// run

// Copyright 2020 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package main

import "math"

type Numeric interface {
	type int, int8, int16, int32, int64,
		uint, uint8, uint16, uint32, uint64, uintptr,
		float32, float64,
		complex64, complex128
}

// NumericAbs matches numeric types with an Abs method.
type NumericAbs[T any] interface {
	Numeric
	Abs() T
}

// AbsDifference computes the absolute value of the difference of
// a and b, where the absolute value is determined by the Abs method.
func AbsDifference[T NumericAbs[T]](a, b T) T {
	d := a - b
	return d.Abs()
}

// OrderedNumeric matches numeric types that support the < operator.
type OrderedNumeric interface {
	type int, int8, int16, int32, int64,
		uint, uint8, uint16, uint32, uint64, uintptr,
		float32, float64
}

// Complex matches the two complex types, which do not have a < operator.
type Complex interface {
	type complex64, complex128
}

// OrderedAbs is a helper type that defines an Abs method for
// ordered numeric types.
type OrderedAbs[T OrderedNumeric] T

func (a OrderedAbs[T]) Abs() OrderedAbs[T] {
	if a < 0 {
		return -a
	}
	return a
}

// ComplexAbs is a helper type that defines an Abs method for
// complex types.
type ComplexAbs[T Complex] T

func (a ComplexAbs[T]) Abs() ComplexAbs[T] {
	r := float64(real(a))
	i := float64(imag(a))
	d := math.Sqrt(r * r + i * i)
	return ComplexAbs[T](complex(d, 0))
}

// OrderedAbsDifference returns the absolute value of the difference
// between a and b, where a and b are of an ordered type.
func OrderedAbsDifference[T OrderedNumeric](a, b T) T {
	return T(AbsDifference(OrderedAbs[T](a), OrderedAbs[T](b)))
}

// ComplexAbsDifference returns the absolute value of the difference
// between a and b, where a and b are of a complex type.
func ComplexAbsDifference[T Complex](a, b T) T {
	return T(AbsDifference(ComplexAbs[T](a), ComplexAbs[T](b)))
}

func main() {
	if d := OrderedAbsDifference(1.0, -2.0); d != 3 {
		panic(d)
	}
	if d := OrderedAbsDifference(-1.0, 2.0); d != 3 {
		panic(d)
	}
	if d := ComplexAbsDifference(5.0 + 2.0i, 2.0 - 2.0i); d != 5 {
		panic(d)
	}
	if d := ComplexAbsDifference(2.0 - 2.0i, 5.0 + 2.0i); d != 5 {
		panic(d)
	}
}