cell/docs/spec/dec64.md

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DEC64 Numbers	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.

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