Is super-accuracy matters?

[Albert Chan]

(10-09-2023 07:24 PM)johnb Wrote:  "how do you convince others that additional accuracy/precision is/is-not needed?"

It may be hard to show benefit, but we can go for how little cost it take.

Example, I recently upgraded old luajit 1.1.8 with openlibm, for better accuracy.
Old luajit was using msvcrt.dll FSIN/FCOS/FPTAN, with only 68 bits of pi
see Intel Underestimates Error Bounds by 1.3 quintillion

Code:

                OLD       NEW = luajit + openlibm
luajit.exe    48142     48142
lua51.dll    283662    351758
mathx.dll     35342         0
complex.dll   34830         0   
-----------------------------
             401976    399900

Adding openlibm code to luajit (*) does not bloat up dll's.
(and, no cheating! libopenlibm.a is a static library)

I don't quite understand how angle reduction code work, but result is amazing!
Performance is OK, see Accurate trigonometric functions for large arguments

lua> x = 1e22
lua> sin(x), dtoh(x)
-0.8522008497671888             +0x1.0f0cf064dd592p+73
lua> !spigot --printf "%.17g" sin(0x1.0f0cf064dd592p+73)
-0.8522008497671888

lua> x = 1e308
lua> sin(x), dtoh(x)
0.4533964905016491             +0x1.1ccf385ebc8a0p+1023
lua> !spigot --printf "%.17g" sin(0x1.1ccf385ebc8a0p+1023)
0.45339649050164912

Last 2 numbers actually matched. luajit use dtoa-fast for numeric output.
Default is output minimum digits that round-trip, same as python 3.

(*) the reason math related code move *inside* lua is due to mingw compiler design.
If openlibm is *inside* lua51.dll, its code should get picked first, before msvcrt.dll

---

Luajit 1.1.8, -O2 or higher, use hardware FSIN/FCOS/FPTAN for speed.
Below patch would remove this optimization, and use libm versions instead.

ljit_x86.h add sin/cos/tan (exact order!) partially inlined math functions. (patch in bold)
Then, remove jit_inline_math() sin/cos/tan cases, and use default (libm) instead.

ljit_x86.h Wrote:/* Partially inlined math functions. */
/* CHECK: must match with jit_hints.h and jit.opt_lib. */
// ALBERT: sin/cos/tan use libm too, 10-11-2023
static const mathfunc_11 jit_mathfuncs_11[JIT_IH_MATH_SIN + 3] = {
log, log10, exp, sinh, cosh, tanh, asin, acos, atan, sin, cos, tan
};

Proper way is to patch ljit_x86_inline.dash, then auto-generate ljit_x86.h
But, that required working lua is available.