src/DoubleToString.cc

   1 #include "DoubleToString.hh"
   2
   3 #include <cmath>
   4 using namespace std;
   5
   6 /**
   7          @author: Dov Kruger
   8          Ultrafast float formatting for fast printing
   9          This code is not well tested, and it definitely does not print every
  10    floating point value Given that we have a known range and a known precision,
  11    this code is a model for how we might print numbers into gcode at high speed.
  12          We determine how big the number is and pull off digits in order.
  13          Given exactly 6 digits after the decimal we print using two groups of 3
  14    digits which are loaded from an array lookup.
  15  */
  16
  17 // code below generated by builddigits.cc
  18 char* formatDouble(double d, char* p)
  19 {
  20     if (d < 0)
  21     {
  22         *p++ = '-';
  23         d    = -d;
  24     }
  25     static const int exponent[] = {0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3,
  26                                    3, 3, 3, 4, 4, 4, 5, 5, 5, 6};
  27     static const int div[]      = {1,      1,      1,      10,    10,    10,
  28                               10,     100,    100,    100,   1000,  1000,
  29                               1000,   1000,   10000,  10000, 10000, 100000,
  30                               100000, 100000, 1000000};
  31     int e;
  32     double m     = frexp(d, &e);
  33     int whole    = int(d);
  34     int fdivisor = 1000000;  // starting divisor for 6 digits after the decimal
  35     int fracDigits =
  36         int((d - whole) *
  37             fdivisor);  // mult by constant to give desired number of digits
  38     if (e >= 0)
  39     {
  40         int divisor = div[e];
  41         for (int numdig = exponent[e]; numdig > 0; numdig--, divisor /= 10)
  42         {
  43             int dig = whole / divisor;
  44             *p++    = dig + '0';
  45             whole -= dig * divisor;
  46             //          cout << dig;
  47         }
  48     }
  49     *p++ = whole + '0';
  50     *p++ = '.';
  51
  52     int first3 = (*(int*)(digits + (fracDigits / 1000 * 4))) >> 8;
  53     *p++       = first3;
  54     first3 >>= 8;
  55     *p++ = first3;
  56     first3 >>= 8;
  57     *p++        = first3;
  58     int second3 = (*(int*)(digits + fracDigits % 1000 * 4)) >> 8;
  59     *p++        = second3;
  60     second3 >>= 8;
  61     *p++ = second3;
  62     second3 >>= 8;
  63     *p++ = second3;
  64
  65     //*p++= '\0';
  66     // cerr << "e=" << e << '\n';
  67     return p;
  68 }
  69
  70 const char digits[4000] = {
  71     '0', '0', '0', '0', '0', '0', '0', '1', '0', '0', '0', '2', '0', '0', '0',
  72     '3', '0', '0', '0', '4', '0', '0', '0', '5', '0', '0', '0', '6', '0', '0',
  73     '0', '7', '0', '0', '0', '8', '0', '0', '0', '9', '0', '0', '1', '0', '0',
  74     '0', '1', '1', '0', '0', '1', '2', '0', '0', '1', '3', '0', '0', '1', '4',
  75     '0', '0', '1', '5', '0', '0', '1', '6', '0', '0', '1', '7', '0', '0', '1',
