gistfile1.md

From Fabrice Bellard, with minor name change (umulh):

// return the high 32 bit part of the 64 bit addition of (hi0, lo0) and (hi1, lo1)
Math.iaddh(lo0, hi0, lo1, hi1)

// return the high 32 bit part of the 64 bit subtraction of (hi0, lo0) and (hi1, lo1)
Math.isubh(lo0, hi0, lo1, hi1)

// return the high 32 bit part of the signed 64 bit product of the 32 bit numbers a and b
Math.imulh(a, b)

// return the high 32 bit part of the unsigned 64 bit product of the 32 bit numbers a and b
Math.umulh(a, b)

All these functions convert their argument to 32 bit integers. They return a signed 32 bit integer.

With these functions, the 64 bit operations are easy to implement :

// (hi_res, lo_res) = (hi0, lo0) + (hi1, lo1) (64 bit addition):

lo_res = (lo0 + lo1) | 0;
hi_res = Math.iaddh(lo0, hi0, lo1, hi1);

// (hi_res, lo_res) = (hi0, lo0) - (hi1, lo1) (64 bit subtraction):

lo_res = (lo0 - lo1) | 0;
hi_res = Math.isubh(lo0, hi0, lo1, hi1);

// (hi_res, lo_res) = a * b (signed 64 bit product of 32 bit integers):

lo_res = Math.imul(a, b);
hi_res = Math.imulh(a, b);

// (hi_res, lo_res) = a * b (unsigned 64 bit product of 32 bit integers):

lo_res = Math.imul(a, b);
hi_res = Math.umulh(a, b);

// (hi_res, lo_res) = (hi0, lo0) * (hi1, lo1) (signed 64 bit product of 64 bit integers):

lo_res = Math.imul(lo0, lo1);
hi_res = (Math.imulh(lo0, lo1) + Math.imul(lo0, hi1)) | 0;
hi_res = (hi_res + Math.imul(lo1, hi0)) | 0;

// (hi_res, lo_res) = (hi0, lo0) * (hi1, lo1) (unsigned 64 bit product of 64 bit integers):

lo_res = Math.imul(lo0, lo1);
hi_res = (Math.umulh(lo0, lo1) + Math.imul(lo0, hi1)) | 0;
hi_res = (hi_res + Math.imul(lo1, hi0)) | 0;

Fabrice wrote:

"It is easy for the compiler to optimize the code because only 32 bit integers are used and because the functions have no side effect. Even if the compiler does not remove the duplicate operation for the low 32 bit parts, the overhead is very small on a 32 bit CPU (1 more instruction than the optimal code)."

UPDATE to provide 64x64=64 functions:

// (hi_res, lo_res) = (hi0, lo0) * (hi1, lo1) (signed 64 bit product of 64 bit integers):

lo_res = Math.imul(lo0, lo1);
hi_res = Math.imulx(lo0, hi0, lo1, hi1);

// (hi_res, lo_res) = (hi0, lo0) * (hi1, lo1) (unsigned 64 bit product of 64 bit integers):

lo_res = Math.imul(lo0, lo1);
hi_res = Math.umulx(lo0, hi0, lo1, hi1);

The x suffix is straw, it could be hx to connote hi_res is the result, or something longer.

/be

@trevnorris: division when you can strength-reduce by right-shifting is best done by shifting, but that only works for 32 bits. Bigger dividends want specific hard-coded solutions for div-by-power-of-2. Anything general wants Newton-Raphson or better, in library code.

/be

@BrendanEich Hm. I missed that the API in your gist is only for math operations. My example was to turn an existing value into the hi and low 32 bits.

So say someone has a value within (2^32, 2^53] and wants to turn it into the hi and low 32 bit range. Is there a proposed API to perform that operation?

@trevnorris, sorry, I know you asked @BrendanEich about it, but I'd like to reply anyway.

I think this API mostly applies to the (2^32, 2^32) ( lo+hi ) pairs. You could just store number in this format, as I'm planning to do in bn.js, or you could as well convert 2^53 floating point number to it using division and binary &. I don't think that there is a big value in introducing new API methods, considering that they'll convert FP number to 64bit pair in the quite similar way internally.

As noted on twitter, see also https://github.com/dherman/float.js for cracking JS 64-bit doubles via typed arrays and their aliasing powers.

/be

I'm finding the naming of these functions pretty confusing. Are they acronyms?

They're abbreviated: imulh is short for "integer, multiply, high bits". It's consistent with the naming of functions like Math.imul.

I also suggest add Math.popcnt Math.popcnt64 support

https://msdn.microsoft.com/zh-cn/library/bb385231.aspx

Maybe also Math.popcnt16 support

Pardon my ignorance, but instead of these specific functions, wouldn't it be great to have custom types work with normal operators? I always thought that JS might benefit from more custom-ish types like matrixes and simply have them work with +-/*<>... operators instead of creating whole new objects/methods like Math.iaddh and SIMD.%type%.mul()

@BrendanEich is this proposal alive or I should remove it from the next version of core-js? -)