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// base/kaldi-math-test.cc
//
// Copyright 2009-2011 Microsoft Corporation; Yanmin Qian; Jan Silovsky
// See ../../COPYING for clarification regarding multiple authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
// MERCHANTABLITY OR NON-INFRINGEMENT.
// See the Apache 2 License for the specific language governing permissions and
// limitations under the License.
#include "base/kaldi-math.h"
#include <limits>
#include "base/timer.h"
namespace kaldi {
template<class I> void UnitTestGcdLcmTpl() {
for (I a = 1; a < 15; a++) { // a is min gcd.
I b = (I)(Rand() % 10);
I c = (I)(Rand() % 10);
if (std::numeric_limits<I>::is_signed) {
if (Rand() % 2 == 0) b = -b;
if (Rand() % 2 == 0) c = -c;
}
if (b == 0 && c == 0) continue; // gcd not defined for such numbers.
I g = Gcd(b*a, c*a);
KALDI_ASSERT(g >= a);
KALDI_ASSERT((b*a) % g == 0);
KALDI_ASSERT((c*a) % g == 0);
// test least common multiple
if (b <= 0 || c <= 0) continue; // lcm not defined unless both positive.
I h = Lcm(b*a, c*a);
KALDI_ASSERT(h != 0 && (h % (b*a)) == 0 &&
(h % (c*a)) == 0);
}
}
void UnitTestRoundUpToNearestPowerOfTwo() {
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(1) == 1);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(2) == 2);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(3) == 4);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(4) == 4);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(7) == 8);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(8) == 8);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(255) == 256);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(256) == 256);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(257) == 512);
KALDI_ASSERT(RoundUpToNearestPowerOfTwo(1073700000) == 1073741824);
}
void UnitTestDivideRoundingDown() {
for (int32 i = 0; i < 100; i++) {
int32 a = RandInt(-100, 100);
int32 b = 0;
while (b == 0)
b = RandInt(-100, 100);
KALDI_ASSERT(DivideRoundingDown(a, b) ==
std::floor(static_cast<double>(a) / static_cast<double>(b)));
}
}
void UnitTestGcdLcm() {
UnitTestGcdLcmTpl<int>();
UnitTestGcdLcmTpl<size_t>();
UnitTestGcdLcmTpl<int16>();
}
void UnitTestRand() {
// Testing random-number generation.
std::cout << "Testing random-number generation. "
<< "If there is an error this may not terminate.\n";
std::cout << "If this does not terminate, look more closely. "
<< "There might be a problem [but might not be]\n";
for (int i = 1; i < 10; i++) {
{ // test RandUniform.
std::cout << "Test RandUniform\n";
KALDI_ASSERT(RandUniform() >= 0 && RandUniform() <= 1);
float sum = RandUniform()-0.5;
for (int j = 0; ; j++) {
sum += RandUniform()-0.5;
if (std::abs(sum) < 0.5*sqrt(static_cast<double>(j))) break;
}
}
{ // test RandGauss.
float sum = RandGauss();
for (int j = 0; ; j++) {
sum += RandGauss();
if (std::abs(sum) < 0.5*sqrt(static_cast<double>(j))) break;
}
}
{ // test RandGauss.
float sum = RandGauss();
for (int j = 0; ; j++) {
float a, b;
RandGauss2(&a, &b);
if (i % 2 == 0) sum += a;
else
sum += b;
if (std::abs(sum) < 0.5*sqrt(static_cast<double>(j))) break;
}
}
{ // test poisson_Rand().
KALDI_ASSERT(RandPoisson(3.0) >= 0);
KALDI_ASSERT(RandPoisson(0.0) == 0);
std::cout << "Test RandPoisson\n";
float lambda = RandUniform() * 3.0; // between 0 and 3.
double sum = RandPoisson(lambda) - lambda; // expected value is zero.
for (int j = 0; ; j++) {
sum += RandPoisson(lambda) - lambda;
if (std::abs(sum) < 0.5*sqrt(static_cast<double>(j))) break;
}
}
{ // test WithProb().
for (int32 i = 0; i < 10; i++) {
KALDI_ASSERT((WithProb(0.0) == false) && (WithProb(1.0) == true));
}
{
int32 tot = 0, n = 10000;
BaseFloat p = 0.5;
for (int32 i = 0; i < n; i++)
tot += WithProb(p);
KALDI_ASSERT(tot > (n * p * 0.8) && tot < (n * p * 1.2));
}
{
int32 tot = 0, n = 10000;
BaseFloat p = 0.25;
for (int32 i = 0; i < n; i++)
tot += WithProb(p);
KALDI_ASSERT(tot > (n * p * 0.8) && tot < (n * p * 1.2));
}
}
{ // test RandInt().
