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Math

Arithmetic Expansion

Pros:

  • fast
  • performance-critical scripts
  • built into Bash

Cons:

  • no decimals
  • no floating point
  • Limited to your system e.g.: 64-bit signed integers (−2⁶³ to 2⁶³−1 or −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807)
  • Silent overflow = no warning
  • No built-in math functions
  • No fractional precision
  • no complex math
  • no trigonometric functions
a=5
b=3
echo $(( a + b ))     # addition
echo $(( a - b ))     # subtraction
echo $(( a * b ))     # multiplication
echo $(( a / b ))     # division
echo $(( a % b ))     # modulus
echo $(( a ** b ))    # exponentiation

Increment and Decrement

n=0                # n by default will be 0 when added to arithmetic expressions, not required, just for demonstration
echo $(( n++ ))    # post-increment
echo $(( ++n ))    # pre-increment
echo $(( n-- ))    # post-decrement
echo $(( --n ))    # pre-decrement

Grouping

a=2
b=3
echo $(( (a + b) * 4 ))    # prioritizes addition before multiplication

Comparisons

a=10
b=20
echo $(( a + b > 10 ))     # 1 (true)
echo $(( a + b > 100 ))    # 0 (false)

Binary, Hex, Octal

echo $(( 2#11111111 ))    # 255 (base 2, binary; range 0–255 has 256 values)
echo $(( 16#FF ))         # 255 (base 16) (hex)
echo $(( 017 ))           # 15 (base 8) (octal)

Random Numbers

echo $(( RANDOM ))            # random number between 0 and 32767 (15 bit, 2¹⁵ – 1)
echo $(( RANDOM % 100 ))      # random number between 0 and 99
echo $(( RANDOM % 100 + 1 ))  # random number between 1 and 100

Bitwise Operations

a=5    # 0101 in binary
b=6    # 0110 in binary

echo $(( a & b ))    # Bitwise AND

   0101    (5)
&  0110    (6)
--------------
   0100    (4)

echo $(( a | b ))    # Bitwise OR

   0101    (5)
|  0110    (6)
--------------
   0111    (7)

echo $(( a ^ b ))    # Bitwise XOR

   0101    (5)
^  0110    (6)
--------------
   0011    (3)

echo $(( a << 3 ))   # Left Shift [2ⁿ]

   0000 0101   (5)
--------------------
   0000 1010   (shift 1)
--------------------
   0001 0100   (shift 2)
--------------------
   0010 1000   (shift 3)
--------------------
   0010 1000   (40)

echo $(( a >> 2 ))   # Right Shift [division by 2ⁿ]

   0101    (5)
--------------------
   0010    (shift 1)
--------------------
   0001    (shift 2)
--------------------
   0001    (1)

echo $(( ~a ))       # Bitwise NOT (two's complement) [~a = -(a + 1)]

~   0000 0101    (5)
---------------------
    1111 1010    (-6)

BC; Basic Calculator

Pros:

  • good for financial calculations
  • math library
  • decimals (arbitrary precision, good for currency)

Cons:

  • slower than arithmetic expansion
  • not built into Bash

Decimal Numbers

a=5
b=3
echo "$a / $b" | bc -l          # division with decimal result
echo "scale=2; $a / $b" | bc    # division with 2 decimal digits

Square Root

echo "sqrt(25)" | bc -l    # 5

Trigonometric Functions

SIN

echo "s(1.5708)" | bc -l    # approximately sin(π/2)