346 lines
12 KiB
C
346 lines
12 KiB
C
/*
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* ratio.c
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*
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* functions for rational number cells.
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*
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* (c) 2017 Simon Brooke <simon@journeyman.cc>
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* Licensed under GPL version 2.0, or, at your option, any later version.
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*/
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#define _GNU_SOURCE
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#include <math.h>
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#include <stdio.h>
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#include "memory/conspage.h"
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#include "memory/consspaceobject.h"
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#include "debug.h"
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#include "ops/equal.h"
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#include "arith/integer.h"
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#include "ops/lispops.h"
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#include "arith/peano.h"
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#include "io/print.h"
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#include "arith/ratio.h"
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/**
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* return, as a int64_t, the greatest common divisor of `m` and `n`,
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*/
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int64_t greatest_common_divisor( int64_t m, int64_t n ) {
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int o;
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while ( m ) {
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o = m;
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m = n % m;
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n = o;
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}
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return o;
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}
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/**
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* return, as a int64_t, the least common multiple of `m` and `n`,
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*/
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int64_t least_common_multiple( int64_t m, int64_t n ) {
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return m / greatest_common_divisor( m, n ) * n;
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}
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struct cons_pointer simplify_ratio( struct cons_pointer pointer ) {
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struct cons_pointer result = pointer;
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struct cons_space_object cell = pointer2cell( pointer );
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struct cons_space_object dividend =
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pointer2cell( cell.payload.ratio.dividend );
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struct cons_space_object divisor =
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pointer2cell( cell.payload.ratio.divisor );
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if ( divisor.payload.integer.value == 1 ) {
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result = pointer2cell( pointer ).payload.ratio.dividend;
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} else {
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if ( ratiop( pointer ) ) {
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int64_t ddrv = dividend.payload.integer.value,
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drrv = divisor.payload.integer.value,
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gcd = greatest_common_divisor( ddrv, drrv );
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if ( gcd > 1 ) {
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if ( drrv / gcd == 1 ) {
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result = acquire_integer( ddrv / gcd, NIL );
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} else {
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result =
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make_ratio( acquire_integer( ddrv / gcd, NIL ),
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acquire_integer( drrv / gcd, NIL ) );
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}
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}
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}
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}
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return result;
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}
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/**
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* return a cons_pointer indicating a number which is the sum of
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* the ratios indicated by `arg1` and `arg2`.
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* @exception will return an exception if either `arg1` or `arg2` is not a
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* rational number.
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*/
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struct cons_pointer add_ratio_ratio( struct cons_pointer arg1,
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struct cons_pointer arg2 ) {
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struct cons_pointer r, result;
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debug_print( L"add_ratio_ratio( arg1 = ", DEBUG_ARITH );
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debug_print_object( arg1, DEBUG_ARITH );
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debug_print( L"; arg2 = ", DEBUG_ARITH );
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debug_print_object( arg2, DEBUG_ARITH );
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debug_print( L")\n", DEBUG_ARITH );
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if ( ratiop( arg1 ) && ratiop( arg2 ) ) {
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struct cons_space_object cell1 = pointer2cell( arg1 );
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struct cons_space_object cell2 = pointer2cell( arg2 );
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int64_t dd1v =
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pointer2cell( cell1.payload.ratio.dividend ).payload.integer.value,
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dd2v =
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pointer2cell( cell2.payload.ratio.dividend ).payload.integer.value,
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dr1v =
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pointer2cell( cell1.payload.ratio.divisor ).payload.integer.value,
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dr2v =
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pointer2cell( cell2.payload.ratio.divisor ).payload.integer.value,
