485 lines
16 KiB
C
485 lines
16 KiB
C
/*
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* peano.c
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*
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* Basic peano arithmetic
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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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#include <ctype.h>
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#include <stdbool.h>
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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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#include <math.h>
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#include "consspaceobject.h"
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#include "conspage.h"
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#include "equal.h"
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#include "integer.h"
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#include "intern.h"
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#include "lispops.h"
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#include "print.h"
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#include "read.h"
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#include "real.h"
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#include "stack.h"
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long double to_long_double( struct cons_pointer arg );
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long int to_long_int( struct stack_frame *frame, struct cons_pointer arg );
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struct cons_pointer add_2( struct stack_frame *frame, struct cons_pointer arg1,
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struct cons_pointer arg2 );
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bool zerop( struct cons_pointer arg ) {
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bool result = false;
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struct cons_space_object cell = pointer2cell( arg );
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switch ( cell.tag.value ) {
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case INTEGERTV:
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result = cell.payload.integer.value == 0;
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break;
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case RATIOTV:
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result = zerop( cell.payload.ratio.dividend );
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break;
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case REALTV:
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result = ( cell.payload.real.value == 0 );
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break;
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}
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return result;
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}
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/**
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* TODO: cannot throw an exception out of here, which is a problem
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* if a ratio may legally have zero as a divisor, or something which is
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* not a number is passed in.
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*/
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long double to_long_double( struct cons_pointer arg ) {
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long double result = 0; /* not a number, as a long double */
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struct cons_space_object cell = pointer2cell( arg );
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switch ( cell.tag.value ) {
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case INTEGERTV:
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result = ( double ) cell.payload.integer.value;
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break;
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case RATIOTV:
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{
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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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result =
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( long double ) dividend.payload.integer.value /
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divisor.payload.integer.value;
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}
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break;
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case REALTV:
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result = cell.payload.real.value;
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break;
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default:
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result = NAN;
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break;
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}
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fputws( L"to_long_double( ", stderr );
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print( stderr, arg );
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fwprintf( stderr, L") => %lf\n", result );
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return result;
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}
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/**
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* TODO: cannot throw an exception out of here, which is a problem
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* if a ratio may legally have zero as a divisor, or something which is
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* not a number (or is a big number) is passed in.
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*/
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long int to_long_int( struct stack_frame *frame, struct cons_pointer arg ) {
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long int result = 0;
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struct cons_space_object cell = pointer2cell( arg );
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switch ( cell.tag.value ) {
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case INTEGERTV:
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result = cell.payload.integer.value;
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break;
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case RATIOTV:
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result = lroundl( to_long_double( arg ) );
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break;
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case REALTV:
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result = lroundl( cell.payload.real.value );
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break;
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}
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return result;
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}
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long int greatest_common_divisor( long int m, long int 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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long int least_common_multiple( long int m, long int n ) {
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return m / greatest_common_divisor( m, n ) * n;
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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`. If you pass non-ratios,
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* this is going to break horribly.
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*/
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struct cons_pointer add_ratio_ratio( struct stack_frame *frame,
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struct cons_pointer arg1,
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struct cons_pointer arg2 ) {
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fputws( L"add_ratio_ratio( arg1 = ", stderr );
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print( stderr, arg1 );
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fputws( L"; arg2 = ", stderr );
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print( stderr, arg2 );
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struct cons_pointer result;
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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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long int 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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fwprintf( stderr, L"); lcm = %ld; m1 = %ld; m2 = %ld", lcm, m1, m2 );
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if ( dr1v == dr2v ) {
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result =
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make_ratio( frame,
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make_integer( dd1v + dd2v ),
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cell1.payload.ratio.divisor );
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long int ddrv =
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pointer2cell( pointer2cell( result ).payload.ratio.
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dividend ).payload.integer.value, drrv =
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pointer2cell( pointer2cell( result ).payload.ratio.
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divisor ).payload.integer.value, gcd =
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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 = make_integer( ddrv / gcd );
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} else {
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result =
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make_ratio( frame, make_integer( ddrv / gcd ),
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make_integer( drrv / gcd ) );
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}
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}
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} else {
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result = add_ratio_ratio( frame,
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make_ratio( frame,
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make_integer( dd1v * m1 ),
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make_integer( dr1v * m1 ) ),
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make_ratio( frame,
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make_integer( dd2v * m2 ),
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make_integer( dr2v * m2 ) ) );
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}
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fputws( L" => ", stderr );
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print( stderr, result );
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fputws( L"\n", stderr );
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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`. If you pass non-ratios,
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* this is going to break horribly.
