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// Copyright 2016 Google Inc. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package grumpy
import (
"errors"
"fmt"
"math"
"math/cmplx"
"reflect"
"regexp"
"strconv"
"strings"
)
// ComplexType is the object representing the Python 'complex' type.
var ComplexType = newBasisType("complex", reflect.TypeOf(Complex{}), toComplexUnsafe, ObjectType)
// Complex represents Python 'complex' objects.
type Complex struct {
Object
value complex128
}
// NewComplex returns a new Complex holding the given complex value.
func NewComplex(value complex128) *Complex {
return &Complex{Object{typ: ComplexType}, value}
}
func toComplexUnsafe(o *Object) *Complex {
return (*Complex)(o.toPointer())
}
// ToObject upcasts c to an Object.
func (c *Complex) ToObject() *Object {
return &c.Object
}
// Value returns the underlying complex value held by c.
func (c *Complex) Value() complex128 {
return c.value
}
func complexAbs(f *Frame, o *Object) (*Object, *BaseException) {
c := toComplexUnsafe(o).Value()
return NewFloat(cmplx.Abs(c)).ToObject(), nil
}
func complexAdd(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__add__", v, w, func(lhs, rhs complex128) complex128 {
return lhs + rhs
})
}
func complexCompareNotSupported(f *Frame, v, w *Object) (*Object, *BaseException) {
if w.isInstance(IntType) || w.isInstance(LongType) || w.isInstance(FloatType) || w.isInstance(ComplexType) {
return nil, f.RaiseType(TypeErrorType, "no ordering relation is defined for complex numbers")
}
return NotImplemented, nil
}
func complexComplex(f *Frame, o *Object) (*Object, *BaseException) {
return o, nil
}
func complexDiv(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__div__", v, w, func(v, w complex128) (complex128, bool) {
if w == 0 {
return 0, false
}
return v / w, true
})
}
func complexDivMod(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivAndModOp(f, "__divmod__", v, w, func(v, w complex128) (complex128, complex128, bool) {
if w == 0 {
return 0, 0, false
}
return complexFloorDivOp(v, w), complexModOp(v, w), true
})
}
func complexEq(f *Frame, v, w *Object) (*Object, *BaseException) {
e, ok := complexCompare(toComplexUnsafe(v), w)
if !ok {
return NotImplemented, nil
}
return GetBool(e).ToObject(), nil
}
func complexFloorDiv(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__floordiv__", v, w, func(v, w complex128) (complex128, bool) {
if w == 0 {
return 0, false
}
return complexFloorDivOp(v, w), true
})
}
func complexHash(f *Frame, o *Object) (*Object, *BaseException) {
v := toComplexUnsafe(o).Value()
hashCombined := hashFloat(real(v)) + 1000003*hashFloat(imag(v))
if hashCombined == -1 {
hashCombined = -2
}
return NewInt(hashCombined).ToObject(), nil
}
func complexMod(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__mod__", v, w, func(v, w complex128) (complex128, bool) {
if w == 0 {
return 0, false
}
return complexModOp(v, w), true
})
}
func complexMul(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__mul__", v, w, func(lhs, rhs complex128) complex128 {
return lhs * rhs
})
}
func complexNE(f *Frame, v, w *Object) (*Object, *BaseException) {
e, ok := complexCompare(toComplexUnsafe(v), w)
if !ok {
return NotImplemented, nil
}
return GetBool(!e).ToObject(), nil
}
func complexNeg(f *Frame, o *Object) (*Object, *BaseException) {
c := toComplexUnsafe(o).Value()
return NewComplex(-c).ToObject(), nil
}
func complexNew(f *Frame, t *Type, args Args, _ KWArgs) (*Object, *BaseException) {
argc := len(args)
if argc == 0 {
return newObject(t), nil
}
if argc > 2 {
return nil, f.RaiseType(TypeErrorType, "'__new__' of 'complex' requires at most 2 arguments")
}
if t != ComplexType {
// Allocate a plain complex then copy it's value into an object
// of the complex subtype.
