1548 lines
39 KiB
C
1548 lines
39 KiB
C
//---------------------------------------------------------------------------
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// Package Title ratpak
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// File conv.c
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// Author Timothy David Corrie Jr. (timc@microsoft.com)
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// Copyright (C) 1995-97 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 conversion, input and output routines for numbers rationals
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// and longs.
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//
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//
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//
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//---------------------------------------------------------------------------
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#include <stdio.h>
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#include <tchar.h> // TCHAR version of sprintf
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#include <string.h>
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#include <malloc.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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BOOL fparserror=FALSE;
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BOOL gbinexact=FALSE;
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// digits 0..64 used by bases 2 .. 64
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TCHAR digits[65]=TEXT("0123456789")
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TEXT("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
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TEXT("abcdefghijklmnopqrstuvwxyz_@");
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// ratio of internal 'digits' to output 'digits'
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// Calculated elsewhere as part of initialization and when base is changed
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long ratio; // int(log(2L^BASEXPWR)/log(nRadix))
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// Used to strip trailing zeroes, and prevent combinatorial explosions
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BOOL stripzeroesnum( PNUMBER pnum, long starting );
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// returns int(lognRadix(x)) quickly.
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long longlognRadix( long x );
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//----------------------------------------------------------------------------
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//
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// FUNCTION: fail
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//
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// ARGUMENTS: pointer to an error message.
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//
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// RETURN: None
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//
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// DESCRIPTION: fail dumps the error message then throws an exception
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//
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//----------------------------------------------------------------------------
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void fail( IN long errmsg )
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{
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#ifdef DEBUG
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fprintf( stderr, "%s\n", TEXT("Out of Memory") );
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#endif
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throw( CALC_E_OUTOFMEMORY );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: _destroynum
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//
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// ARGUMENTS: pointer to a number
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//
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// RETURN: None
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//
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// DESCRIPTION: Deletes the number and associated allocation
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//
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//-----------------------------------------------------------------------------
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void _destroynum( IN PNUMBER pnum )
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{
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if ( pnum != NULL )
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{
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zfree( pnum );
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}
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: _destroyrat
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//
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// ARGUMENTS: pointer to a rational
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//
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// RETURN: None
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//
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// DESCRIPTION: Deletes the rational and associated
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// allocations.
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//
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//-----------------------------------------------------------------------------
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void _destroyrat( IN PRAT prat )
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{
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if ( prat != NULL )
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{
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destroynum( prat->pp );
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destroynum( prat->pq );
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zfree( prat );
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}
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: _createnum
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//
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// ARGUMENTS: size of number in 'digits'
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//
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// RETURN: pointer to a number
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//
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// DESCRIPTION: allocates and zeroes out number type.
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//
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//-----------------------------------------------------------------------------
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PNUMBER _createnum( IN long size )
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{
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PNUMBER pnumret=NULL;
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// sizeof( MANTTYPE ) is the size of a 'digit'
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pnumret = (PNUMBER)zmalloc( (int)(size+1) * sizeof( MANTTYPE ) +
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sizeof( NUMBER ) );
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if ( pnumret == NULL )
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{
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fail( CALC_E_OUTOFMEMORY );
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}
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return( pnumret );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: _createrat
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//
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// ARGUMENTS: none
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//
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// RETURN: pointer to a rational
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//
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// DESCRIPTION: allocates a rational structure but does not
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// allocate the numbers that make up the rational p over q
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// form. These number pointers are left pointing to null.
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//
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//-----------------------------------------------------------------------------
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PRAT _createrat( void )
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{
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PRAT prat=NULL;
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prat = (PRAT)zmalloc( sizeof( RAT ) );
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if ( prat == NULL )
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{
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fail( CALC_E_OUTOFMEMORY );
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}
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prat->pp = NULL;
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prat->pq = NULL;
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return( prat );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: numtorat
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//
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// ARGUMENTS: pointer to a number, nRadix number is in.
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//
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// RETURN: Rational representation of number.
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//
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// DESCRIPTION: The rational representation of the number
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// is guaranteed to be in the form p (number with internal
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// base representation) over q (number with internal base
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// representation) Where p and q are integers.
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//
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//-----------------------------------------------------------------------------
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PRAT numtorat( IN PNUMBER pin, IN unsigned long nRadix )
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{
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PRAT pout=NULL;
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PNUMBER pnRadixn=NULL;
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PNUMBER qnRadixn=NULL;
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DUPNUM( pnRadixn, pin );
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qnRadixn=longtonum( 1, nRadix );
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// Ensure p and q start out as integers.
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if ( pnRadixn->exp < 0 )
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{
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qnRadixn->exp -= pnRadixn->exp;
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pnRadixn->exp = 0;
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}
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createrat(pout);
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// There is probably a better way to do this.
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pout->pp = numtonRadixx( pnRadixn, nRadix, ratio );
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pout->pq = numtonRadixx( qnRadixn, nRadix, ratio );
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destroynum( pnRadixn );
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destroynum( qnRadixn );
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return( pout );
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}
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//----------------------------------------------------------------------------
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//
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// FUNCTION: nRadixxtonum
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//
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// ARGUMENTS: pointer to a number, base requested.
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//
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// RETURN: number representation in nRadix requested.
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//
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// DESCRIPTION: Does a base conversion on a number from
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// internal to requested base. Assumes number being passed
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// in is really in internal base form.
