diff --git a/AGENTS.md b/AGENTS.md
index 6fc879a..5c0a286 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -121,7 +121,7 @@ Do not weaken them.
cmd/simplexcalc/ main(), a single call into internal/cli
internal/api/ the HTTP API: its credential, headers and endpoints
internal/bot/ startup, address setup, and the reply to a message
-internal/calc/ the arithmetic: go/parser and go/constant
+internal/calc/ the arithmetic: its own parser, and go/constant
internal/cli/ cobra command tree: run and version
internal/config/ viper-backed configuration; the abort-on-garbage rule
internal/logger/ log/slog, JSON always
diff --git a/README.md b/README.md
index 7e30288..e8eac27 100644
--- a/README.md
+++ b/README.md
@@ -5,9 +5,10 @@ SimpleX Chat network: it accepts every contact request and answers
arithmetic such as `2 + 2` with the result.
Send it `2 + 2` and it replies `4`; send `5 * 5/2` and it replies
-`12.5`. It understands decimal numbers, `+ - * /`, unary minus and
-parentheses, and computes exactly, so `0.1 + 0.2` is `0.3`. Anything
-else gets a short explanation instead of a result.
+`12.5`. It understands decimal numbers, `+ - * /`, powers written `2^10`
+or `2**10`, remainders written `7 % 3`, signs and parentheses, and
+computes exactly, so `0.1 + 0.2` is `0.3`. Anything else gets a short
+explanation instead of a result.
## Getting Started
@@ -232,16 +233,33 @@ container.
- **Replies**: for each text message a contact sends in a direct chat,
the bot sends back the result, as a reply quoting the message. Group
messages, files and the bot's own messages are ignored.
-- **Arithmetic** (`internal/calc`): the text is parsed as a Go
- expression with `go/parser`, and only numbers, `+ - * /`, unary signs
- and parentheses are evaluated; anything else in the syntax tree is
- refused. `go/constant` computes with exact rationals. Numbers are read
- as decimal, so `010` is ten. Input over 256 bytes is refused, so a
+- **Arithmetic** (`internal/calc`): a small parser of its own reads
+ numbers, `+ - * / % ^`, signs and parentheses, and refuses anything
+ else. `go/constant` computes with exact rationals. `^`, also written
+ `**`, is a power: it binds tighter than `*`, `/`, `%` and a sign on
+ its left, and groups to the right, so `2^3^2` is `512`, `-2^2` is
+ `-4`, `(-2)^2` is `4` and `2^-1` is `0.5`. `%` is the remainder and
+ ranks with `*` and `/`; its result takes the sign of the divisor, as
+ in Python, so `7 % 3` is `1`, `-7 % 3` is `2` and `7.5 % 2` is `1.5`.
+ A power with a whole exponent is exact, so `0.1^2` is `0.01` and
+ `2^-1400 * 2^1400` is `1`, unless `go/constant` could hold the result
+ only rounded; that power, and one with a fractional exponent, is
+ computed as a double, so `2^0.5` is `1.4142135623730951`. A negative
+ number to a fractional power is refused, as having no real result.
+ Numbers are read as decimal, so `010` is ten. Input over 256 bytes is
+ refused, exact powers are capped, and every number is held as a
+ fraction, whole numbers too, under the 4096-bit limit below, so a
message cannot make the bot do unbounded work. Whole numbers below
1021 are written exactly; other results in the shortest
form that reads back as the same double, in exponent notation from
- 1021 up and below 10-6. A result beyond the
- range of a double is refused as too large.
+ 1021 up and below 10-6. Refused as too large or
+ too small: any number whose numerator or denominator reaches 4096
+ bits, wherever it appears, as `go/constant` rounds a fraction that
+ grows that large (`1e-1300 + 1`); a power computed as a double whose
+ base or result is outside the normal range of a double, about 2.2e-308
+ to 1.8e308 in magnitude, where a double keeps all its digits
+ (`1e-400^0.5`); and a result other than zero outside that range, as it
+ is written through a double (`1e400`, `2^-1400`).
- **Failure is an exit.** If the chat client exits or the connection to
it drops, the bot exits with an error and the container's restart
policy starts both again. `SIGTERM` stops the bot, which stops the
diff --git a/docs/TODO.md b/docs/TODO.md
index bd8496f..3b09904 100644
--- a/docs/TODO.md
+++ b/docs/TODO.md
@@ -30,6 +30,9 @@ with no deprecation warning.
