In the following test case, the "n & 4" test is redundant and should be eliminated, since the "n &= 7;" statement limits n's potential values to [0,7].  The "n >= 4" test further narrows its potential values to [4,7], making the "n & 4" test always true, allowing the elimination of the code path calling bar().  

bergner@ltcden2-lp1:~$ cat test.c 
extern long foo (void);
extern long bar (void);

long
test (long n)
{
  n &= 7;
  if (n >= 4) {
    if (n & 4)
      return foo ();
    else
      return bar ();
  }
  return 0;
}

Current gcc (-O2) does optimize this on powerpc64le-linux and removes the bar() code path. However, if we change the "n >= 4" test to either "n > 4" or "n == 4", then we fail to eliminate the code path to bar(), even though the "n & 4" test remains redundant.

Using -O2 -mcpu=power10 (-mcpu=power10 allows tail calls making the resulting asm easier to read, but it isn't required) produces for the "n >= 4" test:

test:
	andi. 3,3,0x4
	bne 0,.L4
	li 3,0
	blr
	.p2align 4,,15
.L4:
	b foo@notoc

Where as the "n > 4" test results in:

test:
	rldicl 2,3,0,61
	cmpdi 0,2,4
	ble 0,.L2
	andi. 3,3,0x4
	beq 0,.L3
	b foo@notoc
	.p2align 4,,15
.L2:
	li 3,0
	blr
	.p2align 4,,15
.L3:
	b bar@notoc

Interestingly to me, the optimized code keeps the inner redundant "n & 4" test (andi. 3,3,0x4) and removes the outer tests.  I didn't expect that.