CODEWITHSUNDEEP
floating-point
Vons
Vons

Reputation: 3335

Interpreting the bit pattern of FLT_MAX

FLT_MAX has a bit pattern of 01111111011111111111111111111111.

If I understand correctly, such a bit pattern should represent 1.111...1 * 2^128 (with twenty-three 1's after the decimal). However, the actual value of FLT_MAX is just 1.0 * 2^128. What's going on here?

Upvotes: 1

Views: 1527

Answers (1)

Daniel Fischer
Daniel Fischer

Reputation: 183948

Your exponent is wrong, it's 1.111...1 * 2^127 = 2^128 - 2^104. That is pretty close (relatively) to 2^128, and you need to print it out with more than default precision in C or C++ to see the difference (note, as a float - if that is an IEEE754 32-bit float - 2^128 is infinity, so you need a double).

The bit pattern yields

  0   11111110  11111111111111111111111
  ^      ^             ^
sign  exponent     mantissa
       254-127     2 - 2^(-23)

Printing the full values:

340282346638528859811704183484516925440.0   // FLT_MAX
340282366920938463463374607431768211456.0   // 2^128

you can see the difference at the eighth digit.

Upvotes: 3

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