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// 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
}
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