CODEWITHSUNDEEP
floating-pointinteger
Jayron Hubbard
Jayron Hubbard

Reputation: 121

Questions about 32 bit float values

Can all 16-bit unsigned integer (unsigned short) values be stored EXACTLY in a 32-bit floating point value? Can all 32-bit unsigned integer (unsigned int) values be stored EXACTLY in a 32-bit floating point value? Which of the numbers below can be represented EXACTLY with a 32-bit float value? 1.648, 2.75, 2.125, 10.999, 9.351, 0.625

Upvotes: 0

Views: 652

Answers (1)

Pascal Cuoq
Pascal Cuoq

Reputation: 80276

  • All integers between -224 and 224 can be represented as single-precision floats.
  • Neither -224-1 nor 224+1 can be represented as floats.

As a consequence all unsigned 16-bit integers can be represented exactly as floats, but not all unsigned 32-bit integers.

The explanation is that some bit patterns are used to represent fractional numbers such as 0.125 and 1.5, so fewer than 232 bit patterns are available for integers.

A simple program in your programming language of choice can tell you which of 1.648, 2.75, 2.125, 10.999, 9.351, 0.625 are exactly representable in single-precision: print, to 26 significant decimal digits (say, with the format %.25e using a printf-like function), the values of 1.648f, …

When you type the floating-point constant 1.648f in a program in most programming languages, it is translated to the single-precision float closest to 1648/1000. If this number prints as 1.64800000, it means that the number 1.648 is exactly representable as a float. If it prints as something else, then 1.648 isn't representable (and the output tell you how far the nearest float happens to be).

Upvotes: 1

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