Example
If ULP(x) is less than or equal to 1, then x + 1 > x. Otherwise, x + 1 = x. This is demonstrated in the following Haskell code typed at an interactive prompt:
> until (\x -> x == x+1) (+1) 0 :: Float 1.6777216e7 > it-1 1.6777215e7 > it+1 1.6777216e7Here we start with 0 in 32-bit single-precision and repeatedly add 1 until the operation is idempotent. The result is equal to 224 (in hex, 4b800000) since the significand for a single-precision number in this example contains 24 bits.
Another example, in Python, also typed at an interactive prompt, is:
>>> x = 1.0 >>> p = 0 >>> while x != x + 1: ... x = x * 2 ... p = p + 1 ... >>> x 9007199254740992.0 >>> p 53In this case, we start with x = 1 and repeatedly double it until x = x + 1. The result is 253, because the double-precision floating-point used a 53-bit significand.
Read more about this topic: Unit In The Last Place
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