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//
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//----------------------------------------------------------------------------
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PNUMBER nRadixxtonum( IN PNUMBER a, IN unsigned long nRadix )
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{
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PNUMBER sum=NULL;
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PNUMBER powofnRadix=NULL;
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unsigned long bitmask;
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unsigned long cdigits;
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MANTTYPE *ptr;
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sum = longtonum( 0, nRadix );
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powofnRadix = longtonum( BASEX, nRadix );
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// A large penalty is paid for conversion of digits no one will see anyway.
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// limit the digits to the minimum of the existing precision or the
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// requested precision.
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cdigits = maxout + 1;
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if ( cdigits > (unsigned long)a->cdigit )
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{
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cdigits = (unsigned long)a->cdigit;
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}
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// scale by the internal base to the internal exponent offset of the LSD
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numpowlong( &powofnRadix, a->exp + (a->cdigit - cdigits), nRadix );
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// Loop over all the relative digits from MSD to LSD
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for ( ptr = &(MANT(a)[a->cdigit-1]); cdigits > 0 && !fhalt;
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ptr--, cdigits-- )
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{
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// Loop over all the bits from MSB to LSB
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for ( bitmask = BASEX/2; bitmask > 0; bitmask /= 2 )
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{
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addnum( &sum, sum, nRadix );
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if ( *ptr & bitmask )
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{
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sum->mant[0] |= 1;
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}
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}
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}
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// Scale answer by power of internal exponent.
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mulnum( &sum, powofnRadix, nRadix );
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destroynum( powofnRadix );
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sum->sign = a->sign;
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return( sum );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: numtonRadixx
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//
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// ARGUMENTS: pointer to a number, nRadix of that number.
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// previously calculated ratio
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//
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// RETURN: number representation in internal nRadix.
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//
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// DESCRIPTION: Does a nRadix conversion on a number from
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// specified nRadix to requested nRadix. Assumes the nRadix
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// specified is the nRadix of the number passed in.
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//
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//-----------------------------------------------------------------------------
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PNUMBER numtonRadixx( IN PNUMBER a, IN unsigned long nRadix, IN long ratio )
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{
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PNUMBER pnumret = NULL; // pnumret is the number in internal form.
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PNUMBER thisdigit = NULL; // thisdigit holds the current digit of a
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// being summed into result.
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PNUMBER powofnRadix = NULL; // offset of external base exponent.
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MANTTYPE *ptrdigit; // pointer to digit being worked on.
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long idigit; // idigit is the iterate of digits in a.
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pnumret = longtonum( 0, BASEX );
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ptrdigit = MANT(a);
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// Digits are in reverse order, back over them LSD first.
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ptrdigit += a->cdigit-1;
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for ( idigit = 0; idigit < a->cdigit; idigit++ )
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{
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mulnumx( &pnumret, num_nRadix );
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// WARNING:
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// This should just smack in each digit into a 'special' thisdigit.
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// and not do the overhead of recreating the number type each time.
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thisdigit = longtonum( *ptrdigit--, BASEX );
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addnum( &pnumret, thisdigit, BASEX );
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destroynum( thisdigit );
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}
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DUPNUM( powofnRadix, num_nRadix );
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// Calculate the exponent of the external base for scaling.
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numpowlongx( &powofnRadix, a->exp );
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// ... and scale the result.
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mulnumx( &pnumret, powofnRadix );
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destroynum( powofnRadix );
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// And propagate the sign.
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pnumret->sign = a->sign;
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return( pnumret );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: inrat
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//
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// ARGUMENTS:
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// fMantIsNeg true if mantissa is less than zero
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// pszMant a string representation of a number
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// fExpIsNeg true if exponent is less than zero
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// pszExp a string representation of a number
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//
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// RETURN: prat representation of string input.
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// Or NULL if no number scanned.
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//
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// EXPLANATION: This is for calc.
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//
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//
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//-----------------------------------------------------------------------------
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PRAT inrat( IN BOOL fMantIsNeg, IN LPTSTR pszMant, IN BOOL fExpIsNeg,
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IN LPTSTR pszExp )
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{
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PNUMBER pnummant=NULL; // holds mantissa in number form.
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PNUMBER pnumexp=NULL; // holds exponent in number form.
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PRAT pratexp=NULL; // holds exponent in rational form.
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PRAT prat=NULL; // holds exponent in rational form.
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long expt; // holds exponent
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// Deal with Mantissa
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if ( ( pszMant == NULL ) || ( *pszMant == TEXT('\0') ) )
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{
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// Preset value if no mantissa
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if ( ( pszExp == NULL ) || ( *pszExp == TEXT('\0') ) )
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{
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// Exponent not specified, preset value to zero
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DUPRAT(prat,rat_zero);
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}
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else
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{
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// Exponent specified, preset value to one
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DUPRAT(prat,rat_one);
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}
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}
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else
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{
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// Mantissa specified, convert to number form.
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pnummant = innum( pszMant );
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if ( pnummant == NULL )
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{
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return( NULL );
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}
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prat = numtorat( pnummant, nRadix );
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// convert to rational form, and cleanup.
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destroynum(pnummant);
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}
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if ( ( pszExp == NULL ) || ( *pszExp == TEXT('\0') ) )
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{
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// Exponent not specified, preset value to zero
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expt=0;
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}
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else
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{
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// Exponent specified, convert to number form.
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// Don't use native stuff, as it is restricted in the bases it can
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// handle.
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pnumexp = innum( pszExp );
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if ( pnumexp == NULL )
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{
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return( NULL );
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}
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// Convert exponent number form to native integral form, and cleanup.
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expt = numtolong( pnumexp, nRadix );
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destroynum( pnumexp );
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}
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// Convert native integral exponent form to rational multiplier form.
