[Someone]

https://wiki.c2.com/?IeeeSevenFiftyFour:

“IEEE 754 […] Has the interesting and useful property that two's complement comparisons of the underlying bit pattern of any two IEEE 754 numbers will have the same result as comparing the numbers that are represented”

That means that, if you interpret the bits of a float/double as an int32/int64, increase that integer by one, and then interpret the bits of the result as a float/double, you get the smallest float/double that’s larger than what you started with (with exceptions for NaN, infinities, +/- zero, and, possibly, some categories I forget)

That can be useful if you want to iterate over all floats between 0.0 and 1.0, for example, but may not be that efficient on some modern hardware, where moving data from the “float side” of the CPU to the “integer side” is expensive)

[saagarjha]

This has more to do with the mantissa than the biased exponent.

[Someone]

No, it has to do with bothequally.

Changing a 0 bit to a 1 in an integer increases its value, and by the rule I gave, should also increase the value of the floating point number with the same bit pattern. It doesn’t matter whether that flipped bit is in the mantissa or the exponent.

That requires the use of the biased number in the exponent. In particular, the “all zeroes” bit pattern for the exponent must be the representation for the lowest possible exponent, and the “all ones” one that for the highest. It cannot be the ‘normal’ two’s complement representation of -1.

[saagarjha]

This is a different claim than the one above, which was about incrementing the least significant bit.

[Someone]

But it trivially follows from it. If operation foo (increasing x by one) makes something larger, repeated operation of foo (increasing x by 2^n) makes it larger, too.