+#include "DoubleToString.hh"
+
+#include <cmath>
+using namespace std;
+
+/**
+ @author: Dov Kruger
+ Ultrafast float formatting for fast printing
+ This code is not well tested, and it definitely does not print every
+ floating point value Given that we have a known range and a known precision,
+ this code is a model for how we might print numbers into gcode at high speed.
+ We determine how big the number is and pull off digits in order.
+ Given exactly 6 digits after the decimal we print using two groups of 3
+ digits which are loaded from an array lookup.
+ */
+
+// code below generated by builddigits.cc
+char* formatDouble(double d, char* p)
+{
+ if (d < 0)
+ {
+ *p++ = '-';
+ d = -d;
+ }
+ static const int exponent[] = {0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3,
+ 3, 3, 3, 4, 4, 4, 5, 5, 5, 6};
+ static const int div[] = {1, 1, 1, 10, 10, 10,
+ 10, 100, 100, 100, 1000, 1000,
+ 1000, 1000, 10000, 10000, 10000, 100000,
+ 100000, 100000, 1000000};
+ int e;
+ double m = frexp(d, &e);
+ int whole = int(d);
+ int fdivisor = 1000000; // starting divisor for 6 digits after the decimal
+ int fracDigits =
+ int((d - whole) *
+ fdivisor); // mult by constant to give desired number of digits
+ if (e >= 0)
+ {
+ int divisor = div[e];
+ for (int numdig = exponent[e]; numdig > 0; numdig--, divisor /= 10)
+ {
+ int dig = whole / divisor;
+ *p++ = dig + '0';
+ whole -= dig * divisor;
+ // cout << dig;
+ }
+ }
+ *p++ = whole + '0';
+ *p++ = '.';
+
+ int first3 = (*(int*)(digits + (fracDigits / 1000 * 4))) >> 8;
+ *p++ = first3;
+ first3 >>= 8;
+ *p++ = first3;
+ first3 >>= 8;
+ *p++ = first3;
+ int second3 = (*(int*)(digits + fracDigits % 1000 * 4)) >> 8;
+ *p++ = second3;
+ second3 >>= 8;
+ *p++ = second3;
+ second3 >>= 8;
+ *p++ = second3;
+
+ //*p++= '\0';
+ // cerr << "e=" << e << '\n';
+ return p;
+}
+
+const char digits[4000] = {
+ '0', '0', '0', '0', '0', '0', '0', '1', '0', '0', '0', '2', '0', '0', '0',
+ '3', '0', '0', '0', '4', '0', '0', '0', '5', '0', '0', '0', '6', '0', '0',
+ '0', '7', '0', '0', '0', '8', '0', '0', '0', '9', '0', '0', '1', '0', '0',
+ '0', '1', '1', '0', '0', '1', '2', '0', '0', '1', '3', '0', '0', '1', '4',
+ '0', '0', '1', '5', '0', '0', '1', '6', '0', '0', '1', '7', '0', '0', '1',
+ '8', '0', '0', '1', '9', '0', '0', '2', '0', '0', '0', '2', '1', '0', '0',
+ '2', '2', '0', '0', '2', '3', '0', '0', '2', '4', '0', '0', '2', '5', '0',
+ '0', '2', '6', '0', '0', '2', '7', '0', '0', '2', '8', '0', '0', '2', '9',
+ '0', '0', '3', '0', '0', '0', '3', '1', '0', '0', '3', '2', '0', '0', '3',
+ '3', '0', '0', '3', '4', '0', '0', '3', '5', '0', '0', '3', '6', '0', '0',
