doc_Text.cpp File Reference

#include <stdio.h>
#include <string.h>
#include "doc_Text.hh"
#include "compatibility.hh"
#include <string>
#include <vector>
#include <iostream>
#include <sstream>
#include <assert.h>
#include <cmath>
#include "floats.hh"

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Defines
#define	M_PI   3.14159265358979323846
#define	M_PI_2   1.57079632679489661923
#define	M_PI_4   0.785398163397448309616
#define	M_E   2.71828182845904523536
Functions
const string	symbolicNumber (double n)
	Return symbolic or numerical representation of n.
string	docT (char *c)
string	docT (int n)
string	docT (long n)
string	docT (double n)
float	fltEpsilon ()
	Compute the smallest float representable difference epsilon such that 1 != 1+epsilon.
double	dblEpsilon ()
	Compute the smallest double representable difference epsilon such that 1 != 1+epsilon.
static bool	AlmostEqual (double A, double B)
	Check if two floating point numbers are (almost) equal Abs(x-y) < epsilon.
bool	isPiPower (double n, string &s)
	Return true if n>0 is equal to PI^k for some small integer k.
bool	isExpPower (double n, string &s)
	Return true if n>0 is equal to e^k for some small integer k.
bool	isSymbolicPower (double n, string &s)
	Return true if n>0 is equal to e^k or PI^k for some integer k The symbolic latex representation is returned in string s.
const string	addFraction (int num, int denom, const string &exp)
	Return exp or num.exp, or exp/denom, or num/denom.exp.
const string	positiveSymbolicNumber (double n)
	Return symbolic or numerical representation of n>0.
Variables
bool	gInternDoubleSwitch

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Define Documentation

#define M_E   2.71828182845904523536

Definition at line 50 of file doc_Text.cpp.

#define M_PI   3.14159265358979323846

Definition at line 38 of file doc_Text.cpp.

Referenced by isPiPower().

#define M_PI_2   1.57079632679489661923

Definition at line 42 of file doc_Text.cpp.

#define M_PI_4   0.785398163397448309616

Definition at line 46 of file doc_Text.cpp.

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Function Documentation

const string addFraction	(	int	num,
		int	denom,
		const string &	exp
	)

Return exp or num.exp, or exp/denom, or num/denom.exp.

Definition at line 198 of file doc_Text.cpp.

Referenced by positiveSymbolicNumber().

{
    stringstream ss (stringstream::out|stringstream::in);

    if ((num==1) & (denom==1)) {
        ss << exp;
    } else if ((num==1) & (denom!=1)) {
        ss << "\\frac{"<< exp <<  "}{" << denom << "}";
    } else if ((num!=1) & (denom==1)) {
        ss << num << "*" << exp;
    } else {
        ss << "\\frac{"<< num <<  "}{" << denom << "}*" << exp;
    }
    return ss.str();
}

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static bool AlmostEqual	(	double	A,
		double	B
	)		[static]

Check if two floating point numbers are (almost) equal Abs(x-y) < epsilon.

Definition at line 118 of file doc_Text.cpp.

References dblEpsilon().

Referenced by isExpPower(), and isPiPower().

{
    double maxRelativeError = 2*dblEpsilon();
    double maxAbsoluteError = maxRelativeError;


    if (fabs(A - B) < maxAbsoluteError)
        return true;
    double relativeError;
    if (fabs(B) > fabs(A))
        relativeError = fabs((A - B) / B);
    else
        relativeError = fabs((A - B) / A);
    if (relativeError <= maxRelativeError)
        return true;
    return false;
}

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double dblEpsilon

(

)

Compute the smallest double representable difference epsilon such that 1 != 1+epsilon.

Definition at line 104 of file doc_Text.cpp.

Referenced by AlmostEqual().

{
   double machEps = 1.0f;
   do {
      machEps /= 2.0f;
   } while ((1.0 + (machEps/2.0)) != 1.0);
   return machEps;
}

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string docT

(

char *

c

)

Definition at line 76 of file doc_Text.cpp.

Referenced by DocCompiler::compileLateq(), DocCompiler::generateCode(), DocCompiler::generateIota(), DocCompiler::getFreshID(), and DocCompiler::prepareIntervallicUI().

