/*
Copyright 2019 The Kubernetes Authors.

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 testing

import (
	"math"
	"sync"
	"time"

	"k8s.io/apimachinery/pkg/util/clock"
)

// Integrator computes the integral of some variable X over time as
// read from a particular clock.  The integral starts when the
// Integrator is created, and ends at the latest operation on the
// Integrator.
type Integrator interface {
	Set(float64) // set the value of X
	Add(float64) // add the given quantity to X
	GetResults() IntegratorResults
}

// IntegratorResults holds statistical abstracts of the integration
type IntegratorResults struct {
	Duration  float64 //seconds
	Average   float64
	Deviation float64 //sqrt(avg((value-avg)^2))
}

type integrator struct {
	sync.Mutex
	clk       clock.PassiveClock
	lastTime  time.Time
	x         float64
	integrals [3]float64 // integral of x^0, x^1, and x^2
}

// NewIntegrator makes one that uses the given clock
func NewIntegrator(clk clock.PassiveClock) Integrator {
	return &integrator{
		clk:      clk,
		lastTime: clk.Now(),
	}
}

func (igr *integrator) Set(x float64) {
	igr.Lock()
	igr.updateLocked()
	igr.x = x
	igr.Unlock()
}

func (igr *integrator) Add(deltaX float64) {
	igr.Lock()
	igr.updateLocked()
	igr.x += deltaX
	igr.Unlock()
}

func (igr *integrator) updateLocked() {
	now := igr.clk.Now()
	dt := now.Sub(igr.lastTime).Seconds()
	igr.lastTime = now
	igr.integrals[0] += dt
	igr.integrals[1] += dt * igr.x
	igr.integrals[2] += dt * igr.x * igr.x
}

func (igr *integrator) GetResults() (results IntegratorResults) {
	igr.Lock()
	defer func() { igr.Unlock() }()
	igr.updateLocked()
	results.Duration = igr.integrals[0]
	if results.Duration <= 0 {
		results.Average = math.NaN()
		results.Deviation = math.NaN()
		return
	}
	results.Average = igr.integrals[1] / igr.integrals[0]
	// Deviation is sqrt( Integral( (x - xbar)^2 dt) / Duration )
	// = sqrt( Integral( x^2 + xbar^2 -2*x*xbar dt ) / Duration )
	// = sqrt( ( Integral( x^2 dt ) + Duration * xbar^2 - 2*xbar*Integral(x dt) ) / Duration)
	// = sqrt( Integral(x^2 dt)/Duration - xbar^2 )
	variance := igr.integrals[2]/igr.integrals[0] - results.Average*results.Average
	if variance > 0 {
		results.Deviation = math.Sqrt(variance)
	}
	return
}