x, raised := complexNew(f, ComplexType, args, nil)
if raised != nil {
return nil, raised
}
result := toComplexUnsafe(newObject(t))
result.value = toComplexUnsafe(x).Value()
return result.ToObject(), nil
}
if complexSlot := args[0].typ.slots.Complex; complexSlot != nil && argc == 1 {
c, raised := complexConvert(complexSlot, f, args[0])
if raised != nil {
return nil, raised
}
return c.ToObject(), nil
}
if args[0].isInstance(StrType) {
if argc > 1 {
return nil, f.RaiseType(TypeErrorType, "complex() can't take second arg if first is a string")
}
s := toStrUnsafe(args[0]).Value()
result, err := parseComplex(s)
if err != nil {
return nil, f.RaiseType(ValueErrorType, "complex() arg is a malformed string")
}
return NewComplex(result).ToObject(), nil
}
if argc > 1 && args[1].isInstance(StrType) {
return nil, f.RaiseType(TypeErrorType, "complex() second arg can't be a string")
}
cr, raised := complex128Convert(f, args[0])
if raised != nil {
return nil, raised
}
var ci complex128
if argc > 1 {
ci, raised = complex128Convert(f, args[1])
if raised != nil {
return nil, raised
}
}
// Logically it should be enough to return this:
// NewComplex(cr + ci*1i).ToObject()
// But Go complex arithmatic is not satisfying all conditions, for instance:
// cr := complex(math.Inf(1), 0)
// ci := complex(math.Inf(-1), 0)
// fmt.Println(cr + ci*1i)
// Output is (NaN-Infi), instead of (+Inf-Infi).
return NewComplex(complex(real(cr)-imag(ci), imag(cr)+real(ci))).ToObject(), nil
}
func complexNonZero(f *Frame, o *Object) (*Object, *BaseException) {
return GetBool(toComplexUnsafe(o).Value() != 0).ToObject(), nil
}
func complexPos(f *Frame, o *Object) (*Object, *BaseException) {
return o, nil
}
func complexPow(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__pow__", v, w, func(lhs, rhs complex128) complex128 {
return cmplx.Pow(lhs, rhs)
})
}
func complexRAdd(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__radd__", v, w, func(lhs, rhs complex128) complex128 {
return lhs + rhs
})
}
func complexRDiv(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__rdiv__", v, w, func(v, w complex128) (complex128, bool) {
if v == 0 {
return 0, false
}
return w / v, true
})
}
func complexRDivMod(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivAndModOp(f, "__rdivmod__", v, w, func(v, w complex128) (complex128, complex128, bool) {
if v == 0 {
return 0, 0, false
}
return complexFloorDivOp(w, v), complexModOp(w, v), true
})
}
func complexRepr(f *Frame, o *Object) (*Object, *BaseException) {
c := toComplexUnsafe(o).Value()
rs, is := "", ""
pre, post := "", ""
sign := ""
if real(c) == 0.0 {
is = strconv.FormatFloat(imag(c), 'g', -1, 64)
} else {
pre = "("
rs = strconv.FormatFloat(real(c), 'g', -1, 64)
is = strconv.FormatFloat(imag(c), 'g', -1, 64)
if imag(c) >= 0.0 || math.IsNaN(imag(c)) {
sign = "+"
}
post = ")"
}
rs = unsignPositiveInf(strings.ToLower(rs))
is = unsignPositiveInf(strings.ToLower(is))
return NewStr(fmt.Sprintf("%s%s%s%sj%s", pre, rs, sign, is, post)).ToObject(), nil
}
func complexRFloorDiv(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__rfloordiv__", v, w, func(v, w complex128) (complex128, bool) {
if v == 0 {
return 0, false
}
return complexFloorDivOp(w, v), true
})
}
func complexRMod(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexDivModOp(f, "__rmod__", v, w, func(v, w complex128) (complex128, bool) {
if v == 0 {
return 0, false
}
return complexModOp(w, v), true
})
}
func complexRMul(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__rmul__", v, w, func(lhs, rhs complex128) complex128 {
return rhs * lhs
})
}
