add parseFraction to Rational struct (round trip toFractionString)

engine/src/Rational.zig

@@ -622,6 +622,45 @@ pub fn toFractionString(self: Rational, allocator: Allocator) Error![]u8 {
         Error.OutOfMemory;
 }
 
+/// The inverse of `toFractionString`, at any size: `"-781250/12573"`, `"7"`.
+///
+/// `parse` caps literals at 512 digits, which is right for what a person types and
+/// wrong for a value the engine produced itself: `factorial(1000)` has 2,568 digits and
+/// has to come back exactly when a saved session is loaded. Only the canonical form is
+/// accepted - an optional minus, digits, and optionally a slash and more digits - and
+/// the result is reduced, so an unreduced fraction is still read as the right value.
+pub fn parseFraction(allocator: Allocator, text: []const u8) Error!Rational {
+    const slash = std.mem.indexOfScalar(u8, text, '/');
+    const num_text = if (slash) |s| text[0..s] else text;
+    const den_text = if (slash) |s| text[s + 1 ..] else "1";
+    const magnitude = if (num_text.len > 0 and num_text[0] == '-') num_text[1..] else num_text;
+    if (!allDigits(magnitude) or !allDigits(den_text)) return Error.InvalidNumber;
+
+    var num = try Managed.init(allocator);
+    errdefer num.deinit();
+    try setDecimal(&num, num_text);
+    var den = try Managed.init(allocator);
+    errdefer den.deinit();
+    try setDecimal(&den, den_text);
+    return finish(allocator, &num, &den);
+}
+
+fn allDigits(text: []const u8) bool {
+    if (text.len == 0) return false;
+    for (text) |c| {
+        if (!std.ascii.isDigit(c)) return false;
+    }
+    return true;
+}
+
+fn setDecimal(value: *Managed, text: []const u8) Error!void {
+    value.setString(10, text) catch |err| return switch (err) {
+        error.OutOfMemory => Error.OutOfMemory,
+        // Unreachable after `allDigits`, and reported rather than asserted.
+        else => Error.InvalidNumber,
+    };
+}
+
 pub const DecimalResult = struct {
     /// Decimal text. Caller owns the memory.
     text: []u8,
@@ -2124,3 +2163,43 @@ fn bodyScientificRendering(a: Allocator) anyerror!void {
 test "OOM safety: scientific rendering" {
     try oomSweep(bodyScientificRendering);
 }
+
+// -- parseFraction --
+
+test "parseFraction reads back what toFractionString writes, at any size" {
+    for ([_][]const u8{ "0", "7", "-7", "1/3", "-1/3", "781250/12573" }) |text| {
+        var r = try parseFraction(alloc, text);
+        defer r.deinit();
+        try expectFrac(text, r);
+    }
+
+    // Far past `parse`'s 512-digit limit: a value the engine can produce must load.
+    const digits = "9" ** 3000;
+    // Over 2, because 10^3000 - 1 is odd: over 7 it would reduce, since 7 divides it.
+    var big = try parseFraction(alloc, digits ++ "/2");
+    defer big.deinit();
+    const back = try big.toFractionString(alloc);
+    defer alloc.free(back);
+    try testing.expectEqualStrings(digits ++ "/2", back);
+    try testing.expectError(Error.TooManyDigits, parse(alloc, digits));
+}
+
+test "parseFraction reduces, and refuses anything but the canonical form" {
+    var half = try parseFraction(alloc, "2/4");
+    defer half.deinit();
+    try expectFrac("1/2", half);
+
+    try testing.expectError(Error.DivisionByZero, parseFraction(alloc, "1/0"));
+    for ([_][]const u8{ "", "-", "1/", "/2", "1/-2", "+1", "1.5", "1e3", "1 / 2", "0x10", "--1" }) |text| {
+        try testing.expectError(Error.InvalidNumber, parseFraction(alloc, text));
+    }
+}
+
+test "parseFraction releases everything on any allocation failure" {
+    try testing.checkAllAllocationFailures(testing.allocator, struct {
+        fn run(a: Allocator) !void {
+            var r = try parseFraction(a, "-123456789012345678901234567890/98765432109876543210");
+            r.deinit();
+        }
+    }.run, .{});
+}