New log, log2, exp, exp2 and pow implementations

[MaxGraey]

Status

• new Mathf.pow
• new Mathf.exp
• new Mathf.log2
• new Mathf.log
• new Math.pow
• new Math.exp
• new Math.log2
• new Math.log
• new Math.exp2 (non standard for symmetry with Math.log2 and opt in future)

Benchmark for Math.pow [f64]

Results

• Firefox 71

old as pow: 190ms
NEW as pow: 31ms
js pow:     52ms

• Chrome 79.0.3945.79

old as pow: 235.450927734375ms
NEW as pow: 91.623046875ms
js pow:     146.000732421875ms

Benchmark for Mathf.pow [f32]

• Firefox 71

old as pow: 106ms
NEW as pow: 16ms
js pow:     26ms

• Chrome 79.0.3945.79

old as pow: 136.93701171875ms
NEW as pow: 39.447265625ms
js pow:     51.557861328125ms

UPDATE

Benchmark for Math.pow [f64] using internal loops in AssemblyScript

• Chrome 79.0.3945.88

old as pow: 153.734130859375ms
NEW as pow: 21.9619140625ms
js pow: 137.114990234375ms

[MaxGraey]

I decided add new non-std Math functions Math.exp2 / Mathf.exp2 and Math.exp10 / Mathf.exp10. Not necessary use it explicitly but its will use for special lowering during Math.pow optimization when first argument known at compile time like:

2 ** y   ->  exp2(y)

10 ** y -> exp10(y) figure out this hasn't any benefits compare to pow(10, y)

e ** y   ->  exp(y)

// where y is f32 or f64 and result also f32 or f64

[dcodeIO]

Can you explain a bit what's the theory behind these improvements? For instance, what did the old implementation do that made it slow, and does the new implementation do that makes it fast? What are the algorithms used here and where are they from? Stuff like that :)

[MaxGraey]

Basicaly it's adoption of new ARM math lib: https://github.com/ARM-software/optimized-routines/tree/master/math (MIT). This link present in musl's implementation. New routines use lookup tables and more clever handling special cases when we could simplify path using twofold fast arithmetic some of LUTs need for speedup FMA emulation. All this significantly speedup pow/log/exp. But sometimes increase code size, so I use this routines mostly for ASC_SHRINK_LEVEL == 0. except Mathf.pow which accidentally decrease size.

[dcodeIO]

Great, thanks!