
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addnum(&(pret->pp),num_one, BASEX);
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addnum(&(pret->pq),num_one, BASEX);
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DUPRAT(thisterm,pret);
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n2=longtonum(0L, BASEX);
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do {
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NEXTTERM(*px, INC(n2) DIVNUM(n2));
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} while ( !SMALL_ENOUGH_RAT( thisterm ) && !fhalt );
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DESTROYTAYLOR();
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}
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void exprat( PRAT *px )
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{
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PRAT pwr=NULL;
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PRAT pint=NULL;
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long intpwr;
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if ( rat_gt( *px, rat_max_exp ) || rat_lt( *px, rat_min_exp ) )
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{
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// Don't attempt exp of anything large.
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throw( CALC_E_DOMAIN );
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}
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DUPRAT(pwr,rat_exp);
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DUPRAT(pint,*px);
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intrat(&pint);
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intpwr = rattolong(pint);
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ratpowlong( &pwr, intpwr );
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subrat(px,pint);
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// It just so happens to be an integral power of e.
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if ( rat_gt( *px, rat_negsmallest ) && rat_lt( *px, rat_smallest ) )
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{
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DUPRAT(*px,pwr);
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}
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else
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{
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_exprat(px);
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mulrat(px,pwr);
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}
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destroyrat( pwr );
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destroyrat( pint );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: lograt, _lograt
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//
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// ARGUMENTS: x PRAT representation of number to logarithim
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//
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// RETURN: log of x in PRAT form.
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//
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// EXPLANATION: This uses Taylor series
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//
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// n
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// ___
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// \ ] j*(1-X)
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// \ thisterm ; where thisterm = thisterm * ---------
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// / j j+1 j j+1
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// /__]
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// j=0
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//
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// thisterm = X ; and stop when thisterm < precision used.
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// 0 n
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//
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// Number is scaled between one and e_to_one_half prior to taking the
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// log. This is to keep execution time from exploding.
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//
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//
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//-----------------------------------------------------------------------------
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void _lograt( PRAT *px )
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{
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CREATETAYLOR();
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createrat(thisterm);
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// sub one from x
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(*px)->pq->sign *= -1;
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addnum(&((*px)->pp),(*px)->pq, BASEX);
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(*px)->pq->sign *= -1;
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DUPRAT(pret,*px);
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DUPRAT(thisterm,*px);
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n2=longtonum(1L, BASEX);
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(*px)->pp->sign *= -1;
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do {
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NEXTTERM(*px, MULNUM(n2) INC(n2) DIVNUM(n2));
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TRIMTOP(*px);
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} while ( !SMALL_ENOUGH_RAT( thisterm ) && !fhalt );
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DESTROYTAYLOR();
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}
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void lograt( PRAT *px )
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{
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BOOL fneglog;
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PRAT pwr=NULL; // pwr is the large scaling factor.
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PRAT offset=NULL; // offset is the incremental scaling factor.
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// Check for someone taking the log of zero or a negative number.
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if ( rat_le( *px, rat_zero ) )
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{
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throw( CALC_E_DOMAIN );
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}
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// Get number > 1, for scaling
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fneglog = rat_lt( *px, rat_one );
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if ( fneglog )
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{
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// WARNING: This is equivalent to doing *px = 1 / *px
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PNUMBER pnumtemp=NULL;
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pnumtemp = (*px)->pp;
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(*px)->pp = (*px)->pq;
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(*px)->pq = pnumtemp;
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}
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// Scale the number within BASEX factor of 1, for the large scale.
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// log(x*2^(BASEXPWR*k)) = BASEXPWR*k*log(2)+log(x)
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if ( LOGRAT2(*px) > 1 )
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{
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// Take advantage of px's base BASEX to scale quickly down to
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// a reasonable range.
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long intpwr;
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intpwr=LOGRAT2(*px)-1;
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(*px)->pq->exp += intpwr;
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pwr=longtorat(intpwr*BASEXPWR);
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mulrat(&pwr,ln_two);
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// ln(x+e)-ln(x) looks close to e when x is close to one using some
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// expansions. This means we can trim past precision digits+1.
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TRIMTOP(*px);
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}
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else
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{
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DUPRAT(pwr,rat_zero);
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}
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DUPRAT(offset,rat_zero);
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// Scale the number between 1 and e_to_one_half, for the small scale.