  76     '8', '0', '0', '1', '9', '0', '0', '2', '0', '0', '0', '2', '1', '0', '0',
  77     '2', '2', '0', '0', '2', '3', '0', '0', '2', '4', '0', '0', '2', '5', '0',
  78     '0', '2', '6', '0', '0', '2', '7', '0', '0', '2', '8', '0', '0', '2', '9',
  79     '0', '0', '3', '0', '0', '0', '3', '1', '0', '0', '3', '2', '0', '0', '3',
  80     '3', '0', '0', '3', '4', '0', '0', '3', '5', '0', '0', '3', '6', '0', '0',
  81     '3', '7', '0', '0', '3', '8', '0', '0', '3', '9', '0', '0', '4', '0', '0',
  82     '0', '4', '1', '0', '0', '4', '2', '0', '0', '4', '3', '0', '0', '4', '4',
  83     '0', '0', '4', '5', '0', '0', '4', '6', '0', '0', '4', '7', '0', '0', '4',
  84     '8', '0', '0', '4', '9', '0', '0', '5', '0', '0', '0', '5', '1', '0', '0',
  85     '5', '2', '0', '0', '5', '3', '0', '0', '5', '4', '0', '0', '5', '5', '0',
  86     '0', '5', '6', '0', '0', '5', '7', '0', '0', '5', '8', '0', '0', '5', '9',
  87     '0', '0', '6', '0', '0', '0', '6', '1', '0', '0', '6', '2', '0', '0', '6',
  88     '3', '0', '0', '6', '4', '0', '0', '6', '5', '0', '0', '6', '6', '0', '0',
  89     '6', '7', '0', '0', '6', '8', '0', '0', '6', '9', '0', '0', '7', '0', '0',
  90     '0', '7', '1', '0', '0', '7', '2', '0', '0', '7', '3', '0', '0', '7', '4',
  91     '0', '0', '7', '5', '0', '0', '7', '6', '0', '0', '7', '7', '0', '0', '7',
  92     '8', '0', '0', '7', '9', '0', '0', '8', '0', '0', '0', '8', '1', '0', '0',
  93     '8', '2', '0', '0', '8', '3', '0', '0', '8', '4', '0', '0', '8', '5', '0',
  94     '0', '8', '6', '0', '0', '8', '7', '0', '0', '8', '8', '0', '0', '8', '9',
  95     '0', '0', '9', '0', '0', '0', '9', '1', '0', '0', '9', '2', '0', '0', '9',
  96     '3', '0', '0', '9', '4', '0', '0', '9', '5', '0', '0', '9', '6', '0', '0',
  97     '9', '7', '0', '0', '9', '8', '0', '0', '9', '9', '0', '1', '0', '0', '0',
  98     '1', '0', '1', '0', '1', '0', '2', '0', '1', '0', '3', '0', '1', '0', '4',
  99     '0', '1', '0', '5', '0', '1', '0', '6', '0', '1', '0', '7', '0', '1', '0',
 100     '8', '0', '1', '0', '9', '0', '1', '1', '0', '0', '1', '1', '1', '0', '1',
 101     '1', '2', '0', '1', '1', '3', '0', '1', '1', '4', '0', '1', '1', '5', '0',
 102     '1', '1', '6', '0', '1', '1', '7', '0', '1', '1', '8', '0', '1', '1', '9',
 103     '0', '1', '2', '0', '0', '1', '2', '1', '0', '1', '2', '2', '0', '1', '2',
 104     '3', '0', '1', '2', '4', '0', '1', '2', '5', '0', '1', '2', '6', '0', '1',
 105     '2', '7', '0', '1', '2', '8', '0', '1', '2', '9', '0', '1', '3', '0', '0',
 106     '1', '3', '1', '0', '1', '3', '2', '0', '1', '3', '3', '0', '1', '3', '4',
 107     '0', '1', '3', '5', '0', '1', '3', '6', '0', '1', '3', '7', '0', '1', '3',
 108     '8', '0', '1', '3', '9', '0', '1', '4', '0', '0', '1', '4', '1', '0', '1',
 109     '4', '2', '0', '1', '4', '3', '0', '1', '4', '4', '0', '1', '4', '5', '0',
 110     '1', '4', '6', '0', '1', '4', '7', '0', '1', '4', '8', '0', '1', '4', '9',