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*/
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struct cons_pointer add_integer_ratio( struct stack_frame *frame,
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struct cons_pointer intarg,
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struct cons_pointer ratarg ) {
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return add_ratio_ratio( frame,
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make_ratio( frame, intarg, make_integer( 1 ) ),
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ratarg );
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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 numbers indicated by `arg1` and `arg2`.
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*/
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struct cons_pointer add_2( struct stack_frame *frame, struct cons_pointer arg1,
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struct cons_pointer arg2 ) {
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struct cons_pointer result;
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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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fputws( L"add_2( arg1 = ", stderr );
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print( stderr, arg1 );
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fputws( L"; arg2 = ", stderr );
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print( stderr, arg2 );
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if ( zerop( arg1 ) ) {
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result = arg2;
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} else if ( zerop( arg2 ) ) {
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result = arg1;
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} else {
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switch ( cell1.tag.value ) {
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case EXCEPTIONTV:
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result = arg1;
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break;
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case INTEGERTV:
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switch ( cell2.tag.value ) {
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case EXCEPTIONTV:
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result = arg2;
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break;
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case INTEGERTV:
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result = make_integer( cell1.payload.integer.value +
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cell2.payload.integer.value );
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break;
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case RATIOTV:
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result = add_integer_ratio( frame, arg1, arg2 );
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break;
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case REALTV:
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result =
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make_real( to_long_double( arg1 ) +
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to_long_double( arg2 ) );
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break;
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default:
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result = lisp_throw( c_string_to_lisp_string
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( "Cannot add: not a number" ),
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frame );
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}
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break;
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case RATIOTV:
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switch ( cell2.tag.value ) {
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case EXCEPTIONTV:
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result = arg2;
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break;
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case INTEGERTV:
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result = add_integer_ratio( frame, arg2, arg1 );
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break;
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case RATIOTV:
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result = add_ratio_ratio( frame, arg1, arg2 );
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break;
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case REALTV:
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result =
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make_real( to_long_double( arg1 ) +
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to_long_double( arg2 ) );
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break;
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}
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break;
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case REALTV:
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result =
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make_real( to_long_double( arg1 ) +
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to_long_double( arg2 ) );
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break;
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default:
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result = lisp_throw( c_string_to_lisp_string
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( "Cannot add: not a number" ), frame );
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}
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}
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fputws( L"}; => ", stderr );
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print( stderr, arg2 );
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fputws( L"\n", stderr );
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return result;
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}
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/**
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* Add an indefinite number of numbers together
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* @param env the evaluation environment - ignored;
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* @param frame the stack frame.
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* @return a pointer to an integer or real.
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*/
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struct cons_pointer lisp_add( struct stack_frame
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*frame, struct
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cons_pointer env ) {
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struct cons_pointer result = make_integer( 0 );
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for ( int i = 0;
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i < args_in_frame &&
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!nilp( frame->arg[i] ) && !exceptionp( result ); i++ ) {
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result = add_2( frame, result, frame->arg[i] );
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}
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struct cons_pointer more = frame->more;
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while ( consp( more ) && !exceptionp( result ) ) {
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result = add_2( frame, result, c_car( more ) );
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more = c_cdr( more );
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}
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return result;
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}
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/**
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* Internal guts of multiply. Dark and mysterious.
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*/
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struct cons_pointer multiply_accumulate( struct
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cons_pointer arg, struct
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stack_frame
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*frame, long
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int
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*i_accumulator, long
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double
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*d_accumulator, int
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*is_int ) {
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struct cons_pointer result = NIL;
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struct cons_space_object cell = pointer2cell( arg );
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switch ( cell.tag.value ) {
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case INTEGERTV:
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( *i_accumulator ) *= cell.payload.integer.value;
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( *d_accumulator ) *= numeric_value( arg );
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break;
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case REALTV:
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( *d_accumulator ) *= cell.payload.real.value;
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( *is_int ) &= false;
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break;
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case EXCEPTIONTV:
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result = arg;
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break;
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default:
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result =
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lisp_throw
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( c_string_to_lisp_string
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( "Cannot multiply: not a number" ), frame );
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}
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return result;
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}
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/**
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* Multiply an indefinite number of numbers together
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* @param env the evaluation environment - ignored;
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* @param frame the stack frame.