+ '3', '7', '0', '0', '3', '8', '0', '0', '3', '9', '0', '0', '4', '0', '0',
+ '0', '4', '1', '0', '0', '4', '2', '0', '0', '4', '3', '0', '0', '4', '4',
+ '0', '0', '4', '5', '0', '0', '4', '6', '0', '0', '4', '7', '0', '0', '4',
+ '8', '0', '0', '4', '9', '0', '0', '5', '0', '0', '0', '5', '1', '0', '0',
+ '5', '2', '0', '0', '5', '3', '0', '0', '5', '4', '0', '0', '5', '5', '0',
+ '0', '5', '6', '0', '0', '5', '7', '0', '0', '5', '8', '0', '0', '5', '9',
+ '0', '0', '6', '0', '0', '0', '6', '1', '0', '0', '6', '2', '0', '0', '6',
+ '3', '0', '0', '6', '4', '0', '0', '6', '5', '0', '0', '6', '6', '0', '0',
+ '6', '7', '0', '0', '6', '8', '0', '0', '6', '9', '0', '0', '7', '0', '0',
+ '0', '7', '1', '0', '0', '7', '2', '0', '0', '7', '3', '0', '0', '7', '4',
+ '0', '0', '7', '5', '0', '0', '7', '6', '0', '0', '7', '7', '0', '0', '7',
+ '8', '0', '0', '7', '9', '0', '0', '8', '0', '0', '0', '8', '1', '0', '0',
+ '8', '2', '0', '0', '8', '3', '0', '0', '8', '4', '0', '0', '8', '5', '0',
+ '0', '8', '6', '0', '0', '8', '7', '0', '0', '8', '8', '0', '0', '8', '9',
+ '0', '0', '9', '0', '0', '0', '9', '1', '0', '0', '9', '2', '0', '0', '9',
+ '3', '0', '0', '9', '4', '0', '0', '9', '5', '0', '0', '9', '6', '0', '0',
+ '9', '7', '0', '0', '9', '8', '0', '0', '9', '9', '0', '1', '0', '0', '0',
+ '1', '0', '1', '0', '1', '0', '2', '0', '1', '0', '3', '0', '1', '0', '4',
+ '0', '1', '0', '5', '0', '1', '0', '6', '0', '1', '0', '7', '0', '1', '0',
+ '8', '0', '1', '0', '9', '0', '1', '1', '0', '0', '1', '1', '1', '0', '1',
+ '1', '2', '0', '1', '1', '3', '0', '1', '1', '4', '0', '1', '1', '5', '0',
+ '1', '1', '6', '0', '1', '1', '7', '0', '1', '1', '8', '0', '1', '1', '9',
+ '0', '1', '2', '0', '0', '1', '2', '1', '0', '1', '2', '2', '0', '1', '2',
+ '3', '0', '1', '2', '4', '0', '1', '2', '5', '0', '1', '2', '6', '0', '1',
+ '2', '7', '0', '1', '2', '8', '0', '1', '2', '9', '0', '1', '3', '0', '0',
+ '1', '3', '1', '0', '1', '3', '2', '0', '1', '3', '3', '0', '1', '3', '4',
+ '0', '1', '3', '5', '0', '1', '3', '6', '0', '1', '3', '7', '0', '1', '3',
+ '8', '0', '1', '3', '9', '0', '1', '4', '0', '0', '1', '4', '1', '0', '1',
+ '4', '2', '0', '1', '4', '3', '0', '1', '4', '4', '0', '1', '4', '5', '0',
+ '1', '4', '6', '0', '1', '4', '7', '0', '1', '4', '8', '0', '1', '4', '9',
+ '0', '1', '5', '0', '0', '1', '5', '1', '0', '1', '5', '2', '0', '1', '5',
+ '3', '0', '1', '5', '4', '0', '1', '5', '5', '0', '1', '5', '6', '0', '1',
+ '5', '7', '0', '1', '5', '8', '0', '1', '5', '9', '0', '1', '6', '0', '0',
+ '1', '6', '1', '0', '1', '6', '2', '0', '1', '6', '3', '0', '1', '6', '4',
