// Copyright (c) 2021 Quan guanyu
// randomness is licensed under Mulan PSL v2.
// You can use this software according to the terms and conditions of the Mulan PSL v2.
// You may obtain a copy of Mulan PSL v2 at:
//          http://license.coscl.org.cn/MulanPSL2
// THIS SOFTWARE IS PROVIDED ON AN "AS IS" BASIS, WITHOUT WARRANTIES OF ANY KIND,
// EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO NON-INFRINGEMENT,
// MERCHANTABILITY OR FIT FOR A PARTICULAR PURPOSE.
// See the Mulan PSL v2 for more details.

package randomness

import (
	"math"
)

// Cumulative 累加和检测
func Cumulative(data []byte) *TestResult {
	p, q := CumulativeTestBytes(data, true)
	return &TestResult{Name: "累加和检测", P: p, Q: q, Pass: p >= Alpha}
}

// CumulativeTestBytes 累加和检测
// forward: true 前向, false 后向
func CumulativeTestBytes(data []byte, forward bool) (float64, float64) {
	return CumulativeTest(B2bitArr(data), forward)
}

// CumulativeTest 累加和检测
// forward: true 前向, false 后向
func CumulativeTest(bits []bool, forward bool) (float64, float64) {
	n := len(bits)

	if n == 0 {
		panic("please provide test bits")
	}

	var S int = 0
	var Z int = 0
	var P float64 = 1.0

	for i := 0; i < n; i++ {
		if forward {
			if bits[i] {
				S++
			} else {
				S--
			}
		} else {
			if bits[n-1-i] {
				S++
			} else {
				S--
			}
		}
		Z = max(Z, abs(S))
	}

	sqrtN := math.Sqrt(float64(n)) // 提前求平方根，避免下面多次求平方根
	for i := ((-n / Z) + 1) / 4; i <= ((n/Z)-1)/4; i++ {
		P -= normal_CDF(float64((4*i+1)*Z)/sqrtN) - normal_CDF(float64((4*i-1)*Z)/sqrtN)
	}
	for i := ((-n / Z) - 3) / 4; i <= ((n/Z)-1)/4; i++ {
		P += normal_CDF(float64((4*i+3)*Z)/sqrtN) - normal_CDF(float64((4*i+1)*Z)/sqrtN)
	}
	return P, P
}