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lcm = least_common_multiple( dr1v, dr2v ),
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m1 = lcm / dr1v, m2 = lcm / dr2v;
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debug_printf( DEBUG_ARITH, L"); lcm = %ld; m1 = %ld; m2 = %ld", lcm,
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m1, m2 );
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if ( dr1v == dr2v ) {
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r = make_ratio( acquire_integer( dd1v + dd2v, NIL ),
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cell1.payload.ratio.divisor );
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} else {
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struct cons_pointer dd1vm = acquire_integer( dd1v * m1, NIL ),
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dr1vm = acquire_integer( dr1v * m1, NIL ),
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dd2vm = acquire_integer( dd2v * m2, NIL ),
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dr2vm = acquire_integer( dr2v * m2, NIL ),
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r1 = make_ratio( dd1vm, dr1vm ),
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r2 = make_ratio( dd2vm, dr2vm );
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r = add_ratio_ratio( r1, r2 );
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if (!eq( r, r1)) { dec_ref( r1);}
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if (!eq( r, r2)) { dec_ref( r2);}
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/* because the references on dd1vm, dr1vm, dd2vm and dr2vm were
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* never incremented except when making r1 and r2, decrementing
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* r1 and r2 should be enought to garbage collect them. */
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}
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result = simplify_ratio( r );
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if ( !eq( r, result ) ) {
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dec_ref( r );
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}
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} else {
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result =
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throw_exception( make_cons( c_string_to_lisp_string
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( L"Shouldn't happen: bad arg to add_ratio_ratio" ),
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make_cons( arg1,
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make_cons( arg2, NIL ) ) ),
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NIL );
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}
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debug_print( L" => ", DEBUG_ARITH );
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debug_print_object( result, DEBUG_ARITH );
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debug_print( L"\n", DEBUG_ARITH );
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return result;
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}
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/**
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* return a cons_pointer indicating a number which is the sum of
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* the intger indicated by `intarg` and the ratio indicated by
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* `ratarg`.
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* @exception if either `intarg` or `ratarg` is not of the expected type.
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*/
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struct cons_pointer add_integer_ratio( struct cons_pointer intarg,
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struct cons_pointer ratarg ) {
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struct cons_pointer result;
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if ( integerp( intarg ) && ratiop( ratarg ) ) {
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// TODO: not longer works
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struct cons_pointer one = acquire_integer( 1, NIL ),
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ratio = make_ratio( intarg, one );
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result = add_ratio_ratio( ratio, ratarg );
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release_integer( one );
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dec_ref( ratio );
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} else {
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result =
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throw_exception( make_cons( c_string_to_lisp_string
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( L"Shouldn't happen: bad arg to add_integer_ratio" ),
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make_cons( intarg,
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make_cons( ratarg,
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NIL ) ) ), NIL );
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}
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return result;
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}
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/**
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* return a cons_pointer to a ratio which represents the value of the ratio
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* indicated by `arg1` divided by the ratio indicated by `arg2`.
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* @exception will return an exception if either `arg1` or `arg2` is not a
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* rational number.
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*/
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struct cons_pointer divide_ratio_ratio( struct cons_pointer arg1,
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struct cons_pointer arg2 ) {
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// TODO: this now has to work if `arg1` is an integer
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struct cons_pointer i =
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make_ratio( pointer2cell( arg2 ).payload.ratio.divisor,
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pointer2cell( arg2 ).payload.ratio.dividend ), result =
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multiply_ratio_ratio( arg1, i );
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dec_ref( i );
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return result;
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}
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/**
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* return a cons_pointer indicating a number which is the product of
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* the ratios indicated by `arg1` and `arg2`.
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* @exception will return an exception if either `arg1` or `arg2` is not a
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* rational number.
