209 lines
4.5 KiB
C
209 lines
4.5 KiB
C
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//-----------------------------------------------------------------------------
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// Package Title ratpak
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// File transh.c
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// Author Timothy David Corrie Jr. (timc@microsoft.com)
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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 hyperbolic sin, cos, and tan 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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#include <string.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: sinhrat, _sinhrat
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//
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// ARGUMENTS: x PRAT representation of number to take the sine hyperbolic
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// of
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// RETURN: sinh 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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// ___ 2j+1
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// \ ] X
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// \ ---------
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// / (2j+1)!
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// /__]
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// j=0
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// or,
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// n
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// ___ 2
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// \ ] X
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// \ thisterm ; where thisterm = thisterm * ---------
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// / j j+1 j (2j)*(2j+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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// if x is bigger than 1.0 (e^x-e^-x)/2 is used.
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//
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//-----------------------------------------------------------------------------
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void _sinhrat( PRAT *px )
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{
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CREATETAYLOR();
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DUPRAT(pret,*px);
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DUPRAT(thisterm,pret);
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DUPNUM(n2,num_one);
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do {
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NEXTTERM(xx,INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2));
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} while ( !SMALL_ENOUGH_RAT( thisterm ) );
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DESTROYTAYLOR();
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}
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void sinhrat( PRAT *px )
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{
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PRAT pret=NULL;
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PRAT tmpx=NULL;
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if ( rat_ge( *px, rat_one ) )
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{
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DUPRAT(tmpx,*px);
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exprat(px);
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tmpx->pp->sign *= -1;
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exprat(&tmpx);
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subrat( px, tmpx );
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divrat( px, rat_two );
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destroyrat( tmpx );
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}
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else
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{
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_sinhrat( px );
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}
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: coshrat
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//
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// ARGUMENTS: x PRAT representation of number to take the cosine
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// hyperbolic of
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//
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// RETURN: cosh 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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// ___ 2j
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// \ ] X
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// \ ---------
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// / (2j)!
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// /__]
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// j=0
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// or,
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// n
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// ___ 2
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// \ ] X
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// \ thisterm ; where thisterm = thisterm * ---------
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// / j j+1 j (2j)*(2j+1)
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// /__]
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// j=0
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//
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// thisterm = 1 ; and stop when thisterm < precision used.
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// 0 n
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//
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// if x is bigger than 1.0 (e^x+e^-x)/2 is used.
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//
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//-----------------------------------------------------------------------------
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void _coshrat( PRAT *px )
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{
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CREATETAYLOR();
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pret->pp=longtonum( 1L, nRadix );
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pret->pq=longtonum( 1L, nRadix );
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DUPRAT(thisterm,pret)
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n2=longtonum(0L, nRadix);
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do {
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NEXTTERM(xx,INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2));
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} while ( !SMALL_ENOUGH_RAT( thisterm ) );
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DESTROYTAYLOR();
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}
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void coshrat( PRAT *px )
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{
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PRAT tmpx=NULL;
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(*px)->pp->sign = 1;
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(*px)->pq->sign = 1;
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if ( rat_ge( *px, rat_one ) )
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{
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DUPRAT(tmpx,*px);
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exprat(px);
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tmpx->pp->sign *= -1;
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exprat(&tmpx);
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addrat( px, tmpx );
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divrat( px, rat_two );
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destroyrat( tmpx );
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}
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else
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{
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_coshrat( px );
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}
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// Since *px might be epsilon below 1 due to TRIMIT
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// we need this trick here.
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if ( rat_lt(*px,rat_one) )
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{
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DUPRAT(*px,rat_one);
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}
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: tanhrat
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//
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// ARGUMENTS: x PRAT representation of number to take the tangent
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// hyperbolic of
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//
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// RETURN: tanh of x in PRAT form.
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//
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// EXPLANATION: This uses sinhrat and coshrat
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//
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//-----------------------------------------------------------------------------
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void tanhrat( PRAT *px )
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{
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PRAT ptmp=NULL;
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DUPRAT(ptmp,*px);
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sinhrat(px);
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coshrat(&ptmp);
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mulnumx(&((*px)->pp),ptmp->pq);
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mulnumx(&((*px)->pq),ptmp->pp);
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destroyrat(ptmp);
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}
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