KALDI_ASSERT(RandInt(0, 3) >= 0 && RandInt(0, 3) <= 3);
std::cout << "Test RandInt\n";
int minint = Rand() % 200;
int maxint = minint + 1 + Rand() % 20;
float sum = RandInt(minint, maxint) + 0.5*(minint+maxint);
for (int j = 0; ; j++) {
sum += RandInt(minint, maxint) - 0.5*(minint+maxint);
if (std::abs(static_cast<float>(sum)) <
0.5*sqrt(static_cast<double>(j))*(maxint-minint)) break;
}
}
{ // test RandPrune in basic way.
KALDI_ASSERT(RandPrune(1.1, 1.0) == 1.1);
KALDI_ASSERT(RandPrune(0.0, 0.0) == 0.0);
KALDI_ASSERT(RandPrune(-1.1, 1.0) == -1.1);
KALDI_ASSERT(RandPrune(0.0, 1.0) == 0.0);
KALDI_ASSERT(RandPrune(0.5, 1.0) >= 0.0);
KALDI_ASSERT(RandPrune(-0.5, 1.0) <= 0.0);
BaseFloat f = RandPrune(-0.5, 1.0);
KALDI_ASSERT(f == 0.0 || f == -1.0);
f = RandPrune(0.5, 1.0);
KALDI_ASSERT(f == 0.0 || f == 1.0);
}
}
}
void UnitTestLogAddSub() {
for (int i = 0; i < 100; i++) {
double f1 = Rand() % 10000, f2 = Rand() % 20;
double add1 = Exp(LogAdd(Log(f1), Log(f2)));
double add2 = Exp(LogAdd(Log(f2), Log(f1)));
double add = f1 + f2, thresh = add*0.00001;
KALDI_ASSERT(std::abs(add-add1) < thresh && std::abs(add-add2) < thresh);
try {
double f2_check = Exp(LogSub(Log(add), Log(f1))),
thresh = (f2*0.01)+0.001;
KALDI_ASSERT(std::abs(f2_check-f2) < thresh);
} catch(...) {
KALDI_ASSERT(f2 == 0); // It will probably crash for f2=0.
}
}
}
void UnitTestDefines() { // Yes, we even unit-test the preprocessor statements.
KALDI_ASSERT(Exp(kLogZeroFloat) == 0.0);
KALDI_ASSERT(Exp(kLogZeroDouble) == 0.0);
BaseFloat den = 0.0;
KALDI_ASSERT(KALDI_ISNAN(0.0 / den));
KALDI_ASSERT(!KALDI_ISINF(0.0 / den));
KALDI_ASSERT(!KALDI_ISFINITE(0.0 / den));
KALDI_ASSERT(!KALDI_ISNAN(1.0 / den));
KALDI_ASSERT(KALDI_ISINF(1.0 / den));
KALDI_ASSERT(!KALDI_ISFINITE(1.0 / den));
KALDI_ASSERT(KALDI_ISFINITE(0.0));
KALDI_ASSERT(!KALDI_ISINF(0.0));
KALDI_ASSERT(!KALDI_ISNAN(0.0));
std::cout << 1.0+DBL_EPSILON;
std::cout << 1.0 + 0.5*DBL_EPSILON;
KALDI_ASSERT(1.0 + DBL_EPSILON != 1.0 && 1.0 + (0.5*DBL_EPSILON) == 1.0
&& "If this test fails, you can probably just comment it out-- "
"may mean your CPU exceeds expected floating point precision");
KALDI_ASSERT(1.0f + FLT_EPSILON != 1.0f && 1.0f + (0.5f*FLT_EPSILON) == 1.0f
&& "If this test fails, you can probably just comment it out-- "
"may mean your CPU exceeds expected floating point precision");
KALDI_ASSERT(std::abs(sin(M_PI)) < 1.0e-05
&& std::abs(cos(M_PI)+1.0) < 1.0e-05);
KALDI_ASSERT(std::abs(sin(M_2PI)) < 1.0e-05
&& std::abs(cos(M_2PI)-1.0) < 1.0e-05);
KALDI_ASSERT(std::abs(sin(Exp(M_LOG_2PI))) < 1.0e-05);
KALDI_ASSERT(std::abs(cos(Exp(M_LOG_2PI)) - 1.0) < 1.0e-05);
}
void UnitTestAssertFunc() { // Testing Assert** *functions
for (int i = 1; i < 100; i++) {
float f1 = Rand() % 10000 + 1, f2 = Rand() % 20 + 1;
float tmp1 = f1 * f2;
float tmp2 = (1/f1 + 1/f2);
float add = f1 + f2;
float addeql = tmp1 * tmp2;
float thresh = 0.00001;
AssertEqual(add, addeql, thresh); // test AssertEqual()
}
}
template<class I> void UnitTestFactorizeTpl() {
for (int p= 0; p < 100; p++) {
I m = Rand() % 100000;
if (m >= 1) {
std::vector<I> factors;
Factorize(m, &factors);
I m2 = 1;
for (size_t i = 0; i < factors.size(); i++) {
m2 *= factors[i];
if (i+1 < factors.size())
KALDI_ASSERT(factors[i+1] >= factors[i]); // check sorted.
