Fix parsing of pow(), ToBaseN hangs, and three numeric-precision bugs (#625, #584, #602, #210, #561, #542)

Sources/AngouriMath/Convenience/MathS.cs

@@ -1,4 +1,4 @@
-//
+//
 // Copyright (c) 2019-2022 Angouri.
 // AngouriMath is licensed under MIT.
 // Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
@@ -3760,9 +3760,9 @@ public static ParsingResult Parse(string source)
         /// Console.WriteLine(ToBaseN(13.125m, 2));
         /// Console.WriteLine(ToBaseN(13.125m, 10));
         /// 
-        /// // uncomment when https://github.com/asc-community/AngouriMath/issues/584
-        /// // is fixed
-        /// // Console.WriteLine(ToBaseN(13.125m, 5));
+        /// // A repeating expansion is cut off at the configured decimal precision
+        /// // instead of hanging; see https://github.com/asc-community/AngouriMath/issues/584.
+        /// Console.WriteLine(ToBaseN(13.125m, 5).Substring(0, 12) + "...");
         /// 
         /// Console.WriteLine(ToBaseN(13.125m, 8));
         /// Console.WriteLine("-----------------------");
@@ -3778,6 +3778,7 @@ public static ParsingResult Parse(string source)
         /// 11.11
         /// 1101.001
         /// 13.125
+        /// 23.030303030...
         /// 15.1
         /// -----------------------
         /// 255
@@ -3806,9 +3807,9 @@ public static ParsingResult Parse(string source)
         /// Console.WriteLine(ToBaseN(13.125m, 2));
         /// Console.WriteLine(ToBaseN(13.125m, 10));
         /// 
-        /// // uncomment when https://github.com/asc-community/AngouriMath/issues/584
-        /// // is fixed
-        /// // Console.WriteLine(ToBaseN(13.125m, 5));
+        /// // A repeating expansion is cut off at the configured decimal precision
+        /// // instead of hanging; see issue 584.
+        /// Console.WriteLine(ToBaseN(13.125m, 5).Substring(0, 12) + "...");
         /// 
         /// Console.WriteLine(ToBaseN(13.125m, 8));
         /// Console.WriteLine("-----------------------");
@@ -3824,6 +3825,7 @@ public static ParsingResult Parse(string source)
         /// 11.11
         /// 1101.001
         /// 13.125
+        /// 23.030303030...
         /// 15.1
         /// -----------------------
         /// 255
@@ -5464,6 +5466,37 @@ public sealed record NewtonSetting
             public static Setting<EDecimal> PrecisionErrorZeroRange => precisionErrorZeroRange ??= EDecimal.Create(1, -16);
             [ThreadStatic] private static Setting<EDecimal>? precisionErrorZeroRange;
 
+            /// <summary>
+            /// The tolerance within which downcasting rounds a number onto a nearby integer.
+            /// </summary>
+            /// <remarks>
+            /// This is <see cref="PrecisionErrorZeroRange"/> whenever a caller has set it,
+            /// but its default of 1e-16 is far too coarse to be applied blindly: numbers are
+            /// evaluated to <see cref="DecimalPrecisionContext"/> digits, 100 by default, so
+            /// 1e-16 sits nowhere near the noise floor. Applying it destroyed every legitimate
+            /// small value -- <c>1e-20</c> parsed to zero and <c>e^(-40)</c> evaluated to zero.
+            /// Residuals genuinely left over by exact cancellation, such as the one from
+            /// <c>sin(pi)</c>, land around 1e-99, so half the working digits separates the two
+            /// cases with room to spare. Never looser than the setting's own default, so that
+            /// lowering the precision cannot silently widen the tolerance.
+            /// </remarks>
+            internal static EDecimal DowncastingTolerance
+            {
+                get
+                {
+                    var configured = PrecisionErrorZeroRange.Value;
+                    if (PrecisionErrorZeroRange.IsOverriden)
+                        return configured;
+                    var precision = DecimalPrecisionContext.Value.Precision;
+                    if (precision.IsZero)
+                        return configured;
+                    // Built from EIntegers throughout: the precision is user-supplied and
+                    // need not fit in an int.
+                    var derived = EDecimal.Create(EInteger.One, precision.Divide(2).Negate());
+                    return derived.LessThan(configured) ? derived : configured;
+                }
+            }
+
             /// <summary>
             /// If you only need analytical solutions and an empty set if no analytical solutions were found, disable Newton's method
             /// </summary>

Sources/AngouriMath/Convenience/SettingClass.cs

@@ -126,6 +126,14 @@ public TReturnType As<TReturnType>(T value, Func<TReturnType> action)
         /// </summary>
         public T Default { get; }
 
+        /// <summary>
+        /// Whether anyone has called <see cref="Set"/> on this setting, i.e. whether
+        /// <see cref="Value"/> is anything other than the value the constructor pushed.
+        /// Lets a default be treated as "nobody expressed an opinion" rather than as a
+        /// deliberate choice.
+        /// </summary>
+        internal bool IsOverriden => values.Count > 1;
+
         /// <summary>
         /// This tiny struct is needed to be under `using` operator, so that your settings
         /// are automatically rolled back on the end of your method
@@ -158,6 +166,8 @@ internal sealed class KeyStack<TKey, TValue>
     {
         private readonly List<(TKey key, TValue value)> list = new();
 
