Question

if I do:

int x = 4;
pow(2, x);

Is that really that much less efficient than just doing:

1 << 4

?

Answer 1

Yes. An easy way to show this is to compile the following two functions that do the same thing and then look at the disassembly.

#include <stdint.h>
#include <math.h>

uint32_t foo1(uint32_t shftAmt) {
    return pow(2, shftAmt);
}

uint32_t foo2(uint32_t shftAmt) {
    return (1 << shftAmt);
}

cc -arch armv7 -O3 -S -o - shift.c (I happen to find ARM asm easier to read but if you want x86 just remove the arch flag)

    _foo1:
@ BB#0:
    push    {r7, lr}
    vmov    s0, r0
    mov r7, sp
    vcvt.f64.u32    d16, s0
    vmov    r0, r1, d16
    blx _exp2
    vmov    d16, r0, r1
    vcvt.u32.f64    s0, d16
    vmov    r0, s0
    pop {r7, pc}

_foo2:
@ BB#0:
    movs    r1, #1
    lsl.w   r0, r1, r0
    bx  lr

You can see foo2 only takes 2 instructions vs foo1 which takes several instructions. It has to move the data to the FP HW registers (vmov), convert the integer to a float (vcvt.f64.u32) call the exp function and then convert the answer back to an uint (vcvt.u32.f64) and move it from the FP HW back to the GP registers.