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Commitbb1d1b2

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Organized Simplifications and Edited Sgn Functions
1 parentb733886 commitbb1d1b2

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2 files changed

+371
-189
lines changed

2 files changed

+371
-189
lines changed

‎src/compute-engine/library/arithmetic.ts‎

Lines changed: 51 additions & 23 deletions
Original file line numberDiff line numberDiff line change
@@ -163,7 +163,10 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
163163
type:([x])=>x.type,
164164
sgn:([x])=>{
165165
if(x.is(0))return'zero';
166-
returnx.isNumberLiteral ?'positive' :'non-negative';
166+
if(x.isNumberLiteral){
167+
return'positive';
168+
}
169+
returnx.isNumberLiteral ?'positive' :'non-negative';//|x^2+1| fails
167170
},
168171
evaluate:([x])=>evaluateAbs(x),
169172
},
@@ -183,13 +186,12 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
183186
type:addType,
184187

185188
sgn:(ops)=>{
186-
if(ops.some((x)=>x.isReal===false||x.isNaN))return'unsigned';
189+
if(ops.some((x)=>x.isNaN))return'unsigned';
187190
if(ops.every((x)=>x.is(0)))return'zero';
188191
if(ops.every((x)=>x.isNonNegative))
189192
returnops.some((x)=>x.isPositive) ?'positive' :'non-negative';
190193
if(ops.every((x)=>x.isNonPositive))
191194
returnops.some((x)=>x.isNegative) ?'negative' :'non-positive';
192-
if(ops.every((x)=>x.isReal))return'real';
193195
returnundefined;
194196
},
195197

@@ -273,12 +275,14 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
273275

274276
sgn:(ops)=>{
275277
const[n,d]=[ops[0],ops[1]];
278+
consts=d.sgn;
279+
consts1=n.sgn;
276280
if(d.is(0))return'unsigned';
277-
if(d.is(0)===false&&n.is(0))return'zero';
278-
if(d.isPositive)returnn.sgn;
279-
if(d.isNegative)returnoppositeSgn(n.sgn);
280-
if(n.is(0)||(n.isFinite&&d.isInfinity))return'zero';
281-
if(!n.is(0)&&!d.is(0))return'not-zero';
281+
if(d.isPositive)returns1;
282+
if(d.isNegative)returnoppositeSgn(s1);
283+
if((n.is(0)&&s==='not-zero')||(n.isFinite&&d.isInfinity))
284+
return'zero';
285+
if(s1==='not-zero'&&s==='not-zero')return'not-zero';
282286
returnundefined;
283287
},
284288

@@ -653,7 +657,10 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
653657
:undefined;
654658
if(
655659
ops.some((x)=>x.isFinite===false||x.isFinite===undefined)&&
656-
ops.some((x)=>x.is(0)===undefined)
660+
ops.some((x)=>{
661+
consts=x.sgn;
662+
s!=='positive'&&s!=='negative'&&s!=='not-zero';
663+
})
657664
)
658665
returnundefined;
659666
if(ops.every((x)=>x.isPositive||x.isNegative)){
@@ -670,11 +677,17 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
670677
});
671678
returnsumNeg%2===0 ?'non-positive' :'non-negative';
672679
}
673-
if(ops.every((x)=>!x.is(0)))return'not-zero';
674-
if(ops.every((x)=>x.isReal))return'real';
680+
if(
681+
ops.every(
682+
(x)=>
683+
x.sgn==='not-zero'||
684+
x.sgn==='positive'||
685+
x.sgn==='negative'
686+
)
687+
)
688+
return'not-zero';
675689
returnundefined;
676690
},
677-
678691
evaluate:(ops,{ numericApproximation})=>
679692
// Use evaluate i both cases: do not introduce premature rounding errors
680693
numericApproximation
@@ -756,9 +769,13 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
756769
returna.sgn;
757770

758771
if(b.numerator.isEven&&b.denominator.isOdd){
759-
if(a.isReal)return!a.is(0) ?'positive' :'non-negative';
772+
if(a.isReal){
773+
lets=a.sgn;
774+
returns==='positive'||s==='not-zero'||s==='negative'
775+
?'positive'
776+
:'non-negative';
777+
}
760778
if(a.type==='imaginary')return'negative';
761-
return!a.is(0) ?'not-zero' :undefined;//already accounted for a.is(0)
762779
}
763780

764781
if(
@@ -847,19 +864,26 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
847864
sgn:([x,n])=>{
848865
// Note: we can't simplify this to a power, then get the sgn of that because this may cause an infinite loop
849866
if(x.isReal===false||n.isReal===false)return'unsigned';
850-
if(x.is(0))returnn.is(0) ?'unsigned' :'zero';
867+
if(x.is(0)){
868+
if(n.isNonPositive){
869+
return'unsigned';
870+
}
871+
if(n.isPositive)return'zero';
872+
}
851873
if(x.isPositive===true)return'positive';
852-
if(n.isOdd===true)return'negative';
853-
if(n.isEven===true)return'unsigned';
874+
if(x.isNonNegative===true)return'non-negative';
875+
if(n.isOdd===true||(n.numerator.isOdd&&n.denominator.isOdd)){
876+
returnx.sgn;
877+
}
878+
if(x.isNegative&&n.isOdd===false)return'unsigned';
854879
returnundefined;
855880
},
856881
canonical:(args,{ engine})=>{
857882
args=checkNumericArgs(engine,args,2);
858883
const[base,exp]=args;
859884
returncanonicalRoot(base,exp);
860885
},
861-
evaluate:([x,n],{ numericApproximation})=>
862-
root(x,n,{ numericApproximation}),
886+
evaluate:([x,n],{ numericApproximation})=>x.root(n),
863887
},
864888

865889
Round:{
@@ -882,7 +906,6 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
882906
if(x.isLess(0.5)&&x.isGreater(-0.5))return'zero';
883907
if(x.isNonNegative)return'non-negative';
884908
if(x.isNonPositive)return'non-positive';
885-
if(x.isReal)return'real';
886909
returnundefined;
887910
},
888911
evaluate:([x])=>
@@ -958,7 +981,7 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
958981
if(x.isPositive)return'positive';
959982
if(x.isNegative)return'unsigned';
960983
if(x.isNonNegative)return'non-negative';
961-
if(!x.is(0))return'not-zero';
984+
if(x.sgn==='not-zero')return'not-zero';
962985
returnundefined;
963986
},
964987
evaluate:([x],{ numericApproximation, engine})=>{
@@ -979,8 +1002,13 @@ export const ARITHMETIC_LIBRARY: IdentifierDefinitions[] = [
9791002
signature:'number -> number',
9801003
sgn:([x])=>{
9811004
if(x.is(0))return'zero';
982-
if(x.isReal)return!x.is(0) ?'positive' :'non-negative';
983-
if(x.type==='imaginary'||x.type==='complex')return'negative';
1005+
if(x.isReal){
1006+
lets=x.sgn;
1007+
returns==='not-zero'||s==='positive'||s==='negative'
1008+
?'positive'
1009+
:'non-negative';
1010+
}
1011+
if(x.type==='imaginary')return'negative';
9841012
if(x.isReal==false||x.isNaN)return'unsigned';
9851013
returnundefined;
9861014
},

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