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docs/spec/dec64.md

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+---
+title: "DEC64 Numbers"
+description: "Decimal floating point representation"
+---
+
+## Overview
+
+ƿit uses DEC64 as its number format. DEC64 represents numbers as `coefficient * 10^exponent` in a 64-bit word. This eliminates the rounding errors that plague IEEE 754 binary floating point — `0.1 + 0.2` is exactly `0.3`.
+
+DEC64 was designed by Douglas Crockford as a general-purpose number type suitable for both business and scientific computation.
+
+## Format
+
+A DEC64 number is a 64-bit value:
+
+```
+[coefficient: 56 bits][exponent: 8 bits]
+```
+
+- **Coefficient** — a 56-bit signed integer (two's complement)
+- **Exponent** — an 8-bit signed integer (range: -127 to 127)
+
+The value of a DEC64 number is: `coefficient * 10^exponent`
+
+### Examples
+
+| Value | Coefficient | Exponent | Hex |
+|-------|------------|----------|-----|
+| `0` | 0 | 0 | `0000000000000000` |
+| `1` | 1 | 0 | `0000000000000100` |
+| `3.14159` | 314159 | -5 | `000000004CB2FFFB` |
+| `-1` | -1 | 0 | `FFFFFFFFFFFFFF00` |
+| `1000000` | 1 | 6 | `0000000000000106` |
+
+## Special Values
+
+### Null
+
+The exponent `0x80` (-128) indicates null. This is the only special value — there is no infinity, no NaN, no negative zero. Operations that would produce undefined results (such as division by zero) return null.
+
+```
+coefficient: any, exponent: 0x80  →  null
+```
+
+## Arithmetic Properties
+
+- **Exact decimals**: All decimal fractions with up to 17 significant digits are represented exactly
+- **No rounding**: `0.1 + 0.2 == 0.3` is true
+- **Integer range**: Exact integers up to 2^55 (about 3.6 * 10^16)
+- **Normalized on demand**: The runtime normalizes coefficients to remove trailing zeros when needed for comparison
+
+## Comparison with IEEE 754
+
+| Property | DEC64 | IEEE 754 double |
+|----------|-------|----------------|
+| Decimal fractions | Exact | Approximate |
+| Significant digits | ~17 | ~15-16 |
+| Special values | null only | NaN, ±Infinity, -0 |
+| Rounding errors | None (decimal) | Common |
+| Financial arithmetic | Correct | Requires libraries |
+| Scientific range | ±10^127 | ±10^308 |
+
+DEC64 trades a smaller exponent range for exact decimal arithmetic. Most applications never need exponents beyond ±127.
+
+## In ƿit
+
+All numbers in ƿit are DEC64. There is no separate integer type at the language level — the distinction is internal. The `is_integer` function checks whether a number has no fractional part.
+
+```javascript
+var x = 42        // coefficient: 42, exponent: 0
+var y = 3.14      // coefficient: 314, exponent: -2
+var z = 1000000   // coefficient: 1, exponent: 6 (normalized)
+
+is_integer(x)     // true
+is_integer(y)     // false
+1 / 0             // null
+```