 111     '0', '1', '5', '0', '0', '1', '5', '1', '0', '1', '5', '2', '0', '1', '5',
 112     '3', '0', '1', '5', '4', '0', '1', '5', '5', '0', '1', '5', '6', '0', '1',
 113     '5', '7', '0', '1', '5', '8', '0', '1', '5', '9', '0', '1', '6', '0', '0',
 114     '1', '6', '1', '0', '1', '6', '2', '0', '1', '6', '3', '0', '1', '6', '4',
 115     '0', '1', '6', '5', '0', '1', '6', '6', '0', '1', '6', '7', '0', '1', '6',
 116     '8', '0', '1', '6', '9', '0', '1', '7', '0', '0', '1', '7', '1', '0', '1',
 117     '7', '2', '0', '1', '7', '3', '0', '1', '7', '4', '0', '1', '7', '5', '0',
 118     '1', '7', '6', '0', '1', '7', '7', '0', '1', '7', '8', '0', '1', '7', '9',
 119     '0', '1', '8', '0', '0', '1', '8', '1', '0', '1', '8', '2', '0', '1', '8',
 120     '3', '0', '1', '8', '4', '0', '1', '8', '5', '0', '1', '8', '6', '0', '1',
 121     '8', '7', '0', '1', '8', '8', '0', '1', '8', '9', '0', '1', '9', '0', '0',
 122     '1', '9', '1', '0', '1', '9', '2', '0', '1', '9', '3', '0', '1', '9', '4',
 123     '0', '1', '9', '5', '0', '1', '9', '6', '0', '1', '9', '7', '0', '1', '9',
 124     '8', '0', '1', '9', '9', '0', '2', '0', '0', '0', '2', '0', '1', '0', '2',
 125     '0', '2', '0', '2', '0', '3', '0', '2', '0', '4', '0', '2', '0', '5', '0',
 126     '2', '0', '6', '0', '2', '0', '7', '0', '2', '0', '8', '0', '2', '0', '9',
 127     '0', '2', '1', '0', '0', '2', '1', '1', '0', '2', '1', '2', '0', '2', '1',
 128     '3', '0', '2', '1', '4', '0', '2', '1', '5', '0', '2', '1', '6', '0', '2',
 129     '1', '7', '0', '2', '1', '8', '0', '2', '1', '9', '0', '2', '2', '0', '0',
 130     '2', '2', '1', '0', '2', '2', '2', '0', '2', '2', '3', '0', '2', '2', '4',
 131     '0', '2', '2', '5', '0', '2', '2', '6', '0', '2', '2', '7', '0', '2', '2',
 132     '8', '0', '2', '2', '9', '0', '2', '3', '0', '0', '2', '3', '1', '0', '2',
 133     '3', '2', '0', '2', '3', '3', '0', '2', '3', '4', '0', '2', '3', '5', '0',
 134     '2', '3', '6', '0', '2', '3', '7', '0', '2', '3', '8', '0', '2', '3', '9',
 135     '0', '2', '4', '0', '0', '2', '4', '1', '0', '2', '4', '2', '0', '2', '4',
 136     '3', '0', '2', '4', '4', '0', '2', '4', '5', '0', '2', '4', '6', '0', '2',
 137     '4', '7', '0', '2', '4', '8', '0', '2', '4', '9', '0', '2', '5', '0', '0',
 138     '2', '5', '1', '0', '2', '5', '2', '0', '2', '5', '3', '0', '2', '5', '4',
 139     '0', '2', '5', '5', '0', '2', '5', '6', '0', '2', '5', '7', '0', '2', '5',
 140     '8', '0', '2', '5', '9', '0', '2', '6', '0', '0', '2', '6', '1', '0', '2',
 141     '6', '2', '0', '2', '6', '3', '0', '2', '6', '4', '0', '2', '6', '5', '0',
 142     '2', '6', '6', '0', '2', '6', '7', '0', '2', '6', '8', '0', '2', '6', '9',
 143     '0', '2', '7', '0', '0', '2', '7', '1', '0', '2', '7', '2', '0', '2', '7',
 144     '3', '0', '2', '7', '4', '0', '2', '7', '5', '0', '2', '7', '6', '0', '2',
 145     '7', '7', '0', '2', '7', '8', '0', '2', '7', '9', '0', '2', '8', '0', '0',
 146     '2', '8', '1', '0', '2', '8', '2', '0', '2', '8', '3', '0', '2', '8', '4',
