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// ulps.h: Counts the FP intervals between two FP numbers

// ulps.h: Counts the FP intervals between two FP numbers. #include <algorithm>. #include <cassert>. #include <cstdlib>. #include <cmath>. #include <limits>. template<typename FType>. int sign(const FType& x) {. return x < FType(0) ? -1 : x > FType(0) ? 1 : 0;. }.

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// ulps.h: Counts the FP intervals between two FP numbers

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  1. // ulps.h: Counts the FP intervals between two FP numbers

  2. #include <algorithm>

  3. #include <cassert>

  4. #include <cstdlib>

  5. #include <cmath>

  6. #include <limits>

  7. template<typename FType>

  8. int sign(const FType& x) {

  9. return x < FType(0) ? -1 : x > FType(0) ? 1 : 0;

  10. }

  11. template<typename FType>

  12. int lowerexp(FType z, FType& glb) {

  13. int base = std::numeric_limits<FType>::radix;

  14. // Find largest exponent of base <= z ("glb" = "base"^"exp").

  15. // z is bracketed by [glb, lub)

  16. // First, search above 1

  17. FType lub = 1;

  18. int exp = 0;

  19. while (lub <= z) {

  20. lub *= base;

  21. ++exp;

  22. }

  23. glb = lub/base;

  24. --exp;

  25. // In case z < 1, search there

  26. while (glb > z) {

  27. lub = glb;

  28. glb /= base;

  29. --exp;

  30. }

  31. assert(glb <= z && z < lub);

  32. return exp;

  33. }

  34. template<typename FType>

  35. long double ulps(FType x, FType y) {

  36. // Handle special cases first

  37. long double inf = std::numeric_limits<long double>::infinity();

  38. if (x == y)

  39. return 0;

  40. else if (sign(x)*sign(y) <= 0 || x == inf || y == inf)

  41. return inf;

  42. // Ignore sign for the result; make x <= y

  43. x = std::abs(x);

  44. y = std::abs(y);

  45. if (x > y)

  46. std::swap(x, y);

  47. // Get needed floating-point parameters

  48. // (The cast is to force long double arithmetic below)

  49. long double eps =

  50. static_cast<long double>(std::numeric_limits<FType>::epsilon());

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