- 2026-09-29 Added the HTTP API in `internal/api`: the server on `PORT`,
the bearer credential from `API_TOKEN_FILE`, security headers and
limits, and `GET /api/v1/chats`
+- 2026-09-28 Powers (`^`, also written `**`) and remainders (`%`) in
+ `internal/calc`, which now reads expressions with a parser of its own
+ in place of `go/parser`
- 2026-09-28 Moved the command tree and the `run` and `version` commands
from `cmd/simplexcalc/` into `internal/cli`; `cmd/simplexcalc/main.go`
is now a single call to `cli.Main`
diff --git a/internal/bot/bot.go b/internal/bot/bot.go
index e0d3738..ce7924e 100644
--- a/internal/bot/bot.go
+++ b/internal/bot/bot.go
@@ -25,7 +25,7 @@ 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."
// ChatPort is where the chat client serves its API, on localhost inside
@@ -275,10 +275,12 @@ func Reply(text string) string {
calc.MaxInputLength)
case errors.Is(err, calc.ErrDivisionByZero):
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.ErrOutOfRange):
+ return "That needs a number too large or too small 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."
}
}
diff --git a/internal/bot/bot_test.go b/internal/bot/bot_test.go
index 3f7971e..3bbb661 100644
--- a/internal/bot/bot_test.go
+++ b/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 +25,11 @@ 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": "That needs a number too large or too small for me.",
+ "1e-1300": "That needs a number too large or too small 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) {
diff --git a/internal/calc/calc.go b/internal/calc/calc.go
index 2f2bd65..606a1f7 100644
--- a/internal/calc/calc.go
+++ b/internal/calc/calc.go
@@ -1,29 +1,45 @@
// Package calc evaluates the arithmetic people send the bot: decimal
-// numbers, + - * /, unary minus and parentheses.
+// numbers, + - * / % ^, signs and parentheses.
//
-// The expression is parsed by go/parser and computed by go/constant,
-// which does exact rational arithmetic: 5 * 5/2 is exactly 12.5, and
-// 0.1 + 0.2 is exactly 0.3, so a result carries no binary floating
-// point noise until the moment it is formatted.
+// The expression is read by a small parser of its own, because Go's
+// grammar has no power operator (^ is XOR there), and computed by
+// go/constant, which does exact rational arithmetic: 5 * 5/2 is exactly
+// 12.5, and 0.1 + 0.2 is exactly 0.3, so a result carries no binary
+// floating point noise until the moment it is formatted. A power is the
+// exception: one with a fractional exponent, or whose result go/constant
+// cannot hold exactly, is computed in float64.
package calc
import (
"errors"
- "go/ast"
"go/constant"
- "go/parser"
"go/token"
"math"
+ "math/big"
"regexp"
"strconv"
"strings"
)
-// MaxInputLength caps an expression, in bytes, so a message cannot make
-// the bot do unbounded work. Every operation's cost grows with the size
-// of its operands, and the operands can only grow with the input.
+// MaxInputLength caps an expression, in bytes. With maxExactExponent,
+// which caps a power computed exactly, and bitLimit, which caps every
+// number, it keeps a message from making the bot do unbounded work.
const MaxInputLength = 256
+// bitLimit caps the numerator and denominator of every number: see
+// exact.
+const bitLimit = 4096
+
+// maxExactExponent is the largest exponent, either way, of a power
+// computed exactly. Past it, x^n has a numerator or denominator of more
+// than 4096 bits, which go/constant holds only rounded, unless x is 0 or
+// 1, and float64 computes those exactly.
+const maxExactExponent = 4096
+
+// smallestNormal is the smallest positive normal double, about 2.2e-308.
+// Below it a double keeps fewer digits, down to one.
+const smallestNormal = 0x1p-1022
+
// Results of magnitude plainUpper or more are written in exponent form
// (1e+21 rather than twenty-two digits), and so are fractions smaller
// than plainLower (1e-07 rather than 0.0000001).
@@ -32,20 +48,37 @@ const (
plainLower = 1e-6
)
+// The precedence of the binary operators: the higher, the tighter the
+// operator binds.
+const (
+ sumPrecedence = iota + 1
+ productPrecedence
+ powerPrecedence
+)
+
// Errors returned by Evaluate. The bot turns each into a reply.
var (
ErrTooLong = errors.New("expression too long")
ErrNotArithmetic = errors.New("not an arithmetic expression")
ErrDivisionByZero = errors.New("division by zero")
- ErrTooLarge = errors.New("result too large")
+ ErrOutOfRange = errors.New("number too large or too small")
+ ErrNoRealResult = errors.New("no real result")
)
-// decimalLiteral is the only number syntax accepted. Go's own literal
-// syntax is wider, and parts of it are traps for someone typing
-// arithmetic: 010 is octal 8, and 0x10, 1_000 and 1i are not what a
-// calculator user means by a number.
-var decimalLiteral = regexp.MustCompile(
- `^([0-9]+\.?[0-9]*|\.[0-9]+)([eE][+-]?[0-9]+)?$`,
+// decimal is the only number syntax accepted. Go's own literal syntax is
+// wider, and parts of it are traps for someone typing arithmetic: 010 is
+// octal 8, and 0x10, 1_000 and 1i are not what a calculator user means
+// by a number. Here the x, _ or i matches no token and is refused.
