Use [1 1>@0.inf as the canonical not-a-number

ref #320

documentation/interchange.md

@@ -109,16 +109,16 @@ To support tempering after interchanging data, the special `1°` basis element i
 ```
 
 ### Not-a-number
-The special token `nan` indicates a value that can't be interpreted as an interval.
+The special combination `[1 1>@0.inf` indicates a value that can't be interpreted as an interval.
 ```c
-nan "asin(2)" niente
+[1 1>@0.inf "asin(2)" niente
 ```
 
 ## Example
 See [examples/interchange.sw](https://github.com/xenharmonic-devs/sonic-weave/blob/main/examples/interchange.sw) for various extreme values supported by the original SonicWeave runtime.
 
 ```c
-// Created using SonicWeave 0.0.37
+// Created using SonicWeave 0.1.0
 
 "Various values to test the .swi interchange format"
 
@@ -151,5 +151,5 @@ See [examples/interchange.sw](https://github.com/xenharmonic-devs/sonic-weave/bl
 [-5 1 5/2 1 1>@1°.Hz.2.3.37 "" niente
 [1>@inf "infinity" niente
 [1 1>@-1.inf "negative infinity" niente
-nan "not-a-number" niente
+[1 1>@0.inf "not-a-number" niente
 ```

src/__tests__/cli.spec.ts

@@ -14,7 +14,7 @@ describe('Interchange format', () => {
 
   it('has representation for nan', () => {
     const result = toSonicWeaveInterchange('nan');
-    expect(result).toContain('nan');
+    expect(result).toContain('[1 1>@0.inf');
   });
 
   it('has representation for negative infinity Hz', () => {
@@ -24,6 +24,6 @@ describe('Interchange format', () => {
 
   it('has representation for nan Hz (normalizes)', () => {
     const result = toSonicWeaveInterchange('nan * 1 Hz');
-    expect(result).toContain('nan');
+    expect(result).toContain('[1 1>@0.inf');
   });
 });

src/interval.ts

@@ -1078,7 +1078,7 @@ export class Interval {
    * @param interchange Boolean flag to format everything explicitly.
    * @returns A virtual monzo literal.
    */
-  asMonzoLiteral(interchange = false): MonzoLiteral | undefined {
+  asMonzoLiteral(interchange = false): MonzoLiteral {
     let node: MonzoLiteral;
     if (
       interchange &&
@@ -1089,11 +1089,7 @@ export class Interval {
       clone.numberOfComponents = NUM_INTERCHANGE_COMPONENTS;
       node = clone.asMonzoLiteral();
     } else {
-      const maybeNode = this.value.asMonzoLiteral();
-      if (maybeNode === undefined) {
-        return undefined;
-      }
-      node = maybeNode;
+      node = this.value.asMonzoLiteral();
     }
     if (
       interchange &&
@@ -1129,11 +1125,7 @@ export class Interval {
         result = `${this.steps}°`;
       } else {
         const node = this.asMonzoLiteral();
-        if (node) {
-          result = literalToString(node);
-        } else {
-          result = this.value.toString();
-        }
+        result = literalToString(node);
       }
       if (this.domain === 'linear') {
         return `linear(${result})`;

src/monzo.ts

@@ -745,12 +745,16 @@ export class TimeReal {
    * @param interchange Boolean flag to use Hz basis for the absolute echelon.
    * @returns Monzo literal.
    */
-  asMonzoLiteral(interchange = false): MonzoLiteral | undefined {
-    if (isNaN(this.value)) {
-      return undefined;
-    }
+  asMonzoLiteral(interchange = false): MonzoLiteral {
     const components: VectorComponent[] = [];
     const basis: BasisElement[] = [];
+    if (isNaN(this.value)) {
+      basis.push({numerator: 0, denominator: null, radical: false});
+      components.push({sign: '', left: 1, right: '', exponent: null});
+      basis.push('inf');
+      components.push({sign: '', left: 1, right: '', exponent: null});
+      return {type: 'MonzoLiteral', components, ups: 0, lifts: 0, basis};
+    }
     if (interchange) {
       if (this.timeExponent) {
         basis.push('Hz');
@@ -817,7 +821,7 @@ export class TimeReal {
    * Obtain an AST node representing the time monzo as a monzo literal suitable for interchange between programs.
    * @returns Monzo literal.
    */
-  asInterchangeLiteral(): MonzoLiteral | undefined {
+  asInterchangeLiteral(): MonzoLiteral {
     return this.asMonzoLiteral(true);
   }
 

src/parser/__tests__/expression.spec.ts

@@ -2410,4 +2410,10 @@ describe('Poor grammar / Fun with "<"', () => {
     expect(interval.valueOf()).toBe(0);
     expect(interval.value).toBeInstanceOf(TimeReal);
   });
+
+  it('parses the universal not-a-number', () => {
+    const interval = evaluate('[1 1>@0.inf') as Interval;
+    expect(interval.valueOf()).toBeNaN();
+    expect(interval.value).toBeInstanceOf(TimeReal);
+  });
 });