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decimal.md

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Decimals

If an opcode has a high nibble of 0x7_, it represents a decimal. Low nibble values indicate the number of trailing bytes used to encode the decimal.

The body of the decimal is encoded as a FlexInt representing its exponent, followed by a FixedInt representing its coefficient. The width of the coefficient is the total length of the decimal encoding minus the length of the exponent. It is possible for the coefficient to have a width of zero, indicating a coefficient of 0. When the coefficient is present but has a value of 0, the coefficient is -0.

Decimal values that require more than 15 bytes can be encoded using the variable-length decimal opcode: 0xF7.

0xEB 0x03 represents null.decimal.

Encoding of decimal 0d0
┌──── Opcode in range 70-7F indicates a decimal
│┌─── Low nibble 0 indicates a zero-byte
││    decimal; 0d0
70
Encoding of decimal 7d0
┌──── Opcode in range 70-7F indicates a decimal
│┌─── Low nibble 2 indicates a 2-byte decimal
││
72 01 07
   |  └─── Coefficient: 1-byte FixedInt 7
   └─── Exponent: FlexInt 0
Encoding of decimal 1.27
┌──── Opcode in range 70-7F indicates a decimal
│┌─── Low nibble 2 indicates a 2-byte decimal
││
72 FD 7F
   |  └─── Coefficient: FixedInt 127
   └─── Exponent: 1-byte FlexInt -2
Variable-length encoding of decimal 1.27
┌──── Opcode F7 indicates a variable-length decimal
│
F7 05 FD 7F
   |  |  └─── Coefficient: FixedInt 127
   |  └───── Exponent: 1-byte FlexInt -2
   └─────── Decimal length: FlexUInt 2
Encoding of 0d3, which has a coefficient of zero
┌──── Opcode in range 70-7F indicates a decimal
│┌─── Low nibble 1 indicates a 1-byte decimal
││
71 07
   └────── Exponent: FlexInt 3; no more bytes follow, so the coefficient is implicitly 0
Encoding of -0d3, which has a coefficient of negative zero
┌──── Opcode in range 70-7F indicates a decimal
│┌─── Low nibble 2 indicates a 2-byte decimal
││
72 07 00
   |  └─── Coefficient: 1-byte FixedInt 0, indicating a coefficient of -0
   └────── Exponent: FlexInt 3
Encoding of null.decimal
┌──── Opcode 0xEB indicates a typed null; a byte follows specifying the type
│  ┌─── Null type: decimal
│  │
EB 03