gcc -O optimization: Help me understand the effect

Question

So, I'm learning C and I'm currently going through Computer Systems: A Programmer's Perspective 3rd Edition and associated labs. I'm now doing the first lab for which I have to implement (and have thus implemented) the following function.

/* 
* fitsBits - return 1 if x can be represented as an 
*  n-bit, two's complement integer.
*   1 <= n <= 32
*   Examples: fitsBits(5,3) = 0, fitsBits(-4,3) = 1
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 15
*   Rating: 2
*/
int fitsBits(int x, int n) {
  int sign_bit = (x >> 31 & 1);
  int minus_one = ~1+1;
  int n_minus_one = n + minus_one;
  return  (!(x >> n_minus_one) & !sign_bit)
           | (!(~(x >> n_minus_one)) & sign_bit);
}

This function will run _a_lot_ of testcases against the following test function.

int test_fitsBits(int x, int n)
{
  int TMin_n = -(1 << (n-1));
  int TMax_n = (1 << (n-1)) - 1;
  return x >= TMin_n && x <= TMax_n;
}

Now, here is where the weird stuff happens: by default the code is compiled with the following flags -O -Wall -m32

Running my code against the test function produces the following assertion fail: ERROR: Test fitsBits(-2147483648[0x80000000],32[0x20]) failed... ...Gives 1[0x1]. Should be 0[0x0]

It seems that my code is correct and the testcode is bogus. Upon further investigation it seems that the test_function produces following intermediary results:

> Tmin:-2147483648 
> TMax_n:2147483647 
> x: -2147483648 
> x >= TMin_n: 1
> x <= TMax_n: 0
> result: 0

Obviously -2147483648 <= 2147483647, but the comparison somehow produces a 0.

If I compile this program without the -O flag, all the tests pass successfully. Can somebody shed some light on this behaviour please?

EDIT: Sorry the Assembly Code is horrible layout, don't know exactly how to fix quickly

Assembly Code without -O;

.section    __TEXT,__text,regular,pure_instructions
.macosx_version_min 10, 11
.globl  _test_fitsBits
.align  4, 0x90
_test_fitsBits:                         ## @test_fitsBits
.cfi_startproc
## BB#0:
pushq   %rbp
Ltmp0:
.cfi_def_cfa_offset 16
Ltmp1:
.cfi_offset %rbp, -16
movq    %rsp, %rbp
Ltmp2:
.cfi_def_cfa_register %rbp
xorl    %eax, %eax
movb    %al, %cl
movl    $1, %eax
xorl    %edx, %edx
movl    %edi, -4(%rbp)
movl    %esi, -8(%rbp)
movl    -8(%rbp), %esi
subl    $1, %esi
movb    %cl, -17(%rbp)          ## 1-byte Spill
movl    %esi, %ecx
                                    ## kill: CL<def> ECX<kill>
movl    %eax, %esi
shll    %cl, %esi
subl    %esi, %edx
movl    %edx, -12(%rbp)
movl    -8(%rbp), %edx
subl    $1, %edx
movl    %edx, %ecx
                                    ## kill: CL<def> ECX<kill>
shll    %cl, %eax
subl    $1, %eax
movl    %eax, -16(%rbp)
movl    -4(%rbp), %eax
cmpl    -12(%rbp), %eax
movb    -17(%rbp), %cl          ## 1-byte Reload
movb    %cl, -18(%rbp)          ## 1-byte Spill
jl  LBB0_2
## BB#1:
movl    -4(%rbp), %eax
cmpl    -16(%rbp), %eax
setle   %cl
movb    %cl, -18(%rbp)          ## 1-byte Spill
LBB0_2:
movb    -18(%rbp), %al          ## 1-byte Reload
andb    $1, %al
movzbl  %al, %eax
popq    %rbp
retq
.cfi_endproc

.globl  _main
.align  4, 0x90
_main:                                  ## @main
.cfi_startproc
## BB#0:
pushq   %rbp
Ltmp3:
.cfi_def_cfa_offset 16
Ltmp4:
.cfi_offset %rbp, -16
movq    %rsp, %rbp
Ltmp5:
.cfi_def_cfa_register %rbp
xorl    %eax, %eax
movl    $0, -4(%rbp)
movl    %edi, -8(%rbp)
movq    %rsi, -16(%rbp)
popq    %rbp
retq
.cfi_endproc


.subsections_via_symbols

Assembly Code with -O:

.section    __TEXT,__text,regular,pure_instructions
.macosx_version_min 10, 11
.globl  _test_fitsBits
.align  4, 0x90
_test_fitsBits:                         ## @test_fitsBits
.cfi_startproc
## BB#0:
pushq   %rbp
Ltmp0:
.cfi_def_cfa_offset 16
Ltmp1:
.cfi_offset %rbp, -16
movq    %rsp, %rbp
Ltmp2:
.cfi_def_cfa_register %rbp
                                    ## kill: ESI<def> ESI<kill>       RSI<def>
leal    -1(%rsi), %ecx
movl    $1, %eax
                                    ## kill: CL<def> CL<kill> ECX<kill>
shll    %cl, %eax
movl    %eax, %ecx
negl    %ecx
cmpl    %edi, %eax
setg    %al
cmpl    %ecx, %edi
setge   %cl
andb    %al, %cl
movzbl  %cl, %eax
popq    %rbp
retq
.cfi_endproc

.globl  _main
.align  4, 0x90
_main:                                  ## @main
.cfi_startproc
## BB#0:
pushq   %rbp
Ltmp3:
.cfi_def_cfa_offset 16
Ltmp4:
.cfi_offset %rbp, -16
movq    %rsp, %rbp
Ltmp5:
.cfi_def_cfa_register %rbp
xorl    %eax, %eax
popq    %rbp
retq
.cfi_endproc


.subsections_via_symbols

Answer 1

int TMin_n = -(1 << (n-1));
int TMax_n = (1 << (n-1)) - 1;

On a system with 32-bit int the two bitwise shift expressions above invoke undefined behavior when n is 32. When int is 32-bit then 1 << 31 is UB in C as 1 << 31 is not representable in a int.