+const decimal = `([0-9]+\.?[0-9]*|\.[0-9]+)([eE][+-]?[0-9]+)?`
+
+var (
+ // nextToken matches the token at the start of the input, after any
+ // whitespace: an operator, a parenthesis or a number. ** comes
+ // before * so that it is read as one token.
+ nextToken = regexp.MustCompile(`^\s*(\*\*|[-+*/%^()]|` + decimal + `)`)
+
+ // decimalLiteral matches a token that is a number.
+ decimalLiteral = regexp.MustCompile(`^` + decimal + `$`)
)
// Evaluate computes an arithmetic expression and returns its result as
@@ -57,114 +90,384 @@ func Evaluate(input string) (string, error) {
return "", ErrTooLong
}
- if s == "" {
- return "", ErrNotArithmetic
- }
-
- expr, err := parser.ParseExpr(s)
- if err != nil {
- return "", ErrNotArithmetic
- }
-
- v, err := eval(expr)
+ tokens, err := tokenize(s)
if err != nil {
return "", err
}
+ p := parser{tokens: tokens}
+
+ v, err := p.expr(sumPrecedence)
+ if err != nil {
+ return "", err
+ }
+
+ if p.next() != "" {
+ return "", ErrNotArithmetic
+ }
+
return format(v)
}
-// eval walks the syntax tree, allowing only the node types and
-// operators of arithmetic. Anything else — identifiers, calls, strings,
-// shifts, comparisons — is refused, not evaluated.
-func eval(e ast.Expr) (constant.Value, error) {
- switch n := e.(type) {
- case *ast.BasicLit:
- return literal(n)
- case *ast.ParenExpr:
- return eval(n.X)
- case *ast.UnaryExpr:
- if n.Op != token.ADD && n.Op != token.SUB {
+// tokenize splits an expression into operators, parentheses and
+// numbers, and refuses anything else. ** is returned as ^.
+func tokenize(s string) ([]string, error) {
+ var tokens []string
+
+ for strings.TrimSpace(s) != "" {
+ m := nextToken.FindStringSubmatch(s)
+ if m == nil {
return nil, ErrNotArithmetic
}
- x, err := eval(n.X)
+ tok := m[1]
+ if tok == "**" {
+ tok = "^"
+ }
+
+ tokens = append(tokens, tok)
+ s = s[len(m[0]):]
+ }
+
+ return tokens, nil
+}
+
+// parser computes an expression as it reads it, by precedence climbing:
+// expr reads operands joined by operators of at least a given
+// precedence, and hands the right operand of each to a deeper call that
+// takes only the operators that bind tighter, so those are applied
+// first.
+type parser struct {
+ tokens []string
+}
+
+// next removes and returns the next token, or "" at the end.
+func (p *parser) next() string {
+ tok := p.peek()
+ if tok != "" {
+ p.tokens = p.tokens[1:]
+ }
+
+ return tok
+}
+
+// peek returns the next token, or "" at the end, and leaves it unread.
+func (p *parser) peek() string {
+ if len(p.tokens) == 0 {
+ return ""
+ }
+
+ return p.tokens[0]
+}
+
+// expr reads and computes an expression whose binary operators all have
+// at least minPrecedence. Operators of equal precedence group to the
+// left, 8/2/2 is (8/2)/2, except ^, which groups to the right: 2^3^2 is
+// 2^(3^2).
+func (p *parser) expr(minPrecedence int) (constant.Value, error) {
+ x, err := p.operand()
+ if err != nil {
+ return nil, err
+ }
+
+ for {
+ op := p.peek()
+
+ prec := precedence(op)
+ if prec < minPrecedence {
+ return x, nil
+ }
+
+ p.next()
+
+ rightPrecedence := prec + 1
+ if op == "^" {
+ rightPrecedence = prec
+ }
+
+ y, err := p.expr(rightPrecedence)
if err != nil {
return nil, err
}
- return constant.UnaryOp(n.Op, x, 0), nil
- case *ast.BinaryExpr:
- return binary(n)
- default:
- return nil, ErrNotArithmetic
+ x, err = apply(x, op, y)
+ if err != nil {
+ return nil, err
+ }
}
}
-func binary(n *ast.BinaryExpr) (constant.Value, error) {
- switch n.Op { //nolint:exhaustive // every other operator is refused.
- case token.ADD, token.SUB, token.MUL, token.QUO:
+// operand reads a number, an expression in parentheses, or a sign and
+// its operand. A sign binds more loosely than a power that follows it,
+// so -2^2 is -(2^2), and 2^-1 is 2^(-1).
