// base/kaldi-math.h
// Copyright 2009-2011 Ondrej Glembek; Microsoft Corporation; Yanmin Qian;
// Jan Silovsky; Saarland University
//
// 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.
#ifndef KALDI_BASE_KALDI_MATH_H_
#define KALDI_BASE_KALDI_MATH_H_ 1
#ifdef _MSC_VER
#include <float.h>
#endif
#include <cmath>
#include <limits>
#include <vector>
#include "base/kaldi-types.h"
#include "base/kaldi-common.h"
#ifndef DBL_EPSILON
#define DBL_EPSILON 2.2204460492503131e-16
#endif
#ifndef FLT_EPSILON
#define FLT_EPSILON 1.19209290e-7f
#endif
#ifndef M_PI
# define M_PI 3.1415926535897932384626433832795
#endif
#ifndef M_SQRT2
# define M_SQRT2 1.4142135623730950488016887
#endif
#ifndef M_2PI
# define M_2PI 6.283185307179586476925286766559005
#endif
#ifndef M_SQRT1_2
# define M_SQRT1_2 0.7071067811865475244008443621048490
#endif
#ifndef M_LOG_2PI
#define M_LOG_2PI 1.8378770664093454835606594728112
#endif
#ifndef M_LN2
#define M_LN2 0.693147180559945309417232121458
#endif
#ifdef _MSC_VER
# define KALDI_ISNAN _isnan
# define KALDI_ISINF(x) (!_isnan(x) && _isnan(x-x))
# define KALDI_ISFINITE _finite
#else
# define KALDI_ISNAN std::isnan
# define KALDI_ISINF std::isinf
# define KALDI_ISFINITE(x) std::isfinite(x)
#endif
#if !defined(KALDI_SQR)
# define KALDI_SQR(x) ((x) * (x))
#endif
namespace kaldi {
// -infinity
const float kLogZeroFloat = -std::numeric_limits<float>::infinity();
const double kLogZeroDouble = -std::numeric_limits<double>::infinity();
const BaseFloat kLogZeroBaseFloat = -std::numeric_limits<BaseFloat>::infinity();
// Returns a random integer between 0 and RAND_MAX, inclusive
int Rand(struct RandomState* state=NULL);
// State for thread-safe random number generator
struct RandomState {
RandomState();
unsigned seed;
};
// Returns a random integer between min and max inclusive.
int32 RandInt(int32 min, int32 max, struct RandomState* state=NULL);
bool WithProb(BaseFloat prob, struct RandomState* state=NULL); // Returns true with probability "prob",
// with 0 <= prob <= 1 [we check this].
// Internally calls Rand(). This function is carefully implemented so
// that it should work even if prob is very small.
/// Returns a random number strictly between 0 and 1.
inline float RandUniform(struct RandomState* state = NULL) {
return static_cast<float>((Rand(state) + 1.0) / (RAND_MAX+2.0));
}
inline float RandGauss(struct RandomState* state = NULL) {
return static_cast<float>(sqrtf (-2 * logf(RandUniform(state)))
* cosf(2*M_PI*RandUniform(state)));
}
// Returns poisson-distributed random number. Uses Knuth's algorithm.
// Take care: this takes time proportinal
// to lambda. Faster algorithms exist but are more complex.
int32 RandPoisson(float lambda, struct RandomState* state=NULL);
// Returns a pair of gaussian random numbers. Uses Box-Muller transform
void RandGauss2(float *a, float *b, RandomState *state = NULL);
void RandGauss2(double *a, double *b, RandomState *state = NULL);
// Also see Vector<float,double>::RandCategorical().
// This is a randomized pruning mechanism that preserves expectations,
// that we typically use to prune posteriors.
template<class Float>
inline Float RandPrune(Float post, BaseFloat prune_thresh, struct RandomState* state=NULL) {
KALDI_ASSERT(prune_thresh >= 0.0);
if (post == 0.0 || std::abs(post) >= prune_thresh)
return post;
return (post >= 0 ? 1.0 : -1.0) *
(RandUniform(state) <= fabs(post)/prune_thresh ? prune_thresh : 0.0);
}
static const double kMinLogDiffDouble = std::log(DBL_EPSILON); // negative!
static const float kMinLogDiffFloat = std::log(FLT_EPSILON); // negative!
inline double LogAdd(double x, double y) {
double diff;
if (x < y) {
diff = x - y;
x = y;
} else {
diff = y - x;
}
// diff is negative. x is now the larger one.
if (diff >= kMinLogDiffDouble) {
double res;
#ifdef _MSC_VER
res = x + log(1.0 + exp(diff));
#else
res = x + log1p(exp(diff));
#endif
return res;
} else {
return x; // return the larger one.
