#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 <stdlib.h>
#include "floats.hh"

Include dependency graph for doc_Text.cpp:

Macros
#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. More...

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. More...

double	dblEpsilon ()
	Compute the smallest double representable difference epsilon such that 1 != 1+epsilon. More...

static bool	AlmostEqual (double A, double B)
	Check if two floating point numbers are (almost) equal Abs(x-y) < epsilon. More...

bool	isPiPower (double n, string &s)
	Return true if n>0 is equal to PI^k for some small integer k. More...

bool	isExpPower (double n, string &s)
	Return true if n>0 is equal to e^k for some small integer k. More...

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. More...

const string	addFraction (int num, int denom, const string &exp)
	Return exp or num.exp, or exp/denom, or num/denom.exp. More...

const string	positiveSymbolicNumber (double n)
	Return symbolic or numerical representation of n>0. More...

Variables
bool	gInternDoubleSwitch

Macro Definition Documentation

#define M_E 2.71828182845904523536

Definition at line 51 of file doc_Text.cpp.

#define M_PI 3.14159265358979323846

Definition at line 39 of file doc_Text.cpp.

Referenced by isPiPower().

#define M_PI_2 1.57079632679489661923

Definition at line 43 of file doc_Text.cpp.

#define M_PI_4 0.785398163397448309616

Definition at line 47 of file doc_Text.cpp.

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 199 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();
 }

Here is the caller graph for this function:

static bool AlmostEqual	(	double	A,
		double	B
	)

static

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

Definition at line 119 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;
 }

Here is the call graph for this function:

Here is the caller graph for this function:

double dblEpsilon ( )

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

Definition at line 105 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;
 }

Here is the caller graph for this function:

string docT ( char * c )

Definition at line 77 of file doc_Text.cpp.

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

77 { return string(c); }

Here is the caller graph for this function:

string docT ( int n )

Definition at line 78 of file doc_Text.cpp.

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

string docT ( long n )

Definition at line 79 of file doc_Text.cpp.

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

string docT ( double n )

Definition at line 80 of file doc_Text.cpp.

References symbolicNumber().

80 { return symbolicNumber(n); }

symbolicNumber

const string symbolicNumber(double n)

Return symbolic or numerical representation of n.

Definition: doc_Text.cpp:260

Here is the call graph for this function:

float fltEpsilon ( )

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

Definition at line 91 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 163 of file doc_Text.cpp.

References abs(), and AlmostEqual().

Referenced by isSymbolicPower().

 {
     assert(n>0);
     stringstream ss (stringstream::out|stringstream::in);
     int k = (int)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;
     }
 }

Here is the call graph for this function:

Here is the caller graph for this function:

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 143 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 = (int)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;
     }
 }

Here is the call graph for this function:

Here is the caller graph for this function:

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 183 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;
     }
 }

Here is the call graph for this function:

Here is the caller graph for this function:

const string positiveSymbolicNumber ( double n )

Return symbolic or numerical representation of n>0.

Definition at line 219 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;
 
 }

Here is the call graph for this function:

Here is the caller graph for this function:

const string symbolicNumber ( double n )

Return symbolic or numerical representation of n.

Definition at line 260 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";
     }
 }

Here is the call graph for this function:

Here is the caller graph for this function:

Variable Documentation

bool gInternDoubleSwitch

Macros

Functions

Variables

Macro Definition Documentation

Function Documentation

Variable Documentation