Why is there no `nand` instruction in modern CPUs?

http://www.ibm.com/support/knowledgecenter/ssw_aix_61/com.ibm.aix.alangref/idalangref_nand_nd_instrs.htm : POWER has NAND.

But generally modern CPUs are built to match automated code generation by compilers, and bitwise NAND is very rarely called for. Bitwise AND and OR get used more often for manipulating bitfields in data structures. In fact, SSE has AND-NOT but not NAND.

Every instruction has a cost in the decode logic and consumes an opcode that could be used for something else. Especially in variable-length encodings like x86, you can run out of short opcodes and have to use longer ones, which potentially slows down all code.

The cost of such an ALU functions is

1) the logic that performs the function itself

2) the selector that selects this function result instead of the others out of all ALU functions

3) the cost of having this option in the instruction set (and not having some other usefull function)

I agree with you that the 1) cost is very small. The 2) and 3) cost however is almost independent of the function. I think in this case the 3) cost (the bits occupied in the instruction) were the reason not to have this specific instruction. Bits in an instruction are a very scarce resource for a CPU/architecture designer.

Turn it around - first see why Nand was popular in hardware logic design - it has several useful properties there. Then ask whether those properties still apply in a CPU instruction...

TL/DR - they don't, so there's no downside to using And, Or or Not instead.

The biggest advantage to hardwired Nand logic was speed, gained by reducing the number of logic levels (transistor stages) between a circuit's inputs and outputs. In a CPU, the clock speed is determined by the speed of much more complex operations like addition, so speeding up an AND operation won't enable you to increase clock rate.

And the number of times you need to combine other instructions is vanishingly small - enough so that Nand really doesn't earn its space in the instrucnion set.