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*/
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struct cons_pointer multiply_ratio_ratio( struct
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cons_pointer arg1, struct
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cons_pointer arg2 ) {
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// TODO: this now has to work if arg1 is an integer
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struct cons_pointer result;
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debug_print( L"multiply_ratio_ratio( arg1 = ", DEBUG_ARITH );
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debug_print_object( arg1, DEBUG_ARITH );
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debug_print( L"; arg2 = ", DEBUG_ARITH );
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debug_print_object( arg2, DEBUG_ARITH );
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debug_print( L")\n", DEBUG_ARITH );
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if ( ratiop( arg1 ) && ratiop( arg2 ) ) {
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struct cons_space_object cell1 = pointer2cell( arg1 );
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struct cons_space_object cell2 = pointer2cell( arg2 );
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int64_t dd1v =
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pointer2cell( cell1.payload.ratio.dividend ).payload.integer.value,
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dd2v =
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pointer2cell( cell2.payload.ratio.dividend ).payload.integer.value,
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dr1v =
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pointer2cell( cell1.payload.ratio.divisor ).payload.integer.value,
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dr2v =
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pointer2cell( cell2.payload.ratio.divisor ).payload.integer.value,
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ddrv = dd1v * dd2v, drrv = dr1v * dr2v;
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struct cons_pointer dividend = acquire_integer( ddrv, NIL );
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struct cons_pointer divisor = acquire_integer( drrv, NIL );
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struct cons_pointer unsimplified =
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make_ratio( dividend, divisor);
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result = simplify_ratio( unsimplified );
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release_integer( dividend);
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release_integer( divisor);
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if ( !eq( unsimplified, result ) ) {
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dec_ref( unsimplified );
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}
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} else {
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result =
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throw_exception( c_string_to_lisp_string
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( L"Shouldn't happen: bad arg to multiply_ratio_ratio" ),
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NIL );
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}
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return result;
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}
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/**
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* return a cons_pointer indicating a number which is the product of
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* the intger indicated by `intarg` and the ratio indicated by
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* `ratarg`.
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* @exception if either `intarg` or `ratarg` is not of the expected type.
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*/
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struct cons_pointer multiply_integer_ratio( struct cons_pointer intarg,
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struct cons_pointer ratarg ) {
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struct cons_pointer result;
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if ( integerp( intarg ) && ratiop( ratarg ) ) {
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// TODO: no longer works; fix
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struct cons_pointer one = acquire_integer( 1, NIL ),
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ratio = make_ratio( intarg, one );
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result = multiply_ratio_ratio( ratio, ratarg );
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release_integer( one );
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} else {
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result =
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throw_exception( c_string_to_lisp_string
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( L"Shouldn't happen: bad arg to multiply_integer_ratio" ),
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NIL );
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}
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return result;
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}
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/**
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* return a cons_pointer indicating a number which is the difference of
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* the ratios indicated by `arg1` and `arg2`.
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* @exception will return an exception if either `arg1` or `arg2` is not a
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* rational number.
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*/
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struct cons_pointer subtract_ratio_ratio( struct cons_pointer arg1,
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struct cons_pointer arg2 ) {
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struct cons_pointer i = negative( arg2 ),
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result = add_ratio_ratio( arg1, i );
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dec_ref( i );
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return result;
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}
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/**
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* Construct a ratio frame from this `dividend` and `divisor`, expected to
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* be integers, in the context of the stack_frame indicated by this
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* `frame_pointer`.
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* @exception if either `dividend` or `divisor` is not an integer.
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*/
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struct cons_pointer make_ratio( struct cons_pointer dividend,
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struct cons_pointer divisor ) {
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struct cons_pointer result;
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if ( integerp( dividend ) && integerp( divisor ) ) {
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inc_ref( dividend );
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inc_ref( divisor );
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result = allocate_cell( RATIOTV );
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struct cons_space_object *cell = &pointer2cell( result );
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cell->payload.ratio.dividend = dividend;
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cell->payload.ratio.divisor = divisor;
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} else {
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result =
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throw_exception( c_string_to_lisp_string
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( L"Dividend and divisor of a ratio must be integers" ),
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NIL );
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}
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debug_dump_object( result, DEBUG_ARITH );
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return result;
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}
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/**
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* True if a and be are identical ratios, else false.
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*/
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bool equal_ratio_ratio( struct cons_pointer a, struct cons_pointer b ) {
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bool result = false;
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if ( ratiop( a ) && ratiop( b ) ) {
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struct cons_space_object *cell_a = &pointer2cell( a );
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struct cons_space_object *cell_b = &pointer2cell( b );
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result = equal_integer_integer( cell_a->payload.ratio.dividend,
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cell_b->payload.ratio.dividend ) &&
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equal_integer_integer( cell_a->payload.ratio.divisor,
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cell_b->payload.ratio.divisor );
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}
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return result;
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}
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