func complexRPow(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__rpow__", v, w, func(lhs, rhs complex128) complex128 {
return cmplx.Pow(rhs, lhs)
})
}
func complexRSub(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__rsub__", v, w, func(lhs, rhs complex128) complex128 {
return rhs - lhs
})
}
func complexSub(f *Frame, v, w *Object) (*Object, *BaseException) {
return complexArithmeticOp(f, "__sub__", v, w, func(lhs, rhs complex128) complex128 {
return lhs - rhs
})
}
func initComplexType(dict map[string]*Object) {
ComplexType.slots.Abs = &unaryOpSlot{complexAbs}
ComplexType.slots.Add = &binaryOpSlot{complexAdd}
ComplexType.slots.Complex = &unaryOpSlot{complexComplex}
ComplexType.slots.Div = &binaryOpSlot{complexDiv}
ComplexType.slots.DivMod = &binaryOpSlot{complexDivMod}
ComplexType.slots.Eq = &binaryOpSlot{complexEq}
ComplexType.slots.FloorDiv = &binaryOpSlot{complexFloorDiv}
ComplexType.slots.GE = &binaryOpSlot{complexCompareNotSupported}
ComplexType.slots.GT = &binaryOpSlot{complexCompareNotSupported}
ComplexType.slots.Hash = &unaryOpSlot{complexHash}
ComplexType.slots.LE = &binaryOpSlot{complexCompareNotSupported}
ComplexType.slots.LT = &binaryOpSlot{complexCompareNotSupported}
ComplexType.slots.Mod = &binaryOpSlot{complexMod}
ComplexType.slots.Mul = &binaryOpSlot{complexMul}
ComplexType.slots.NE = &binaryOpSlot{complexNE}
ComplexType.slots.Neg = &unaryOpSlot{complexNeg}
ComplexType.slots.New = &newSlot{complexNew}
ComplexType.slots.NonZero = &unaryOpSlot{complexNonZero}
ComplexType.slots.Pos = &unaryOpSlot{complexPos}
ComplexType.slots.Pow = &binaryOpSlot{complexPow}
ComplexType.slots.RAdd = &binaryOpSlot{complexRAdd}
ComplexType.slots.RDiv = &binaryOpSlot{complexRDiv}
ComplexType.slots.RDivMod = &binaryOpSlot{complexRDivMod}
ComplexType.slots.RFloorDiv = &binaryOpSlot{complexRFloorDiv}
ComplexType.slots.Repr = &unaryOpSlot{complexRepr}
ComplexType.slots.RMod = &binaryOpSlot{complexRMod}
ComplexType.slots.RMul = &binaryOpSlot{complexRMul}
ComplexType.slots.RPow = &binaryOpSlot{complexRPow}
ComplexType.slots.RSub = &binaryOpSlot{complexRSub}
ComplexType.slots.Sub = &binaryOpSlot{complexSub}
}
func complex128Convert(f *Frame, o *Object) (complex128, *BaseException) {
if complexSlot := o.typ.slots.Complex; complexSlot != nil {
c, raised := complexConvert(complexSlot, f, o)
if raised != nil {
return complex(0, 0), raised
}
return c.Value(), nil
} else if floatSlot := o.typ.slots.Float; floatSlot != nil {
result, raised := floatConvert(floatSlot, f, o)
if raised != nil {
return complex(0, 0), raised
}
return complex(result.Value(), 0), nil
} else {
return complex(0, 0), f.RaiseType(TypeErrorType, "complex() argument must be a string or a number")
}
}
func complexArithmeticOp(f *Frame, method string, v, w *Object, fun func(v, w complex128) complex128) (*Object, *BaseException) {
if w.isInstance(ComplexType) {
return NewComplex(fun(toComplexUnsafe(v).Value(), toComplexUnsafe(w).Value())).ToObject(), nil
}
floatW, ok := floatCoerce(w)
if !ok {
if math.IsInf(floatW, 0) {
return nil, f.RaiseType(OverflowErrorType, "long int too large to convert to float")
}
return NotImplemented, nil
}
return NewComplex(fun(toComplexUnsafe(v).Value(), complex(floatW, 0))).ToObject(), nil
}
// complexCoerce will coerce any numeric type to a complex. If all is
// well, it will return the complex128 value, and true (OK). If an overflow
// occurs, it will return either (+Inf, false) or (-Inf, false) depending
// on whether the source value was too large or too small. Note that if the
// source number is an infinite float, the result will be infinite without
// overflow, (+-Inf, true).
// If the input is not a number, it will return (0, false).
