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The <<= operator is the bitwise left shift assignment operator in Bash. It shifts the binary representation of a variable’s integer value to the left by a specified number of bits, appending zeros to the least significant bits, and assigns the newly computed value back to the original variable. 
(( variable <<= shift_amount ))

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Execution Context

Because Bash treats variables as strings by default, <<= must be executed within an arithmetic evaluation context. This is typically achieved using double parentheses (( )) or the let built-in command. 

# Double parentheses syntax
(( x <<= 3 ))


# let command syntax
let "x <<= 3"

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Mechanics and Behavior

  • Equivalence: The expression (( x <<= y )) is a syntactic shorthand for (( x = x << y )).
  • Mathematical Translation: Shifting an integer left by n bits is mathematically equivalent to multiplying that integer by 2n2^n. For example, (( x <<= 2 )) multiplies x by 4.
  • Data Type Constraints and Evaluation: The operator evaluates operands strictly as integers. If a variable contains a non-integer string, Bash attempts recursive arithmetic evaluation. If the string is a valid, unset variable identifier (e.g., "foo"), it evaluates to 0. However, if the string contains characters that are invalid in an arithmetic context (such as a decimal point in "3.14" or spaces in "invalid string"), Bash will throw a syntax error (e.g., syntax error: invalid arithmetic operator).
  • Bit Width and Overflow: During arithmetic evaluation, Bash typically treats numbers as 64-bit signed integers (on 64-bit architectures). Bits shifted beyond the most significant bit boundary are discarded. If the shift alters the sign bit (the 64th bit), the resulting integer will become negative due to two’s complement representation.

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Evaluation Example

x=5             # Binary representation: ...00000101
(( x <<= 2 ))   # Shift left by 2 bits:  ...00010100
echo $x         # Output: 20
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