+func (p *parser) operand() (constant.Value, error) {
+ switch tok := p.next(); tok {
+ case "+", "-":
+ x, err := p.expr(powerPrecedence)
+ if err != nil {
+ return nil, err
+ }
+
+ if tok == "-" {
+ x = constant.UnaryOp(token.SUB, x, 0)
+ }
+
+ return x, nil
+ case "(":
+ x, err := p.expr(sumPrecedence)
+ if err != nil {
+ return nil, err
+ }
+
+ if p.next() != ")" {
+ return nil, ErrNotArithmetic
+ }
+
+ return x, nil
default:
+ return number(tok)
+ }
+}
+
+// precedence returns the precedence of a binary operator, and 0 for any
+// other token, which ends an expression.
+func precedence(op string) int {
+ switch op {
+ case "+", "-":
+ return sumPrecedence
+ case "*", "/", "%":
+ return productPrecedence
+ case "^":
+ return powerPrecedence
+ default:
+ return 0
+ }
+}
+
+func number(tok string) (constant.Value, error) {
+ if !decimalLiteral.MatchString(tok) {
return nil, ErrNotArithmetic
}
- x, err := eval(n.X)
+ // Read as FLOAT, which makes every literal decimal and a fraction
+ // (see exact): as INT, a leading zero would make it octal.
+ v := constant.MakeFromLiteral(tok, token.FLOAT, 0)
+
+ // A literal such as 1e1300 or 1e-1233 is past bitLimit: see exact.
+ if !exact(v) {
+ return nil, ErrOutOfRange
+ }
+
+ // One too small even to be held rounded, such as 1e-999999999, is
+ // read as 0.
+ mantissa, _, _ := strings.Cut(strings.ToLower(tok), "e")
+ if constant.Sign(v) == 0 && strings.ContainsAny(mantissa, "123456789") {
+ return nil, ErrOutOfRange
+ }
+
+ return v, nil
+}
+
+// apply computes x op y.
+func apply(x constant.Value, op string, y constant.Value) (constant.Value, error) {
+ var (
+ v constant.Value
+ err error
+ )
+
+ switch op {
+ case "+":
+ v = constant.BinaryOp(x, token.ADD, y)
+ case "-":
+ v = constant.BinaryOp(x, token.SUB, y)
+ case "*":
+ v = constant.BinaryOp(x, token.MUL, y)
+ case "/":
+ v, err = divide(x, y)
+ case "%":
+ v, err = modulo(x, y)
+ case "^":
+ v, err = power(x, y)
+ default:
+ err = ErrNotArithmetic
+ }
+
if err != nil {
return nil, err
}
- y, err := eval(n.Y)
- if err != nil {
- return nil, err
+ if !exact(v) {
+ return nil, ErrOutOfRange
}
+ return v, nil
+}
+
+func divide(x, y constant.Value) (constant.Value, error) {
// constant.BinaryOp panics on a zero divisor.
- if n.Op == token.QUO && constant.Sign(y) == 0 {
+ if constant.Sign(y) == 0 {
return nil, ErrDivisionByZero
}
// token.QUO divides exactly, integers included: 25/2 is 12.5.
- v := constant.BinaryOp(x, n.Op, y)
+ return constant.BinaryOp(x, token.QUO, y), nil
+}
- // go/constant represents an overflow to infinity as Unknown.
- if v.Kind() == constant.Unknown {
- return nil, ErrTooLarge
+// modulo computes x % y, whose result takes the sign of y, as in Python:
+// -7 % 3 is 2 and 7 % -3 is -2. It is exact for decimals too: 7.5 % 2
+// is 1.5.
+func modulo(x, y constant.Value) (constant.Value, error) {
+ q, err := divide(x, y)
+ if err != nil {
+ return nil, err
+ }
+
+ // The fractional part of a rounded quotient, and so the remainder,
+ // would be wrong.
+ if !exact(q) {
+ return nil, ErrOutOfRange
+ }
+
+ // x % y is y times the fractional part of x/y, which is at least 0
+ // and less than 1, so the result has the sign of y. It is not
+ // computed as x minus y times the whole part of x/y: that product
+ // can be too large to hold exactly when the remainder is not.
+ //
+ // For x/y = n/d the fractional part is (n mod d)/d, exact because d
+ // is. token.REM truncates, leaving the sign of n; adding d brings a
+ // negative one into range.
+ n, d := constant.Num(q), constant.Denom(q)
+
+ m := constant.BinaryOp(n, token.REM, d)
+ if constant.Sign(m) < 0 {
+ m = constant.BinaryOp(m, token.ADD, d)
+ }
+
+ return constant.BinaryOp(y, token.MUL, constant.BinaryOp(m, token.QUO, d)), nil
+}
+
+// power computes x^y. A negative x needs a whole y, and its sign is
+// applied here: math.Pow would take it from the parity of y's float64
+// value, and every float64 from 2^53 up is even.
