Remove "except in benchmarks" exception for fp math

[laanwj]

Convert bench.h to fixed-point math, removing all use of float math from the repository:

• Use 64-bit integer microsecond timestamps
• Use decimal fixed-point math for formatting numbers

It turned out to be a little trickier than I expected because of formatting and rounding. But, output should be the same before and after.

I used the following to test the number formatting: https://gist.github.com/laanwj/f971bfbe018e39c19677a21ff954d0c7

[real-or-random]

ACK 8a7dea1 I've read the code in detail and I've tested it. I haven't explicitly tested the formatting function with known/hardcoded inputs.

[real-or-random]

Nice! Now I don't want to work on the related #680 because I may end up removing parts of your excellent formatting function...

[laanwj]

I searched around a bit and it doesn't seem there's currently any way to tell the compiler (gcc or otherwise) to fail on any use on floating point. So we can't easily check this policy in the CI. Not that it matters, it's a relatively small project and changes here are well-reviewed.

Nice! Now I don't want to work on the related #680 because I may end up removing parts of your excellent formatting function...

Haha yes I leave the "how to show the benchmark" part up to you. I think there's different preferences in that regard.

I made that it's straightforward to split up in a "how many decimals to show" and generic "format fixed-point with n decimals" part.

[apoelstra]

FWIW the output of git grep 'double ' is only two lines, both of which are comments. And git grep float is empty. We could just have CI check this :P

[gmaxwell]

Very nice. One thing that wasn't clear to me was what is protecting overflow in the fixed point scaling?

[laanwj]

Very nice. One thing that wasn't clear to me was what is protecting overflow in the fixed point scaling?

You mean this part?

    printf("%s: min ", name);
    print_number(min * FP_MULT / iter);
    printf("us / avg ");
    print_number(((sum * FP_MULT) / count) / iter);
    printf("us / max ");
    print_number(max * FP_MULT / iter)

The value is in microseconds and is multiplied with 1e6, so if my computation is correct ((1<<63)/1e6/1e6) it takes 9.2 megasecond (~1/3th year) until an overflow can happen. Do you think anyone is going to wait that long for a benchmark?

It would definitely be possible to add overflow checks here but it seemed overkill.

[gmaxwell]

Indeed, that seems more than adequate. I should have done the math!

[laanwj]

Anything left to do here?

[real-or-random]

I think there's nothing left do to here.

But can we get a second (untested) ACK here? @gmaxwell You apparently looked at it, do you mind ACKing it?

[gmaxwell]

ACK

[real-or-random]

ACK bde2a32 I've read the code in detail and I've tested it. I haven't explicitly tested the formatting function with known/hardcoded inputs.