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Author SHA1 Message Date
Markus Hitter fc7365b320 preprocessor_math.h: fix errorneous comment. 2014-08-31 19:32:09 +02:00
Markus Hitter 2ad7517e27 preprocessor_math.h, SQRT(): take a better initial guess. 
Now results are apparently accurate across the whole uint32 range.
At least, this test passes with all numbers being exact:

  #include "preprocessor_math.h"
  #include <math.h>
  ... in main() ...
  sersendf_P(PSTR("0:  %lu  %lu\n"), (uint32_t)SQRT(0), (uint32_t)sqrt(0));
  sersendf_P(PSTR("1:  %lu  %lu\n"), (uint32_t)SQRT(1), (uint32_t)sqrt(1));
  sersendf_P(PSTR("2:  %lu  %lu\n"), (uint32_t)SQRT(2), (uint32_t)sqrt(2));
  sersendf_P(PSTR("3:  %lu  %lu\n"), (uint32_t)SQRT(3), (uint32_t)sqrt(3));
  sersendf_P(PSTR("4:  %lu  %lu\n"), (uint32_t)SQRT(4), (uint32_t)sqrt(4));
  sersendf_P(PSTR("5:  %lu  %lu\n"), (uint32_t)SQRT(5), (uint32_t)sqrt(5));
  sersendf_P(PSTR("6:  %lu  %lu\n"), (uint32_t)SQRT(6), (uint32_t)sqrt(6));
  sersendf_P(PSTR("7:  %lu  %lu\n"), (uint32_t)SQRT(7), (uint32_t)sqrt(7));
  sersendf_P(PSTR("8:  %lu  %lu\n"), (uint32_t)SQRT(8), (uint32_t)sqrt(8));
  sersendf_P(PSTR("9:  %lu  %lu\n"), (uint32_t)SQRT(9), (uint32_t)sqrt(9));
  sersendf_P(PSTR("10:  %lu  %lu\n"), (uint32_t)SQRT(10), (uint32_t)sqrt(10));
  sersendf_P(PSTR("20:  %lu  %lu\n"), (uint32_t)SQRT(20), (uint32_t)sqrt(20));
  sersendf_P(PSTR("30:  %lu  %lu\n"), (uint32_t)SQRT(30), (uint32_t)sqrt(30));
  sersendf_P(PSTR("40:  %lu  %lu\n"), (uint32_t)SQRT(40), (uint32_t)sqrt(40));
  sersendf_P(PSTR("50:  %lu  %lu\n"), (uint32_t)SQRT(50), (uint32_t)sqrt(50));
  sersendf_P(PSTR("60:  %lu  %lu\n"), (uint32_t)SQRT(60), (uint32_t)sqrt(60));
  sersendf_P(PSTR("70:  %lu  %lu\n"), (uint32_t)SQRT(70), (uint32_t)sqrt(70));
  sersendf_P(PSTR("80:  %lu  %lu\n"), (uint32_t)SQRT(80), (uint32_t)sqrt(80));
  sersendf_P(PSTR("90:  %lu  %lu\n"), (uint32_t)SQRT(90), (uint32_t)sqrt(90));
  sersendf_P(PSTR("100:  %lu  %lu\n"), (uint32_t)SQRT(100), (uint32_t)sqrt(100));
  sersendf_P(PSTR("200:  %lu  %lu\n"), (uint32_t)SQRT(200), (uint32_t)sqrt(200));
  sersendf_P(PSTR("300:  %lu  %lu\n"), (uint32_t)SQRT(300), (uint32_t)sqrt(300));
  sersendf_P(PSTR("400:  %lu  %lu\n"), (uint32_t)SQRT(400), (uint32_t)sqrt(400));
  sersendf_P(PSTR("500:  %lu  %lu\n"), (uint32_t)SQRT(500), (uint32_t)sqrt(500));
  sersendf_P(PSTR("600:  %lu  %lu\n"), (uint32_t)SQRT(600), (uint32_t)sqrt(600));
  sersendf_P(PSTR("700:  %lu  %lu\n"), (uint32_t)SQRT(700), (uint32_t)sqrt(700));
  sersendf_P(PSTR("800:  %lu  %lu\n"), (uint32_t)SQRT(800), (uint32_t)sqrt(800));
  sersendf_P(PSTR("900:  %lu  %lu\n"), (uint32_t)SQRT(900), (uint32_t)sqrt(900));
  sersendf_P(PSTR("1000:  %lu  %lu\n"), (uint32_t)SQRT(1000), (uint32_t)sqrt(1000));
