When does underflow occur?

by

Underflow is not only a question of range, but also of precision/rounding.

7.12.1 Treatment of error conditions
The result underflows if the magnitude of the mathematical result is so small that the mathematical result cannot be represented, without extraordinary roundoff error, in an object of the specified type. C11 ยง7.12.1 6

1.777e-308, converted to the nearest binary64 0x1.98e566222bcfcp-1023, happens to have a significand (0x198E566222BCFC, 7193376082541820) that is a multiple of 10. So dividing by 10 is exact. No roundoff error.

I find this easier to demo with hex notation. Note that dividing by 2 is always exact, except for the smallest value.

#include <float.h>
#include <stdio.h>
#include <fenv.h>
#include <math.h>

int uf_test(double x, double denominator){
  printf("%.17e %24a ", x, x);
  feclearexcept(FE_ALL_EXCEPT);
  double y=x/denominator;
  int uf = !!fetestexcept(FE_UNDERFLOW);
  printf("%-24a %s\n", y, uf ? "Underflow" : "");
  return uf;
}

int main(void) {
  uf_test(DBL_MIN, 2.0);
  uf_test(1.777e-308, 2.0);
  uf_test(1.77e-308, 2.0);
  uf_test(DBL_TRUE_MIN, 2.0);

  uf_test(pow(2.0, -1000), 10.0);
  uf_test(DBL_MIN, 10.0);
  uf_test(1.777e-308, 10.0);
  uf_test(1.77e-308, 10.0);
  uf_test(DBL_TRUE_MIN, 10.0);
  return 0;
}

Output

2.22507385850720138e-308                0x1p-1022 0x1p-1023                
1.77700000000000015e-308  0x1.98e566222bcfcp-1023 0x1.98e566222bcfcp-1024  
1.77000000000000003e-308  0x1.97490d21e478cp-1023 0x1.97490d21e478cp-1024  
4.94065645841246544e-324                0x1p-1074 0x0p+0                   Underflow

// No underflow as inexact result is not too small
9.33263618503218879e-302                0x1p-1000 0x1.999999999999ap-1004  
// Underflow as result is too small and inexact
2.22507385850720138e-308                0x1p-1022 0x1.99999999999ap-1026   Underflow
// No underflow as result is exact
1.77700000000000015e-308  0x1.98e566222bcfcp-1023 0x1.471deb4e8973p-1026   
1.77000000000000003e-308  0x1.97490d21e478cp-1023 0x1.45d40a818394p-1026   Underflow
4.94065645841246544e-324                0x1p-1074 0x0p+0                   Underflow

More Related Contents:

  1. error: incompatible types for a function that returns float in C
  2. Why does >= operator work as > operator in C when compared with 0.9 [duplicate]
  3. How do I restrict a float value to only two places after the decimal point in C?
  4. Correct format specifier for double in printf
  5. Dividing 1/n always returns 0.0 [duplicate]
  6. How to get the sign, mantissa and exponent of a floating point number
  7. How to compare double numbers?
  8. What operations and functions on +0.0 and -0.0 give different arithmetic results?
  9. Question about C behaviour for unsigned integer underflow
  10. Simd matmul program gives different numerical results
  11. Floating point comparison `a != 0.7` [duplicate]
  12. Representing integers in doubles
  13. C: Casting minimum 32-bit integer (-2147483648) to float gives positive number (2147483648.0)
  14. Are floating point operations in C associative?
  15. Comparing float and double in C
  16. Is it safe to assume floating point is represented using IEEE754 floats in C?
  17. Is there a tool to know whether a value has an exact binary representation as a floating point variable?
  18. problems in floating point comparison [duplicate]
  19. Is my fma() broken?
  20. C – Serialization of the floating point numbers (floats, doubles)
  21. Variadic function (va_arg) doesn’t work with float?
  22. sin, cos, tan and rounding error
  23. Why does printf print random value with float and integer format specifier
  24. C printf using %d and %f
  25. Comparing float and double
  26. Why do you need an explicit `-lm` compiler option? [duplicate]
  27. pow() cast to integer, unexpected result
  28. C fundamentals: double variable not equal to double expression?
  29. C dynamically printf double, no loss of precision and no trailing zeroes
  30. How can floating point calculations be made deterministic?

Leave a Comment