Bitwise ternary logic instructions can logically implement all possible bitwise operations between three inputs (256 permutations). They take three registers as input and an 8-bit immediate field. Each bit in the output is generated using an 8-bit Lookup table of the three corresponding bits in the inputs to select one of the 8 positions in the 8-bit immediate. Since only 8 combinations are possible using three bits, this allow all possible 3-input bitwise operations to be performed. In mathematical terminology: each corresponding bit of the three inputs is a ternary Boolean function with a Hasse diagram of order n=8. Also known as minterms.
A full table showing all 256 possible 3-operand logical bitwise instruction may be found in the Power ISA description of . An additional insight is that if the 8-bit immediate were an operand (register) then in FPGA terminology, bitwise ternary logical instructions would implement an array of Hardware LUT3s.
One of the typical applications is an implementation bit manipulation for the symmetric cyphers.
In pseudocode the output from three single-bit inputs is illustrated by using r2, r1 and r0 as three binary digits of a 3-bit index, to treat the 8-bit immediate as a lookup table and to simply return the indexed bit: result := imm8(r2<<2 + r1<<1 + r0)
A readable implementation in Python of three single-bit inputs (r0 r1 and r2) is shown below:
If the input registers are 64-bit then the output is correspondingly 64-bit, and would be constructed from selecting each indexed bit of the three inputs to create the corresponding indexed bit of the output:
An example table of just three possible permutations out of the total 256 for the 8-bit immediate is shown below - Double-AND, Double-OR and Bitwise-blend. The immediate (the 8-bit lookup table) is named , below. Note that the column has the value in binary of its corresponding header: is binary in the "Bitwise blend" column:
The number of uses is significant: anywhere that three logical bitwise operations are used in algorithms. Carry-save, SHA-1 SHA-2, MD5, and exactly-one and exactly-two bitcounting used in Harley-Seal Popcount. speeds up MD5 by 20%
Although unusual due to the high cost in hardware this instruction is found in a number of instruction set architectures