  sersendf_P(PSTR("2000:  %lu  %lu\n"), (uint32_t)SQRT(2000), (uint32_t)sqrt(2000));
  sersendf_P(PSTR("3000:  %lu  %lu\n"), (uint32_t)SQRT(3000), (uint32_t)sqrt(3000));
  sersendf_P(PSTR("4000:  %lu  %lu\n"), (uint32_t)SQRT(4000), (uint32_t)sqrt(4000));
  sersendf_P(PSTR("5000:  %lu  %lu\n"), (uint32_t)SQRT(5000), (uint32_t)sqrt(5000));
  sersendf_P(PSTR("6000:  %lu  %lu\n"), (uint32_t)SQRT(6000), (uint32_t)sqrt(6000));
  sersendf_P(PSTR("7000:  %lu  %lu\n"), (uint32_t)SQRT(7000), (uint32_t)sqrt(7000));
  sersendf_P(PSTR("8000:  %lu  %lu\n"), (uint32_t)SQRT(8000), (uint32_t)sqrt(8000));
  sersendf_P(PSTR("9000:  %lu  %lu\n"), (uint32_t)SQRT(9000), (uint32_t)sqrt(9000));
  sersendf_P(PSTR("10000:  %lu  %lu\n"), (uint32_t)SQRT(10000), (uint32_t)sqrt(10000));
  sersendf_P(PSTR("20000:  %lu  %lu\n"), (uint32_t)SQRT(20000), (uint32_t)sqrt(20000));
  sersendf_P(PSTR("30000:  %lu  %lu\n"), (uint32_t)SQRT(30000), (uint32_t)sqrt(30000));
  sersendf_P(PSTR("40000:  %lu  %lu\n"), (uint32_t)SQRT(40000), (uint32_t)sqrt(40000));
  sersendf_P(PSTR("50000:  %lu  %lu\n"), (uint32_t)SQRT(50000), (uint32_t)sqrt(50000));
  sersendf_P(PSTR("60000:  %lu  %lu\n"), (uint32_t)SQRT(60000), (uint32_t)sqrt(60000));
  sersendf_P(PSTR("70000:  %lu  %lu\n"), (uint32_t)SQRT(70000), (uint32_t)sqrt(70000));
  sersendf_P(PSTR("80000:  %lu  %lu\n"), (uint32_t)SQRT(80000), (uint32_t)sqrt(80000));
  sersendf_P(PSTR("90000:  %lu  %lu\n"), (uint32_t)SQRT(90000), (uint32_t)sqrt(90000));
  sersendf_P(PSTR("100000:  %lu  %lu\n"), (uint32_t)SQRT(100000), (uint32_t)sqrt(100000));
  sersendf_P(PSTR("200000:  %lu  %lu\n"), (uint32_t)SQRT(200000), (uint32_t)sqrt(200000));
  sersendf_P(PSTR("300000:  %lu  %lu\n"), (uint32_t)SQRT(300000), (uint32_t)sqrt(300000));
  sersendf_P(PSTR("400000:  %lu  %lu\n"), (uint32_t)SQRT(400000), (uint32_t)sqrt(400000));
  sersendf_P(PSTR("500000:  %lu  %lu\n"), (uint32_t)SQRT(500000), (uint32_t)sqrt(500000));
  sersendf_P(PSTR("600000:  %lu  %lu\n"), (uint32_t)SQRT(600000), (uint32_t)sqrt(600000));
  sersendf_P(PSTR("700000:  %lu  %lu\n"), (uint32_t)SQRT(700000), (uint32_t)sqrt(700000));
  sersendf_P(PSTR("800000:  %lu  %lu\n"), (uint32_t)SQRT(800000), (uint32_t)sqrt(800000));
  sersendf_P(PSTR("900000:  %lu  %lu\n"), (uint32_t)SQRT(900000), (uint32_t)sqrt(900000));
  sersendf_P(PSTR("1000000:  %lu  %lu\n"), (uint32_t)SQRT(1000000), (uint32_t)sqrt(1000000));
  sersendf_P(PSTR("2000000:  %lu  %lu\n"), (uint32_t)SQRT(2000000), (uint32_t)sqrt(2000000));
  sersendf_P(PSTR("3000000:  %lu  %lu\n"), (uint32_t)SQRT(3000000), (uint32_t)sqrt(3000000));
  sersendf_P(PSTR("4000000:  %lu  %lu\n"), (uint32_t)SQRT(4000000), (uint32_t)sqrt(4000000));
  sersendf_P(PSTR("5000000:  %lu  %lu\n"), (uint32_t)SQRT(5000000), (uint32_t)sqrt(5000000));