 147     '0', '2', '8', '5', '0', '2', '8', '6', '0', '2', '8', '7', '0', '2', '8',
 148     '8', '0', '2', '8', '9', '0', '2', '9', '0', '0', '2', '9', '1', '0', '2',
 149     '9', '2', '0', '2', '9', '3', '0', '2', '9', '4', '0', '2', '9', '5', '0',
 150     '2', '9', '6', '0', '2', '9', '7', '0', '2', '9', '8', '0', '2', '9', '9',
 151     '0', '3', '0', '0', '0', '3', '0', '1', '0', '3', '0', '2', '0', '3', '0',
 152     '3', '0', '3', '0', '4', '0', '3', '0', '5', '0', '3', '0', '6', '0', '3',
 153     '0', '7', '0', '3', '0', '8', '0', '3', '0', '9', '0', '3', '1', '0', '0',
 154     '3', '1', '1', '0', '3', '1', '2', '0', '3', '1', '3', '0', '3', '1', '4',
 155     '0', '3', '1', '5', '0', '3', '1', '6', '0', '3', '1', '7', '0', '3', '1',
 156     '8', '0', '3', '1', '9', '0', '3', '2', '0', '0', '3', '2', '1', '0', '3',
 157     '2', '2', '0', '3', '2', '3', '0', '3', '2', '4', '0', '3', '2', '5', '0',
 158     '3', '2', '6', '0', '3', '2', '7', '0', '3', '2', '8', '0', '3', '2', '9',
 159     '0', '3', '3', '0', '0', '3', '3', '1', '0', '3', '3', '2', '0', '3', '3',
 160     '3', '0', '3', '3', '4', '0', '3', '3', '5', '0', '3', '3', '6', '0', '3',
 161     '3', '7', '0', '3', '3', '8', '0', '3', '3', '9', '0', '3', '4', '0', '0',
 162     '3', '4', '1', '0', '3', '4', '2', '0', '3', '4', '3', '0', '3', '4', '4',
 163     '0', '3', '4', '5', '0', '3', '4', '6', '0', '3', '4', '7', '0', '3', '4',
 164     '8', '0', '3', '4', '9', '0', '3', '5', '0', '0', '3', '5', '1', '0', '3',
 165     '5', '2', '0', '3', '5', '3', '0', '3', '5', '4', '0', '3', '5', '5', '0',
 166     '3', '5', '6', '0', '3', '5', '7', '0', '3', '5', '8', '0', '3', '5', '9',
 167     '0', '3', '6', '0', '0', '3', '6', '1', '0', '3', '6', '2', '0', '3', '6',
 168     '3', '0', '3', '6', '4', '0', '3', '6', '5', '0', '3', '6', '6', '0', '3',
 169     '6', '7', '0', '3', '6', '8', '0', '3', '6', '9', '0', '3', '7', '0', '0',
 170     '3', '7', '1', '0', '3', '7', '2', '0', '3', '7', '3', '0', '3', '7', '4',
 171     '0', '3', '7', '5', '0', '3', '7', '6', '0', '3', '7', '7', '0', '3', '7',
 172     '8', '0', '3', '7', '9', '0', '3', '8', '0', '0', '3', '8', '1', '0', '3',
 173     '8', '2', '0', '3', '8', '3', '0', '3', '8', '4', '0', '3', '8', '5', '0',
 174     '3', '8', '6', '0', '3', '8', '7', '0', '3', '8', '8', '0', '3', '8', '9',
 175     '0', '3', '9', '0', '0', '3', '9', '1', '0', '3', '9', '2', '0', '3', '9',
 176     '3', '0', '3', '9', '4', '0', '3', '9', '5', '0', '3', '9', '6', '0', '3',
 177     '9', '7', '0', '3', '9', '8', '0', '3', '9', '9', '0', '4', '0', '0', '0',
 178     '4', '0', '1', '0', '4', '0', '2', '0', '4', '0', '3', '0', '4', '0', '4',
 179     '0', '4', '0', '5', '0', '4', '0', '6', '0', '4', '0', '7', '0', '4', '0',
 180     '8', '0', '4', '0', '9', '0', '4', '1', '0', '0', '4', '1', '1', '0', '4',
 181     '1', '2', '0', '4', '1', '3', '0', '4', '1', '4', '0', '4', '1', '5', '0',
 182     '4', '1', '6', '0', '4', '1', '7', '0', '4', '1', '8', '0', '4', '1', '9',
