interpreter/preprocessor/faust-0.9.47mr3/compiler/documentator/doc_Text.cpp

   1 /************************************************************************
   2  ************************************************************************
   3     FAUST compiler
   4         Copyright (C) 2003-2004 GRAME, Centre National de Creation Musicale
   5     ---------------------------------------------------------------------
   6     This program is free software; you can redistribute it and/or modify
   7     it under the terms of the GNU General Public License as published by
   8     the Free Software Foundation; either version 2 of the License, or
   9     (at your option) any later version.
  10
  11     This program is distributed in the hope that it will be useful,
  12     but WITHOUT ANY WARRANTY; without even the implied warranty of
  13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14     GNU General Public License for more details.
  15
  16     You should have received a copy of the GNU General Public License
  17     along with this program; if not, write to the Free Software
  18     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  19  ************************************************************************
  20  ************************************************************************/
  21
  22
  23
  24 #include <stdio.h>
  25 #include <string.h>
  26 #include "doc_Text.hh"
  27 #include "compatibility.hh"
  28 #include <string>
  29 #include <vector>
  30 #include <iostream>
  31 #include <sstream>
  32 #include <assert.h>
  33 #include <cmath>
  34 #include <stdlib.h>
  35
  36 #include "floats.hh"
  37
  38 #ifndef M_PI
  39 #define M_PI 3.14159265358979323846
  40 #endif
  41
  42 #ifndef M_PI_2
  43 #define M_PI_2 1.57079632679489661923
  44 #endif
  45
  46 #ifndef M_PI_4
  47 #define M_PI_4 0.785398163397448309616
  48 #endif
  49
  50 #ifndef M_E
  51 #define M_E 2.71828182845904523536
  52 #endif
  53
  54 extern bool gInternDoubleSwitch;
  55 const string symbolicNumber (double n);
  56
  57
  58
  59 #if 0
  60 /**
  61  * Suppress trailing zero in a string representating a floating point number.
  62  * example : 1.00000  -> 1.0
  63  * example : 1.00000f -> 1.0f
  64  */
  65
  66 static void zdel(char* c)
  67 {
  68     int     l = strlen(c) - 1;
  69     bool    f = (c[l] == 'f');
  70
  71     if (f) c[l--] = 0;      // remove trailing if any f
  72     while ( l>1 && c[l-1] != '.' && c[l] == '0')  c[l--] = 0;
  73     if (f) c[++l] = 'f';    // restaure trailing f if needed
  74 }
  75 #endif
  76
  77 string docT (char* c)   { return string(c); }
  78 string docT (int n)     { char c[64]; snprintf(c, 63, "%d",n);  return string(c); }
  79 string docT (long n)    { char c[64]; snprintf(c, 63, "%ld",n); return string(c); }
  80 string docT (double n) { return symbolicNumber(n); }
  81
  82
  83 //
  84 //*****************************SYMBOLIC NUMBER REPRESENTATION*******************
  85 //
  86
  87 /**
  88  * Compute the smallest float representable
  89  * difference epsilon such that 1 != 1+epsilon
  90  */
  91 float fltEpsilon()
  92 {
  93    float machEps = 1.0f;
  94    do {
  95       machEps /= 2.0f;
  96    } while ((float)(1.0 + (machEps/2.0)) != 1.0);
  97    return machEps;
  98 }
  99
 100
 101 /**
 102  * Compute the smallest double representable
 103  * difference epsilon such that 1 != 1+epsilon
 104  */
 105 double dblEpsilon()
 106 {
 107    double machEps = 1.0f;
 108    do {
 109       machEps /= 2.0f;
 110    } while ((1.0 + (machEps/2.0)) != 1.0);
 111    return machEps;
 112 }
 113
 114
 115 /**
 116  * Check if two floating point numbers are (almost) equal
 117  * Abs(x-y) < epsilon
 118  */
 119 static bool AlmostEqual(double A, double B)
 120 {
 121     double maxRelativeError = 2*dblEpsilon();
 122     double maxAbsoluteError = maxRelativeError;
 123
 124
 125     if (fabs(A - B) < maxAbsoluteError)
 126         return true;
 127     double relativeError;
 128     if (fabs(B) > fabs(A))
 129         relativeError = fabs((A - B) / B);
 130     else
 131         relativeError = fabs((A - B) / A);
 132     if (relativeError <= maxRelativeError)
 133         return true;
 134     return false;
 135 }
 136
 137
 138 /**
 139  * Return true if n>0 is equal to PI^k for some small integer k.