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pnumexp=longtonum( nRadix, BASEX );
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numpowlongx(&(pnumexp),abs(expt));
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createrat(pratexp);
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DUPNUM( pratexp->pp, pnumexp );
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pratexp->pq = longtonum( 1, BASEX );
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destroynum(pnumexp);
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if ( fExpIsNeg )
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{
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// multiplier is less than 1, this means divide.
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divrat( &prat, pratexp );
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}
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else
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{
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if ( expt > 0 )
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{
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// multiplier is greater than 1, this means divide.
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mulrat(&prat, pratexp);
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}
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// multiplier can be 1, in which case it'd be a waste of time to
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// multiply.
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}
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if ( fMantIsNeg )
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{
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// A negative number was used, adjust the sign.
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prat->pp->sign *= -1;
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}
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return( prat );
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: innum
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//
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// ARGUMENTS:
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// TCHAR *buffer
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//
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// RETURN: pnumber representation of string input.
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// Or NULL if no number scanned.
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//
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// EXPLANATION: This is a state machine,
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//
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// State Description Example, ^shows just read position.
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// which caused the transition
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//
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// START Start state ^1.0
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// MANTS Mantissa sign -^1.0
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// LZ Leading Zero 0^1.0
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// LZDP Post LZ dec. pt. 000.^1
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// LD Leading digit 1^.0
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// DZ Post LZDP Zero 000.0^1
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// DD Post Decimal digit .01^2
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// DDP Leading Digit dec. pt. 1.^2
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// EXPB Exponent Begins 1.0e^2
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// EXPS Exponent sign 1.0e+^5
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// EXPD Exponent digit 1.0e1^2 or even 1.0e0^1
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// EXPBZ Exponent begin post 0 0.000e^+1
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// EXPSZ Exponent sign post 0 0.000e+^1
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// EXPDZ Exponent digit post 0 0.000e+1^2
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// ERR Error case 0.0.^
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//
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// Terminal Description
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//
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// DP '.'
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// ZR '0'
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// NZ '1'..'9' 'A'..'Z' 'a'..'z' '@' '_'
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// SG '+' '-'
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// EX 'e' '^' e is used for nRadix 10, ^ for all other nRadixs.
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//
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//-----------------------------------------------------------------------------
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#define DP 0
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#define ZR 1
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#define NZ 2
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#define SG 3
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#define EX 4
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#define START 0
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#define MANTS 1
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#define LZ 2
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#define LZDP 3
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#define LD 4
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#define DZ 5
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#define DD 6
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#define DDP 7
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#define EXPB 8
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#define EXPS 9
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#define EXPD 10
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#define EXPBZ 11
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#define EXPSZ 12
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#define EXPDZ 13
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#define ERR 14
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|
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#if defined( DEBUG )
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char *statestr[] = {
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"START",
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"MANTS",
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"LZ",
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"LZDP",
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"LD",
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"DZ",
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"DD",
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"DDP",
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"EXPB",
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"EXPS",
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"EXPD",
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"EXPBZ",
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"EXPSZ",
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"EXPDZ",
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"ERR",
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};
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#endif
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// New state is machine[state][terminal]
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char machine[ERR+1][EX+1]= {
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// DP, ZR, NZ, SG, EX
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// START
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{ LZDP, LZ, LD, MANTS, ERR },
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// MANTS
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{ LZDP, LZ, LD, ERR, ERR },
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// LZ
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{ LZDP, LZ, LD, ERR, EXPBZ },
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// LZDP
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{ ERR, DZ, DD, ERR, EXPB },
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// LD
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{ DDP, LD, LD, ERR, EXPB },
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// DZ
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{ ERR, DZ, DD, ERR, EXPBZ },
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// DD
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{ ERR, DD, DD, ERR, EXPB },
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// DDP
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{ ERR, DD, DD, ERR, EXPB },
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// EXPB
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{ ERR, EXPD, EXPD, EXPS, ERR },
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// EXPS
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{ ERR, EXPD, EXPD, ERR, ERR },
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// EXPD
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{ ERR, EXPD, EXPD, ERR, ERR },
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// EXPBZ
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{ ERR, EXPDZ, EXPDZ, EXPSZ, ERR },
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// EXPSZ
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{ ERR, EXPDZ, EXPDZ, ERR, ERR },
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// EXPDZ
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{ ERR, EXPDZ, EXPDZ, ERR, ERR },
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// ERR
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{ ERR, ERR, ERR, ERR, ERR }
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};
|
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|
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|
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PNUMBER innum( IN TCHAR *buffer )
|
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|
|
{
|
|
int c; // c is character being worked on currently.
|
|
int state; // state is the state of the input state machine.
|
|
long exps = 1L; // exps is exponent sign ( +/- 1 )
|
|
long expt = 0L; // expt is exponent mantissa, should be unsigned
|
|
long length = 0L; // length is the length of the input string.
|
|
MANTTYPE *pmant; //
|
|
PNUMBER pnumret=NULL; //
|
|
|
|
length = _tcslen(buffer);
|
|
createnum( pnumret, length );
|
|
pnumret->sign = 1L;
|
|
pnumret->cdigit = 0;
|
|
pnumret->exp = 0;
|
|
pmant = MANT(pnumret)+length-1;
|
|
state = START;
|
|
fparserror=FALSE; // clear global flag for parse error initially.
|
|
while ( ( c = *buffer ) && c != TEXT('\n') )
|
|
{
|
|
int dp;
|
|
dp = 0;
|
|
// Added code to deal with international decimal point.