+func power(x, y constant.Value) (constant.Value, error) {
+ // n is y if y is a whole number, and Unknown otherwise.
+ n := constant.ToInt(y)
+
+ switch {
+ case constant.Sign(x) == 0 && constant.Sign(y) < 0:
+ return nil, ErrDivisionByZero
+ case constant.Sign(x) >= 0:
+ return nonNegativePower(x, y, n)
+ case n.Kind() != constant.Int:
+ return nil, ErrNoRealResult
+ }
+
+ // x is negative and n whole: x^n is (-x)^n, negated if n is odd.
+ v, err := nonNegativePower(constant.UnaryOp(token.SUB, x, 0), y, n)
+ if err != nil {
+ return nil, err
+ }
+
+ odd := constant.BinaryOp(n, token.AND, constant.MakeInt64(1))
+ if constant.Sign(odd) != 0 {
+ v = constant.UnaryOp(token.SUB, v, 0)
}
return v, nil
}
-func literal(n *ast.BasicLit) (constant.Value, error) {
- if n.Kind != token.INT && n.Kind != token.FLOAT {
- return nil, ErrNotArithmetic
+// nonNegativePower computes x^y for x of at least zero, and y not below
+// zero if x is zero: exactly if y is a whole number n and go/constant
+// holds the result exactly, otherwise in float64.
+func nonNegativePower(x, y, n constant.Value) (constant.Value, error) {
+ e, ok := constant.Int64Val(n)
+ if ok && -maxExactExponent <= e && e <= maxExactExponent {
+ v := exactPower(x, e)
+ if exact(v) {
+ return v, nil
+ }
}
- if !decimalLiteral.MatchString(n.Value) {
- return nil, ErrNotArithmetic
+ // y is above zero here if x is zero.
+ if constant.Sign(x) == 0 {
+ return x, nil
}
- // Read as FLOAT whatever the token says, which makes every literal
- // decimal: as INT, a leading zero would make it octal.
- v := constant.MakeFromLiteral(n.Value, token.FLOAT, 0)
+ xf, _ := constant.Float64Val(x)
+ yf, _ := constant.Float64Val(y)
+ f := math.Pow(xf, yf)
- // The syntax was checked above, so Unknown here means the exponent
- // overflowed.
- if v.Kind() == constant.Unknown {
- return nil, ErrTooLarge
+ // Neither x nor x^y is zero. If either is not a normal double, it
+ // has lost digits, or all of them.
+ if !normal(xf) || !normal(f) {
+ return nil, ErrOutOfRange
}
- return v, nil
+ return constant.MakeFloat64(f), nil
+}
+
+// exactPower computes x^e by repeated squaring. x is not zero if e is
+// negative. It starts from 1 as a fraction, a Float to go/constant, so
+// that x^0 is a fraction like every other number (see exact). Each
+// step's numbers stay small: go/constant holds one whose numerator or
+// denominator reaches 4096 bits as a 512-bit float.
+func exactPower(x constant.Value, e int64) constant.Value {
+ one := constant.MakeFloat64(1)
+ result := one
+
+ for n := max(e, -e); n > 0; n >>= 1 {
+ if n&1 == 1 {
+ result = constant.BinaryOp(result, token.MUL, x)
+ }
+
+ x = constant.BinaryOp(x, token.MUL, x)
+ }
+
+ if e < 0 {
+ result = constant.BinaryOp(one, token.QUO, result)
+ }
+
+ return result
+}
+
+// exact reports whether v is a fraction whose numerator and denominator
+// are both below bitLimit bits, as every number here must be, so that
+// each step of arithmetic stays small. go/constant never rounds an
+// integer, however large, so every number is made a fraction: literals
+// are read as FLOAT, and a power starts from the fraction 1. It rounds
+// a fraction that grows past the limit, to a 512-bit float and past
+// that float's range to Unknown, but not one it reads from a literal,
+// such as 1e-1233, so the limit is checked here.
+//
+// A number that is not exact is refused wherever it appears: a sum can
+// lose the answer entirely (7^1000*7^1000 + 5 - 7^1000*7^1000 would be
+// 0), and a remainder, or whether an exponent is whole or odd, cannot be
+// read from one.
+func exact(v constant.Value) bool {
+ r, ok := constant.Val(v).(*big.Rat)
+
+ return ok && r.Num().BitLen() < bitLimit && r.Denom().BitLen() < bitLimit
+}
+
+// normal reports whether f is a normal double, finite and at least
+// smallestNormal in magnitude: a number other than zero keeps all of a
+// double's digits only as one.
+func normal(f float64) bool {
+ abs := math.Abs(f)
+
+ return abs >= smallestNormal && abs <= math.MaxFloat64
}
// format writes a result for a person to read. A whole number of
// ordinary size is written exactly, digit for digit; anything else goes
// through float64, whose shortest round-trip form is free of the noise
// (0.30000000000000004) that printing a binary fraction to a fixed
-// precision produces.