+ '0', '1', '6', '5', '0', '1', '6', '6', '0', '1', '6', '7', '0', '1', '6',
+ '8', '0', '1', '6', '9', '0', '1', '7', '0', '0', '1', '7', '1', '0', '1',
+ '7', '2', '0', '1', '7', '3', '0', '1', '7', '4', '0', '1', '7', '5', '0',
+ '1', '7', '6', '0', '1', '7', '7', '0', '1', '7', '8', '0', '1', '7', '9',
+ '0', '1', '8', '0', '0', '1', '8', '1', '0', '1', '8', '2', '0', '1', '8',
+ '3', '0', '1', '8', '4', '0', '1', '8', '5', '0', '1', '8', '6', '0', '1',
+ '8', '7', '0', '1', '8', '8', '0', '1', '8', '9', '0', '1', '9', '0', '0',
+ '1', '9', '1', '0', '1', '9', '2', '0', '1', '9', '3', '0', '1', '9', '4',
+ '0', '1', '9', '5', '0', '1', '9', '6', '0', '1', '9', '7', '0', '1', '9',
+ '8', '0', '1', '9', '9', '0', '2', '0', '0', '0', '2', '0', '1', '0', '2',
+ '0', '2', '0', '2', '0', '3', '0', '2', '0', '4', '0', '2', '0', '5', '0',
+ '2', '0', '6', '0', '2', '0', '7', '0', '2', '0', '8', '0', '2', '0', '9',
+ '0', '2', '1', '0', '0', '2', '1', '1', '0', '2', '1', '2', '0', '2', '1',
+ '3', '0', '2', '1', '4', '0', '2', '1', '5', '0', '2', '1', '6', '0', '2',
+ '1', '7', '0', '2', '1', '8', '0', '2', '1', '9', '0', '2', '2', '0', '0',
+ '2', '2', '1', '0', '2', '2', '2', '0', '2', '2', '3', '0', '2', '2', '4',
+ '0', '2', '2', '5', '0', '2', '2', '6', '0', '2', '2', '7', '0', '2', '2',
+ '8', '0', '2', '2', '9', '0', '2', '3', '0', '0', '2', '3', '1', '0', '2',
+ '3', '2', '0', '2', '3', '3', '0', '2', '3', '4', '0', '2', '3', '5', '0',
+ '2', '3', '6', '0', '2', '3', '7', '0', '2', '3', '8', '0', '2', '3', '9',
+ '0', '2', '4', '0', '0', '2', '4', '1', '0', '2', '4', '2', '0', '2', '4',
+ '3', '0', '2', '4', '4', '0', '2', '4', '5', '0', '2', '4', '6', '0', '2',
+ '4', '7', '0', '2', '4', '8', '0', '2', '4', '9', '0', '2', '5', '0', '0',
+ '2', '5', '1', '0', '2', '5', '2', '0', '2', '5', '3', '0', '2', '5', '4',
+ '0', '2', '5', '5', '0', '2', '5', '6', '0', '2', '5', '7', '0', '2', '5',
+ '8', '0', '2', '5', '9', '0', '2', '6', '0', '0', '2', '6', '1', '0', '2',
+ '6', '2', '0', '2', '6', '3', '0', '2', '6', '4', '0', '2', '6', '5', '0',
+ '2', '6', '6', '0', '2', '6', '7', '0', '2', '6', '8', '0', '2', '6', '9',
+ '0', '2', '7', '0', '0', '2', '7', '1', '0', '2', '7', '2', '0', '2', '7',
+ '3', '0', '2', '7', '4', '0', '2', '7', '5', '0', '2', '7', '6', '0', '2',
+ '7', '7', '0', '2', '7', '8', '0', '2', '7', '9', '0', '2', '8', '0', '0',
+ '2', '8', '1', '0', '2', '8', '2', '0', '2', '8', '3', '0', '2', '8', '4',
+ '0', '2', '8', '5', '0', '2', '8', '6', '0', '2', '8', '7', '0', '2', '8',
+ '8', '0', '2', '8', '9', '0', '2', '9', '0', '0', '2', '9', '1', '0', '2',