}
KALDI_ASSERT(m2 == m); // check correctness.
}
}
}
void UnitTestFactorize() {
UnitTestFactorizeTpl<int>();
UnitTestFactorizeTpl<size_t>();
UnitTestFactorizeTpl<int16>();
}
void UnitTestApproxEqual() {
KALDI_ASSERT(ApproxEqual(1.0, 1.00001));
KALDI_ASSERT(ApproxEqual(1.0, 1.00001, 0.001));
KALDI_ASSERT(!ApproxEqual(1.0, 1.1));
KALDI_ASSERT(!ApproxEqual(1.0, 1.01, 0.001));
KALDI_ASSERT(!ApproxEqual(1.0, 0.0));
KALDI_ASSERT(ApproxEqual(0.0, 0.0));
KALDI_ASSERT(!ApproxEqual(0.0, 0.00001));
KALDI_ASSERT(!ApproxEqual(std::numeric_limits<float>::infinity(),
-std::numeric_limits<float>::infinity()));
KALDI_ASSERT(ApproxEqual(std::numeric_limits<float>::infinity(),
std::numeric_limits<float>::infinity()));
KALDI_ASSERT(ApproxEqual(-std::numeric_limits<float>::infinity(),
-std::numeric_limits<float>::infinity()));
KALDI_ASSERT(!ApproxEqual(-std::numeric_limits<float>::infinity(),
0));
KALDI_ASSERT(!ApproxEqual(-std::numeric_limits<float>::infinity(),
1));
}
template<class Real>
void UnitTestExpSpeed() {
Real sum = 0.0; // compute the sum to avoid optimizing it away.
Real time = 0.01; // how long this should last.
int block_size = 10;
int num_ops = 0;
Timer tim;
while (tim.Elapsed() < time) {
for (int i = 0; i < block_size; i++) {
sum += Exp((Real)i);
}
num_ops += block_size;
}
KALDI_ASSERT(sum > 0.0); // make it harder for the compiler to optimize Exp
// away, as we have a conditional.
Real flops = 1.0e-06 * num_ops / tim.Elapsed();
KALDI_LOG << "Megaflops doing Exp("
<< (sizeof(Real) == 4 ? "float" : "double") << ") is " << flops;
}
template<class Real>
void UnitTestLogSpeed() {
Real sum = 0.0; // compute the sum to avoid optimizing it away.
Real time = 0.01; // how long this should last.
int block_size = 10;
int num_ops = 0;
Timer tim;
while (tim.Elapsed() < time) {
for (int i = 0; i < block_size; i++) {
sum += Log(static_cast<float>(i + 1));
}
num_ops += block_size;
}
KALDI_ASSERT(sum > 0.0); // make it harder for the compiler to optimize Log
// away, as we have a conditional.
Real flops = 1.0e-06 * num_ops / tim.Elapsed();
KALDI_LOG << "Megaflops doing Log("
<< (sizeof(Real) == 4 ? "float" : "double") << ") is " << flops;
}
} // end namespace kaldi.
int main() {
using namespace kaldi;
UnitTestApproxEqual();
UnitTestGcdLcm();
UnitTestFactorize();
UnitTestDefines();
UnitTestLogAddSub();
UnitTestRand();
UnitTestAssertFunc();
UnitTestRoundUpToNearestPowerOfTwo();
UnitTestDivideRoundingDown();
UnitTestExpSpeed<float>();
UnitTestExpSpeed<double>();
UnitTestLogSpeed<float>();
UnitTestLogSpeed<double>();
}