`/lib/math` for Urbit

An unjetted library for basic mathematical and special function support.

We support the following functions and special functions:

++add, $+$ addition
++sub, $-$ subtraction
++mul, $\times$ multiplication
++div, $/$ division
++mod, modulo (remainder after division)
++fma, $\text{fma}$ fused multiply-add
++sgn, $\text{sgn}$ signum (also ++sig)
++neg, $-$ unary negation
++factorial, $!$ factorial
++abs, $\text{abs}$
++exp, $\exp$
++sin, $\sin$
++cos, $\cos$
++tan, $\tan$
++pow-n, $\text{pow}$ to integer power
++log, $\log$ (natural logarithm)
++log-10, $\log_{10}$ (log base-10)
++log-2, $\log_{2}$ (log base-2)
++pow, $\text{pow}$
++sqrt, $\sqrt$ (also ++sqt)
++cbrt, $\cbrt$ (also ++cbt)
++arg (alias for ++abs in real values)

Logical functions:

++lth, $<$
++lte $\leq$ (also ++leq)
++gth, $>$
++gte, $\geq$ (also ++geq)
++equ, $=$
++neq, $\neq$
is-close
all-close
is-int

Constants (to machine accuracy):

++tau, $\tau = 2 \pi$
++pi, $\pi$
++e, $e$ (base of natural logarithm)
++phi, $\phi$, Euler's constant
++sqt2, $\sqrt{2}$
++invsqt2, $\frac{1}{\sqrt{2}}$
++log2, $\log 2$
++invlog2, $\frac{1}{\log 2}$
++log10, $\log 10$
++huge, largest valid number in bloq width
++tiny, smallest valid number in bloq size

It would be nice to have the following special functions as well:

$\arcsin$
$\arccos$
$\arctan$
$\sinh$
$\cosh$
$\tanh$

We do not envision including the Bessel functions and other more abstruse functions.

We use naïve algorithms which are highly reproducible. We special-case some arguments to make them tractable without catastrophic cancellation.