+ '9', '2', '0', '2', '9', '3', '0', '2', '9', '4', '0', '2', '9', '5', '0',
+ '2', '9', '6', '0', '2', '9', '7', '0', '2', '9', '8', '0', '2', '9', '9',
+ '0', '3', '0', '0', '0', '3', '0', '1', '0', '3', '0', '2', '0', '3', '0',
+ '3', '0', '3', '0', '4', '0', '3', '0', '5', '0', '3', '0', '6', '0', '3',
+ '0', '7', '0', '3', '0', '8', '0', '3', '0', '9', '0', '3', '1', '0', '0',
+ '3', '1', '1', '0', '3', '1', '2', '0', '3', '1', '3', '0', '3', '1', '4',
+ '0', '3', '1', '5', '0', '3', '1', '6', '0', '3', '1', '7', '0', '3', '1',
+ '8', '0', '3', '1', '9', '0', '3', '2', '0', '0', '3', '2', '1', '0', '3',
+ '2', '2', '0', '3', '2', '3', '0', '3', '2', '4', '0', '3', '2', '5', '0',
+ '3', '2', '6', '0', '3', '2', '7', '0', '3', '2', '8', '0', '3', '2', '9',
+ '0', '3', '3', '0', '0', '3', '3', '1', '0', '3', '3', '2', '0', '3', '3',
+ '3', '0', '3', '3', '4', '0', '3', '3', '5', '0', '3', '3', '6', '0', '3',
+ '3', '7', '0', '3', '3', '8', '0', '3', '3', '9', '0', '3', '4', '0', '0',
+ '3', '4', '1', '0', '3', '4', '2', '0', '3', '4', '3', '0', '3', '4', '4',
+ '0', '3', '4', '5', '0', '3', '4', '6', '0', '3', '4', '7', '0', '3', '4',
+ '8', '0', '3', '4', '9', '0', '3', '5', '0', '0', '3', '5', '1', '0', '3',
+ '5', '2', '0', '3', '5', '3', '0', '3', '5', '4', '0', '3', '5', '5', '0',
+ '3', '5', '6', '0', '3', '5', '7', '0', '3', '5', '8', '0', '3', '5', '9',
+ '0', '3', '6', '0', '0', '3', '6', '1', '0', '3', '6', '2', '0', '3', '6',
+ '3', '0', '3', '6', '4', '0', '3', '6', '5', '0', '3', '6', '6', '0', '3',
+ '6', '7', '0', '3', '6', '8', '0', '3', '6', '9', '0', '3', '7', '0', '0',
+ '3', '7', '1', '0', '3', '7', '2', '0', '3', '7', '3', '0', '3', '7', '4',
+ '0', '3', '7', '5', '0', '3', '7', '6', '0', '3', '7', '7', '0', '3', '7',
+ '8', '0', '3', '7', '9', '0', '3', '8', '0', '0', '3', '8', '1', '0', '3',
+ '8', '2', '0', '3', '8', '3', '0', '3', '8', '4', '0', '3', '8', '5', '0',
+ '3', '8', '6', '0', '3', '8', '7', '0', '3', '8', '8', '0', '3', '8', '9',
+ '0', '3', '9', '0', '0', '3', '9', '1', '0', '3', '9', '2', '0', '3', '9',
+ '3', '0', '3', '9', '4', '0', '3', '9', '5', '0', '3', '9', '6', '0', '3',
+ '9', '7', '0', '3', '9', '8', '0', '3', '9', '9', '0', '4', '0', '0', '0',
+ '4', '0', '1', '0', '4', '0', '2', '0', '4', '0', '3', '0', '4', '0', '4',
+ '0', '4', '0', '5', '0', '4', '0', '6', '0', '4', '0', '7', '0', '4', '0',
+ '8', '0', '4', '0', '9', '0', '4', '1', '0', '0', '4', '1', '1', '0', '4',
+ '1', '2', '0', '4', '1', '3', '0', '4', '1', '4', '0', '4', '1', '5', '0',
+ '4', '1', '6', '0', '4', '1', '7', '0', '4', '1', '8', '0', '4', '1', '9',