|
|
while ( szDec[dp] && ( szDec[dp] == *buffer ) )
|
|
{
|
|
dp++;
|
|
buffer++;
|
|
}
|
|
if ( dp )
|
|
{
|
|
if ( szDec[dp] == TEXT('\0') )
|
|
{
|
|
// OK pretend that was a decimal point for the state machine
|
|
c = TEXT('.');
|
|
buffer--;
|
|
}
|
|
else
|
|
{
|
|
// Backup that was no decimal point
|
|
buffer -= (dp-1);
|
|
c = *buffer++;
|
|
}
|
|
}
|
|
switch ( c )
|
|
{
|
|
case TEXT('-'):
|
|
case TEXT('+'):
|
|
state=machine[state][SG];
|
|
break;
|
|
case TEXT('.'):
|
|
state=machine[state][DP];
|
|
break;
|
|
case TEXT('0'):
|
|
state=machine[state][ZR];
|
|
break;
|
|
case TEXT('^'):
|
|
case TEXT('e'):
|
|
if ( ( c == TEXT('^') ) || ( nRadix == 10 ) )
|
|
{
|
|
state=machine[state][EX];
|
|
break;
|
|
}
|
|
// WARNING tricky dropthrough in the TEXT('e') as a digit case!!!
|
|
default:
|
|
state=machine[state][NZ];
|
|
break;
|
|
}
|
|
switch ( state )
|
|
{
|
|
case MANTS:
|
|
pnumret->sign = ( ( c == TEXT('-') ) ? -1 : 1);
|
|
break;
|
|
case EXPSZ:
|
|
case EXPS:
|
|
exps = ( ( c == TEXT('-') ) ? -1 : 1);
|
|
break;
|
|
case EXPDZ:
|
|
case EXPD:
|
|
{
|
|
TCHAR *ptr; // offset into digit table.
|
|
if ( ( nRadix <= 36 ) && ( nRadix > 10 ) )
|
|
{
|
|
c = toupper( c );
|
|
}
|
|
ptr = _tcschr( digits, (TCHAR)c );
|
|
if ( ptr != NULL )
|
|
{
|
|
expt *= nRadix;
|
|
expt += (long)(ptr - digits);
|
|
}
|
|
else
|
|
{
|
|
state=ERR;
|
|
}
|
|
}
|
|
break;
|
|
case LD:
|
|
pnumret->exp++;
|
|
case DD:
|
|
{
|
|
TCHAR *ptr; // offset into digit table.
|
|
if ( ( nRadix <= 36 ) && ( nRadix > 10 ) )
|
|
{
|
|
// Allow upper and lower case letters as equivalent, base
|
|
// is in the range where this is not ambiguous.
|
|
c = toupper( c );
|
|
}
|
|
ptr = _tcschr( digits, (TCHAR)c );
|
|
if ( ptr != NULL && ( (ptr - digits) < nRadix ) )
|
|
{
|
|
*pmant-- = (MANTTYPE)(ptr - digits);
|
|
pnumret->exp--;
|
|
pnumret->cdigit++;
|
|
}
|
|
else
|
|
{
|
|
state=ERR;
|
|
// set global flag for parse error just in case anyone cares.
|
|
fparserror=TRUE;
|
|
}
|
|
}
|
|
break;
|
|
case DZ:
|
|
pnumret->exp--;
|
|
break;
|
|
case LZ:
|
|
case LZDP:
|
|
case DDP:
|
|
break;
|
|
}
|
|
buffer++;
|
|
}
|
|
if ( state == DZ || state == EXPDZ )
|
|
{
|
|
pnumret->cdigit = 1;
|
|
pnumret->exp=0;
|
|
pnumret->sign=1;
|
|
}
|
|
else
|
|
{
|
|
while ( pnumret->cdigit < length )
|
|
{
|
|
pnumret->cdigit++;
|
|
pnumret->exp--;
|
|
}
|
|
pnumret->exp += exps*expt;
|
|
}
|
|
|
|
|
|
if ( pnumret->cdigit == 0 )
|
|
{
|
|
destroynum( pnumret );
|
|
pnumret = NULL;
|
|
}
|
|
stripzeroesnum( pnumret, maxout );
|
|
return( pnumret );
|
|
}
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: longtorat
|
|
//
|
|
// ARGUMENTS: long
|
|
//
|
|
// RETURN: Rational representation of long input.
|
|
//
|
|
// DESCRIPTION: Converts long input to rational (p over q)
|
|
// form, where q is 1 and p is the long.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PRAT longtorat( IN long inlong )
|
|
|
|
{
|
|
PRAT pratret=NULL;
|
|
createrat( pratret );
|
|
pratret->pp = longtonum(inlong, BASEX );
|
|
pratret->pq = longtonum(1L, BASEX );
|
|
return( pratret );
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: realtorat
|
|
//
|
|
// ARGUMENTS: double real value.
