Souper says:

; Function: fn1
%0:i32 = var 
%1:i32 = srem 1:i32, %0
%2:i32 = lshr %1, 1:i32
%3:i1 = ne 0:i32, %2
cand %3 0:i1

COMMAND: /home/regehr/souper/build/souper -stp-path=/usr/local/bin/stp reduce_537/foo.bc

LLVM says:

define void @fn1() #0 {
entry:
  %0 = load i32* @a, align 4, !tbaa !1
  %rem = srem i32 1, %0
  %shr1 = lshr i32 %rem, 1
  %tobool = icmp ne i32 %shr1, 0
  %shr. = select i1 %tobool, i32 %shr1, i32 1
  store i32 %shr., i32* @a, align 4, !tbaa !1
  ret void
}

COMMAND: /home/regehr/souper/third_party/llvm/Debug/bin/clang -c -w -emit-llvm -O3 reduce_537/foo.c -o reduce_537/foo.bc

C source code:

int a;
void fn1() { a = 1 % a >> 1 ?: 1; }

x86-64 from LLVM:

fn1:                                    # @fn1
	movl	$1, %ecx
	movl	$1, %eax
	xorl	%edx, %edx
	idivl	a(%rip)
	shrl	%edx
	cmovel	%ecx, %edx
	movl	%edx, a(%rip)
	retq

COMMAND: /home/regehr/souper/third_party/llvm/Debug/bin/clang -w -O3 reduce_537/foo.c -S -o -

x86-64 from GCC:

fn1:
	movl	$1, %ecx
	movl	%ecx, %eax
	cltd
	idivl	a(%rip)
	sarl	%edx
	cmovne	%edx, %ecx
	movl	%ecx, a(%rip)
	ret

COMMAND: gcc -w -O3 reduce_537/foo.c -S -o -