 140  * k = log(n)/log(pi) is integer => n = exp(int(k)*log(pi))
 141  * The latex representation \pi^{k} is returned in string s
 142  */
 143 bool isPiPower (double n, string& s)
 144 {
 145     assert(n>0);
 146     stringstream ss (stringstream::out|stringstream::in);
 147     int k = floor(log(n)/log(M_PI));
 148     if ( AlmostEqual(n, exp(k * log(M_PI))) && (k!=0) && (abs(k)<5.0) ) {
 149         ss << "\\pi";
 150         if (k!=1)  ss << "^{"<< k <<"}";
 151         s = ss.str();
 152         return true;
 153     } else {
 154         return false;
 155     }
 156 }
 157
 158
 159 /**
 160  * Return true if n>0 is equal to e^k for some small integer k.
 161  * The latex representation e^{k} is returned in string s
 162  */
 163 bool isExpPower (double n, string& s)
 164 {
 165     assert(n>0);
 166     stringstream ss (stringstream::out|stringstream::in);
 167     int k = floor(log(n));
 168     if ( AlmostEqual(n, exp(k)) && (k!=0) && (abs(k)<5.0) ) {
 169         ss << "e";
 170         if (k!=1)  ss << "^{"<< k <<"}";
 171         s = ss.str();
 172         return true;
 173     } else {
 174         return false;
 175     }
 176 }
 177
 178
 179 /**
 180  * Return true if n>0 is equal to e^k or PI^k for some integer k
 181  * The symbolic latex representation is returned in string s
 182  */
 183 bool isSymbolicPower (double n, string& s)
 184 {
 185     assert(n>0);
 186     if (isPiPower(n,s)) {
 187         return true;
 188     } else if (isExpPower(n,s)) {
 189         return true;
 190     } else {
 191         return false;
 192     }
 193 }
 194
 195
 196 /**
 197  * Return exp or num.exp, or exp/denom, or num/denom.exp
 198  */
 199 const string addFraction (int num, int denom, const string& exp)
 200 {
 201     stringstream ss (stringstream::out|stringstream::in);
 202
 203     if ((num==1) & (denom==1)) {
 204         ss << exp;
 205     } else if ((num==1) & (denom!=1)) {
 206         ss << "\\frac{"<< exp <<  "}{" << denom << "}";
 207     } else if ((num!=1) & (denom==1)) {
 208         ss << num << "*" << exp;
 209     } else {
 210         ss << "\\frac{"<< num <<  "}{" << denom << "}*" << exp;
 211     }
 212     return ss.str();
 213 }
 214
 215
 216 /**
 217  * Return symbolic or numerical representation of n>0
 218  */
 219 const string positiveSymbolicNumber (double n)
 220 {
 221     string s;
 222     assert(n>0);
 223
 224     // Try to find a symbolic representation
 225
 226     for (int i=1;i<10;i++) {
 227         for(int j=1;j<10;j++) {
 228             if (isSymbolicPower(i*n/j,s)) {
 229                 return addFraction(j,i,s);
 230             }
 231         }
 232     }
 233
 234     // No symbolic representation,
 235     // Then numerical representation x.10^k
 236
 237     char tmp[64];
 238     string entree = " * 10^{";
 239     char sortie = '}';
 240     string::size_type ps;
 241
 242     snprintf(tmp, 63, "%.15g", n); // Warning: over 15 decimals, results are wrong !!
 243     s = tmp;
 244     ps = s.find('e');
 245
 246     if (ps != string::npos) {
 247         s.replace(ps, 1, "");
 248         s.insert(ps, entree);
 249         s += sortie;
 250     }
 251
 252     return s;
 253
 254 }
 255
 256
 257 /**
 258  * Return symbolic or numerical representation of n
 259  */
 260 const string symbolicNumber (double n)
 261 {
 262     if (n>0.0) {
 263         return positiveSymbolicNumber(n);
 264     } else if (n<0.0) {
 265         return string("-") + positiveSymbolicNumber(-n);
 266     } else {
 267         return "0";
 268     }
 269 }