// Copyright ©2017 The Gonum 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 fd

import (
	"math"
	"runtime"
	"sync"
)

// Derivative estimates the derivative of the function f at the given location.
// The finite difference formula, the step size, and other options are
// specified by settings. If settings is nil, the first derivative will be
// estimated using the Forward formula and a default step size.
func Derivative(f func(float64) float64, x float64, settings *Settings) float64 {
	// Default settings.
	formula := Forward
	step := formula.Step
	var originValue float64
	var originKnown, concurrent bool

	// Use user settings if provided.
	if settings != nil {
		if !settings.Formula.isZero() {
			formula = settings.Formula
			step = formula.Step
			checkFormula(formula)
		}
		if settings.Step != 0 {
			step = settings.Step
		}
		originKnown = settings.OriginKnown
		originValue = settings.OriginValue
		concurrent = settings.Concurrent
	}

	var deriv float64
	if !concurrent || runtime.GOMAXPROCS(0) == 1 {
		for _, pt := range formula.Stencil {
			if originKnown && pt.Loc == 0 {
				deriv += pt.Coeff * originValue
				continue
			}
			deriv += pt.Coeff * f(x+step*pt.Loc)
		}
		return deriv / math.Pow(step, float64(formula.Derivative))
	}

	wg := &sync.WaitGroup{}
	mux := &sync.Mutex{}
	for _, pt := range formula.Stencil {
		if originKnown && pt.Loc == 0 {
			mux.Lock()
			deriv += pt.Coeff * originValue
			mux.Unlock()
			continue
		}
		wg.Add(1)
		go func(pt Point) {
			defer wg.Done()
			fofx := f(x + step*pt.Loc)
			mux.Lock()
			defer mux.Unlock()
			deriv += pt.Coeff * fofx
		}(pt)
	}
	wg.Wait()
	return deriv / math.Pow(step, float64(formula.Derivative))
}