proposal-math-float

JavaScript arithmetic is implemented in a non-standard way, compared to other languages. Over time, there was a demand for performance and precision but the language itself does not give an opportunity for some effective algorithms. This proposal offers to add signbit, inverse square, ldexp that multiplying by 2 raised to the exp power, frexp that decomposes given floating point value arg into a normalized fraction and an integral power of two, scalar FMA instruction that performs multiplication-addition in one step with single rounding, successor/predecessor of floating point number

Proposed syntax

let signbit = Math.signbit(x)
let invsqrt = Math.rsqrt(x);
let ldexp = Math.ldexp(x);
let frexp = Math.frexp(x);
let fma = Math.fma(x, y, z);
let successor = Math.nextUp(x);
let predecessor = Math.nextDown(x);

Similar proposals

• proposal-math-extensions
• proposal-math-signbit

Motivation to add this functions because they can be faster in native code

• signbit() current polyfill to get sign bit is slower that it can be (x = +x) == x && x == 0 ? 1 / x == -Infinity : x < 0
• rsqrt() is used in computer graphics, we have Math.hypot(x, y) in JS but it's not inverted
• ldexp() could be useful for multiplication optimization on 2**n (in Java it is called scalb())
• frexp() could be useful for bit analysis inside float number and correct rounding
• fma() very useful for optimizing multiplication in arbitrary precision floating point libraries
• nextUp()/nextDown() basic blocks for floating-point computations with correct rounding

Pollyfills status

Disclaimer

This proposal based on my R&D projects (1, 2) with floating point numbers and created as alternative to decimal-proposal. I feel frustrated that JS not added this basic blocks 5 years ago and we at that point when something hardcore is computed not as fast as it could be. There are two type of arbitrary precision floating point libraries: based on integers and based on floats. Since javascript don't have integers historically I found that solution based on floats much easier in implementation and equally good as solutions based on integer arithmetic, when it properly cooked. invSqrt() / frexp() was added after inspiration with new WGSL specification, nextUp() / nextDown() exist in Java with same syntax, scalar fma() is the reason why this proposal was created.

Key algorithms for polyfill implementation

1. Chris Lomont. Fast inverse square root
2. Sylvie Boldo, Guillaume Melquiond. Emulation of a FMA and correctly-rounded sums: proved algorithms using rounding to odd.
3. Siegfried Rump, Paul Zimmermann, Sylvie Boldo, Guillaume Melquiond Computing predecessor and successor in rounding to nearest
4. Masahide Kashiwagi Emulation of Rounded Arithmetic in Rounding to Nearest