float64

float64 is a built-in primitive data type in Go that represents a 64-bit double-precision floating-point number, strictly conforming to the IEEE 754 standard. It is the default type inferred by the Go compiler when a variable is initialized with a floating-point literal.

Technical Specifications

• Memory Footprint: 64 bits (8 bytes).
• Bit Layout:
  • Sign: 1 bit
  • Exponent: 11 bits
  • Mantissa (Fraction): 52 bits
• Precision: Approximately 15 to 17 decimal digits.

Syntax and Initialization

Go provides multiple ways to declare and initialize a float64, including explicit typing, type inference, and scientific notation.

package example

// Explicit declaration
var pi float64 = 3.141592653589793

// Type inference (defaults to float64)
var e = 2.71828

// Scientific notation
var avogadro float64 = 6.022e23
var planck float64 = 6.626e-34

Boundary Limits

The math standard library package defines the architectural limits of the float64 type.

package example

import "math"

// Maximum finite float64 value (~1.7976931348623157e+308)
var maxVal float64 = math.MaxFloat64

// Smallest positive, non-zero float64 value (~4.9406564584124654e-324)
var minVal float64 = math.SmallestNonzeroFloat64

Special IEEE 754 Values

Because float64 adheres to IEEE 754, it supports special states representing undefined or unrepresentable mathematical operations. In Go, constant division by zero is caught by the compiler and results in a compile-time error (invalid operation: division by zero). To yield infinity or NaN via arithmetic division, the operands must be variables.

package example

import "math"

func evaluateIEEE754() {
    // Positive and Negative Infinity via the math package
    posInf := math.Inf(1)  
    negInf := math.Inf(-1) 

    // Not a Number via the math package
    nan := math.NaN()      

    // Infinity and NaN via variable division
    numerator := 1.0
    zero := 0.0
    calcInf := numerator / zero     // Evaluates to +Inf
    calcNegInf := -numerator / zero // Evaluates to -Inf
    calcNaN := zero / zero          // Evaluates to NaN

    // Evaluation functions
    isInf := math.IsInf(posInf, 0) // returns true
    isNaN := math.IsNaN(nan)       // returns true

    // Prevent "declared and not used" compile-time errors
    _ = posInf
    _ = negInf
    _ = nan
    _ = calcInf
    _ = calcNegInf
    _ = calcNaN
    _ = isInf
    _ = isNaN
}

Type Conversion

Go’s strong typing system prohibits implicit type coercion. Operations involving float64 and other numeric types (including float32 or integers) require explicit casting. Furthermore, the Go compiler prohibits truncating constant floating-point values directly to integers.

package example

func convertTypes() {
    var integerVal int = 42
    var float32Val float32 = 9.81

    // Explicit conversion to float64
    var convertedInt float64 = float64(integerVal)
    var convertedFloat32 float64 = float64(float32Val)

    // Explicit conversion from float64 (truncates decimal portion)
    // Note: int(3.99) causes a compile-time error ("constant 3.99 truncated to integer")
    f := 3.99
    var truncatedInt int = int(f) // Result: 3

    // Prevent "declared and not used" compile-time errors
    _ = convertedInt
    _ = convertedFloat32
    _ = truncatedInt
}

Precision Characteristics

Due to the base-2 representation of floating-point numbers, certain base-10 fractional values cannot be represented exactly. This results in standard floating-point arithmetic rounding errors.

package example

func precisionExample() {
    a := 0.1
    b := 0.2
    c := a + b 
    
    // c evaluates to 0.30000000000000004, not exactly 0.3
    
    // Prevent "declared and not used" compile-time error
    _ = c 
}

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