Decompressing Half Precision Floats in Javascript

问题:

I'm trying to read a binary file with javascript that contains a lot of 16-bit floating point numbers. Fairly certain it's IEEE standard, little endian. It's pretty straightforward to read the two bytes into an int, but from there I'm not having much success expanding that out into a full floating point number. Any clues?

回答1:

@Toji: Thanks a lot! Here a version with optimizations for NON high-end-engines like V8

function decodeFloat16 (binary) {
    var exponent = (binary & 0x7C00) >> 10,
        fraction = binary & 0x03FF;
    return (binary >> 15 ? -1 : 1) * (
        exponent ?
        (
            exponent === 0x1F ?
            fraction ? NaN : Infinity :
            Math.pow(2, exponent - 15) * (1 + fraction / 0x400)
        ) :
        6.103515625e-5 * (fraction / 0x400)
    );
};

And a more complete IEEE 754 test:

function test() {
    var samples = [
        0x3C00, // = 1
            0xC000, // = −2
            0x7BFF, // = 6.5504 × 10^4 (max half precision)
            0x0400, // = 2^−14 ≈ 6.10352 × 10^−5 (minimum positive normal)
            0x0001, // = 2^−24 ≈ 5.96046 × 10^−8 (minimum strictly positive subnormal)
            0x0000, // = 0
            0x8000, // = −0
            0x7C00, // = Infinity
            0xFC00, // = −Infinity
            0x3555, // ≈ 0.33325... ≈ 1/3
            0x7C01  // = NaN
        ],
        i = samples.length;
    while (i--) samples[i] = decodeFloat16(samples[i]);
    return samples.join("\n");
};

Performance test results compared with the original code from Toji:

• Chrome 17: +30 %
• Safari 5.1: -10 % (don't ask me why)
• Firefox 9: +11 %
• IExplorer 9: +22 %
• IExplorer 7: +14 %

回答2:

I ended up implementing my own parser based on the information on the Wikipedia page. It's probably not the fastest out there, but I'm not too concerned about that. Here it is for those that are curious:

function float16_to_float(h) {
    var s = (h & 0x8000) >> 15;
    var e = (h & 0x7C00) >> 10;
    var f = h & 0x03FF;

    if(e == 0) {
        return (s?-1:1) * Math.pow(2,-14) * (f/Math.pow(2, 10));
    } else if (e == 0x1F) {
        return f?NaN:((s?-1:1)*Infinity);
    }

    return (s?-1:1) * Math.pow(2, e-15) * (1+(f/Math.pow(2, 10)));
}

function test() {
    float16_to_float(parseInt('3C00', 16)); // 1
    float16_to_float(parseInt('C000', 16)); // -2

    float16_to_float(parseInt('7BFF', 16)); // 6.5504 × 10^4 (Maximum half precision)
    float16_to_float(parseInt('3555', 16)); // 0.33325... ≈ 1/3
    // Works with all the test cases on the wikipedia page
}

回答3:

Take inspiration from jspack. A bunch of people tried similar stuff before.

回答4:

Begin reading this wikipedia article. For implementation, I'd create a lookup table. (or maybe two, one for high and low byte.