correct ln, exp and arg on decimal values

fixes #1059.

This commit also makes isclose work with complex values: it only checks
the absolute tolerance.

runtime/scripts/jme-builtins.js

@@ -1016,8 +1016,9 @@ newBuiltin('mod', [TDecimal,TDecimal], TDecimal, function(a,b) {
     }
     return m;
 });
-newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.re.exp(); });
-newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.re.ln(); });
+newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.exp(); });
+newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.ln(); });
+newBuiltin('arg', [TDecimal], TDecimal, function(a) { return a.argument(); } );
 newBuiltin('countsigfigs',[TDecimal], TInt, function(a) {return a.re.countSigFigs(); });
 newBuiltin('round',[TDecimal], TDecimal, function(a) {return a.round(); });
 newBuiltin('sin',[TDecimal], TDecimal, function(a) {return a.re.sin(); });

runtime/scripts/math.js

@@ -510,6 +510,11 @@ var math = Numbas.math = /** @lends Numbas.math */ {
         }
         rel_tol = rel_tol===undefined ? 1e-15 : rel_tol;
         abs_tol = abs_tol===undefined ? 1e-15: abs_tol;
+
+        if(a.complex || b.complex) {
+            return math.abs(math.sub(a,b)) < abs_tol;
+        }
+
         return Math.abs(a-b) <= Math.max( rel_tol * Math.max(Math.abs(a), Math.abs(b)), abs_tol );
     },
 
@@ -2616,8 +2621,14 @@ ComplexDecimal.prototype = {
     },
 
     ln: function() {
-        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument());
+        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument().re);
     },
+
+    exp: function() {
+        var r = this.re.exp();
+        return new ComplexDecimal(r.times(Decimal.cos(this.im)), r.times(Decimal.sin(this.im)));
+    },
+
     isInt: function() {
         return this.re.isInt() && this.im.isInt();
     },

tests/jme-runtime.js

@@ -2685,6 +2685,9 @@ var math = Numbas.math = /** @lends Numbas.math */ {
         }
         rel_tol = rel_tol===undefined ? 1e-15 : rel_tol;
         abs_tol = abs_tol===undefined ? 1e-15: abs_tol;
+        if(a.complex || b.complex) {
+            return math.abs(math.sub(a,b)) < abs_tol;
+        }
         return Math.abs(a-b) <= Math.max( rel_tol * Math.max(Math.abs(a), Math.abs(b)), abs_tol );
     },
 
@@ -4791,8 +4794,14 @@ ComplexDecimal.prototype = {
     },
 
     ln: function() {
-        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument());
+        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument().re);
     },
+
+    exp: function() {
+        var r = this.re.exp();
+        return new ComplexDecimal(r.times(Decimal.cos(this.im)), r.times(Decimal.sin(this.im)));
+    },
+
     isInt: function() {
         return this.re.isInt() && this.im.isInt();
     },
@@ -14126,8 +14135,9 @@ newBuiltin('mod', [TDecimal,TDecimal], TDecimal, function(a,b) {
     }
     return m;
 });
-newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.re.exp(); });
-newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.re.ln(); });
+newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.exp(); });
+newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.ln(); });
+newBuiltin('arg', [TDecimal], TDecimal, function(a) { return a.argument(); } );
 newBuiltin('countsigfigs',[TDecimal], TInt, function(a) {return a.re.countSigFigs(); });
 newBuiltin('round',[TDecimal], TDecimal, function(a) {return a.round(); });
 newBuiltin('sin',[TDecimal], TDecimal, function(a) {return a.re.sin(); });

tests/jme/jme-tests.mjs

@@ -1063,6 +1063,8 @@ Numbas.queueScript('jme_tests',['qunit','jme','jme-rules','jme-display','jme-cal
         closeEqual(assert, evaluate('exp(5)').value,Math.exp(5),'exp(5)');
         closeEqual(assert, evaluate('exp(-2)').value,Math.exp(-2),'exp(-2)');
         deepCloseEqual(assert, evaluate('exp(4-i)').value,math.complex(Math.exp(4)*Math.cos(-1),Math.exp(4)*Math.sin(-1)),'exp(4-i)');
+        assert.ok(evaluate('isclose(ln(dec(-e)), dec(ln(e)) - dec(pi)*i)').value, 'ln(dec(-e))');
+        assert.ok(evaluate('isclose(exp(dec(pi/2)*i), i)').value, 'exp(dec(pi/2)*i)');
 
         closeEqual(assert, evaluate('fact(0)').value,1,'fact(0)');
         closeEqual(assert, evaluate('fact(1)').value,1,'fact(1)');

tests/numbas-runtime.js

@@ -2686,6 +2686,9 @@ var math = Numbas.math = /** @lends Numbas.math */ {
         }
         rel_tol = rel_tol===undefined ? 1e-15 : rel_tol;
         abs_tol = abs_tol===undefined ? 1e-15: abs_tol;
+        if(a.complex || b.complex) {
+            return math.abs(math.sub(a,b)) < abs_tol;
+        }
         return Math.abs(a-b) <= Math.max( rel_tol * Math.max(Math.abs(a), Math.abs(b)), abs_tol );
     },
 
@@ -4792,8 +4795,14 @@ ComplexDecimal.prototype = {
     },
 
     ln: function() {
-        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument());
+        return new ComplexDecimal(this.absoluteValue().re.ln(), this.argument().re);
     },
+
+    exp: function() {
+        var r = this.re.exp();
+        return new ComplexDecimal(r.times(Decimal.cos(this.im)), r.times(Decimal.sin(this.im)));
+    },
+
     isInt: function() {
         return this.re.isInt() && this.im.isInt();
     },
@@ -14114,8 +14123,9 @@ newBuiltin('mod', [TDecimal,TDecimal], TDecimal, function(a,b) {
     }
     return m;
 });
-newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.re.exp(); });
-newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.re.ln(); });
+newBuiltin('exp',[TDecimal], TDecimal, function(a) {return a.exp(); });
+newBuiltin('ln',[TDecimal], TDecimal, function(a) {return a.ln(); });
+newBuiltin('arg', [TDecimal], TDecimal, function(a) { return a.argument(); } );
 newBuiltin('countsigfigs',[TDecimal], TInt, function(a) {return a.re.countSigFigs(); });
 newBuiltin('round',[TDecimal], TDecimal, function(a) {return a.round(); });
 newBuiltin('sin',[TDecimal], TDecimal, function(a) {return a.re.sin(); });
@@ -28884,7 +28894,7 @@ Numbas.queueScript('answer-widgets',['knockout','util','jme','jme-display'],func
                     return '';
                 }
                 if(util.isNumber(n, vm.allowFractions, vm.allowedNotationStyles)) {
-                    return n;
+                    return n + '';
                 }
                 return Numbas.math.niceNumber(n,{style: vm.allowedNotationStyles[0]}) || '';
             }