| /* |
| * 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 "include/core/SkTypes.h" |
| #include "include/private/base/SkMath.h" |
| #include "src/base/SkRandom.h" |
| #include "src/base/SkTSort.h" |
| #include "tests/Test.h" |
| |
| #include <cmath> |
| #include <cstring> |
| |
| 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 + 32); |
| |
| // 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); |
| |
| SkRandom 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); |
| |
| SkRandom 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]; |
| |
| SkRandom 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 = SkLeftShift(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) { |
| SkRandom 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)); |
| } |
| |
| DEF_TEST(Random, 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); |
| } |