Powers and remainders in the calculator (closes #3)

internal/calc gets its own tokenizer and precedence-climbing parser in
place of go/parser, which cannot express a power operator; go/constant
still computes. ^ (also **) binds tighter than * / % and a sign on its
left, and groups to the right. % takes the sign of the divisor and is
exact on decimals. A whole exponent is computed exactly while the
result's numerator and denominator stay within 4096 bits; otherwise,
and for a fractional exponent, in float64. A remainder, or the sign of
a negative base's power, that depends on a value go/constant holds
rounded is refused as too large. The welcome text and the replies
mention the new operators; a negative base with a fractional exponent
gets its own reply.

Model: opus-5-5

internal/bot/bot.go

@@ -22,7 +22,7 @@ import (
 const DisplayName = "calc"
 
 // Welcome is sent to everyone whose contact request the bot accepts.
-const Welcome = "Send me arithmetic, such as 2 + 2 or 5 * 5/2, " +
+const Welcome = "Send me arithmetic, such as 2 + 2, 5 * 5/2, 2^10 or 7 % 3, " +
 	"and I will reply with the result."
 
 const (
@@ -223,8 +223,10 @@ func Reply(text string) string {
 		return "I cannot divide by zero."
 	case errors.Is(err, calc.ErrTooLarge):
 		return "The result is too large for me."
+	case errors.Is(err, calc.ErrNoRealResult):
+		return "A negative number to a fractional power has no real result."
 	default:
-		return "I only understand arithmetic: numbers, + - * / and " +
-			"parentheses, such as 5 * 5/2."
+		return "I only understand arithmetic: numbers, + - * /, ^ for a power, " +
+			"% for a remainder, and parentheses, such as 5 * 5/2 or 2^10."
 	}
 }

internal/bot/bot_test.go

@@ -16,6 +16,8 @@ func TestReply(t *testing.T) {
 	for in, want := range map[string]string{
 		"2 + 2":   "4",
 		"5 * 5/2": "12.5",
+		"2^10":    "1024",
+		"7 % 3":   "1",
 	} {
 		if got := bot.Reply(in); got != want {
 			t.Errorf("Reply(%q) = %q, want %q", in, got, want)
@@ -23,9 +25,10 @@ func TestReply(t *testing.T) {
 	}
 
 	for in, want := range map[string]string{
-		"hello": "I only understand arithmetic",
-		"1 / 0": "I cannot divide by zero.",
-		"1e400": "The result is too large for me.",
+		"hello":    "I only understand arithmetic",
+		"1 / 0":    "I cannot divide by zero.",
+		"1e400":    "The result is too large for me.",
+		"(-8)^0.5": "A negative number to a fractional power has no real",
 		strings.Repeat("1+", calc.MaxInputLength) + "1": "That is too long for me",
 	} {
 		if got := bot.Reply(in); !strings.HasPrefix(got, want) {