MIPS Bitshift Operators

Introduction

MIPS supports several bitshift logical operators. There are all R-type instructions

sll Shift left logical by a constant number of bits
sllv Shift left logical by a variable number of bits
srl Shift right logical by a constant number of bits
srlv Shift right logical by a variable number of bits
sra Shift right arithmetic by a constant number of bits
srav Shift right arithmetic by a variable number of bits

Example and Semantics

sll $rd, $rt, shift_amt
sllv $rd, $rt, $rs
srl $rd, $rt, shift_amt
srlv $rd, $rt, $rs
sra $rd, $rt, shift_amt
srav $rd, $rt, $rs

We'll explain sll and sllv, then point out differences with the right-shifted versions.

In sll, the semantics are:

   R[d] <- R[t]_{31-shift_amt}::0^shift_amt

where the copy of the contents of register t are shifted left (the uppermost bits fall off). Zeroes are shifted in.

The shift amount is recorded in the shift amount field of the instruction (bits B_10-6).

Notice register s is unused.

In sllv, the semantics are

   R[d] <- R[t]_{(31-R[s]_4-0)--0}::0^R[s]_4-0

This complicated expression just means to take the low (32 - R[s]_4-0) bits and shift it left by R[s]_4-0 bits where R[s]_4-0 is interpreted using 5-bit UB (thus the value of R[s]_4-0 ranges from 00000 to 11111).

Recall that shifting left by k bits is like multiplying a number by 2^k. This is true in UB or in 2C, which is why there is no such thing as an arithmetic left shift.

Here are the key differences for right-shifted versions.

srl and srlv behave like sll and sllv but shift right instead of left. Zeroes are shifted in from the most significant end, and bits fall off the least significant end. This is equivalent to dividing by 2_k in UB.
sra and srav behave like sll and sllv but shift right instead of left. The sign bit is shifted in from the most significant end, and bits fall off the least significant end.
Shifting in the sign-bit does the "right thing" for 2C. That is, by shifting in the sign bit, you are dividing by 2^k for 2C.

Machine Code Representation

Here are the representations for bitshift logical operators.

Instruction	B_31-26	B_25-21	B_20-16	B_15-11	B_10-6	B_5-0
	opcode	register s	register t	register d	shift amount	function
sll $rd, $rt, shift_amt	000 000 (SPECIAL)	unused	-	-	shift_amt	000 000
sllv $rd, $rt, $rs	000 000 (SPECIAL)	-	-	-	00000	000 100
srl $rd, $rt, <shift_amt>	000 000 (SPECIAL)	unused	-	-	shift_amt	000 010
srlv $rd, $rt, $rs	000 000 (SPECIAL)	-	-	-	00000	000 110
sra $rd, $rt, <shift_amt>	000 000 (SPECIAL)	unused	-	-	shift_amt	000 011
srav $rd, $rt, $rs	000 000 (SPECIAL)	-	-	-	00000	000 111

The dashes are filled in with 5-bit encoding of the registers (in UB), as usual.

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