+        internal int Count => list.Count;
+
         internal TValue Peek() => list[^1].value;
 
         internal bool Remove(TKey key)

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -267,6 +267,7 @@ atom returns[Entity value]
     | '{' cset_args = cset_arguments '}' { $value = new ConditionalSet($cset_args.couple.variable, $cset_args.couple.predicate); }
     | '{' args = function_arguments '}' { $value = new FiniteSet((IEnumerable<Entity>)$args.list); }
     | 'log(' args = function_arguments ')' { $value = Assert("log", (1, 2), $args.list.Count) ? MathS.Log(10, $args.list[0]) : MathS.Log($args.list[0], $args.list[1]); }
+    | 'pow(' args = function_arguments ')' { Assert("pow", 2, $args.list.Count); $value = MathS.Pow($args.list[0], $args.list[1]); }
     | 'sqrt(' args = function_arguments ')' { Assert("sqrt", 1, $args.list.Count); $value = MathS.Sqrt($args.list[0]); }
     | 'cbrt(' args = function_arguments ')' { Assert("cbrt", 1, $args.list.Count); $value = MathS.Cbrt($args.list[0]); }
     | 'sqr(' args = function_arguments ')' { Assert("sqr", 1, $args.list.Count); $value = MathS.Sqr($args.list[0]); }

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -118,13 +118,14 @@ T__116=117
 T__117=118
 T__118=119
 T__119=120
-NEWLINE=121
-NUMBER=122
-SPECIALSET=123
-BOOLEAN=124
-VARIABLE=125
-COMMENT=126
-WS=127
+T__120=121
+NEWLINE=122
+NUMBER=123
+SPECIALSET=124
+BOOLEAN=125
+VARIABLE=126
+COMMENT=127
+WS=128
 '!'=1
 '^'=2
 '-'=3
@@ -168,80 +169,81 @@ WS=127
 '{'=41
 '}'=42
 'log('=43
-'sqrt('=44
-'cbrt('=45
-'sqr('=46
-'ln('=47
-'sin('=48
-'cos('=49
-'tan('=50
-'cotan('=51
-'cot('=52
-'sec('=53
-'cosec('=54
-'csc('=55
-'arcsin('=56
-'arccos('=57
-'arctan('=58
-'arccotan('=59
-'arcsec('=60
-'arccosec('=61
-'arccsc('=62
-'acsc('=63
-'asin('=64
-'acos('=65
-'atan('=66
-'acotan('=67
-'asec('=68
-'acosec('=69
-'acot('=70
-'arccot('=71
-'sinh('=72
-'sh('=73
-'cosh('=74
-'ch('=75
-'tanh('=76
-'th('=77
-'cotanh('=78
-'coth('=79
-'cth('=80
-'sech('=81
-'sch('=82
-'cosech('=83
-'csch('=84
-'asinh('=85
-'arsinh('=86
-'arsh('=87
-'acosh('=88
-'arcosh('=89
-'arch('=90
-'atanh('=91
-'artanh('=92
-'arth('=93
-'acoth('=94
-'arcoth('=95
-'acotanh('=96
-'arcotanh('=97
-'arcth('=98
-'asech('=99
-'arsech('=100
-'arsch('=101
-'acosech('=102
-'arcosech('=103
-'arcsch('=104
-'acsch('=105
-'gamma('=106
-'derivative('=107
-'integral('=108
-'limit('=109
-'limitleft('=110
-'limitright('=111
-'signum('=112
-'sgn('=113
-'sign('=114
-'abs('=115
-'phi('=116
-'domain('=117
-'piecewise('=118
-'apply('=119
-'lambda('=120
+'pow('=44
+'sqrt('=45
+'cbrt('=46
+'sqr('=47
+'ln('=48
+'sin('=49
+'cos('=50
+'tan('=51
+'cotan('=52
+'cot('=53
+'sec('=54
+'cosec('=55
+'csc('=56
+'arcsin('=57
+'arccos('=58
+'arctan('=59
+'arccotan('=60
+'arcsec('=61
+'arccosec('=62
+'arccsc('=63
+'acsc('=64
+'asin('=65
+'acos('=66
+'atan('=67
+'acotan('=68
+'asec('=69
+'acosec('=70
+'acot('=71
+'arccot('=72
+'sinh('=73
+'sh('=74
+'cosh('=75
+'ch('=76
+'tanh('=77
+'th('=78
+'cotanh('=79
+'coth('=80
+'cth('=81
+'sech('=82
+'sch('=83
+'cosech('=84
+'csch('=85
+'asinh('=86
+'arsinh('=87
+'arsh('=88
+'acosh('=89
+'arcosh('=90
+'arch('=91
+'atanh('=92
+'artanh('=93
+'arth('=94
+'acoth('=95
+'arcoth('=96
+'acotanh('=97
+'arcotanh('=98
+'arcth('=99
+'asech('=100
+'arsech('=101
+'arsch('=102
+'acosech('=103
+'arcosech('=104
+'arcsch('=105
+'acsch('=106
+'gamma('=107
+'derivative('=108
+'integral('=109
+'limit('=110
+'limitleft('=111
+'limitright('=112
+'signum('=113
+'sgn('=114
+'sign('=115
+'abs('=116
+'phi('=117
+'domain('=118
+'piecewise('=119
+'apply('=120
+'lambda('=121