jedahan/ofmath

exploration of floating point numbers, thanks to openframeworks pull request 3824

EPSILON! fixes 3, 4, and 5

A second idea from arturo was compiled into a new pull request - this one really looks like it will work. A modified version is included in ofMath.cpp. The important bit is:

range -= std::numeric_limits<float>::epsilon();

This patch reduces the range of possible return values by epsilon, a special number that means 'the smallest possible amount'. And if we try the proposed fix, it seems to work!

From the title, this cannot be the final fix. And 2bit knows this. 2bit wants to be super sure that -= std::numeric_limits<float>::epsilon() really does reduce the range when working with large numbers, when casting them as integers and devises this rangeTest.cpp:

#include <iostream>

void large_range_check(float low, float high) {
    float range = high - low;
    float little_bit_small_range = (high - low) - std::numeric_limits<float>::epsilon();

    printf("%x\n", *(reinterpret_cast<int *>(&range)));
    printf("%x\n", *(reinterpret_cast<int *>(&little_bit_small_range)));
}

int main(){
  large_range_check(0.0f, std::numeric_limits<float>::max());
  large_range_check(0.0f, 3.0f);
}

We can run rangeTest in the usual manner, g++ rangeTest.cpp -o rangeTest && ./rangeTest

Turns out, not only does it fail when casting to integers with large floats, but it also does with small floats, like 3.0f! The numbers haven't moved at all!

Why is this? Well, time to break out gdb, and do some sluething...

Turns out, at "big" numbers, epsilon is smaller than the 'gap' between two consecutive floats. I think this is so terribly cool.

And the quick fix that 2bit comes up with is to multiply the range by (1.0-epsilon), like so:

float range = high - low;
range *= (1.0f - std::numeric_limits<float>::epsilon());

This is a performance penalty, but at least reduces our MAX_RAND range by 1, as shown in rangeFixed.cpp g++ rangeFixed.cpp -o rangeFixed && ./rangeFixed:

Well, openFrameworks is an international community, and kyle comes up with another solution in parallel to the multiply by epsilon fix...

Next

To move onto the next step, do git checkout nextafter

Overview

This repository contains source code and commentary explored in openFrameworks pull request #3842.

From the sidelines, it was really interesting to follow along the discussion about floating point numbers, and randomness.

I am trying to figure out the best way to expose the code for learning. If you have suggestions, please make an issue on github!

After cloning this repository, I recommend checking out the first commit git checkout initial, and then moving up one commit at a time.

This readme will change, explaining the different approaches taken on the quest for a ofRandom that works well.

ofmath's Issues

maybe we should add assertions to tests

or at least comment on what the correct output would be...

include other floating point weirdness that 2bit discovered

#include <iostream>

void printFloatAsHex(float f) { printf("%0x\n", *(reinterpret_cast<int *>(&f))); }
int main(int argc, char *argv[]) {
    printFloatAsHex((1.1f + 1.2f) + 1.3f);
    printFloatAsHex(1.1f + (1.2f + 1.3f));
}

maybe as an aside or a final "hahah" on the last commit

look at all the comments for each comment and fix them

maybe we should flatten the entire repository

the "git checkout some-random-tag" is less like walking someone through some beautiful scenery, and more like mission impossible:

Ethan Hunt: The only certified technician has to pass a series of security scans. First one is voice activated.
CIA Analyst William Donloe: William Donloe.
Ethan Hunt: Then, he has to put in a 6 digit code.
[Donloe enters the first room]
Ethan Hunt: That only gets him into the outer room. In order to get in the vault, he first has to pass a retina scan. Then, the door will unlock by only two electronic keycards, which we won't have.

.

suggestions on restructuring to both show the code side-by-side, making it easily runnable for verification and exploration, and still reading like a story are all super welcome