Arithmetic Shift

In computer programming, an arithmetic shift is a shift operator, sometimes known as a signed shift (though it is not restricted to signed operands). The two basic flavours are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in. Instead of being filled with all 0s, as in logical shift, when shifting to the right, the leftmost bit (usually the sign bit in signed integer representations) is replicated to fill in all the vacant positions (this is a kind of sign extension).

Arithmetic shifts can be useful as efficient ways of performing multiplication or division of signed integers by powers of two. Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2n. Shifting right by n bits on a two's complement signed binary number has the effect of dividing it by 2n, but it always rounds down (towards negative infinity). This is different from the way rounding is usually done in signed integer division (which rounds towards 0). This discrepancy has led to bugs in more than one compiler.

For example, in the x86 instruction set, the SAR instruction (arithmetic right shift) divides a signed number by a power of two, rounding towards negative infinity. However, the IDIV instruction (signed divide) divides a signed number, rounding towards zero. So a SAR instruction cannot be substituted for an IDIV by power of two instruction nor vice versa.