alt Hacker NewsThere's another gotcha. Consider positive, normal x and y where ulp(y) != ulp(x). Bitwise comparison, regardless of tolerance, will consider x to be far from y, even though they might be adjacent numbers, e.g. if y = x+ulp(x) but y is a power of 2.
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oasisaimlessly • yesterday at 7:18 PM
I don't think this is true. Modulo the sign bit, the "next float" operator is equivalent to the next bitstring or the integer++.
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This case actually works because for finite numbers of a given sign, the integer bit representations are monotonic with the value due to the placement of the exponent and mantissa fields and the implicit mantissa bit. For instance, 1.0 in IEEE float is 0x3F800000, and the next immediate representable value below it 1.0-e is 0x3F7FFFFF.
Signed zero and the sign-magnitude representation is more of an issue, but can be resolved by XORing the sign bit into the mantissa and exponent fields, flipping the negative range. This places -0 adjacent to 0 which is typically enough, and can be fixed up for minimal additional cost (another subtract).