+ '0', '4', '2', '0', '0', '4', '2', '1', '0', '4', '2', '2', '0', '4', '2',
+ '3', '0', '4', '2', '4', '0', '4', '2', '5', '0', '4', '2', '6', '0', '4',
+ '2', '7', '0', '4', '2', '8', '0', '4', '2', '9', '0', '4', '3', '0', '0',
+ '4', '3', '1', '0', '4', '3', '2', '0', '4', '3', '3', '0', '4', '3', '4',
+ '0', '4', '3', '5', '0', '4', '3', '6', '0', '4', '3', '7', '0', '4', '3',
+ '8', '0', '4', '3', '9', '0', '4', '4', '0', '0', '4', '4', '1', '0', '4',
+ '4', '2', '0', '4', '4', '3', '0', '4', '4', '4', '0', '4', '4', '5', '0',
+ '4', '4', '6', '0', '4', '4', '7', '0', '4', '4', '8', '0', '4', '4', '9',
+ '0', '4', '5', '0', '0', '4', '5', '1', '0', '4', '5', '2', '0', '4', '5',
+ '3', '0', '4', '5', '4', '0', '4', '5', '5', '0', '4', '5', '6', '0', '4',
+ '5', '7', '0', '4', '5', '8', '0', '4', '5', '9', '0', '4', '6', '0', '0',
+ '4', '6', '1', '0', '4', '6', '2', '0', '4', '6', '3', '0', '4', '6', '4',
+ '0', '4', '6', '5', '0', '4', '6', '6', '0', '4', '6', '7', '0', '4', '6',
+ '8', '0', '4', '6', '9', '0', '4', '7', '0', '0', '4', '7', '1', '0', '4',
+ '7', '2', '0', '4', '7', '3', '0', '4', '7', '4', '0', '4', '7', '5', '0',
+ '4', '7', '6', '0', '4', '7', '7', '0', '4', '7', '8', '0', '4', '7', '9',
+ '0', '4', '8', '0', '0', '4', '8', '1', '0', '4', '8', '2', '0', '4', '8',
+ '3', '0', '4', '8', '4', '0', '4', '8', '5', '0', '4', '8', '6', '0', '4',
+ '8', '7', '0', '4', '8', '8', '0', '4', '8', '9', '0', '4', '9', '0', '0',
+ '4', '9', '1', '0', '4', '9', '2', '0', '4', '9', '3', '0', '4', '9', '4',
+ '0', '4', '9', '5', '0', '4', '9', '6', '0', '4', '9', '7', '0', '4', '9',
+ '8', '0', '4', '9', '9', '0', '5', '0', '0', '0', '5', '0', '1', '0', '5',
+ '0', '2', '0', '5', '0', '3', '0', '5', '0', '4', '0', '5', '0', '5', '0',
+ '5', '0', '6', '0', '5', '0', '7', '0', '5', '0', '8', '0', '5', '0', '9',
+ '0', '5', '1', '0', '0', '5', '1', '1', '0', '5', '1', '2', '0', '5', '1',
+ '3', '0', '5', '1', '4', '0', '5', '1', '5', '0', '5', '1', '6', '0', '5',
+ '1', '7', '0', '5', '1', '8', '0', '5', '1', '9', '0', '5', '2', '0', '0',
+ '5', '2', '1', '0', '5', '2', '2', '0', '5', '2', '3', '0', '5', '2', '4',
+ '0', '5', '2', '5', '0', '5', '2', '6', '0', '5', '2', '7', '0', '5', '2',
+ '8', '0', '5', '2', '9', '0', '5', '3', '0', '0', '5', '3', '1', '0', '5',
+ '3', '2', '0', '5', '3', '3', '0', '5', '3', '4', '0', '5', '3', '5', '0',
+ '5', '3', '6', '0', '5', '3', '7', '0', '5', '3', '8', '0', '5', '3', '9',
+ '0', '5', '4', '0', '0', '5', '4', '1', '0', '5', '4', '2', '0', '5', '4',
+ '3', '0', '5', '4', '4', '0', '5', '4', '5', '0', '5', '4', '6', '0', '5',
