Integer square root with shift and add

isqrt.c

// assumes unsigned is 32 bits
unsigned isqrt1(unsigned x) {
  unsigned r = 0, r2 = 0; 
  for (int p = 15; p >= 0; --p) {
    unsigned tr2 = r2 + (r << (p + 1)) + (1u << (p << 1));
    if (tr2 <= x) {
      r2 = tr2;
      r |= (1u << p);
    }
  }
  return r;
}

/*
gcc 6.3 -O2

isqrt(unsigned int):
        mov     esi, 15
        xor     r9d, r9d
        xor     eax, eax
        mov     r8d, 1
.L3:
        lea     ecx, [rsi+1]
        mov     edx, eax
        mov     r10d, r8d
        sal     edx, cl
        lea     ecx, [rsi+rsi]
        sal     r10d, cl
        add     edx, r10d
        add     edx, r9d
        cmp     edx, edi
        ja      .L2
        mov     r11d, r8d
        mov     ecx, esi
        mov     r9d, edx
        sal     r11d, cl
        or      eax, r11d
.L2:
        sub     esi, 1
        cmp     esi, -1
        jne     .L3
        rep ret
*/