 183     '0', '4', '2', '0', '0', '4', '2', '1', '0', '4', '2', '2', '0', '4', '2',
 184     '3', '0', '4', '2', '4', '0', '4', '2', '5', '0', '4', '2', '6', '0', '4',
 185     '2', '7', '0', '4', '2', '8', '0', '4', '2', '9', '0', '4', '3', '0', '0',
 186     '4', '3', '1', '0', '4', '3', '2', '0', '4', '3', '3', '0', '4', '3', '4',
 187     '0', '4', '3', '5', '0', '4', '3', '6', '0', '4', '3', '7', '0', '4', '3',
 188     '8', '0', '4', '3', '9', '0', '4', '4', '0', '0', '4', '4', '1', '0', '4',
 189     '4', '2', '0', '4', '4', '3', '0', '4', '4', '4', '0', '4', '4', '5', '0',
 190     '4', '4', '6', '0', '4', '4', '7', '0', '4', '4', '8', '0', '4', '4', '9',
 191     '0', '4', '5', '0', '0', '4', '5', '1', '0', '4', '5', '2', '0', '4', '5',
 192     '3', '0', '4', '5', '4', '0', '4', '5', '5', '0', '4', '5', '6', '0', '4',
 193     '5', '7', '0', '4', '5', '8', '0', '4', '5', '9', '0', '4', '6', '0', '0',
 194     '4', '6', '1', '0', '4', '6', '2', '0', '4', '6', '3', '0', '4', '6', '4',
 195     '0', '4', '6', '5', '0', '4', '6', '6', '0', '4', '6', '7', '0', '4', '6',
 196     '8', '0', '4', '6', '9', '0', '4', '7', '0', '0', '4', '7', '1', '0', '4',
 197     '7', '2', '0', '4', '7', '3', '0', '4', '7', '4', '0', '4', '7', '5', '0',
 198     '4', '7', '6', '0', '4', '7', '7', '0', '4', '7', '8', '0', '4', '7', '9',
 199     '0', '4', '8', '0', '0', '4', '8', '1', '0', '4', '8', '2', '0', '4', '8',
 200     '3', '0', '4', '8', '4', '0', '4', '8', '5', '0', '4', '8', '6', '0', '4',
 201     '8', '7', '0', '4', '8', '8', '0', '4', '8', '9', '0', '4', '9', '0', '0',
 202     '4', '9', '1', '0', '4', '9', '2', '0', '4', '9', '3', '0', '4', '9', '4',
 203     '0', '4', '9', '5', '0', '4', '9', '6', '0', '4', '9', '7', '0', '4', '9',
 204     '8', '0', '4', '9', '9', '0', '5', '0', '0', '0', '5', '0', '1', '0', '5',
 205     '0', '2', '0', '5', '0', '3', '0', '5', '0', '4', '0', '5', '0', '5', '0',
 206     '5', '0', '6', '0', '5', '0', '7', '0', '5', '0', '8', '0', '5', '0', '9',
 207     '0', '5', '1', '0', '0', '5', '1', '1', '0', '5', '1', '2', '0', '5', '1',
 208     '3', '0', '5', '1', '4', '0', '5', '1', '5', '0', '5', '1', '6', '0', '5',
 209     '1', '7', '0', '5', '1', '8', '0', '5', '1', '9', '0', '5', '2', '0', '0',
 210     '5', '2', '1', '0', '5', '2', '2', '0', '5', '2', '3', '0', '5', '2', '4',
 211     '0', '5', '2', '5', '0', '5', '2', '6', '0', '5', '2', '7', '0', '5', '2',
 212     '8', '0', '5', '2', '9', '0', '5', '3', '0', '0', '5', '3', '1', '0', '5',
 213     '3', '2', '0', '5', '3', '3', '0', '5', '3', '4', '0', '5', '3', '5', '0',
 214     '5', '3', '6', '0', '5', '3', '7', '0', '5', '3', '8', '0', '5', '3', '9',
 215     '0', '5', '4', '0', '0', '5', '4', '1', '0', '5', '4', '2', '0', '5', '4',
 216     '3', '0', '5', '4', '4', '0', '5', '4', '5', '0', '5', '4', '6', '0', '5',
 217     '4', '7', '0', '5', '4', '8', '0', '5', '4', '9', '0', '5', '5', '0', '0',
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