Add unum support (posits first)

libmath/README.md

@@ -15,6 +15,7 @@ We support the following functions and special functions:
 - `++factorial`, $!$ factorial
 - `++abs`, $\text{abs}$
 - `++exp`, $\exp$
+- `++expm1`, $\exp - 1$
 - `++sin`, $\sin$
 - `++cos`, $\cos$
 - `++tan`, $\tan$
@@ -35,9 +36,9 @@ Logical functions:
 - `++gte`, $\geq$ (also `++geq`)
 - `++equ`, $=$
 - `++neq`, $\neq$
-- `is-close`
-- `all-close`
-- `is-int`
+- `++is-close`
+- `++all-close`
+- `++is-int`
 
 Constants (to machine accuracy):
 
@@ -67,3 +68,121 @@ It would be nice to have the following special functions as well:
 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.
+
+---
+
+# `/lib/unum` for Urbit
+
+A library for universal numbers (posits, quires, and valids) per the Gustafson (2019) formulation and the 2022 Posit Standard.
+
+- $\text{posit}<8,0>$
+- $\text{posit}<16,1>$
+- $\text{posit}<32,2>$
+
+##  Posit Standard Compliance
+
+Two interfaces are maintained for `/lib/unum`:  one to hew to the `/lib/math` and `/lib/saloon` interface, and another to alias in the 2022 Posit Standard requirements.  The names are slightly modified from the standard to adhere to Hoon name requirements.
+
+### Basic functions of one posit value argument
+
+- `++negate` ← `(sub 0 val)`
+- `++abs` ← no change
+- `++sign` ← `++sgn`
+- `++nearest-int`
+- `++ceil`
+- `++floor`
+- `++next`
+- `++prior`
+
+### Comparison functions of two posit value arguments
+
+- `++compare-equal` ← `++equ`
+- `++compare-not-equal` ← `!(equ val)`
+- `++compare-greater` ← `++gth`
+- `++compare-greater-equal` ← `++gte`
+- `++compare-less` ← `++lth`
+- `++compare-less-equal` ← `++lte`
+
+### Arithmetic functions of two posit value arguments
+
+- `++addition` ← `++add`
+- `++subtraction` ← `++sub`
+- `++multiplication` ← `++mul`
+- `++division` ← `++div`
+
+### Elementary functions of one posit value argument
+
+- `++sqrt` ← no change
+- `++rsqrt` ← TODO
+- `++exp` ← no change
+- `++exp-minus-1` ← `++expm1`
+- `++exp2` ← no change
+- `++exp2-minus-1` ← `++exp2m1`
+- `++exp10` ← no change
+- `++exp10-minus-1` ← `++exp10m1`
+- `++log` ← no change
+- `++log-plus-1` ← `++logp1`
+- `++log2` ← no change
+- `++log2-plus-1` ← `++log2p1`
+- `++log10` ← no change
+- `++log10-plus-1` ← `++log10p1`
+- `++sin` ← no change
+- `++sin-pi` ← `(sin (mul pi val))`
+- `++cos` ← no change
+- `++cos-pi` ← `(cos (mul pi val))`
+- `++tan` ← no change
+- `++tan-pi` ← `(tan (mul pi val))`
+- `++arcsin` ← no change
+- `++arcsin-pi` ← `(arcsin (div val pi))`
+- `++arccos` ← no change
+- `++arccos-pi` ← `(arccos (div val pi))`
+- `++arctan` ← no change
+- `++arctan-pi` ← `(arctan (div val pi))`
+- `++sinh` ← no change
+- `++cosh` ← no change
+- `++tanh` ← no change
+- `++arcsinh` ← no change
+- `++arccosh` ← no change
+- `++arctanh` ← no change
+
+### Elementary functions of two posit value arguments
+
+- `++hypot` ← `(sqt (mul val-1 val-1) (mul val-2 val-2))`
+- `++pow` ← no change
+- `++arctan2` ← ??? complex
+- `++arctan2-pi` ← `(div (arctan2 val) pi)`
+
+### Functions of three posit value arguments
+
+- `++fmm` ← `:(mul val-1 val-2 val-3)`
+
+### Functions of one posit value argument and one integer argument
+
+- `++compound` ← `(pow (add val 1) int)`
+- `++root-n` ← `(pow val (div 1 int))`
+
+### Functions involving quire value arguments
+
+- `++p-to-q`
+- `++q-negate`
+- `++q-abs`
+- `++q-add-p`
+- `++q-sub-p`
+- `++q-add-q`
+- `++q-sub-q`
+- `++q-mul-add`
+- `++q-mul-sub`
+- `++q-to-p`
+
+### Conversions between different precisions
+
+- `++p8-to-16`
+- `++p8-to-32`
+- `++p16-to-8`
+- `++p16-to-32`
+- `++p32-to-8`
+- `++p32-to-16`
+
+### Conversions between posit format and decimal format
+
+### Conversions between posit format and IEEE 754 format