}
}
inline float LogAdd(float x, float y) {
float diff;
if (x < y) {
diff = x - y;
x = y;
} else {
diff = y - x;
}
// diff is negative. x is now the larger one.
if (diff >= kMinLogDiffFloat) {
float res;
#ifdef _MSC_VER
res = x + logf(1.0 + expf(diff));
#else
res = x + log1pf(expf(diff));
#endif
return res;
} else {
return x; // return the larger one.
}
}
// returns exp(x) - exp(y).
inline double LogSub(double x, double y) {
if (y >= x) { // Throws exception if y>=x.
if (y == x)
return kLogZeroDouble;
else
KALDI_ERR << "Cannot subtract a larger from a smaller number.";
}
double diff = y - x; // Will be negative.
double res = x + log(1.0 - exp(diff));
// res might be NAN if diff ~0.0, and 1.0-exp(diff) == 0 to machine precision
if (KALDI_ISNAN(res))
return kLogZeroDouble;
return res;
}
// returns exp(x) - exp(y).
inline float LogSub(float x, float y) {
if (y >= x) { // Throws exception if y>=x.
if (y == x)
return kLogZeroDouble;
else
KALDI_ERR << "Cannot subtract a larger from a smaller number.";
}
float diff = y - x; // Will be negative.
float res = x + logf(1.0 - expf(diff));
// res might be NAN if diff ~0.0, and 1.0-exp(diff) == 0 to machine precision
if (KALDI_ISNAN(res))
return kLogZeroFloat;
return res;
}
/// return abs(a - b) <= relative_tolerance * (abs(a)+abs(b)).
static inline bool ApproxEqual(float a, float b,
float relative_tolerance = 0.001) {
// a==b handles infinities.
if (a==b) return true;
float diff = std::abs(a-b);
if (diff == std::numeric_limits<float>::infinity()
|| diff != diff) return false; // diff is +inf or nan.
return (diff <= relative_tolerance*(std::abs(a)+std::abs(b)));
}
/// assert abs(a - b) <= relative_tolerance * (abs(a)+abs(b))
static inline void AssertEqual(float a, float b,
float relative_tolerance = 0.001) {
// a==b handles infinities.
KALDI_ASSERT(ApproxEqual(a, b, relative_tolerance));
}
// RoundUpToNearestPowerOfTwo does the obvious thing. It crashes if n <= 0.
int32 RoundUpToNearestPowerOfTwo(int32 n);
template<class I> I Gcd(I m, I n) {
if (m == 0 || n == 0) {
if (m == 0 && n == 0) { // gcd not defined, as all integers are divisors.
KALDI_ERR << "Undefined GCD since m = 0, n = 0.";
}
return (m == 0 ? (n > 0 ? n : -n) : ( m > 0 ? m : -m));
// return absolute value of whichever is nonzero
}
// could use compile-time assertion
// but involves messing with complex template stuff.
KALDI_ASSERT(std::numeric_limits<I>::is_integer);
while (1) {
m %= n;
if (m == 0) return (n > 0 ? n : -n);
n %= m;
if (n == 0) return (m > 0 ? m : -m);
}
}
/// Returns the least common multiple of two integers. Will
/// crash unless the inputs are positive.
template<class I> I Lcm(I m, I n) {
KALDI_ASSERT(m > 0 && n > 0);
I gcd = Gcd(m, n);
return gcd * (m/gcd) * (n/gcd);
}
template<class I> void Factorize(I m, std::vector<I> *factors) {
// Splits a number into its prime factors, in sorted order from
// least to greatest, with duplication. A very inefficient
// algorithm, which is mainly intended for use in the
// mixed-radix FFT computation (where we assume most factors
// are small).
KALDI_ASSERT(factors != NULL);
KALDI_ASSERT(m >= 1); // Doesn't work for zero or negative numbers.
factors->clear();
I small_factors[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
// First try sm