  sersendf_P(PSTR("6000000:  %lu  %lu\n"), (uint32_t)SQRT(6000000), (uint32_t)sqrt(6000000));
  sersendf_P(PSTR("7000000:  %lu  %lu\n"), (uint32_t)SQRT(7000000), (uint32_t)sqrt(7000000));
  sersendf_P(PSTR("8000000:  %lu  %lu\n"), (uint32_t)SQRT(8000000), (uint32_t)sqrt(8000000));
  sersendf_P(PSTR("9000000:  %lu  %lu\n"), (uint32_t)SQRT(9000000), (uint32_t)sqrt(9000000));
  sersendf_P(PSTR("10000000:  %lu  %lu\n"), (uint32_t)SQRT(10000000), (uint32_t)sqrt(10000000));
  sersendf_P(PSTR("20000000:  %lu  %lu\n"), (uint32_t)SQRT(20000000), (uint32_t)sqrt(20000000));
  sersendf_P(PSTR("30000000:  %lu  %lu\n"), (uint32_t)SQRT(30000000), (uint32_t)sqrt(30000000));
  sersendf_P(PSTR("40000000:  %lu  %lu\n"), (uint32_t)SQRT(40000000), (uint32_t)sqrt(40000000));
  sersendf_P(PSTR("50000000:  %lu  %lu\n"), (uint32_t)SQRT(50000000), (uint32_t)sqrt(50000000));
  sersendf_P(PSTR("60000000:  %lu  %lu\n"), (uint32_t)SQRT(60000000), (uint32_t)sqrt(60000000));
  sersendf_P(PSTR("70000000:  %lu  %lu\n"), (uint32_t)SQRT(70000000), (uint32_t)sqrt(70000000));
  sersendf_P(PSTR("80000000:  %lu  %lu\n"), (uint32_t)SQRT(80000000), (uint32_t)sqrt(80000000));
  sersendf_P(PSTR("90000000:  %lu  %lu\n"), (uint32_t)SQRT(90000000), (uint32_t)sqrt(90000000));
  sersendf_P(PSTR("100000000:  %lu  %lu\n"), (uint32_t)SQRT(100000000), (uint32_t)sqrt(100000000));
  sersendf_P(PSTR("200000000:  %lu  %lu\n"), (uint32_t)SQRT(200000000), (uint32_t)sqrt(200000000));
  sersendf_P(PSTR("300000000:  %lu  %lu\n"), (uint32_t)SQRT(300000000), (uint32_t)sqrt(300000000));
  sersendf_P(PSTR("400000000:  %lu  %lu\n"), (uint32_t)SQRT(400000000), (uint32_t)sqrt(400000000));
  sersendf_P(PSTR("500000000:  %lu  %lu\n"), (uint32_t)SQRT(500000000), (uint32_t)sqrt(500000000));
  sersendf_P(PSTR("600000000:  %lu  %lu\n"), (uint32_t)SQRT(600000000), (uint32_t)sqrt(600000000));
  sersendf_P(PSTR("700000000:  %lu  %lu\n"), (uint32_t)SQRT(700000000), (uint32_t)sqrt(700000000));
  sersendf_P(PSTR("800000000:  %lu  %lu\n"), (uint32_t)SQRT(800000000), (uint32_t)sqrt(800000000));
  sersendf_P(PSTR("900000000:  %lu  %lu\n"), (uint32_t)SQRT(900000000), (uint32_t)sqrt(900000000));
  sersendf_P(PSTR("1000000000:  %lu  %lu\n"), (uint32_t)SQRT(1000000000), (uint32_t)sqrt(1000000000));
  sersendf_P(PSTR("2000000000:  %lu  %lu\n"), (uint32_t)SQRT(2000000000), (uint32_t)sqrt(2000000000));
  sersendf_P(PSTR("3000000000:  %lu  %lu\n"), (uint32_t)SQRT(3000000000), (uint32_t)sqrt(3000000000));
  sersendf_P(PSTR("4000000000:  %lu  %lu\n"), (uint32_t)SQRT(4000000000), (uint32_t)sqrt(4000000000));
 2014-08-31 19:10:07 +02:00
Markus Hitter 6f83519a1d Add preprocessor math. 
For now this is a square root function which should solve entirely
in the preprocessor. Test results described in the file.