+ '4', '7', '0', '5', '4', '8', '0', '5', '4', '9', '0', '5', '5', '0', '0',
+ '5', '5', '1', '0', '5', '5', '2', '0', '5', '5', '3', '0', '5', '5', '4',
+ '0', '5', '5', '5', '0', '5', '5', '6', '0', '5', '5', '7', '0', '5', '5',
+ '8', '0', '5', '5', '9', '0', '5', '6', '0', '0', '5', '6', '1', '0', '5',
+ '6', '2', '0', '5', '6', '3', '0', '5', '6', '4', '0', '5', '6', '5', '0',
+ '5', '6', '6', '0', '5', '6', '7', '0', '5', '6', '8', '0', '5', '6', '9',
+ '0', '5', '7', '0', '0', '5', '7', '1', '0', '5', '7', '2', '0', '5', '7',
+ '3', '0', '5', '7', '4', '0', '5', '7', '5', '0', '5', '7', '6', '0', '5',
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+ '6', '4', '1', '0', '6', '4', '2', '0', '6', '4', '3', '0', '6', '4', '4',
+ '0', '6', '4', '5', '0', '6', '4', '6', '0', '6', '4', '7', '0', '6', '4',
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+ '5', '2', '0', '6', '5', '3', '0', '6', '5', '4', '0', '6', '5', '5', '0',
+ '6', '5', '6', '0', '6', '5', '7', '0', '6', '5', '8', '0', '6', '5', '9',
+ '0', '6', '6', '0', '0', '6', '6', '1', '0', '6', '6', '2', '0', '6', '6',
+ '3', '0', '6', '6', '4', '0', '6', '6', '5', '0', '6', '6', '6', '0', '6',
+ '6', '7', '0', '6', '6', '8', '0', '6', '6', '9', '0', '6', '7', '0', '0',
+ '6', '7', '1', '0', '6', '7', '2', '0', '6', '7', '3', '0', '6', '7', '4',
+ '0', '6', '7', '5', '0', '6', '7', '6', '0', '6', '7', '7', '0', '6', '7',
+ '8', '0', '6', '7', '9', '0', '6', '8', '0', '0', '6', '8', '1', '0', '6',
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+ '0', '6', '9', '0', '0', '6', '9', '1', '0', '6', '9', '2', '0', '6', '9',
+ '3', '0', '6', '9', '4', '0', '6', '9', '5', '0', '6', '9', '6', '0', '6',
+ '9', '7', '0', '6', '9', '8', '0', '6', '9', '9', '0', '7', '0', '0', '0',
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+ '0', '7', '0', '5', '0', '7', '0', '6', '0', '7', '0', '7', '0', '7', '0',
+ '8', '0', '7', '0', '9', '0', '7', '1', '0', '0', '7', '1', '1', '0', '7',
+ '1', '2', '0', '7', '1', '3', '0', '7', '1', '4', '0', '7', '1', '5', '0',
+ '7', '1', '6', '0', '7', '1', '7', '0', '7', '1', '8', '0', '7', '1', '9',
+ '0', '7', '2', '0', '0', '7', '2', '1', '0', '7', '2', '2', '0', '7', '2',
+ '3', '0', '7', '2', '4', '0', '7', '2', '5', '0', '7', '2', '6', '0', '7',
+ '2', '7', '0', '7', '2', '8', '0', '7', '2', '9', '0', '7', '3', '0', '0',
+ '7', '3', '1', '0', '7', '3', '2', '0', '7', '3', '3', '0', '7', '3', '4',
+ '0', '7', '3', '5', '0', '7', '3', '6', '0', '7', '3', '7', '0', '7', '3',
+ '8', '0', '7', '3', '9', '0', '7', '4', '0', '0', '7', '4', '1', '0', '7',
