Right Shift Assignment

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(( variable >>= shift_amount ))

# or
let "variable >>= shift_amount"

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Operational Mechanics

• Expression Equivalence: The operation (( x >>= y )) is the shorthand assignment equivalent of (( x = x >> y )).
• Context Requirement: The operator requires an explicit arithmetic execution environment, invoked via (( ... )), $(( ... )), or let. Unlike standard assignment operators (= or +=), >>= is not recognized as a valid token in standard shell command contexts, even if the target variable is strictly typed with declare -i.
• Recursive Integer Evaluation: Bash dynamically evaluates variables as signed integers (typically a 64-bit intmax_t on modern architectures). If the variable contains a non-numeric string, Bash evaluates that string recursively as an arithmetic expression or a variable reference. A string evaluates to 0 if it ultimately resolves to an uninitialized variable, an initialized variable currently holding the value 0, or an arithmetic expression that mathematically equals zero (e.g., "10 - 10").
• Sign Bit Propagation (Arithmetic Shift): Because Bash utilizes signed integers, >>= performs an arithmetic right shift rather than a logical right shift. The most significant bit (the sign bit) is preserved and propagated to fill the vacated bit positions on the left.
  • For positive integers (sign bit 0), vacated bits are filled with 0s.
  • For negative integers (sign bit 1, represented in two’s complement), vacated bits are filled with 1s.
• Mathematical Property: A bitwise right shift by n bits is mathematically equivalent to integer floor division by 2ⁿ.

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Evaluation Examples

# Positive integer shift
val=24          # Binary: ...00011000
(( val >>= 2 )) # Shifts right by 2 bits
echo $val       # Output: 6 (Binary: ...00000110)


# Negative integer shift (Two's complement sign propagation)
val=-16         # Binary: ...11110000
(( val >>= 2 )) # Shifts right by 2 bits
echo $val       # Output: -4 (Binary: ...11111100)


# Recursive evaluation of string variables
foo=32
str_val="foo"
(( str_val >>= 3 )) # "foo" recursively resolves to the variable foo (32). 32 >> 3 is 4.
echo $str_val       # Output: 4


# Evaluation of strings resolving to zero
str_val2="10 - 10"
(( str_val2 >>= 1 )) # "10 - 10" mathematically resolves to 0. 0 >> 1 is 0.
echo $str_val2       # Output: 0