+// precision produces. A result that is not zero must therefore be a
+// normal double: 2^-1074 would be written 5e-324.
func format(v constant.Value) (string, error) {
f, _ := constant.Float64Val(v)
- if math.IsInf(f, 0) || math.IsNaN(f) {
- return "", ErrTooLarge
+ if constant.Sign(v) != 0 && !normal(f) {
+ return "", ErrOutOfRange
}
abs := math.Abs(f)
diff --git a/internal/calc/calc_test.go b/internal/calc/calc_test.go
index 9b91d97..21e40ee 100644
--- a/internal/calc/calc_test.go
+++ b/internal/calc/calc_test.go
@@ -4,6 +4,7 @@ import (
"errors"
"strings"
"testing"
+ "time"
"sneak.berlin/go/simplexcalc/internal/calc"
)
@@ -13,7 +14,7 @@ import (
func TestEvaluate(t *testing.T) {
t.Parallel()
- cases := map[string]string{
+ expectResults(t, map[string]string{
// The specification's own examples.
"2 + 2": "4",
"5 * 5/2": "12.5",
@@ -51,7 +52,92 @@ func TestEvaluate(t *testing.T) {
"1234567.5": "1234567.5",
"-1 / 4": "-0.25",
"1e300 * 1e8": "1e+308",
- }
+ })
+}
+
+// TestEvaluatePowers: ^ and ** are one operator, binding tighter than
+// * / % and a sign on its left, and grouping to the right.
+func TestEvaluatePowers(t *testing.T) {
+ t.Parallel()
+
+ expectResults(t, map[string]string{
+ "2^3": "8",
+ "2**3": "8",
+ "2 ** 3 ^ 2": "512",
+ "2^3^2": "512",
+ "(2^3)^2": "64",
+ "-2^2": "-4",
+ "(-2)^2": "4",
+ "(-2)^3": "-8",
+ "(-2)^-3": "-0.125",
+ "2^-1": "0.5",
+ "2**-1": "0.5",
+ "-2^-2": "-0.25",
+ "2^-3^2": "0.001953125",
+ "2 * 3^2": "18",
+ "3^2 * 2": "18",
+ "2^3 / 2^2": "2",
+ "1 + 2^3 - 3^2": "0",
+ "010^2": "100",
+ "0.1^2": "0.01",
+ "2^100 - 2^100 + 1": "1",
+ "2^64": "18446744073709551616",
+ "0^0": "1",
+ "0^3": "0",
+ "1.5^2": "2.25",
+ "2^0.5": "1.4142135623730951",
+ "-2^0.5": "-1.4142135623730951",
+ "4^0.5": "2",
+ "0^0.5": "0",
+ "2^1023": "8.98846567431158e+307",
+ "2^-1022": "2.2250738585072014e-308",
+ // Past 2^53 a float64 cannot tell odd from even.
+ "(-1)^(2^53 + 1)": "-1",
+ "(-1)^(10^30)": "1",
+ "(-1)^-9223372036854775808": "1",
+ // Whole powers beyond the range of a double, held exactly.
+ "2^-1400 * 2^1365 * 2^35": "1",
+ "0.3^900 * 10^470": "0.25652473503365386",
+ "2^1500 / 2^1000": "3.273390607896142e+150",
+ })
+}
+
+// TestEvaluateModulo: % sits with * and /, left to right, and its result
+// takes the sign of the divisor.
+func TestEvaluateModulo(t *testing.T) {
+ t.Parallel()
+
+ expectResults(t, map[string]string{
+ "7 % 3": "1",
+ "-7 % 3": "2",
+ "7 % -3": "-2",
+ "-7 % -3": "-1",
+ "6 % 3": "0",
+ "-6 % 3": "0",
+ "7.5 % 2": "1.5",
+ "0.3 % 0.1": "0",
+ "-0.3 % 0.2": "0.1",
+ "10 % 4 * 3": "6",
+ "2 * 7 % 4": "2",
+ "1 + 7 % 3": "2",
+ "2^10 % 7": "2",
+ "10^400 % 7": "4",
+ "1e-30 % 1": "1e-30",
+ "-1e-30 % 1": "1",
+ "10 / 8 % 1": "0.25",
+ "(7 % 3)^2": "1",
+ "7 % (3 ^ 2)": "7",
+ // Both operands and their quotient are held exactly, but y times
+ // the whole part of x/y is too large to be.
+ "(5^860*3^630/7) % (5^860/2^998/2^998)": "0.5179219763783696",
+ // A whole number made from x^0, just below the 4096-bit limit.
+ "(3^0 + 3^0 + 3^0)^2583 % 10": "7",
+ })
+}
+
+// expectResults checks that each expression evaluates to its result.