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* @return a pointer to an integer or real.
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*/
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struct cons_pointer lisp_multiply( struct
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stack_frame
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*frame, struct
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cons_pointer env ) {
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struct cons_pointer result = NIL;
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long int i_accumulator = 1;
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long double d_accumulator = 1;
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int is_int = true;
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for ( int i = 0; i < args_in_frame && !nilp( frame->arg[i] )
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&& !exceptionp( result ); i++ ) {
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result =
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multiply_accumulate( frame->arg[i],
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frame,
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&i_accumulator, &d_accumulator, &is_int );
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}
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struct cons_pointer more = frame->more;
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while ( consp( more )
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&& !exceptionp( result ) ) {
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result =
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multiply_accumulate( c_car
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( more ),
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frame,
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&i_accumulator, &d_accumulator, &is_int );
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more = c_cdr( more );
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}
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if ( !exceptionp( result ) ) {
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if ( is_int ) {
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result = make_integer( i_accumulator );
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} else {
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result = make_real( d_accumulator );
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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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* Subtract one number from another.
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* @param env the evaluation environment - ignored;
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* @param frame the stack frame.
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* @return a pointer to an integer or real.
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*/
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struct cons_pointer lisp_subtract( struct
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stack_frame
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*frame, struct
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cons_pointer env ) {
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struct cons_pointer result = NIL;
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struct cons_space_object arg0 = pointer2cell( frame->arg[0] );
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struct cons_space_object arg1 = pointer2cell( frame->arg[1] );
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if ( integerp( frame->arg[0] )
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&& integerp( frame->arg[1] ) ) {
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result =
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make_integer( arg0.payload.integer.value
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- arg1.payload.integer.value );
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} else if ( realp( frame->arg[0] )
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&& realp( frame->arg[1] ) ) {
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result =
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make_real( arg0.payload.real.value - arg1.payload.real.value );
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} else if ( integerp( frame->arg[0] )
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&& realp( frame->arg[1] ) ) {
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result =
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make_real( numeric_value
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( frame->arg[0] ) - arg1.payload.real.value );
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} else if ( realp( frame->arg[0] )
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&& integerp( frame->arg[1] ) ) {
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result =
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make_real( arg0.payload.real.value -
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numeric_value( frame->arg[1] ) );
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} else {
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/* TODO: throw an exception */
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lisp_throw
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( c_string_to_lisp_string
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( "Cannot subtract: not a number" ), frame );
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}
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// and if not nilp[frame->arg[2]) we also have an error.
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return result;
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}
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/**
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* Divide one number by another.
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* @param env the evaluation environment - ignored;
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* @param frame the stack frame.
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* @return a pointer to an integer or real.
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*/
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struct cons_pointer lisp_divide( struct
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stack_frame
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*frame, struct
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cons_pointer env ) {
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struct cons_pointer result = NIL;
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struct cons_space_object arg0 = pointer2cell( frame->arg[0] );
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struct cons_space_object arg1 = pointer2cell( frame->arg[1] );
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if ( numberp( frame->arg[1] )
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&& numeric_value( frame->arg[1] ) == 0 ) {
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lisp_throw
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( c_string_to_lisp_string
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( "Cannot divide: divisor is zero" ), frame );
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} else if ( numberp( frame->arg[0] )
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&& numberp( frame->arg[1] ) ) {
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long int i = ( long int )
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numeric_value( frame->arg[0] ) / numeric_value( frame->arg[1] );
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long double r = ( long double )
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numeric_value( frame->arg[0] )
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/ numeric_value( frame->arg[1] );
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if ( fabsl( ( long double ) i - r ) < 0.0000000001 ) {
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result = make_integer( i );
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} else {
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result = make_real( r );
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}
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} else {
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lisp_throw
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( c_string_to_lisp_string
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( "Cannot divide: not a number" ), frame );
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}
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return result;
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}
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