✨ feat(simplify): Add fraction simplification method.

Author: make-github-pseudonymous-again

src/index.js

@@ -4,3 +4,4 @@ export * from './mul' ;
 export * from './sub' ;
 export * from './cmp' ;
 export * from './cmp_no_bounds' ;
+export * from './simplify' ;

src/simplify.js

@@ -0,0 +1,9 @@
+export function _simplify ( { egcd , sgn , neg } ) {
+	return function ( a , b ) {
+		const { u , v } = egcd(a , b) ;
+		return [
+			sgn(v) === sgn(a) ? v : neg(v) ,
+			sgn(u) === sgn(b) ? u : neg(u)
+		] ;
+	} ;
+}

test/src/core.js

@@ -1,16 +1,15 @@
 import test from 'ava';
-import { _add , _sub , _mul , _div , _cmp , _cmp_no_bounds } from '../../src';
+import { _add , _sub , _mul , _div , _cmp , _cmp_no_bounds , _simplify } from '../../src';
 
 import int from 'int' ;
 import { ZZ } from '@aureooms/js-integer' ;
 
 const GOOGOL = '10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000' ;
 
-function macro ( t , alu , [ [ _x , _y , factory ] , a , b , c , d , e ] ) {
+function binary ( t , alu , [ [ _x , _y , factory ] , a , b , c , d , e ] ) {
 
 	const apply = factory( alu );
 
-	//const repr = x => `${alu.str(x[0])} / ${alu.str(x[1])}` ;
 	const num  = x => Number(alu.str(x[0])) / Number(alu.str(x[1])) ;
 
 	const a0 = alu.reg(a);
@@ -25,10 +24,29 @@ function macro ( t , alu , [ [ _x , _y , factory ] , a , b , c , d , e ] ) {
 
 }
 
-macro.title = ( _ , alu , [ [ name , op , impl ] , a , b , c , d , e] ) => {
+binary.title = ( _ , alu , [ [ name , op , impl ] , a , b , c , d , e] ) => {
 	return `${name}<${impl.name}, ${alu.name}> ${a}/${b} ${op} ${c}/${d} = ${e}` ;
 } ;
 
+function unary ( t , alu , [ [ _x , _y , factory ] , a , b , e ] ) {
+
+	const apply = factory( alu );
+
+	const repr = x => `${alu.str(x[0])}/${alu.str(x[1])}` ;
+
+	const _a = alu.reg(a);
+	const _b = alu.reg(b);
+
+	const z = apply( _a , _b ) ;
+
+	t.is(e, repr(z));
+
+}
+
+unary.title = ( _ , alu , [ [ name , impl ] , a , b , e ] ) => {
+	return `${name}<${impl.name}, ${alu.name}> ${name}(${a}/${b}) = ${e}` ;
+} ;
+
 const ALU = [
 	{
 		name : 'int',
@@ -42,6 +60,7 @@ const ALU = [
 		lt0 : x => x.lt(0),
 		cmp  : (a,b) => a.cmp(b),
 		neg : x => x.neg(),
+		sgn : x => x.cmp(0),
 		divmod : (a,b) => [a.div(b), a.mod(b)],
 	},
 	{
@@ -55,16 +74,19 @@ const ALU = [
 		jz  : x => x.iszero(),
 		lt0 : x => x.sign() < 0,
 		cmp  : (a,b) => a.cmp(b),
+		sgn : x => x.sign(),
 		neg : x => x.opposite(),
 		divmod : (a,b) => a.divmod(b),
+		egcd : (a,b) => a.egcd(b),
 	}
 ];
 
-const add = [ 'add' , '+' , [ _add ] ] ;
-const sub = [ 'sub' , '-' , [ _sub ] ] ;
-const mul = [ 'mul' , '*' , [ _mul ] ] ;
-const div = [ 'div' , '/' , [ _div ] ] ;
-const cmp = [ 'cmp' , '~' , [ _cmp , _cmp_no_bounds ] ] ;
+const add = [ 'add' , '+' , [ _add ] , binary ] ;
+const sub = [ 'sub' , '-' , [ _sub ] , binary ] ;
+const mul = [ 'mul' , '*' , [ _mul ] , binary ] ;
+const div = [ 'div' , '/' , [ _div ] , binary ] ;
+const cmp = [ 'cmp' , '~' , [ _cmp , _cmp_no_bounds ] , binary ] ;
+const simplify = [ 'simplify' , '=' , [ _simplify ] , unary , alu => alu.egcd ] ;
 
 const PARAMS = [
 
@@ -131,9 +153,23 @@ const PARAMS = [
 	[ cmp , GOOGOL, '3', GOOGOL, '3', 0 ] ,
 	[ cmp , GOOGOL, GOOGOL, GOOGOL, GOOGOL, 0 ] ,
 
+	[ simplify , GOOGOL, GOOGOL, '1/1' ] ,
+	[ simplify , '7', '14', '1/2' ] ,
+	[ simplify , '-7', '14', '-1/2' ] ,
+	[ simplify , '170141183460469231731687303715884105729' , '56713727820156410577229101238628035243' , '3/1' ] ,
+	[ simplify , '56713727820156410577229101238628035243' , '170141183460469231731687303715884105729' , '1/3' ] ,
+	[ simplify , '170141183460469231731687303715884105729' , '3' , '56713727820156410577229101238628035243/1' ] ,
+	[ simplify , '3' , '170141183460469231731687303715884105729' , '1/56713727820156410577229101238628035243' ] ,
+	[ simplify , '-170141183460469231731687303715884105729' , '56713727820156410577229101238628035243' , '-3/1' ] ,
+	[ simplify , '-56713727820156410577229101238628035243' , '170141183460469231731687303715884105729' , '-1/3' ] ,
+	[ simplify , '-170141183460469231731687303715884105729' , '3' , '-56713727820156410577229101238628035243/1' ] ,
+	[ simplify , '-3' , '170141183460469231731687303715884105729' , '-1/56713727820156410577229101238628035243' ] ,
+
 ] ;
 
 for (const alu of ALU)
-for (const [[name, symbol, implementations], ...params] of PARAMS)
-for (const factory of implementations)
-	test(macro, alu, [[name, symbol, factory], ...params]);
+for (const [[name, symbol, implementations, macro, predicate], ...params] of PARAMS)
+if (!predicate || predicate(alu)) {
+	for (const factory of implementations)
+		test(macro, alu, [[name, symbol, factory], ...params]);
+}