{ return string(c); }

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string docT

(

int

n

)

Definition at line 77 of file doc_Text.cpp.

{ char c[64]; snprintf(c, 63, "%d",n);  return string(c); }

string docT

(

long

n

)

Definition at line 78 of file doc_Text.cpp.

{ char c[64]; snprintf(c, 63, "%ld",n); return string(c); }

string docT

(

double

n

)

Definition at line 79 of file doc_Text.cpp.

References symbolicNumber().

{ return symbolicNumber(n); }

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float fltEpsilon

(

)

Compute the smallest float representable difference epsilon such that 1 != 1+epsilon.

Definition at line 90 of file doc_Text.cpp.

{
   float machEps = 1.0f;
   do {
      machEps /= 2.0f;
   } while ((float)(1.0 + (machEps/2.0)) != 1.0);
   return machEps;
}

bool isExpPower	(	double	n,
		string &	s
	)

Return true if n>0 is equal to e^k for some small integer k.

The latex representation e^{k} is returned in string s

Definition at line 162 of file doc_Text.cpp.

References abs(), and AlmostEqual().

Referenced by isSymbolicPower().

{
    assert(n>0);
    stringstream ss (stringstream::out|stringstream::in);
    int k = floor(log(n));
    if ( AlmostEqual(n, exp(k)) && (k!=0) && (abs(k)<5.0) ) {
        ss << "e";
        if (k!=1)  ss << "^{"<< k <<"}";
        s = ss.str();
        return true;
    } else {
        return false;
    }
}

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bool isPiPower	(	double	n,
		string &	s
	)

Return true if n>0 is equal to PI^k for some small integer k.

k = log(n)/log(pi) is integer => n = exp(int(k)*log(pi)) The latex representation ^{k} is returned in string s

Definition at line 142 of file doc_Text.cpp.

References abs(), AlmostEqual(), and M_PI.

Referenced by isSymbolicPower().

{
    assert(n>0);
    stringstream ss (stringstream::out|stringstream::in);
    int k = floor(log(n)/log(M_PI));
    if ( AlmostEqual(n, exp(k * log(M_PI))) && (k!=0) && (abs(k)<5.0) ) {
        ss << "\\pi";
        if (k!=1)  ss << "^{"<< k <<"}";
        s = ss.str();
        return true;
    } else {
        return false;
    }
}

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bool isSymbolicPower	(	double	n,
		string &	s
	)

Return true if n>0 is equal to e^k or PI^k for some integer k The symbolic latex representation is returned in string s.

Definition at line 182 of file doc_Text.cpp.

References isExpPower(), and isPiPower().

Referenced by positiveSymbolicNumber().

{
    assert(n>0);
    if (isPiPower(n,s)) {
        return true;
    } else if (isExpPower(n,s)) {
        return true;
    } else {
        return false;
    }
}

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const string positiveSymbolicNumber

(

double

n

)

Return symbolic or numerical representation of n>0.

Definition at line 218 of file doc_Text.cpp.

References addFraction(), and isSymbolicPower().

Referenced by symbolicNumber().

{
    string s;
    assert(n>0);

    // Try to find a symbolic representation

    for (int i=1;i<10;i++) {
        for(int j=1;j<10;j++) {
            if (isSymbolicPower(i*n/j,s)) {
                return addFraction(j,i,s);
            }
        }
    }

    // No symbolic representation,
    // Then numerical representation x.10^k

    char tmp[64];
    string entree = " * 10^{";
    char sortie = '}';
    string::size_type ps;

    snprintf(tmp, 63, "%.15g", n); // Warning: over 15 decimals, results are wrong !!
    s = tmp;
    ps = s.find('e');

    if (ps != string::npos) {
        s.replace(ps, 1, "");
        s.insert(ps, entree);
        s += sortie;
    }

    return s;

}

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const string symbolicNumber

(

double

n

)

Return symbolic or numerical representation of n.

Definition at line 259 of file doc_Text.cpp.

References positiveSymbolicNumber().

Referenced by docT().

{
    if (n>0.0) {
        return positiveSymbolicNumber(n);
    } else if (n<0.0) {
        return string("-") + positiveSymbolicNumber(-n);
    } else {
        return "0";
    }
}

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Variable Documentation

bool gInternDoubleSwitch