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mathematicalFunctions.cpp (mathematical functions C++ source code file) Print E-mail
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//
// Creator:    http://www.dicelocksecurity.com
// Version:    vers.6.0.0.1
//
// Copyright (C) 2008-2012 DiceLock Security, LLC. All rights reserved.
//
//                               DISCLAIMER
//
// THIS SOFTWARE IS PROVIDED "AS IS" AND ANY EXPRESSED OR IMPLIED WARRANTIES,
// INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
// AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
// REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// 
// DICELOCK IS A REGISTERED TRADEMARK OR TRADEMARK OF THE OWNERS.
// 
 
#include <stdlib.h>
#include <math.h>
#include "mathematicalFunctions.h"
 
 
namespace DiceLockSecurity {
 
  namespace RandomTest {
 
    const double MathematicalFunctions::MACHEP =  1.11022302462515654042E-16;  // 2**-53 
    const double MathematicalFunctions::MAXLOG =  7.09782712893383996732E2;    // log(MAXNUM) 
    const double MathematicalFunctions::MAXNUM =  1.79769313486231570815E308;    // 2**1024*(1-MACHEP) 
    const double MathematicalFunctions::PI     =  3.14159265358979323846;    // pi
    const double MathematicalFunctions::LOGPI = 1.14472988584940017414;      // log(pi) 
    const double MathematicalFunctions::LS2PI  =  0.91893853320467274178;    //( log( sqrt( 2*pi ) ) 
    const double MathematicalFunctions::big = 4.503599627370496e15;
    const double MathematicalFunctions::biginv =  2.22044604925031308085e-16;
    // A[]: Stirling's formula expansion of log gamma
    // B[], C[]: log gamma function between 2 and 3
    double MathematicalFunctions::A_lgam[] = {
      8.11614167470508450300E-4,
      -5.95061904284301438324E-4,
       7.93650340457716943945E-4,
      -2.77777777730099687205E-3,
       8.33333333333331927722E-2
    };
    double MathematicalFunctions::B_lgam[] = {
      -1.37825152569120859100E3,
      -3.88016315134637840924E4,
      -3.31612992738871184744E5,
      -1.16237097492762307383E6,
      -1.72173700820839662146E6,
      -8.53555664245765465627E5
    };
    double MathematicalFunctions::C_lgam[] = {
      -3.51815701436523470549E2,
      -1.70642106651881159223E4,
      -2.20528590553854454839E5,
      -1.13933444367982507207E6,
      -2.53252307177582951285E6,
      -2.01889141433532773231E6
    };
    const double MathematicalFunctions::MAXLGM = 2.556348e305;
 
    // Constructor
    MathematicalFunctions::MathematicalFunctions() {
    }
 
    // Destructor
    MathematicalFunctions::~MathematicalFunctions() {
    }
 
    // Logarithm of gamma function
    double MathematicalFunctions::LGamma(double x) {
      double p, q, u, w, z;
      signed long int i;
      signed long int sgngam = 0;
 
      sgngam = 1;
      this->Error = false;
      this->MathError = None;
      if (x < -34.0) {
             q = -x;
             w = this->LGamma(q); /* note this modifies sgngam! */
             p = floor(q);
        if( p == q ) {
        lgsing:
          goto loverf;
        }
        i = (int)p;
          if ((i & 1) == 0)
          sgngam = -1;
        else
          sgngam = 1;
        z = q - p;
        if (z > 0.5) {
          p += 1.0;
          z = p - q;
        }
        z = q * sin( this->PI * z );
        if (z == 0.0)
          goto lgsing;
        z = this->LOGPI - log( z ) - w;
        return (z);
      }
      if (x < 13.0) {
        z = 1.0;
        p = 0.0;
        u = x;
        while (u >= 3.0) {
          p -= 1.0;
          u = x + p;
          z *= u;
        }
        while (u < 2.0) {
          if (u == 0.0)
            goto lgsing;
          z /= u;
          p += 1.0;
          u = x + p;
        }
        if (z < 0.0) {
          sgngam = -1;
          z = -z;
        }
        else
          sgngam = 1;
        if (u == 2.0)
          return (log(z));
        p -= 2.0;
        x = x + p;
        p = x * this->PolEvl(x, &this->B_lgam[0], 5)/this->P1Evl( x, &this->C_lgam[0], 6);
        return (log(z) + p);
      }
      if (x > this->MAXLGM) {
        loverf:
        this->Error = true;
        this->MathError = Overflow;
        return ( sgngam * this->MAXNUM );
      }
      q = (x - 0.5) * log(x) - x + this->LS2PI;
      if (x > 1.0e8)
        return(q);
      p = 1.0/(x*x);
      if (x >= 1000.0)
        q += ((   7.9365079365079365079365e-4 * p
          - 2.7777777777777777777778e-3) *p
          + 0.0833333333333333333333) / x;
      else
        q += this->PolEvl(p, &this->A_lgam[0], 4)/x;
      return (q);
    }
 
