simplexcalc/internal/calc/calc.go

// Package calc evaluates the arithmetic people send the bot: decimal
// numbers, + - * /, unary minus 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.
package calc

import (
	"errors"
	"go/ast"
	"go/constant"
	"go/parser"
	"go/token"
	"math"
	"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.
const MaxInputLength = 256

// 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).
const (
	plainUpper = 1e21
	plainLower = 1e-6
)

// 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")
)

// 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]+)?$`,
)

// Evaluate computes an arithmetic expression and returns its result as
// text: whole numbers without a decimal point, fractions in the
// shortest form that reads back as the same float64.
func Evaluate(input string) (string, error) {
	s := strings.TrimSpace(input)
	if len(s) > MaxInputLength {
		return "", ErrTooLong
	}

	if s == "" {
		return "", ErrNotArithmetic
	}

	expr, err := parser.ParseExpr(s)
	if err != nil {
		return "", ErrNotArithmetic
	}

	v, err := eval(expr)
	if err != nil {
		return "", err
	}

	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 {
			return nil, ErrNotArithmetic
		}

		x, err := eval(n.X)
		if err != nil {
			return nil, err
		}

		return constant.UnaryOp(n.Op, x, 0), nil
	case *ast.BinaryExpr:
		return binary(n)
	default:
		return nil, ErrNotArithmetic
	}
}

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:
	default:
		return nil, ErrNotArithmetic
	}

	x, err := eval(n.X)
	if err != nil {
		return nil, err
	}

	y, err := eval(n.Y)
	if err != nil {
		return nil, err
	}

	// constant.BinaryOp panics on a zero divisor.
	if n.Op == token.QUO && 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)

	// go/constant represents an overflow to infinity as Unknown.
	if v.Kind() == constant.Unknown {
		return nil, ErrTooLarge
	}

	return v, nil
}

func literal(n *ast.BasicLit) (constant.Value, error) {
	if n.Kind != token.INT && n.Kind != token.FLOAT {
		return nil, ErrNotArithmetic
	}

	if !decimalLiteral.MatchString(n.Value) {
		return nil, ErrNotArithmetic
	}

	// 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)

	// The syntax was checked above, so Unknown here means the exponent
	// overflowed.
	if v.Kind() == constant.Unknown {
		return nil, ErrTooLarge
	}

	return v, nil
}

// 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.
func format(v constant.Value) (string, error) {
	f, _ := constant.Float64Val(v)
	if math.IsInf(f, 0) || math.IsNaN(f) {
		return "", ErrTooLarge
	}

	abs := math.Abs(f)

	if i := constant.ToInt(v); i.Kind() == constant.Int && abs < plainUpper {
		return i.ExactString(), nil
	}

	if abs >= plainUpper || abs < plainLower {
		return strconv.FormatFloat(f, 'g', -1, 64), nil
	}

	return strconv.FormatFloat(f, 'f', -1, 64), nil
}