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+ '7', '4', '6', '0', '7', '4', '7', '0', '7', '4', '8', '0', '7', '4', '9',
+ '0', '7', '5', '0', '0', '7', '5', '1', '0', '7', '5', '2', '0', '7', '5',
+ '3', '0', '7', '5', '4', '0', '7', '5', '5', '0', '7', '5', '6', '0', '7',
+ '5', '7', '0', '7', '5', '8', '0', '7', '5', '9', '0', '7', '6', '0', '0',
+ '7', '6', '1', '0', '7', '6', '2', '0', '7', '6', '3', '0', '7', '6', '4',
+ '0', '7', '6', '5', '0', '7', '6', '6', '0', '7', '6', '7', '0', '7', '6',
+ '8', '0', '7', '6', '9', '0', '7', '7', '0', '0', '7', '7', '1', '0', '7',
+ '7', '2', '0', '7', '7', '3', '0', '7', '7', '4', '0', '7', '7', '5', '0',
+ '7', '7', '6', '0', '7', '7', '7', '0', '7', '7', '8', '0', '7', '7', '9',
+ '0', '7', '8', '0', '0', '7', '8', '1', '0', '7', '8', '2', '0', '7', '8',
+ '3', '0', '7', '8', '4', '0', '7', '8', '5', '0', '7', '8', '6', '0', '7',
+ '8', '7', '0', '7', '8', '8', '0', '7', '8', '9', '0', '7', '9', '0', '0',
+ '7', '9', '1', '0', '7', '9', '2', '0', '7', '9', '3', '0', '7', '9', '4',
+ '0', '7', '9', '5', '0', '7', '9', '6', '0', '7', '9', '7', '0', '7', '9',
+ '8', '0', '7', '9', '9', '0', '8', '0', '0', '0', '8', '0', '1', '0', '8',
+ '0', '2', '0', '8', '0', '3', '0', '8', '0', '4', '0', '8', '0', '5', '0',
+ '8', '0', '6', '0', '8', '0', '7', '0', '8', '0', '8', '0', '8', '0', '9',
+ '0', '8', '1', '0', '0', '8', '1', '1', '0', '8', '1', '2', '0', '8', '1',
+ '3', '0', '8', '1', '4', '0', '8', '1', '5', '0', '8', '1', '6', '0', '8',
+ '1', '7', '0', '8', '1', '8', '0', '8', '1', '9', '0', '8', '2', '0', '0',
+ '8', '2', '1', '0', '8', '2', '2', '0', '8', '2', '3', '0', '8', '2', '4',
+ '0', '8', '2', '5', '0', '8', '2', '6', '0', '8', '2', '7', '0', '8', '2',
+ '8', '0', '8', '2', '9', '0', '8', '3', '0', '0', '8', '3', '1', '0', '8',
+ '3', '2', '0', '8', '3', '3', '0', '8', '3', '4', '0', '8', '3', '5', '0',
+ '8', '3', '6', '0', '8', '3', '7', '0', '8', '3', '8', '0', '8', '3', '9',
+ '0', '8', '4', '0', '0', '8', '4', '1', '0', '8', '4', '2', '0', '8', '4',
+ '3', '0', '8', '4', '4', '0', '8', '4', '5', '0', '8', '4', '6', '0', '8',
+ '4', '7', '0', '8', '4', '8', '0', '8', '4', '9', '0', '8', '5', '0', '0',
+ '8', '5', '1', '0', '8', '5', '2', '0', '8', '5', '3', '0', '8', '5', '4',
+ '0', '8', '5', '5', '0', '8', '5', '6', '0', '8', '5', '7', '0', '8', '5',
+ '8', '0', '8', '5', '9', '0', '8', '6', '0', '0', '8', '6', '1', '0', '8',
+ '6', '2', '0', '8', '6', '3', '0', '8', '6', '4', '0', '8', '6', '5', '0',
+ '8', '6', '6', '0', '8', '6', '7', '0', '8', '6', '8', '0', '8', '6', '9',
+ '0', '8', '7', '0', '0', '8', '7', '1', '0', '8', '7', '2', '0', '8', '7',