|
|
//
|
|
// RETURN: Rational representation of the double
|
|
//
|
|
// DESCRIPTION: returns the rational (p over q)
|
|
// representation of the double.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PRAT realtorat( IN double real )
|
|
|
|
{
|
|
#if !defined( CLEVER )
|
|
// get clever later, right now hack something to work
|
|
TCHAR *ptr;
|
|
PNUMBER pnum=NULL;
|
|
PRAT prat=NULL;
|
|
if ( ( ptr = (TCHAR*)zmalloc( 60 * sizeof(TCHAR) ) ) != NULL )
|
|
{
|
|
_stprintf( ptr, TEXT("%20.20le"), real );
|
|
pnum=innum( ptr );
|
|
prat = numtorat( pnum, nRadix );
|
|
destroynum( pnum );
|
|
zfree( ptr );
|
|
return( prat );
|
|
}
|
|
else
|
|
{
|
|
return( NULL );
|
|
}
|
|
#else
|
|
int i;
|
|
union {
|
|
double real;
|
|
BYTE split[8];
|
|
} unpack;
|
|
long expt;
|
|
long ratio;
|
|
MANTTYPE *pmant;
|
|
PNUMBER pnumret = NULL;
|
|
PRAT pratret = NULL;
|
|
|
|
createrat( pratret );
|
|
|
|
if ( real == 0.0 )
|
|
{
|
|
pnumret=longtonum( 0L, 2L );
|
|
}
|
|
else
|
|
{
|
|
unpack.real=real;
|
|
|
|
expt=unpack.split[7]*0x100+(unpack.split[6]>>4)-1023;
|
|
createnum( pnumret, 52 );
|
|
pmant = MANT(pnumret);
|
|
for ( i = 63; i > 10; i-- )
|
|
{
|
|
*pmant++ = (MANTTYPE)((unpack.split[i/8]&(1<<(i%8)))!=0);
|
|
}
|
|
pnumret->exp=expt-52;
|
|
pnumret->cdigit=52;
|
|
}
|
|
|
|
ratio = 1;
|
|
while ( ratio > BASEX )
|
|
{
|
|
ratio *= 2;
|
|
}
|
|
|
|
pratret->pp = numtonRadixx( pnumret, 2, ratio );
|
|
destroynum( pnumret );
|
|
|
|
pratret->pq=longtonum( 1L, BASEX );
|
|
|
|
if ( pratret->pp->exp < 0 )
|
|
{
|
|
pratret->pq->exp -= pratret->pp->exp;
|
|
pratret->pp->exp = 0;
|
|
}
|
|
|
|
return( pratret );
|
|
#endif
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: longtonum
|
|
//
|
|
// ARGUMENTS: long input and nRadix requested.
|
|
//
|
|
// RETURN: number
|
|
//
|
|
// DESCRIPTION: Returns a number representation in the
|
|
// base requested of the long value passed in.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PNUMBER longtonum( IN long inlong, IN unsigned long nRadix )
|
|
|
|
{
|
|
MANTTYPE *pmant;
|
|
PNUMBER pnumret=NULL;
|
|
|
|
createnum( pnumret, MAX_LONG_SIZE );
|
|
pmant = MANT(pnumret);
|
|
pnumret->cdigit = 0;
|
|
pnumret->exp = 0;
|
|
if ( inlong < 0 )
|
|
{
|
|
pnumret->sign = -1;
|
|
inlong *= -1;
|
|
}
|
|
else
|
|
{
|
|
pnumret->sign = 1;
|
|
}
|
|
|
|
do {
|
|
*pmant++ = (MANTTYPE)(inlong % nRadix);
|
|
inlong /= nRadix;
|
|
pnumret->cdigit++;
|
|
} while ( inlong );
|
|
|
|
return( pnumret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: rattolong
|
|
//
|
|
// ARGUMENTS: rational number in internal base.
|
|
//
|
|
// RETURN: long
|
|
//
|
|
// DESCRIPTION: returns the long representation of the
|
|
// number input. Assumes that the number is in the internal
|
|
// base.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
long rattolong( IN PRAT prat )
|
|
|
|
{
|
|
long lret;
|
|
PRAT pint = NULL;
|
|
|
|
if ( rat_gt( prat, rat_dword ) || rat_lt( prat, rat_min_long ) )
|
|
{
|
|
// Don't attempt rattolong of anything too big or small
|
|
throw( CALC_E_DOMAIN );
|
|
}
|
|
|
|
DUPRAT(pint,prat);
|
|
|
|
intrat( &pint );
|
|
divnumx( &(pint->pp), pint->pq );
|
|
DUPNUM( pint->pq, num_one );
|
|
|
|
lret = numtolong( pint->pp, BASEX );
|
|
|
|
destroyrat(pint);
|
|
|
|
return( lret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: numtolong
|
|
//
|
|
// ARGUMENTS: number input and base of that number.
|
|
//
|
|
// RETURN: long
|
|
//
|
|
// DESCRIPTION: returns the long representation of the
|
|
// number input. Assumes that the number is really in the
|
|
// base claimed.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
long numtolong( IN PNUMBER pnum, IN unsigned long nRadix )
|
|
|
|
{
|
|
long lret;
|
|
long expt;
|
|
long length;
|
|
MANTTYPE *pmant;
|
|
|
|
lret = 0;
|
|
pmant = MANT( pnum );
|
|
pmant += pnum->cdigit - 1;
|
|
|
|
expt = pnum->exp;
|
|
length = pnum->cdigit;
|
|
while ( length > 0 && length + expt > 0 )
|
|
{
|
|
lret *= nRadix;
|
|
lret += *(pmant--);
|
|
length--;
|
|
}
|
|
while ( expt-- > 0 )
|
|
{
|
|
lret *= (long)nRadix;
|
|
}
|
|
lret *= pnum->sign;
|
|
return( lret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: BOOL stripzeroesnum
|
|
//
|
|
// ARGUMENTS: a number representation
|
|
//
|
|
// RETURN: TRUE if stripping done, modifies number in place.
|
|
//
|
|
// DESCRIPTION: Strips off trailing zeroes.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
BOOL stripzeroesnum( IN OUT PNUMBER pnum, long starting )
|
|
|
|
{
|
|
MANTTYPE *pmant;
|
|
long cdigits;
|
|
BOOL fstrip = FALSE;
|
|
|
|
// point pmant to the LeastCalculatedDigit
|
|
pmant=MANT(pnum);
|
|
cdigits=pnum->cdigit;
|
|
// point pmant to the LSD
|
|
if ( cdigits > starting )
|
|
{
|
|
pmant += cdigits - starting;
|
|
cdigits = starting;
|
|
}
|
|
|
|
// Check we haven't gone too far, and we are still looking at zeroes.
