Efficient way to round double precision numbers to a lower precision given in number of bits

by

Dekker’s algorithm will split a floating-point number into high and low parts. If there are s bits in the significand (53 in IEEE 754 64-bit binary), then *x0 receives the high s–b bits, which is what you requested, and *x1 receives the remaining bits, which you may discard. In the code below, Scale should have the value 2b. If b is known at compile time, e.g., the constant 43, you can replace Scale with 0x1p43. Otherwise, you must produce 2b in some way.

This requires round-to-nearest mode. IEEE 754 arithmetic suffices, but other reasonable arithmetic may be okay too. It rounds ties to even, which is not what you requested (ties upward). Is that necessary?

This assumes that x * (Scale + 1) does not overflow. The operations must be evaluated in double precision (not greater).

void Split(double *x0, double *x1, double x)
{
    double d = x * (Scale + 1);
    double t = d - x;
    *x0 = d - t;
    *x1 = x - *x0;
}

More Related Contents:

  1. Math.Round doesn’t behave like i want it to. (X.0xxxxx numbers) [closed]
  2. round() for float in C++
  3. Double to string conversion without scientific notation
  4. Floating point comparison functions for C#
  5. How To Represent 0.1 In Floating Point Arithmetic And Decimal
  6. How can I round up the time to the nearest X minutes?
  7. Formatting a float to 2 decimal places
  8. Formatting doubles for output in C#
  9. Round a double to x significant figures
  10. Is it safe to check floating point values for equality to 0?
  11. Built in .Net algorithm to round value to the nearest 10 interval
  12. C++: How to round a double to an int? [duplicate]
  13. How to round up value C# to the nearest integer?
  14. C#: Convert Byte array into a float
  15. Why is printf round floating point numbers up?
  16. Float/double precision in debug/release modes
  17. Best way to parse float?
  18. Set back default floating point print precision in C++
  19. How can I test for negative zero?
  20. Rounding down to 2 decimal places in c#
  21. Is there a function to round a float in C or do I need to write my own?
  22. Converting String To Float in C#
  23. Comparing floating point values
  24. printf rounding behavior for doubles
  25. sin, cos, tan and rounding error
  26. Round double in two decimal places in C#?
  27. Round a decimal to the nearest quarter in C#
  28. Is floating point arithmetic stable? [duplicate]
  29. Rule of thumb to test the equality of two doubles in C#?
  30. Why does “dtoa.c” contain so much code?

Leave a Comment