+ '3', '0', '8', '7', '4', '0', '8', '7', '5', '0', '8', '7', '6', '0', '8',
+ '7', '7', '0', '8', '7', '8', '0', '8', '7', '9', '0', '8', '8', '0', '0',
+ '8', '8', '1', '0', '8', '8', '2', '0', '8', '8', '3', '0', '8', '8', '4',
+ '0', '8', '8', '5', '0', '8', '8', '6', '0', '8', '8', '7', '0', '8', '8',
+ '8', '0', '8', '8', '9', '0', '8', '9', '0', '0', '8', '9', '1', '0', '8',
+ '9', '2', '0', '8', '9', '3', '0', '8', '9', '4', '0', '8', '9', '5', '0',
+ '8', '9', '6', '0', '8', '9', '7', '0', '8', '9', '8', '0', '8', '9', '9',
+ '0', '9', '0', '0', '0', '9', '0', '1', '0', '9', '0', '2', '0', '9', '0',
+ '3', '0', '9', '0', '4', '0', '9', '0', '5', '0', '9', '0', '6', '0', '9',
+ '0', '7', '0', '9', '0', '8', '0', '9', '0', '9', '0', '9', '1', '0', '0',
+ '9', '1', '1', '0', '9', '1', '2', '0', '9', '1', '3', '0', '9', '1', '4',
+ '0', '9', '1', '5', '0', '9', '1', '6', '0', '9', '1', '7', '0', '9', '1',
+ '8', '0', '9', '1', '9', '0', '9', '2', '0', '0', '9', '2', '1', '0', '9',
+ '2', '2', '0', '9', '2', '3', '0', '9', '2', '4', '0', '9', '2', '5', '0',
+ '9', '2', '6', '0', '9', '2', '7', '0', '9', '2', '8', '0', '9', '2', '9',
+ '0', '9', '3', '0', '0', '9', '3', '1', '0', '9', '3', '2', '0', '9', '3',
+ '3', '0', '9', '3', '4', '0', '9', '3', '5', '0', '9', '3', '6', '0', '9',
+ '3', '7', '0', '9', '3', '8', '0', '9', '3', '9', '0', '9', '4', '0', '0',
+ '9', '4', '1', '0', '9', '4', '2', '0', '9', '4', '3', '0', '9', '4', '4',
+ '0', '9', '4', '5', '0', '9', '4', '6', '0', '9', '4', '7', '0', '9', '4',
+ '8', '0', '9', '4', '9', '0', '9', '5', '0', '0', '9', '5', '1', '0', '9',
+ '5', '2', '0', '9', '5', '3', '0', '9', '5', '4', '0', '9', '5', '5', '0',
+ '9', '5', '6', '0', '9', '5', '7', '0', '9', '5', '8', '0', '9', '5', '9',
+ '0', '9', '6', '0', '0', '9', '6', '1', '0', '9', '6', '2', '0', '9', '6',
+ '3', '0', '9', '6', '4', '0', '9', '6', '5', '0', '9', '6', '6', '0', '9',
+ '6', '7', '0', '9', '6', '8', '0', '9', '6', '9', '0', '9', '7', '0', '0',
+ '9', '7', '1', '0', '9', '7', '2', '0', '9', '7', '3', '0', '9', '7', '4',
+ '0', '9', '7', '5', '0', '9', '7', '6', '0', '9', '7', '7', '0', '9', '7',
+ '8', '0', '9', '7', '9', '0', '9', '8', '0', '0', '9', '8', '1', '0', '9',
+ '8', '2', '0', '9', '8', '3', '0', '9', '8', '4', '0', '9', '8', '5', '0',
+ '9', '8', '6', '0', '9', '8', '7', '0', '9', '8', '8', '0', '9', '8', '9',
+ '0', '9', '9', '0', '0', '9', '9', '1', '0', '9', '9', '2', '0', '9', '9',
+ '3', '0', '9', '9', '4', '0', '9', '9', '5', '0', '9', '9', '6', '0', '9',
+ '9', '7', '0', '9', '9', '8', '0', '9', '9', '9'};