|
|
while ( ( cdigits > 0 ) && !(*pmant) )
|
|
{
|
|
// move to next significant digit and keep track of digits we can
|
|
// ignore later.
|
|
pmant++;
|
|
cdigits--;
|
|
fstrip = TRUE;
|
|
}
|
|
|
|
// If there are zeroes to remove.
|
|
if ( fstrip )
|
|
{
|
|
// Remove them.
|
|
memcpy( MANT(pnum), pmant, (int)(cdigits*sizeof(MANTTYPE)) );
|
|
// And adjust exponent and digit count accordingly.
|
|
pnum->exp += ( pnum->cdigit - cdigits );
|
|
pnum->cdigit = cdigits;
|
|
}
|
|
return( fstrip );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: putnum
|
|
//
|
|
// ARGUMENTS: number representation
|
|
// fmt, one of FMT_FLOAT FMT_SCIENTIFIC or
|
|
// FMT_ENGINEERING
|
|
//
|
|
// RETURN: String representation of number.
|
|
//
|
|
// DESCRIPTION: Converts a number to it's string
|
|
// representation. Returns a string that should be
|
|
// zfree'd after use.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
TCHAR *putnum( IN PNUMBER *ppnum, IN int fmt )
|
|
|
|
{
|
|
TCHAR *psz;
|
|
TCHAR *pret;
|
|
long expt; // Actual number of digits to the left of decimal
|
|
long eout; // Displayed exponent.
|
|
long cexp; // the size of the exponent needed.
|
|
long elen;
|
|
long length;
|
|
MANTTYPE *pmant;
|
|
int fsciform=0; // If true scientific form is called for.
|
|
PNUMBER pnum;
|
|
PNUMBER round=NULL;
|
|
long oldfmt = fmt;
|
|
|
|
|
|
pnum=*ppnum;
|
|
stripzeroesnum( pnum, maxout+2 );
|
|
length = pnum->cdigit;
|
|
expt = pnum->exp+length;
|
|
if ( ( expt > maxout ) && ( fmt == FMT_FLOAT ) )
|
|
{
|
|
// Force scientific mode to prevent user from assuming 33rd digit is
|
|
// exact.
|
|
fmt = FMT_SCIENTIFIC;
|
|
}
|
|
|
|
|
|
// Make length small enough to fit in pret.
|
|
if ( length > maxout )
|
|
{
|
|
length = maxout;
|
|
}
|
|
|
|
eout=expt-1;
|
|
cexp = longlognRadix( expt );
|
|
|
|
// 2 for signs, 1 for 'e'(or leading zero), 1 for dp, 1 for null and
|
|
// 10 for maximum exponent size.
|
|
pret = (TCHAR*)zmalloc( (maxout + 16) * sizeof(TCHAR) );
|
|
psz = pret;
|
|
|
|
if (!psz)
|
|
{
|
|
fail( CALC_E_OUTOFMEMORY );
|
|
}
|
|
|
|
// If there is a chance a round has to occour, round.
|
|
if (
|
|
// if number is zero no rounding.
|
|
!zernum( pnum ) &&
|
|
// if number of digits is less than the maximum output no rounding.
|
|
pnum->cdigit >= maxout
|
|
)
|
|
{
|
|
// Otherwise round.
|
|
round=longtonum( nRadix, nRadix );
|
|
divnum(&round, num_two, nRadix );
|
|
|
|
// Make round number exponent one below the LSD for the number.
|
|
round->exp = pnum->exp + pnum->cdigit - round->cdigit - maxout;
|
|
round->sign = pnum->sign;
|
|
}
|
|
|
|
if ( fmt == FMT_FLOAT )
|
|
{
|
|
// cexp will now contain the size required by exponential.
|
|
// Figure out if the exponent will fill more space than the nonexponent field.
|
|
if ( ( length - expt > maxout + 2 ) || ( expt > maxout + 3 ) )
|
|
{
|
|
// Case where too many zeroes are to the right or left of the
|
|
// decimal pt. And we are forced to switch to scientific form.
|
|
fmt = FMT_SCIENTIFIC;
|
|
}
|
|
else
|
|
{
|
|
// Minimum loss of precision occours with listing leading zeros
|
|
// if we need to make room for zeroes sacrifice some digits.
|
|
if ( length + abs(expt) < maxout )
|
|
{
|
|
if ( round )
|
|
{
|
|
round->exp -= expt;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if ( round != NULL )
|
|
{
|
|
BOOL fstrip=FALSE;
|
|
long offset;
|
|
addnum( ppnum, round, nRadix );
|
|
pnum=*ppnum;
|
|
offset=(pnum->cdigit+pnum->exp) - (round->cdigit+round->exp);
|
|
fstrip = stripzeroesnum( pnum, offset );
|
|
destroynum( round );
|
|
if ( fstrip )
|
|
{
|
|
// WARNING: nesting/recursion, too much has been changed, need to
|
|
// refigure format.
|
|
return( putnum( &pnum, oldfmt ) );
|
|
}
|
|
}
|
|
else
|
|
{
|
|
stripzeroesnum( pnum, maxout );
|
|
}
|
|
|
|
// Set up all the post rounding stuff.
|
|
pmant = MANT(pnum)+pnum->cdigit-1;
|
|
|
|
if (
|
|
// Case where too many digits are to the left of the decimal or
|
|
// FMT_SCIENTIFIC or FMT_ENGINEERING was specified.
