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/*
* Copyright 2013 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "Test.h"
#include "SkRandom.h"
#include "SkTSort.h"
static bool anderson_darling_test(double p[32]) {
// Min and max Anderson-Darling values allowable for k=32
const double kADMin32 = 0.202; // p-value of ~0.1
const double kADMax32 = 3.89; // p-value of ~0.99
// sort p values
SkTQSort<double>(p, p + 31);
// and compute Anderson-Darling statistic to ensure these are uniform
double s = 0.0;
for(int k = 0; k < 32; k++) {
double v = p[k]*(1.0 - p[31-k]);
if (v < 1.0e-30) {
v = 1.0e-30;
}
s += (2.0*(k+1)-1.0)*log(v);
}
double a2 = -32.0 - 0.03125*s;
return (kADMin32 < a2 && a2 < kADMax32);
}
static bool chi_square_test(int bins[256], int e) {
// Min and max chisquare values allowable
const double kChiSqMin256 = 206.3179; // probability of chance = 0.99 with k=256
const double kChiSqMax256 = 311.5603; // probability of chance = 0.01 with k=256
// compute chi-square
double chi2 = 0.0;
for (int j = 0; j < 256; ++j) {
double delta = bins[j] - e;
chi2 += delta*delta/e;
}
return (kChiSqMin256 < chi2 && chi2 < kChiSqMax256);
}
// Approximation to the normal distribution CDF
// From Waissi and Rossin, 1996
static double normal_cdf(double z) {
double t = ((-0.0004406*z*z* + 0.0418198)*z*z + 0.9)*z;
t *= -1.77245385091; // -sqrt(PI)
double p = 1.0/(1.0 + exp(t));
return p;
}
static void test_random_byte(skiatest::Reporter* reporter, int shift) {
int bins[256];
memset(bins, 0, sizeof(int)*256);
SkMWCRandom rand;
for (int i = 0; i < 256*10000; ++i) {
bins[(rand.nextU() >> shift) & 0xff]++;
}
REPORTER_ASSERT(reporter, chi_square_test(bins, 10000));
}
static void test_random_float(skiatest::Reporter* reporter) {
int bins[256];
memset(bins, 0, sizeof(int)*256);
SkMWCRandom rand;
for (int i = 0; i < 256*10000; ++i) {
float f = rand.nextF();
REPORTER_ASSERT(reporter, 0.0f <= f && f < 1.0f);
bins[(int)(f*256.f)]++;
}
REPORTER_ASSERT(reporter, chi_square_test(bins, 10000));
double p[32];
for (int j = 0; j < 32; ++j) {
float f = rand.nextF();
REPORTER_ASSERT(reporter, 0.0f <= f && f < 1.0f);
p[j] = f;
}
REPORTER_ASSERT(reporter, anderson_darling_test(p));
}
// This is a test taken from tuftests by Marsaglia and Tsang. The idea here is that
// we are using the random bit generated from a single shift position to generate
// "strings" of 16 bits in length, shifting the string and adding a new bit with each
// iteration. We track the numbers generated. The ones that we don't generate will
// have a normal distribution with mean ~24108 and standard deviation ~127. By
// creating a z-score (# of deviations from the mean) for one iteration of this step
// we can determine its probability.
//
// The original test used 26 bit strings, but is somewhat slow. This version uses 16
// bits which is less rigorous but much faster to generate.
static double test_single_gorilla(skiatest::Reporter* reporter, int shift) {
const int kWordWidth = 16;
const double kMean = 24108.0;
const double kStandardDeviation = 127.0;
const int kN = (1 << kWordWidth);
const int kNumEntries = kN >> 5; // dividing by 32
unsigned int entries[kNumEntries];
SkMWCRandom rand;
memset(entries, 0, sizeof(unsigned int)*kNumEntries);
// pre-seed our string value
int value = 0;
for (int i = 0; i < kWordWidth-1; ++i) {
value <<= 1;
unsigned int rnd = rand.nextU();
value |= ((rnd >> shift) & 0x1);
}
// now make some strings and track them
for (int i = 0; i < kN; ++i) {
value <<= 1;
unsigned int rnd = rand.nextU();
value |= ((rnd >> shift) & 0x1);
int index = value & (kNumEntries-1);
SkASSERT(index < kNumEntries);
int entry_shift = (value >> (kWordWidth-5)) & 0x1f;
entries[index] |= (0x1 << entry_shift);
}
// count entries
int total = 0;
for (int i = 0; i < kNumEntries; ++i) {
unsigned int entry = entries[i];
while (entry) {
total += (entry & 0x1);
entry >>= 1;
}
}
// convert counts to normal distribution z-score
double z = ((kN-total)-kMean)/kStandardDeviation;
// compute probability from normal distibution CDF
double p = normal_cdf(z);
REPORTER_ASSERT(reporter, 0.01 < p && p < 0.99);
return p;
}
static void test_gorilla(skiatest::Reporter* reporter) {
double p[32];
for (int bit_position = 0; bit_position < 32; ++bit_position) {
p[bit_position] = test_single_gorilla(reporter, bit_position);
}
REPORTER_ASSERT(reporter, anderson_darling_test(p));
}
static void test_range(skiatest::Reporter* reporter) {
SkMWCRandom rand;
// just to make sure we don't crash in this case
(void) rand.nextRangeU(0, 0xffffffff);
// check a case to see if it's uniform
int bins[256];
memset(bins, 0, sizeof(int)*256);
for (int i = 0; i < 256*10000; ++i) {
unsigned int u = rand.nextRangeU(17, 17+255);
REPORTER_ASSERT(reporter, 17 <= u && u <= 17+255);
bins[u - 17]++;
}
REPORTER_ASSERT(reporter, chi_square_test(bins, 10000));
}
static void TestRandom(skiatest::Reporter* reporter) {
// check uniform distributions of each byte in 32-bit word
test_random_byte(reporter, 0);
test_random_byte(reporter, 8);
test_random_byte(reporter, 16);
test_random_byte(reporter, 24);
test_random_float(reporter);
test_gorilla(reporter);
test_range(reporter);
}
#include "TestClassDef.h"
DEFINE_TESTCLASS("Random", RandomTestClass, TestRandom)
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