softposit

A pure Nim implementation of posit arithmetic.

Posit numbers are an alternative to IEEE 754 floating-point, designed to offer higher precision near ±1, a wide dynamic range, and better numerical stability — often matching or exceeding IEEE 754 precision with fewer bits. Unlike IEEE floats, posits use regime bits to encode scale, eliminating the need for infinities, NaNs, and subnormals (replaced by a single NaR — Not a Real — value). For more background, see posithub.org.

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Features

• Posit4[es] — a 4-bit posit type parameterized by the number of exponent bits (es ∈ {0, 1, 2})
• All arithmetic via O(1) compile-time LUTs — addition, subtraction, multiplication, division, negation, absolute value, reciprocal, and square root are pure table lookups with zero runtime branching
• Quire4[es] — an exact float64 accumulator for fused multiply-accumulate (MAC) operations, enabling dot products without intermediate rounding
• Conversion — to/from float64, to/from float32, and cross-es posit casting
• Predicates — isZero, isNaR, isPositive, isNegative
• Comparison operators — ==, <, <= with correct NaR-unordered semantics (mirroring IEEE NaN behaviour)
• Compound assignment — +=, -=, *=, /=
• $ display — prints the raw 4-bit pattern alongside the decoded value, e.g. 0110[4,1]=4.0

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Type overview

Type	Bits	es	useed	minpos	maxpos
Posit4[0]	4	0	2	1/4	4
Posit4[1]	4	1	4	1/16	16
Posit4[2]	4	2	16	1/256	256

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Usage

import softposit

# Construction
let a = Posit4[1].fromFloat(1.5)
let b = Posit4[1].fromFloat(2.0)

# Arithmetic
let c = a + b          # nearest representable sum
let d = a * b
let e = recip(a)       # 1/a
let f = sqrt(b)

# Conversion
echo a.toFloat         # float64
echo a.toFloat32       # float32
echo a                 # "0101[4,1]=1.5"

# Predicates
echo a.isZero          # false
echo a.isNaR           # false
echo a.isPositive      # true

# Cross-es cast
let g = a.to(Posit4[2])

# Fused multiply-accumulate via Quire
var q: Quire4[1]
q += (a, b)            # q.val += a * b  (exact, no rounding)
q += (c, d)
let result = q.toPosit # round once at the end
q.clear

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Design notes

All lookup tables (kAdd, kMul, kSub, kDiv, kNeg, kAbs, kRecip, kSqrt) are built entirely at compile time using Nim's {.compileTime.} functions and baked into the binary as constant arrays. At runtime every operation is a single array index — there are no branches, no floating-point computations, and no dynamic allocation.

The Quire accumulator stores products exactly in float64 (the maximum product magnitude for Posit4 is 256² = 65 536, well within float64's 53-bit mantissa), deferring rounding to a single final toPosit call.

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License

MIT — see LICENSE.