166 lines
3.7 KiB
C
166 lines
3.7 KiB
C
|
//-----------------------------------------------------------------------------
|
||
|
|
// Package Title ratpak
|
||
|
|
// File itransh.c
|
||
|
|
// Author Timothy David Corrie Jr. (timc@microsoft.com)
|
||
|
|
// Copyright (C) 1995-97 Microsoft
|
||
|
|
// Date 01-16-95
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Description
|
||
|
|
//
|
||
|
|
// Contains inverse hyperbolic sin, cos, and tan functions.
|
||
|
|
//
|
||
|
|
// Special Information
|
||
|
|
//
|
||
|
|
//
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
|
||
|
|
#include <stdio.h>
|
||
|
|
#include <stdlib.h>
|
||
|
|
#include <string.h>
|
||
|
|
#if defined( DOS )
|
||
|
|
#include <dosstub.h>
|
||
|
|
#else
|
||
|
|
#include <windows.h>
|
||
|
|
#endif
|
||
|
|
#include <ratpak.h>
|
||
|
|
|
||
|
|
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
//
|
||
|
|
// FUNCTION: asinhrat
|
||
|
|
//
|
||
|
|
// ARGUMENTS: x PRAT representation of number to take the inverse
|
||
|
|
// hyperbolic sine of
|
||
|
|
// RETURN: asinh of x in PRAT form.
|
||
|
|
//
|
||
|
|
// EXPLANATION: This uses Taylor series
|
||
|
|
//
|
||
|
|
// n
|
||
|
|
// ___ 2 2
|
||
|
|
// \ ] -(2j+1) X
|
||
|
|
// \ thisterm ; where thisterm = thisterm * ---------
|
||
|
|
// / j j+1 j (2j+2)*(2j+3)
|
||
|
|
// /__]
|
||
|
|
// j=0
|
||
|
|
//
|
||
|
|
// thisterm = X ; and stop when thisterm < precision used.
|
||
|
|
// 0 n
|
||
|
|
//
|
||
|
|
// For abs(x) < .85, and
|
||
|
|
//
|
||
|
|
// asinh(x) = log(x+sqrt(x^2+1))
|
||
|
|
//
|
||
|
|
// For abs(x) >= .85
|
||
|
|
//
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
|
||
|
|
void asinhrat( PRAT *px )
|
||
|
|
|
||
|
|
{
|
||
|
|
PRAT neg_pt_eight_five = NULL;
|
||
|
|
|
||
|
|
DUPRAT(neg_pt_eight_five,pt_eight_five);
|
||
|
|
neg_pt_eight_five->pp->sign *= -1;
|
||
|
|
if ( rat_gt( *px, pt_eight_five) || rat_lt( *px, neg_pt_eight_five) )
|
||
|
|
{
|
||
|
|
PRAT ptmp = NULL;
|
||
|
|
DUPRAT(ptmp,(*px));
|
||
|
|
mulrat(&ptmp,*px);
|
||
|
|
addrat(&ptmp,rat_one);
|
||
|
|
rootrat(&ptmp,rat_two);
|
||
|
|
addrat(px,ptmp);
|
||
|
|
lograt(px);
|
||
|
|
destroyrat(ptmp);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
CREATETAYLOR();
|
||
|
|
xx->pp->sign *= -1;
|
||
|
|
|
||
|
|
DUPRAT(pret,(*px));
|
||
|
|
DUPRAT(thisterm,(*px));
|
||
|
|
|
||
|
|
DUPNUM(n2,num_one);
|
||
|
|
|
||
|
|
do
|
||
|
|
{
|
||
|
|
NEXTTERM(xx,MULNUM(n2) MULNUM(n2)
|
||
|
|
INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2));
|
||
|
|
}
|
||
|
|
while ( !SMALL_ENOUGH_RAT( thisterm ) );
|
||
|
|
|
||
|
|
DESTROYTAYLOR();
|
||
|
|
}
|
||
|
|
destroyrat(neg_pt_eight_five);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
//
|
||
|
|
// FUNCTION: acoshrat
|
||
|
|
//
|
||
|
|
// ARGUMENTS: x PRAT representation of number to take the inverse
|
||
|
|
// hyperbolic cose of
|
||
|
|
// RETURN: acosh of x in PRAT form.
|
||
|
|
//
|
||
|
|
// EXPLANATION: This uses
|
||
|
|
//
|
||
|
|
// acosh(x)=ln(x+sqrt(x^2-1))
|
||
|
|
//
|
||
|
|
// For x >= 1
|
||
|
|
//
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
|
||
|
|
void acoshrat( PRAT *px )
|
||
|
|
|
||
|
|
{
|
||
|
|
if ( rat_lt( *px, rat_one ) )
|
||
|
|
{
|
||
|
|
throw CALC_E_DOMAIN;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
PRAT ptmp = NULL;
|
||
|
|
DUPRAT(ptmp,(*px));
|
||
|
|
mulrat(&ptmp,*px);
|
||
|
|
subrat(&ptmp,rat_one);
|
||
|
|
rootrat(&ptmp,rat_two);
|
||
|
|
addrat(px,ptmp);
|
||
|
|
lograt(px);
|
||
|
|
destroyrat(ptmp);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
//
|
||
|
|
// FUNCTION: atanhrat
|
||
|
|
//
|
||
|
|
// ARGUMENTS: x PRAT representation of number to take the inverse
|
||
|
|
// hyperbolic tangent of
|
||
|
|
//
|
||
|
|
// RETURN: atanh of x in PRAT form.
|
||
|
|
//
|
||
|
|
// EXPLANATION: This uses
|
||
|
|
//
|
||
|
|
// 1 x+1
|
||
|
|
// atanh(x) = -*ln(----)
|
||
|
|
// 2 x-1
|
||
|
|
//
|
||
|
|
//-----------------------------------------------------------------------------
|
||
|
|
|
||
|
|
void atanhrat( PRAT *px )
|
||
|
|
|
||
|
|
{
|
||
|
|
PRAT ptmp = NULL;
|
||
|
|
DUPRAT(ptmp,(*px));
|
||
|
|
subrat(&ptmp,rat_one);
|
||
|
|
addrat(px,rat_one);
|
||
|
|
divrat(px,ptmp);
|
||
|
|
(*px)->pp->sign *= -1;
|
||
|
|
lograt(px);
|
||
|
|
divrat(px,rat_two);
|
||
|
|
destroyrat(ptmp);
|
||
|
|
}
|
||
|
|
|