+func expectResults(t *testing.T, cases map[string]string) {
+ t.Helper()
for in, want := range cases {
t.Run(in, func(t *testing.T) {
@@ -70,11 +156,11 @@ func TestEvaluate(t *testing.T) {
}
// TestEvaluateRefuses covers what must be answered with an error rather
-// than a number, and never with a panic.
+// than a number.
func TestEvaluateRefuses(t *testing.T) {
t.Parallel()
- cases := map[string]error{
+ expectErrors(t, map[string]error{
"": calc.ErrNotArithmetic,
" ": calc.ErrNotArithmetic,
"hello": calc.ErrNotArithmetic,
@@ -89,20 +175,91 @@ func TestEvaluateRefuses(t *testing.T) {
"2i * 2i": calc.ErrNotArithmetic,
"0x10 + 1": calc.ErrNotArithmetic,
"1_000 + 1": calc.ErrNotArithmetic,
- "7 % 2": calc.ErrNotArithmetic,
- "2 ^ 3": calc.ErrNotArithmetic,
"1 << 10": calc.ErrNotArithmetic,
"1 == 1": calc.ErrNotArithmetic,
"!1": calc.ErrNotArithmetic,
"func() int { return 1 }()": calc.ErrNotArithmetic,
+ "(1 + 2": calc.ErrNotArithmetic,
+ "1 + 2)": calc.ErrNotArithmetic,
+ "()": calc.ErrNotArithmetic,
+ "(2)(3)": calc.ErrNotArithmetic,
+ "2 ^": calc.ErrNotArithmetic,
+ "^ 2": calc.ErrNotArithmetic,
+ "2 ^^ 3": calc.ErrNotArithmetic,
+ "2 *** 3": calc.ErrNotArithmetic,
+ "2 * * 3": calc.ErrNotArithmetic,
+ "% 3": calc.ErrNotArithmetic,
+ "50%": calc.ErrNotArithmetic,
+ "2 × 3": calc.ErrNotArithmetic,
"1 / 0": calc.ErrDivisionByZero,
"1 / (2 - 2)": calc.ErrDivisionByZero,
"5 / 0.0": calc.ErrDivisionByZero,
- "1e400": calc.ErrTooLarge,
- "1e300 * 1e300": calc.ErrTooLarge,
- "1e999999999 * 1e999999999": calc.ErrTooLarge,
- "1 / 1e-400": calc.ErrTooLarge,
- }
+ "7 % 0": calc.ErrDivisionByZero,
+ "7.5 % (1 - 1)": calc.ErrDivisionByZero,
+ "0^-1": calc.ErrDivisionByZero,
+ "0^-0.5": calc.ErrDivisionByZero,
+ "(-2)^0.5": calc.ErrNoRealResult,
+ "(-8)^(1/3)": calc.ErrNoRealResult,
+ "(-1)^-0.5": calc.ErrNoRealResult,
+ })
+}
+
+// TestEvaluateOutOfRange: a number is held exactly, or computed in
+// float64 as a normal double, and a result is written as a normal
+// double. Anything else is refused.
+func TestEvaluateOutOfRange(t *testing.T) {
+ t.Parallel()
+
+ expectErrors(t, map[string]error{
+ // Results that are not normal doubles: 2^-1074 would be written
+ // 5e-324.
+ "1e400": calc.ErrOutOfRange,
+ "1e300 * 1e300": calc.ErrOutOfRange,
+ "1e999999999 * 1e999999999": calc.ErrOutOfRange,
+ "1 / 1e-400": calc.ErrOutOfRange,
+ "2^1024": calc.ErrOutOfRange,
+ "2^5000": calc.ErrOutOfRange,
+ "(-2)^5001": calc.ErrOutOfRange,
+ "0.5^-5000": calc.ErrOutOfRange,
+ "2^-1074": calc.ErrOutOfRange,
+ "2^-1400": calc.ErrOutOfRange,
+ "-1e-310": calc.ErrOutOfRange,
+ // Powers computed in float64 whose base or result is not a
+ // normal double, and so has lost digits, or all of them.
+ "2^-1073.5 * 2^1073": calc.ErrOutOfRange,
+ "1e400^-0.001": calc.ErrOutOfRange,
+ "1e-400^0.001": calc.ErrOutOfRange,
+ "1e-310^0.5": calc.ErrOutOfRange,
+ "(0.5^1100)^4 / (0.5^1100)^4": calc.ErrOutOfRange,
+ "(1/3)^1e400": calc.ErrOutOfRange,
+ // go/constant holds numbers of this size rounded. A sum of them
+ // can lose the answer (this one would be 0), and so can a
+ // remainder or the sign of -1 to such a power.
