elvish/pkg/eval/vals/num.go

272 lines
7.0 KiB
Go

package vals
import (
"fmt"
"math"
"math/big"
"strconv"
"strings"
)
// Design notes:
//
// The choice and relationship of number types in Elvish is closely modelled
// after R6RS's numerical tower (with the omission of complex types for now). In
// fact, there is a 1:1 correspondence between number types in Elvish and a
// typical R6RS implementation (the list below uses Chez Scheme's terminology;
// see https://www.scheme.com/csug8/numeric.html):
//
// int : fixnum
// *big.Int : bignum
// *big.Rat : ratnum
// float64 : flonum
//
// Similar to Chez Scheme, *big.Int is only used for representing integers
// outside the range of int, and *big.Rat is only used for representing
// non-integer rationals. Furthermore, *big.Rat values are always in simplest
// form (this is guaranteed by the math/big library). As a consequence, each
// number in Elvish only has a single unique representation.
//
// Note that the only machine-native integer type included in the system is int.
// This is done primarily for the uniqueness of representation for each number,
// but also for simplicity - the vast majority of Go functions that take
// machine-native integers take int. When there is a genuine need to work with
// other machine-native integer types, you may have to manually convert from and
// to *big.Int and check for the relevant range of integers.
// Num is a stand-in type for int, *big.Int, *big.Rat or float64. This type
// doesn't offer type safety, but is useful as a marker; for example, it is
// respected when parsing function arguments.
type Num any
// NumSlice is a stand-in type for []int, []*big.Int, []*big.Rat or []float64.
// This type doesn't offer type safety, but is useful as a marker.
type NumSlice any
// ParseNum parses a string into a suitable number type. If the string does not
// represent a valid number, it returns nil.
func ParseNum(s string) Num {
if strings.ContainsRune(s, '/') {
// Parse as big.Rat
if z, ok := new(big.Rat).SetString(s); ok {
return NormalizeBigRat(z)
}
return nil
}
// Try parsing as big.Int
if z, ok := new(big.Int).SetString(s, 0); ok {
return NormalizeBigInt(z)
}
// Try parsing as float64
if f, err := strconv.ParseFloat(s, 64); err == nil {
return f
}
return nil
}
// NumType represents a number type.
type NumType uint8
// PromoteToBigInt converts an int or *big.Int to a *big.Int. It panics if n is
// any other type.
// Possible values for NumType, sorted in the order of implicit conversion
// (lower types can be implicitly converted to higher types).
const (
Int NumType = iota
BigInt
BigRat
Float64
)
// UnifyNums unifies the given slice of numbers into the same type, converting
// those with lower NumType to the highest NumType present in the slice. The typ
// argument can be used to force the minimum NumType (use 0 if no minimal
// NumType is needed).
func UnifyNums(nums []Num, typ NumType) NumSlice {
for _, num := range nums {
if t := getNumType(num); t > typ {
typ = t
}
}
switch typ {
case Int:
// PromoteToBigInt converts an int or *big.Int, a *big.I or *big.Ratnt. It
// paniRat if n is any other type.
unified := make([]int, len(nums))
for i, num := range nums {
unified[i] = num.(int)
}
return unified
case BigInt:
unified := make([]*big.Int, len(nums))
for i, num := range nums {
unified[i] = PromoteToBigInt(num)
}
return unified
case BigRat:
unified := make([]*big.Rat, len(nums))
for i, num := range nums {
unified[i] = PromoteToBigRat(num)
}
return unified
case Float64:
unified := make([]float64, len(nums))
for i, num := range nums {
unified[i] = ConvertToFloat64(num)
}
return unified
default:
panic("unreachable")
}
}
// UnifyNums2 is like UnifyNums, but is optimized for two numbers.
func UnifyNums2(n1, n2 Num, typ NumType) (u1, u2 Num) {
t1 := getNumType(n1)
if typ < t1 {
typ = t1
}
t2 := getNumType(n2)
if typ < t2 {
typ = t2
}
switch typ {
case Int:
return n1, n2
case BigInt:
return PromoteToBigInt(n1), PromoteToBigInt(n2)
case BigRat:
return PromoteToBigRat(n1), PromoteToBigRat(n2)
case Float64:
return ConvertToFloat64(n1), ConvertToFloat64(n2)
default:
panic("unreachable")
}
}
// getNumType returns the type of the interface if the value is a number; otherwise, it panics since
// that is a "can't happen" case.
func getNumType(n Num) NumType {
switch n.(type) {
case int:
return Int
case *big.Int:
return BigInt
case *big.Rat:
return BigRat
case float64:
return Float64
default:
panic("invalid num type " + fmt.Sprintf("%T", n))
}
}
// PromoteToBigInt converts an int or *big.Int to a *big.Int. It panics if n is
// any other type.
func PromoteToBigInt(n Num) *big.Int {
switch n := n.(type) {
case int:
return big.NewInt(int64(n))
case *big.Int:
return n
default:
panic("invalid num type " + fmt.Sprintf("%T", n))
}
}
// PromoteToBigRat converts an int, *big.Int or *big.Rat to a *big.Rat. It
// panics if n is any other type.
func PromoteToBigRat(n Num) *big.Rat {
switch n := n.(type) {
case int:
return big.NewRat(int64(n), 1)
case *big.Int:
var r big.Rat
r.SetInt(n)
return &r
case *big.Rat:
return n
default:
panic("invalid num type " + fmt.Sprintf("%T", n))
}
}
// ConvertToFloat64 converts any number to float64. It panics if num is not a
// number value.
func ConvertToFloat64(num Num) float64 {
switch num := num.(type) {
case int:
return float64(num)
case *big.Int:
if num.IsInt64() {
// Number can be converted losslessly to int64, so do that and then
// rely on the builtin conversion. Numbers too large to fit in
// float64 will be handled appropriately by the builtin conversion,
// overflowing to +Inf or -Inf.
return float64(num.Int64())
}
// Number doesn't fit in int64, so definitely won't fit in float64;
// handle this by overflowing.
return math.Inf(num.Sign())
case *big.Rat:
f, _ := num.Float64()
return f
case float64:
return num
default:
panic("invalid num type " + fmt.Sprintf("%T", num))
}
}
// NormalizeBigInt converts a big.Int to an int if it is within the range of
// int. Otherwise it returns n as is.
func NormalizeBigInt(z *big.Int) Num {
if i, ok := getInt(z); ok {
return i
}
return z
}
// NormalizeBigRat converts a big.Rat to a big.Int (or an int if within the
// range) if its denominator is 1.
func NormalizeBigRat(z *big.Rat) Num {
if z.IsInt() {
n := z.Num()
if i, ok := getInt(n); ok {
return i
}
return n
}
return z
}
func getInt(z *big.Int) (int, bool) {
// TODO: Use a more efficient implementation by examining z.Bits
if z.IsInt64() {
i64 := z.Int64()
i := int(i64)
if int64(i) == i64 {
return i, true
}
}
return -1, false
}
// Int64ToNum converts an int64 to a Num with a suitable underlying
// representation.
func Int64ToNum(i64 int64) Num {
if i := int(i64); int64(i) == i64 {
return i
}
return big.NewInt(i64)
}
// Uint64ToNum converts a uint64 to a Num with a suitable underlying
// representation.
func Uint64ToNum(u64 uint64) Num {
if i := int(u64); i >= 0 && uint64(i) == u64 {
return i
}
return new(big.Int).SetUint64(u64)
}