Test code for runtime results, inserted right before the main loop
in mendel.c:

  for (uint32_t i = 0; i < 10000000; i++) {
    uint32_t mathlib = (uint32_t)(sqrt(i) + .5);
    uint32_t preprocessor = (uint32_t)(SQRT(i) + .5);

    if (mathlib != preprocessor) {
      sersendf_P(PSTR("%lu: %lu %lu\n"), i, mathlib, preprocessor);
      break;
    }

    if ((i & 0x00001fff) == 0)
      sersendf_P(PSTR("%lu\n"), i);
  }
  sersendf_P(PSTR("Square root check done.\n"));

Test code for compile time results:

  sersendf_P(PSTR("10000000: %lu\n"), (uint32_t)SQRT(10000000));
  sersendf_P(PSTR("10000000: %lu\n"), (uint32_t)sqrt(10000000));
  sersendf_P(PSTR("20000000: %lu\n"), (uint32_t)SQRT(20000000));
  sersendf_P(PSTR("20000000: %lu\n"), (uint32_t)sqrt(20000000));
  sersendf_P(PSTR("30000000: %lu\n"), (uint32_t)SQRT(30000000));
  sersendf_P(PSTR("30000000: %lu\n"), (uint32_t)sqrt(30000000));
  sersendf_P(PSTR("40000000: %lu\n"), (uint32_t)SQRT(40000000));
  sersendf_P(PSTR("40000000: %lu\n"), (uint32_t)sqrt(40000000));
  sersendf_P(PSTR("50000000: %lu\n"), (uint32_t)SQRT(50000000));
  sersendf_P(PSTR("50000000: %lu\n"), (uint32_t)sqrt(50000000));
  sersendf_P(PSTR("60000000: %lu\n"), (uint32_t)SQRT(60000000));
  sersendf_P(PSTR("60000000: %lu\n"), (uint32_t)sqrt(60000000));
  sersendf_P(PSTR("70000000: %lu\n"), (uint32_t)SQRT(70000000));
  sersendf_P(PSTR("70000000: %lu\n"), (uint32_t)sqrt(70000000));
  sersendf_P(PSTR("80000000: %lu\n"), (uint32_t)SQRT(80000000));
  sersendf_P(PSTR("80000000: %lu\n"), (uint32_t)sqrt(80000000));
  sersendf_P(PSTR("90000000: %lu\n"), (uint32_t)SQRT(90000000));
  sersendf_P(PSTR("90000000: %lu\n"), (uint32_t)sqrt(90000000));
 2014-08-31 19:09:59 +02:00