    // incomplete gamma function
    double MathematicalFunctions::IGamma(double a, double x ) {
      double ans, ax, c, r;
 
      this->Error = false;
      this->MathError = None;
      if ((x <= 0) || (a <= 0))
        return (0.0);
      if ((x > 1.0) && (x > a))
        return (1.e0 - this->IGammaC(a,x));
      ax = a * log(x) - x - this->LGamma(a);
      if (ax < -(this->MAXLOG)) {
        this->Error = true;
        this->MathError = Underflow;
        return( 0.0 );
      }
      ax = exp(ax);
      r = a;
      c = 1.0;
      ans = 1.0;
      do {
        r += 1.0;
        c *= x/r;
        ans += c;
      } while(c/ans > this->MACHEP);
      return(ans * ax/a);
    }
 
    // Complemented incomplete gamma integral
    double MathematicalFunctions::IGammaC(double a, double x) {
      double ans, ax, c, yc, r, t, y, z;
      double pk, pkm1, pkm2, qk, qkm1, qkm2;
 
      this->Error = false;
      this->MathError = None;
      if ((x <= 0) || (a <= 0))
        return (1.0);
      if ((x < 1.0) || (x < a))
        return (1.e0 - this->IGamma(a,x));
      ax = a * log(x) - x - this->LGamma(a);
      if (ax < -(this->MAXLOG)) {
        this->Error = true;
        this->MathError = Underflow;
        return( 0.0 );
      }
      ax = exp(ax);
      y = 1.0 - a;
      z = x + y + 1.0;
      c = 0.0;
      pkm2 = 1.0;
      qkm2 = x;
      pkm1 = x + 1.0;
      qkm1 = z * x;
      ans = pkm1/qkm1;
      do {
        c += 1.0;
        y += 1.0;
        z += 2.0;
        yc = y * c;
        pk = pkm1 * z  -  pkm2 * yc;
        qk = qkm1 * z  -  qkm2 * yc;
        if (qk != 0) {
          r = pk/qk;
          t = fabs((ans - r)/r);
          ans = r;
        }
        else
          t = 1.0;
        pkm2 = pkm1;
        pkm1 = pk;
        qkm2 = qkm1;
        qkm1 = qk;
        if (fabs(pk) > this->big) {
          pkm2 *= this->biginv;
          pkm1 *= this->biginv;
          qkm2 *= this->biginv;
          qkm1 *= this->biginv;
        }
      } while (t > this->MACHEP);
      return (ans * ax);
    }
 
    // Evaluate polynomial of degree N
    double MathematicalFunctions::PolEvl(double x,double coef[], signed long int N) {
      double ans;
      double *p;
      signed long int i;
 
      p = coef;
      ans = *p++;
      i = N;
      do
        ans = ans * x + *p++;
      while (--i);
      return (ans);
    }
 
    //                                          N
    // Evaluate polynomial when coefficient of x  is 1.0.
    double MathematicalFunctions::P1Evl(double x, double coef[], signed long int N) {
      double ans;
      double *p;
      signed long int i;
 
      p = coef;
      ans = x + *p++;
      i = N-1;
      do
        ans = ans * x + *p++;
      while (--i);
      return (ans);
    }
      
    // Error function in double precision 
    double MathematicalFunctions::ErF(double x) {
      static const double two_sqrtpi = 1.128379167095512574;
      static const double  rel_error = 1E-12;
      double  sum = x, term = x, xsqr = x * x;
      signed long int j = 1;
 
      if ( fabs(x) > 2.2 )
        return 1.0 - this->ErFc(x);
      do {
        term *= xsqr/j;
        sum -= term/(2*j+1);
        j++;
        term *= xsqr/j;
        sum += term/(2*j+1);
        j++;
      } while ( fabs(term)/sum > rel_error );
      return two_sqrtpi*sum;
    }
      
    // Error function in double precision 
    double MathematicalFunctions::ErFc(double x) {
      static const double one_sqrtpi = 0.564189583547756287;
      static const double  rel_error = 1E-12;
      double  a = 1, b = x, c = x, d = x*x + 0.5;
      double  q1, q2 = b/d, n = 1.0, t;
 
      if ( fabs(x) < 2.2 )
        return 1.0 - this->ErF(x);
      if ( x < 0 )
        return 2.0 - this->ErFc(-x);
      do {
        t = a*n + b*x;
        a = b;
        b = t;
        t = c*n + d*x;
        c = d;
        d = t;
        n += 0.5;
        q1 = q2;
        q2 = b/d;
      } while ( fabs(q1-q2)/q2 > rel_error );
      return one_sqrtpi * exp(-x*x) * q2;
    }
 
    // Statistical Normal function
    double MathematicalFunctions::Normal(double x) {
      double arg, result, sqrt2=1.414213562373095048801688724209698078569672;
 
      if (x > 0) {
        arg = x/sqrt2;
        result = 0.5 * ( 1 + this->ErF(arg) );
      }  
      else {
        arg = -x/sqrt2;
        result = 0.5 * ( 1 - this->ErF(arg) );
      }
      return(result);
    }
 
    // Class common error handling member
    unsigned short int MathematicalFunctions::GetError() {
 
      return this->Error;
    }
 
    // Class common error handling member
    MathematicalErrors MathematicalFunctions::GetMathError() {
 
      return this->MathError;
    }
   }
}