|
|
( fmt == FMT_SCIENTIFIC ) ||
|
|
( fmt == FMT_ENGINEERING ) )
|
|
|
|
{
|
|
fsciform=1;
|
|
if ( eout != 0 )
|
|
{
|
|
|
|
if ( fmt == FMT_ENGINEERING )
|
|
{
|
|
expt = (eout % 3);
|
|
eout -= expt;
|
|
expt++;
|
|
|
|
// Fix the case where 0.02e-3 should really be 2.e-6 etc.
|
|
if ( expt < 0 )
|
|
{
|
|
expt += 3;
|
|
eout -= 3;
|
|
}
|
|
|
|
}
|
|
else
|
|
{
|
|
expt = 1;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
fsciform=0;
|
|
eout=0;
|
|
}
|
|
|
|
// Make sure negative zeroes aren't allowed.
|
|
if ( ( pnum->sign == -1 ) && ( length > 0 ) )
|
|
{
|
|
*psz++ = TEXT('-');
|
|
}
|
|
|
|
if ( ( expt <= 0 ) && ( fsciform == 0 ) )
|
|
{
|
|
*psz++ = TEXT('0');
|
|
*psz++ = szDec[0];
|
|
// Used up a digit unaccounted for.
|
|
}
|
|
while ( expt < 0 )
|
|
{
|
|
*psz++ = TEXT('0');
|
|
expt++;
|
|
}
|
|
|
|
while ( length > 0 )
|
|
{
|
|
expt--;
|
|
*psz++ = digits[ *pmant-- ];
|
|
length--;
|
|
// Be more regular in using a decimal point.
|
|
if ( expt == 0 )
|
|
{
|
|
*psz++ = szDec[0];
|
|
}
|
|
}
|
|
|
|
while ( expt > 0 )
|
|
{
|
|
*psz++ = TEXT('0');
|
|
expt--;
|
|
// Be more regular in using a decimal point.
|
|
if ( expt == 0 )
|
|
{
|
|
*psz++ = szDec[0];
|
|
}
|
|
}
|
|
|
|
|
|
if ( fsciform )
|
|
{
|
|
if ( nRadix == 10 )
|
|
{
|
|
*psz++ = TEXT('e');
|
|
}
|
|
else
|
|
{
|
|
*psz++ = TEXT('^');
|
|
}
|
|
*psz++ = ( eout < 0 ? TEXT('-') : TEXT('+') );
|
|
eout = abs( eout );
|
|
elen=0;
|
|
do
|
|
{
|
|
// should this be eout % nRadix? or is that insane?
|
|
*psz++ = digits[ eout % nRadix ];
|
|
elen++;
|
|
eout /= nRadix;
|
|
} while ( eout > 0 );
|
|
*psz = TEXT('\0');
|
|
_tcsrev( &(psz[-elen]) );
|
|
}
|
|
*psz = TEXT('\0');
|
|
return( pret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: putrat
|
|
//
|
|
// ARGUMENTS:
|
|
// PRAT *representation of a number.
|
|
// long representation of base to dump to screen.
|
|
// fmt, one of FMT_FLOAT FMT_SCIENTIFIC or FMT_ENGINEERING
|
|
//
|
|
// RETURN: string
|
|
//
|
|
// DESCRIPTION: returns a string representation of rational number passed
|
|
// in, at least to the maxout digits. String returned should be zfree'd
|
|
// after use.
|
|
//
|
|
// NOTE: It may be that doing a GCD() could shorten the rational form
|
|
// And it may eventually be worthwhile to keep the result. That is
|
|
// why a pointer to the rational is passed in.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
TCHAR *putrat( IN OUT PRAT *pa, IN unsigned long nRadix, IN int fmt )
|
|
|
|
{
|
|
TCHAR *psz;
|
|
PNUMBER p=NULL;
|
|
PNUMBER q=NULL;
|
|
long scaleby=0;
|
|
|
|
|
|
// Convert p and q of rational form from internal base to requested base.
|
|
|
|
// Scale by largest power of BASEX possible.
|
|
|
|
scaleby=min((*pa)->pp->exp,(*pa)->pq->exp);
|
|
if ( scaleby < 0 )
|
|
{
|
|
scaleby = 0;
|
|
}
|
|
(*pa)->pp->exp -= scaleby;
|
|
(*pa)->pq->exp -= scaleby;
|
|
|
|
p = nRadixxtonum( (*pa)->pp, nRadix );
|
|
|
|
q = nRadixxtonum( (*pa)->pq, nRadix );
|
|
|
|
// finally take the time hit to actually divide.
|
|
divnum( &p, q, nRadix );
|
|
|
|
psz = putnum( &p, fmt );
|
|
destroynum( p );
|
|
destroynum( q );
|
|
return( psz );
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: gcd
|
|
//
|
|
// ARGUMENTS:
|
|
// PNUMBER representation of a number.
|
|
// PNUMBER representation of a number.
|
|
//
|
|
// RETURN: Greatest common divisor in internal BASEX PNUMBER form.
|
|
//
|
|
// DESCRIPTION: gcd uses remainders to find the greatest common divisor.
|
|
//
|
|
// ASSUMPTIONS: gcd assumes inputs are integers.
|
|
//
|
|
// NOTE: Before GregSte and TimC proved the TRIM macro actually kept the
|
|
// size down cheaper than GCD, this routine was used extensively.