+ "7^1000 * 7^1000 + 5 - 7^1000 * 7^1000": calc.ErrOutOfRange,
+ "7^1000 * 7^1000 / 7^1000 % 10": calc.ErrOutOfRange,
+ "(-1)^(3^1365 * 3^1365 / 3^1365)": calc.ErrOutOfRange,
+ "(-1)^1e1300": calc.ErrOutOfRange,
+ "1e-1300": calc.ErrOutOfRange,
+ "1e-1300 + 1": calc.ErrOutOfRange,
+ "1e-700 * 1e-700": calc.ErrOutOfRange,
+ "0.1^800 * 0.1^800": calc.ErrOutOfRange,
+ // Both operands are held exactly, but their quotient is not.
+ "3^1365 % 7^-1000": calc.ErrOutOfRange,
+ // The same limit for a whole number made from x^0, which
+ // go/constant would hold as an integer and never round, and for
+ // a literal it reads exactly as a fraction past the limit.
+ "(2^0 + 2^0)^4095 % 10": calc.ErrOutOfRange,
+ "1e-1233 * 0": calc.ErrOutOfRange,
+ // go/constant reads this literal as 0.
+ "1e-999999999": calc.ErrOutOfRange,
+ "1 / 1e-999999999": calc.ErrOutOfRange,
+ })
+}
+
+// expectErrors checks that each expression is refused with its error,
+// and never with a panic.
+func expectErrors(t *testing.T, cases map[string]error) {
+ t.Helper()
for in, want := range cases {
t.Run(in, func(t *testing.T) {
@@ -116,6 +273,62 @@ func TestEvaluateRefuses(t *testing.T) {
}
}
+// TestEvaluateBoundsWork: computed exactly, each of these powers would
+// need more time and memory than any machine has. They must be answered
+// at once.
+func TestEvaluateBoundsWork(t *testing.T) {
+ t.Parallel()
+
+ cases := []struct {
+ in string
+ want string
+ err error
+ }{
+ {in: "9^9^9^9^9", err: calc.ErrOutOfRange},
+ {in: "((9^999)^999)^999", err: calc.ErrOutOfRange},
+ {in: "(3^2583)^4096", err: calc.ErrOutOfRange},
+ {in: "1.0000001^99999", want: "1.01005006557947"},
+ {in: "0.5^99999999999999999999", err: calc.ErrOutOfRange},
+ {in: "2^-9223372036854775808", err: calc.ErrOutOfRange},
+ {in: "(-1)^99999999999999999999", want: "-1"},
+ // The longest tower that fits.
+ {in: strings.Repeat("9^", 127) + "9", err: calc.ErrOutOfRange},
+ // The largest power of 3 computed exactly, as often as fits.
+ {in: "0" + strings.Repeat("*3^2583", 36), want: "0"},
+ // Whole numbers made from x^0, through each operation. Held as
+ // integers, which go/constant never rounds, they would escape
+ // the 4096-bit limit: the first needs about 69 billion bits.
+ {in: "(((2^0+2^0)^4096)^4096)^4096", err: calc.ErrOutOfRange},
+ {in: "(((0^0+0^0)^4096)^4096)^4096", err: calc.ErrOutOfRange},
+ {in: "(((-2^0-2^0)^4096)^4096)^4096", err: calc.ErrOutOfRange},
+ {in: "((2^0+2^0)^4000*(2^0+2^0)^4000)^4096", err: calc.ErrOutOfRange},
+ {in: "((((2^0+2^0)/2^0)^4096)^4096)^4096", err: calc.ErrOutOfRange},
+ {in: "((((2^0+2^0) % 3)^4096)^4096)^4096", err: calc.ErrOutOfRange},
+ {in: "(((2^0+2^0)^4096)^4096)^4096 * 0", err: calc.ErrOutOfRange},
+ // A fraction whose numerator and denominator are both just below
+ // the limit, and a literal whose exponent is too large to read.
+ {in: "(3^2583/5^1760)^4096", err: calc.ErrOutOfRange},
+ {in: "1e99999999999999999999", err: calc.ErrOutOfRange},
+ }
+
+ for _, c := range cases {
+ t.Run(c.in, func(t *testing.T) {
+ t.Parallel()
+
+ start := time.Now()
+ got, err := calc.Evaluate(c.in)
+
+ if elapsed := time.Since(start); elapsed > time.Second {
+ t.Errorf("Evaluate(%q) took %v", c.in, elapsed)
+ }
+
+ if !errors.Is(err, c.err) || got != c.want {
+ t.Errorf("Evaluate(%q) = %q, %v; want %q, %v", c.in, got, err, c.want, c.err)
+ }
+ })
+ }
+}
+
// TestEvaluateCapsInput: the length cap is what bounds the work a
// message can cause, so it must hold exactly at the boundary.
func TestEvaluateCapsInput(t *testing.T) {