// base/kaldi-math.cc
  
  // Copyright 2009-2011  Microsoft Corporation;  Yanmin Qian;
  //                      Saarland University;  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"
  #ifndef _MSC_VER
  #include <stdlib.h>
  #include <unistd.h>
  #endif
  #include <string>
  #include <mutex>
  
  namespace kaldi {
  // These routines are tested in matrix/matrix-test.cc
  
  int32 RoundUpToNearestPowerOfTwo(int32 n) {
    KALDI_ASSERT(n > 0);
    n--;
    n |= n >> 1;
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;
    return n+1;
  }
  
  static std::mutex _RandMutex;
  
  int Rand(struct RandomState* state) {
  #if !defined(_POSIX_THREAD_SAFE_FUNCTIONS)
    // On Windows and Cygwin, just call Rand()
    return rand();
  #else
    if (state) {
      return rand_r(&(state->seed));
    } else {
      std::lock_guard<std::mutex> lock(_RandMutex);
      return rand();
    }
  #endif
  }
  
  RandomState::RandomState() {
    // we initialize it as Rand() + 27437 instead of just Rand(), because on some
    // systems, e.g. at the very least Mac OSX Yosemite and later, it seems to be
    // the case that rand_r when initialized with rand() will give you the exact
    // same sequence of numbers that rand() will give if you keep calling rand()
    // after that initial call.  This can cause problems with repeated sequences.
    // For example if you initialize two RandomState structs one after the other
    // without calling rand() in between, they would give you the same sequence
    // offset by one (if we didn't have the "+ 27437" in the code).  27437 is just
    // a randomly chosen prime number.
    seed = Rand() + 27437;
  }
  
  bool WithProb(BaseFloat prob, struct RandomState* state) {
    KALDI_ASSERT(prob >= 0 && prob <= 1.1);  // prob should be <= 1.0,
    // but we allow slightly larger values that could arise from roundoff in
    // previous calculations.
    KALDI_COMPILE_TIME_ASSERT(RAND_MAX > 128 * 128);
    if (prob == 0) return false;
    else if (prob == 1.0) return true;
    else if (prob * RAND_MAX < 128.0) {
      // prob is very small but nonzero, and the "main algorithm"
      // wouldn't work that well.  So: with probability 1/128, we
      // return WithProb (prob * 128), else return false.
      if (Rand(state) < RAND_MAX / 128) {  // with probability 128...
        // Note: we know that prob * 128.0 < 1.0, because
        // we asserted RAND_MAX > 128 * 128.
        return WithProb(prob * 128.0);
      } else {
        return false;
      }
    } else {
      return (Rand(state) < ((RAND_MAX + static_cast<BaseFloat>(1.0)) * prob));
    }
  }
  
  int32 RandInt(int32 min_val, int32 max_val, struct RandomState* state) {
    // This is not exact.
    KALDI_ASSERT(max_val >= min_val);
    if (max_val == min_val) return min_val;
  
  #ifdef _MSC_VER
    // RAND_MAX is quite small on Windows -> may need to handle larger numbers.
    if (RAND_MAX > (max_val-min_val)*8) {
          // *8 to avoid large inaccuracies in probability, from the modulus...
      return min_val +
        ((unsigned int)Rand(state) % (unsigned int)(max_val+1-min_val));
    } else {
      if ((unsigned int)(RAND_MAX*RAND_MAX) >
          (unsigned int)((max_val+1-min_val)*8)) {
          // *8 to avoid inaccuracies in probability, from the modulus...
        return min_val + ( (unsigned int)( (Rand(state)+RAND_MAX*Rand(state)))
                      % (unsigned int)(max_val+1-min_val));
      } else {
        KALDI_ERR << "rand_int failed because we do not support such large "
            "random numbers. (Extend this function).";
      }
    }
  #else
    return min_val +
        (static_cast<int32>(Rand(state)) % static_cast<int32>(max_val+1-min_val));
  #endif
  }
  
  // Returns poisson-distributed random number.
  // Take care: this takes time proportinal
  // to lambda.  Faster algorithms exist but are more complex.
  int32 RandPoisson(float lambda, struct RandomState* state) {
    // Knuth's algorithm.
    KALDI_ASSERT(lambda >= 0);
    float L = expf(-lambda), p = 1.0;
    int32 k = 0;
    do {
      k++;
      float u = RandUniform(state);
      p *= u;
    } while (p > L);
    return k-1;
  }
  
  void RandGauss2(float *a, float *b, RandomState *state) {
    KALDI_ASSERT(a);
    KALDI_ASSERT(b);
    float u1 = RandUniform(state);
    float u2 = RandUniform(state);
    u1 = sqrtf(-2.0f * logf(u1));
    u2 =  2.0f * M_PI * u2;
    *a = u1 * cosf(u2);
    *b = u1 * sinf(u2);
  }
  
  void RandGauss2(double *a, double *b, RandomState *state) {
    KALDI_ASSERT(a);
    KALDI_ASSERT(b);
    float a_float, b_float;
    // Just because we're using doubles doesn't mean we need super-high-quality
    // random numbers, so we just use the floating-point version internally.
    RandGauss2(&a_float, &b_float, state);
    *a = a_float;
    *b = b_float;
  }
  
  
  }  // end namespace kaldi