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while ( rat_gt( *px, e_to_one_half ) && !fhalt )
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{
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divrat( px, e_to_one_half );
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addrat( &offset, rat_one );
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}
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_lograt(px);
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// Add the large and small scaling factors, take into account
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// small scaling was done in e_to_one_half chunks.
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divrat(&offset,rat_two);
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addrat(&pwr,offset);
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// And add the resulting scaling factor to the answer.
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addrat(px,pwr);
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trimit(px);
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// If number started out < 1 rescale answer to negative.
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if ( fneglog )
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{
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(*px)->pp->sign *= -1;
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}
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destroyrat(pwr);
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}
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void log10rat( PRAT *px )
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{
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lograt(px);
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divrat(px,ln_ten);
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}
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//---------------------------------------------------------------------------
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//
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// FUNCTION: powrat
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//
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// ARGUMENTS: PRAT *px, and PRAT y
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//
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// RETURN: none, sets *px to *px to the y.
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//
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// EXPLANATION: This uses x^y=e(y*ln(x)), or a more exact calculation where
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// y is an integer.
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// Assumes, all checking has been done on validity of numbers.
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//
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//
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//---------------------------------------------------------------------------
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void powrat( PRAT *px, PRAT y )
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{
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PRAT podd=NULL;
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PRAT plnx=NULL;
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long sign=1;
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sign=( (*px)->pp->sign * (*px)->pq->sign );
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// Take the absolute value
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(*px)->pp->sign = 1;
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(*px)->pq->sign = 1;
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if ( zerrat( *px ) )
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{
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// *px is zero.
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if ( rat_lt( y, rat_zero ) )
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{
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throw( CALC_E_DOMAIN );
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}
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else if ( zerrat( y ) )
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{
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// *px and y are both zero, special case a 1 return.
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DUPRAT(*px,rat_one);
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// Ensure sign is positive.
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sign = 1;
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}
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}
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else
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{
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PRAT pxint=NULL;
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DUPRAT(pxint,*px);
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subrat(&pxint,rat_one);
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if ( rat_gt( pxint, rat_negsmallest ) &&
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rat_lt( pxint, rat_smallest ) && ( sign == 1 ) )
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{
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// *px is one, special case a 1 return.
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DUPRAT(*px,rat_one);
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// Ensure sign is positive.
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sign = 1;
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}
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else
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{
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// Only do the exp if the number isn't zero or one
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DUPRAT(podd,y);
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fracrat(&podd);
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if ( rat_gt( podd, rat_negsmallest ) && rat_lt( podd, rat_smallest ) )
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{
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// If power is an integer let ratpowlong deal with it.
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PRAT iy = NULL;
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long inty;
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DUPRAT(iy,y);
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subrat(&iy,podd);
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inty = rattolong(iy);
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DUPRAT(plnx,*px);
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lograt(&plnx);
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mulrat(&plnx,iy);
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if ( rat_gt( plnx, rat_max_exp ) || rat_lt( plnx, rat_min_exp ) )
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{
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// Don't attempt exp of anything large or small.A
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destroyrat(plnx);
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destroyrat(iy);
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throw( CALC_E_DOMAIN );
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}
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destroyrat(plnx);
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ratpowlong(px,inty);
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if ( ( inty & 1 ) == 0 )
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{
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sign=1;
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}
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destroyrat(iy);
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}
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else
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{
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// power is a fraction
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if ( sign == -1 )
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{
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// And assign the sign after computations, if appropriate.
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if ( rat_gt( y, rat_neg_one ) && rat_lt( y, rat_zero ) )
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{
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// Check to see if reciprocal is odd.
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DUPRAT(podd,rat_one);
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divrat(&podd,y);
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// Only interested in the absval for determining oddness.
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podd->pp->sign = 1;
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podd->pq->sign = 1;
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divrat(&podd,rat_two);
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fracrat(&podd);
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addrat(&podd,podd);
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subrat(&podd,rat_one);
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if ( rat_lt( podd, rat_zero ) )
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{
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// Negative nonodd root of negative number.
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destroyrat(podd);
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throw( CALC_E_DOMAIN );
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}
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}
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else
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{
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// Negative nonodd power of negative number.
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destroyrat(podd);
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throw( CALC_E_DOMAIN );
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}
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}
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else
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{
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// If the exponent is not odd disregard the sign.
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sign = 1;
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}
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lograt( px );
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mulrat( px, y );
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exprat( px );
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}
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destroyrat(podd);
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}
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destroyrat(pxint);
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}
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(*px)->pp->sign *= sign;
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}
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