Number

Standard 64-bit floating-point numbers in Internet Object

A Number in Internet Object represents a 64-bit double-precision floating-point value conforming to the IEEE 754 standard. Numbers are scalar primitives used to express integers, fractional values, and special numeric constants.

Numbers in Internet Object support various representations including different bases (binary, octal, hexadecimal), scientific notation, and special values like NaN and Infinity.

Syntax

A number can be expressed in multiple forms:

number = ["-" | "+"] (
    decimalNumber
  | binaryNumber
  | octalNumber
  | hexNumber
  | scientificNumber
) | specialValue

decimalNumber = digit+ ["." digit+]
binaryNumber = "0b" binaryDigit+
octalNumber = "0o" octalDigit+
hexNumber = "0x" hexDigit+
scientificNumber = (digit+ ["." digit+] | "." digit+) ("e" | "E") ["-" | "+"] digit+
specialValue = "NaN" | "Inf" | "-Inf" | "+Inf"

digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
binaryDigit = "0" | "1"
octalDigit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7"
hexDigit = digit | "A" | "B" | "C" | "D" | "E" | "F" | "a" | "b" | "c" | "d" | "e" | "f"

Structural Characters

Symbol	Name	Unicode	Description
0-9	Digits	Multiple	Standard decimal digits
.	Decimal Point	U+002E	Separates integer and fraction
-	Minus Sign	U+002D	Indicates negative numbers
+	Plus Sign	U+002B	Optional positive indicator
e/E	Exponent	Multiple	Scientific notation exponent
0b	Binary Prefix	Multiple	Binary number indicator
0o	Octal Prefix	Multiple	Octal number indicator
0x	Hex Prefix	Multiple	Hexadecimal number indicator

Valid Forms

Decimal Base Number

Numbers in decimal format can include integers and fractional values, with optional sign prefixes:

# Simple integers
42                   # Integer
-17                  # Negative integer
+17                  # Positive integer (explicit)

# Fractional numbers
3.14159              # Fractional number
-0.5                 # Negative fractional
+0.5                 # Positive fractional (explicit)

# Zero
0                    # Zero
+0                   # Positive zero (explicit)
-0                   # Negative zero (explicit)

A decimal number consists of one or more digits, optionally preceded by a sign (+ or -), and optionally including a decimal point followed by one or more digits.

Alternative Bases

Numbers can be expressed in binary, octal, or hexadecimal notation:

Binary Numbers (Base-2)

Binary representation uses 0b or 0B prefix followed by binary digits (0-1):

0b1010               # Binary 1010 (10 in decimal)
0B1111               # Binary 1111 (15 in decimal)
0b0                  # Binary 0
-0b1010              # Negative binary (-10 in decimal)
+0B1100              # Positive binary (12 in decimal)

Octal Numbers (Base-8)

Octal representation uses 0o or 0O prefix followed by octal digits (0-7):

0o755                # Octal 755 (493 in decimal)
0O644                # Octal 644 (420 in decimal)
0o0                  # Octal 0
-0o755               # Negative octal (-493 in decimal)
+0O377               # Positive octal (255 in decimal)

Hexadecimal Numbers (Base-16)

Hexadecimal representation uses 0x or 0X prefix followed by hex digits (0-9, A-F):

0xFF                 # Hexadecimal FF (255 in decimal)
0x10                 # Hexadecimal 10 (16 in decimal)
0XDeadBeef           # Mixed case hex (3735928559 in decimal)
-0xFF                # Negative hex (-255 in decimal)
+0x10                # Positive hex (16 in decimal)

Case Sensitivity

• Prefixes: Both lowercase (0b, 0o, 0x) and uppercase (0B, 0O, 0X) are supported

• Hex digits: Both uppercase (A-F) and lowercase (a-f) are valid

0xFF                 # ✅ Lowercase prefix, uppercase digits
0XFF                 # ✅ Uppercase prefix, uppercase digits
0xff                 # ✅ Lowercase prefix, lowercase digits
0Xff                 # ✅ Mixed case (all equivalent)

Scientific Notation

Scientific notation expresses numbers using exponential form with e or E:

1.23e4               # 1.23 × 10⁴ = 12300
1.23E4               # Same as above (case insensitive)
1.23e-4              # 1.23 × 10⁻⁴ = 0.000123
-2.5e+3              # -2.5 × 10³ = -2500
5e3                  # 5 × 10³ = 5000
.5e2                 # 0.5 × 10² = 50
6.022e23             # Avogadro's number
1e-10                # Very small number
-3.14159e0           # -3.14159 × 10⁰ = -3.14159

Scientific Notation Components

• Mantissa: The significant digits (before e/E)

• Exponent marker: e or E (case insensitive)

• Exponent: The power of 10 (can be positive, negative, or zero)

# Format: [sign]mantissa[e|E][sign]exponent
1.5e+10              # Explicit positive exponent
1.5e-10              # Negative exponent
1.5e10               # Implicit positive exponent

Optional Behaviors

Literal and Alternate Forms

Numbers support multiple equivalent representations:

42                  # ✅ Standard decimal
0x2A                # ✅ Hexadecimal (equivalent to 42)
0b101010            # ✅ Binary (equivalent to 42)
0o52                # ✅ Octal (equivalent to 42)
4.2e1               # ✅ Scientific notation (equivalent to 42)

Invalid Forms

.5                  # ❌ Must have leading digit
5.                  # ❌ Must have trailing digit if decimal point used
0b                  # ❌ Missing binary digits
0b12                # ❌ Invalid binary digit '2'
0o89                # ❌ Invalid octal digits '8' and '9'
0x                  # ❌ Missing hex digits
0xGH                # ❌ Invalid hex digits 'G' and 'H'
1.2.3               # ❌ Multiple decimal points
0b 1010             # ❌ Space between prefix and digits
0o 755              # ❌ Space between prefix and digits
0x FF               # ❌ Space between prefix and digits
1e                  # ❌ Missing exponent in scientific notation
1e+                 # ❌ Missing exponent digits
1.23ee4             # ❌ Multiple exponent markers
1.2.3e4             # ❌ Multiple decimal points in mantissa

Preservation of Structure

Internet Object preserves:

• The chosen representation form (decimal, binary, octal, hex, scientific)

• Whitespace (non-significant in interpretation)

• Syntactic fidelity (as written, except that an explicit plus sign is not preserved)

However, it does not interpret:

• Mathematical relationships between values

• Precision requirements beyond IEEE 754

• Domain-specific numeric constraints

Such semantics are the responsibility of the schema layer, validators, or application logic.

See Also

• Number Types Overview - Launcher for all number types and formats

• BigInt - For arbitrary-precision integers

• Decimal - For fixed-precision decimal arithmetic

• Special Numeric Values - NaN and Infinity

• Schema for Numbers

• Values