func complexCoerce(o *Object) (complex128, bool) {
if o.isInstance(ComplexType) {
return toComplexUnsafe(o).Value(), true
}
floatO, ok := floatCoerce(o)
if !ok {
if math.IsInf(floatO, 0) {
return complex(floatO, 0.0), false
}
return 0, false
}
return complex(floatO, 0.0), true
}
func complexCompare(v *Complex, w *Object) (bool, bool) {
lhsr := real(v.Value())
rhs, ok := complexCoerce(w)
if !ok {
return false, false
}
return lhsr == real(rhs) && imag(v.Value()) == imag(rhs), true
}
func complexConvert(complexSlot *unaryOpSlot, f *Frame, o *Object) (*Complex, *BaseException) {
result, raised := complexSlot.Fn(f, o)
if raised != nil {
return nil, raised
}
if !result.isInstance(ComplexType) {
exc := fmt.Sprintf("__complex__ returned non-complex (type %s)", result.typ.Name())
return nil, f.RaiseType(TypeErrorType, exc)
}
return toComplexUnsafe(result), nil
}
func complexDivModOp(f *Frame, method string, v, w *Object, fun func(v, w complex128) (complex128, bool)) (*Object, *BaseException) {
complexW, ok := complexCoerce(w)
if !ok {
if cmplx.IsInf(complexW) {
return nil, f.RaiseType(OverflowErrorType, "long int too large to convert to complex")
}
return NotImplemented, nil
}
x, ok := fun(toComplexUnsafe(v).Value(), complexW)
if !ok {
return nil, f.RaiseType(ZeroDivisionErrorType, "complex division or modulo by zero")
}
return NewComplex(x).ToObject(), nil
}
func complexDivAndModOp(f *Frame, method string, v, w *Object, fun func(v, w complex128) (complex128, complex128, bool)) (*Object, *BaseException) {
complexW, ok := complexCoerce(w)
if !ok {
if cmplx.IsInf(complexW) {
return nil, f.RaiseType(OverflowErrorType, "long int too large to convert to complex")
}
return NotImplemented, nil
}
q, m, ok := fun(toComplexUnsafe(v).Value(), complexW)
if !ok {
return nil, f.RaiseType(ZeroDivisionErrorType, "complex division or modulo by zero")
}
return NewTuple2(NewComplex(q).ToObject(), NewComplex(m).ToObject()).ToObject(), nil
}
func complexFloorDivOp(v, w complex128) complex128 {
return complex(math.Floor(real(v/w)), 0)
}
func complexModOp(v, w complex128) complex128 {
return v - complexFloorDivOp(v, w)*w
}
const (
blank = iota
real1
imag1
real2
sign2
imag3
real4
sign5
onlyJ
)
// ParseComplex converts the string s to a complex number.
// If string is well-formed (one of these forms: <float>, <float>j,
// <float><signed-float>j, <float><sign>j, <sign>j or j, where <float> is
// any numeric string that's acceptable by strconv.ParseFloat(s, 64)),
// ParseComplex returns the respective complex128 number.
func parseComplex(s string) (complex128, error) {
c := strings.Count(s, "(")
if (c > 1) || (c == 1 && strings.Count(s, ")") != 1) {
return complex(0, 0), errors.New("Malformed complex string, more than one matching parantheses")
}
ts := strings.TrimSpace(s)
ts = strings.Trim(ts, "()")
ts = strings.TrimSpace(ts)
re := `(?i)(?:(?:(?:(?:\d*\.\d+)|(?:\d+\.?))(?:[Ee][+-]?\d+)?)|(?:infinity)|(?:nan)|(?:inf))`
fre := `[-+]?` + re
sre := `[-+]` + re
fsfj := `(?:(?P<real1>` + fre + `)(?P<imag1>` + sre + `)j)`
fsj := `(?:(?P<real2>` + fre + `)(?P<sign2>[-+])j)`
fj := `(?P<imag3>` + fre + `)j`
f := `(?P<real4>` + fre + `)`
sj := `(?P<sign5>[-+])j`
j := `(?P<onlyJ>j)`
r := regexp.MustCompile(`^(?:` + fsfj + `|` + fsj + `|` + fj + `|` + f + `|` + sj + `|` + j + `)$`)
subs := r.FindStringSubmatch(ts)
if subs == nil {
return complex(0, 0), errors.New("Malformed complex string, no mathing pattern found")
}
if subs[real1] != "" && subs[imag1] != "" {
r, _ := strconv.ParseFloat(unsignNaN(subs[real1]), 64)
i, err := strconv.ParseFloat(unsignNaN(subs[imag1]), 64)
return complex(r, i), err
}
if subs[real2] != "" && subs[sign2] != "" {
r, err := strconv.ParseFloat(unsignNaN(subs[real2]), 64)
if subs[sign2] == "-" {
return complex(r, -1), err
}
return complex(r, 1), err
}
if subs[imag3] != "" {
i, err := strconv.ParseFloat(unsignNaN(subs[imag3]), 64)
return complex(0, i), err
}
if subs[real4] != "" {
r, err := strconv.ParseFloat(unsignNaN(subs[real4]), 64)
return complex(r, 0), err
}
if subs[sign5] != "" {
if subs[sign5] == "-" {
return complex(0, -1), nil
}
return complex(0, 1), nil
}
if subs[onlyJ] != "" {
return complex(0, 1), nil
}
return complex(0, 0), errors.New("Malformed complex string")
}
func unsignNaN(s string) string {
ls := strings.ToLower(s)
if ls == "-nan" || ls == "+nan" {
return "nan"
}
return s
}
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