---
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
```