|
|
// now it is not used but might be later.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PNUMBER gcd( IN PNUMBER a, IN PNUMBER b )
|
|
|
|
{
|
|
PNUMBER r=NULL;
|
|
PNUMBER tmpa=NULL;
|
|
PNUMBER tmpb=NULL;
|
|
|
|
if ( lessnum( a, b ) )
|
|
{
|
|
DUPNUM(tmpa,b);
|
|
if ( zernum(a) )
|
|
{
|
|
return(tmpa);
|
|
}
|
|
DUPNUM(tmpb,a);
|
|
}
|
|
else
|
|
{
|
|
DUPNUM(tmpa,a);
|
|
if ( zernum(b) )
|
|
{
|
|
return(tmpa);
|
|
}
|
|
DUPNUM(tmpb,b);
|
|
}
|
|
|
|
remnum( &tmpa, tmpb, nRadix );
|
|
while ( !zernum( tmpa ) )
|
|
{
|
|
// swap tmpa and tmpb
|
|
r = tmpa;
|
|
tmpa = tmpb;
|
|
tmpb = r;
|
|
remnum( &tmpa, tmpb, nRadix );
|
|
}
|
|
destroynum( tmpa );
|
|
return( tmpb );
|
|
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: longfactnum
|
|
//
|
|
// ARGUMENTS:
|
|
// long integer to factorialize.
|
|
// long integer representing base of answer.
|
|
//
|
|
// RETURN: Factorial of input in nRadix PNUMBER form.
|
|
//
|
|
// NOTE: Not currently used.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PNUMBER longfactnum( IN long inlong, IN unsigned long nRadix )
|
|
|
|
{
|
|
PNUMBER lret=NULL;
|
|
PNUMBER tmp=NULL;
|
|
PNUMBER tmp1=NULL;
|
|
|
|
lret = longtonum( 1, nRadix );
|
|
|
|
while ( inlong > 0 )
|
|
{
|
|
tmp = longtonum( inlong--, nRadix );
|
|
mulnum( &lret, tmp, nRadix );
|
|
destroynum( tmp );
|
|
}
|
|
return( lret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: longprodnum
|
|
//
|
|
// ARGUMENTS:
|
|
// long integer to factorialize.
|
|
// long integer representing base of answer.
|
|
//
|
|
// RETURN: Factorial of input in base PNUMBER form.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
PNUMBER longprodnum( IN long start, IN long stop, IN unsigned long nRadix )
|
|
|
|
{
|
|
PNUMBER lret=NULL;
|
|
PNUMBER tmp=NULL;
|
|
|
|
lret = longtonum( 1, nRadix );
|
|
|
|
while ( start <= stop )
|
|
{
|
|
if ( start )
|
|
{
|
|
tmp = longtonum( start, nRadix );
|
|
mulnum( &lret, tmp, nRadix );
|
|
destroynum( tmp );
|
|
}
|
|
start++;
|
|
}
|
|
return( lret );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: numpowlong
|
|
//
|
|
// ARGUMENTS: root as number power as long and nRadix of
|
|
// number.
|
|
//
|
|
// RETURN: None root is changed.
|
|
//
|
|
// DESCRIPTION: changes numeric representation of root to
|
|
// root ** power. Assumes nRadix is the nRadix of root.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void numpowlong( IN OUT PNUMBER *proot, IN long power,
|
|
IN unsigned long nRadix )
|
|
|
|
{
|
|
PNUMBER lret=NULL;
|
|
|
|
lret = longtonum( 1, nRadix );
|
|
|
|
while ( power > 0 )
|
|
{
|
|
if ( power & 1 )
|
|
{
|
|
mulnum( &lret, *proot, nRadix );
|
|
}
|
|
mulnum( proot, *proot, nRadix );
|
|
TRIMNUM(*proot);
|
|
power >>= 1;
|
|
}
|
|
destroynum( *proot );
|
|
*proot=lret;
|
|
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: ratpowlong
|
|
//
|
|
// ARGUMENTS: root as rational, power as long.
|
|
//
|
|
// RETURN: None root is changed.
|
|
//
|
|
// DESCRIPTION: changes rational representation of root to
|
|
// root ** power.
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void ratpowlong( IN OUT PRAT *proot, IN long power )
|
|
|
|
{
|
|
if ( power < 0 )
|
|
{
|
|
// Take the positive power and invert answer.
|
|
PNUMBER pnumtemp = NULL;
|
|
ratpowlong( proot, -power );
|
|
pnumtemp = (*proot)->pp;
|
|
(*proot)->pp = (*proot)->pq;
|
|
(*proot)->pq = pnumtemp;
|
|
}
|
|
else
|
|
{
|
|
PRAT lret=NULL;
|
|
|
|
lret = longtorat( 1 );
|
|
|
|
while ( power > 0 )
|
|
{
|
|
if ( power & 1 )
|
|
{
|
|
mulnumx( &(lret->pp), (*proot)->pp );
|
|
mulnumx( &(lret->pq), (*proot)->pq );
|
|
}
|
|
mulrat( proot, *proot );
|
|
trimit(&lret);
|
|
trimit(proot);
|
|
power >>= 1;
|
|
}
|
|
destroyrat( *proot );
|
|
*proot=lret;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//
|
|
// FUNCTION: longlog10
|
|
//
|
|
// ARGUMENTS: number as long.
|
|
//
|
|
// RETURN: returns int(log10(abs(number)+1)), useful in formatting output
|
|
//
|
|
//-----------------------------------------------------------------------------
|
|
|
|
long longlognRadix( long x )
|
|
|
|
{
|
|
long ret = 0;
|
|
x--;
|
|
if ( x < 0 )
|
|
{
|
|
x = -x;
|
|
}
|
|
while ( x )
|
|
{
|
|
ret++;
|
|
x /= nRadix;
|
|
}
|
|
return( ret );
|
|
}
|