[PATCH] Analyze niter for until-wrap condition [PR101145]

guojiufu guojiufu@linux.ibm.com
Fri Jul 2 07:55:58 GMT 2021


On 2021-07-01 20:35, Richard Biener wrote:
> On Thu, 1 Jul 2021, Jiufu Guo wrote:
> 
>> For code like:
>> unsigned foo(unsigned val, unsigned start)
>> {
>>   unsigned cnt = 0;
>>   for (unsigned i = start; i > val; ++i)
>>     cnt++;
>>   return cnt;
>> }
>> 
>> The number of iterations should be about UINT_MAX - start.
> 
> For
> 
> unsigned foo(unsigned val, unsigned start)
> {
>   unsigned cnt = 0;
>   for (unsigned i = start; i >= val; ++i)
>     cnt++;
>   return cnt;
> }
> 
> and val == 0 the loop never terminates.  I don't see anywhere
> in the patch that you disregard GE_EXPR and I remember
> the code handles GE as well as GT?  From a quick look this is
> also not covered by a testcase you add - not exactly sure
> how it would materialize in a miscompilation.
> 
Find a similar issue on the below code with the trunk.
The below code should run infinite, but it exits quickly.

#include <limits.h>
__attribute__ ((noinline))
unsigned foo(unsigned val, unsigned start)
{
   unsigned cnt = 0;
   for (unsigned i = start; i <= val; i+=16)
     cnt++;
   return cnt;
}

int main()
{
   return foo (UINT_MAX-7, 8);
}

Just opened https://gcc.gnu.org/bugzilla/show_bug.cgi?id=101291

BR,
Jiufu Guo.

>> There is function adjust_cond_for_loop_until_wrap which
>> handles similar work for const bases.
>> Like adjust_cond_for_loop_until_wrap, this patch enhance
>> function number_of_iterations_cond/number_of_iterations_lt
>> to analyze number of iterations for this kind of loop.
>> 
>> Bootstrap and regtest pass on powerpc64le, is this ok for trunk?
>> 
>> gcc/ChangeLog:
>> 
>> 	PR tree-optimization/101145
>> 	* tree-ssa-loop-niter.c
>> 	(number_of_iterations_until_wrap): New function.
>> 	(number_of_iterations_lt): Invoke above function.
>> 	(adjust_cond_for_loop_until_wrap):
>> 	Merge to number_of_iterations_until_wrap.
>> 	(number_of_iterations_cond): Update invokes for
>> 	adjust_cond_for_loop_until_wrap and number_of_iterations_lt.
>> 
>> gcc/testsuite/ChangeLog:
>> 
>> 	PR tree-optimization/101145
>> 	* gcc.dg/vect/pr101145.c: New test.
>> 	* gcc.dg/vect/pr101145.inc: New test.
>> 	* gcc.dg/vect/pr101145_1.c: New test.
>> 	* gcc.dg/vect/pr101145_2.c: New test.
>> 	* gcc.dg/vect/pr101145_3.c: New test.
>> ---
>>  gcc/testsuite/gcc.dg/vect/pr101145.c   | 187 
>> +++++++++++++++++++++++++
>>  gcc/testsuite/gcc.dg/vect/pr101145.inc |  63 +++++++++
>>  gcc/testsuite/gcc.dg/vect/pr101145_1.c |  15 ++
>>  gcc/testsuite/gcc.dg/vect/pr101145_2.c |  15 ++
>>  gcc/testsuite/gcc.dg/vect/pr101145_3.c |  15 ++
>>  gcc/tree-ssa-loop-niter.c              | 150 +++++++++++---------
>>  6 files changed, 380 insertions(+), 65 deletions(-)
>>  create mode 100644 gcc/testsuite/gcc.dg/vect/pr101145.c
>>  create mode 100644 gcc/testsuite/gcc.dg/vect/pr101145.inc
>>  create mode 100644 gcc/testsuite/gcc.dg/vect/pr101145_1.c
>>  create mode 100644 gcc/testsuite/gcc.dg/vect/pr101145_2.c
>>  create mode 100644 gcc/testsuite/gcc.dg/vect/pr101145_3.c
>> 
>> diff --git a/gcc/testsuite/gcc.dg/vect/pr101145.c 
>> b/gcc/testsuite/gcc.dg/vect/pr101145.c
>> new file mode 100644
>> index 00000000000..74031b031cf
>> --- /dev/null
>> +++ b/gcc/testsuite/gcc.dg/vect/pr101145.c
>> @@ -0,0 +1,187 @@
>> +/* { dg-require-effective-target vect_int } */
>> +/* { dg-options "-O3 -fdump-tree-vect-details" } */
>> +#include <limits.h>
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  while (n < ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo_1 (int *__restrict__ a, int *__restrict__ b, unsigned l, 
>> unsigned)
>> +{
>> +  while (UINT_MAX - 64 < ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo_2 (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  l = UINT_MAX - 32;
>> +  while (n < ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo_3 (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  while (n <= ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo_4 (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{  // infininate
>> +  while (0 <= ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +foo_5 (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  //no loop
>> +  l = UINT_MAX;
>> +  while (n < ++l)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +bar (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  while (--l < n)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +bar_1 (int *__restrict__ a, int *__restrict__ b, unsigned l, 
>> unsigned)
>> +{
>> +  while (--l < 64)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +unsigned __attribute__ ((noinline))
>> +bar_2 (int *__restrict__ a, int *__restrict__ b, unsigned l, unsigned 
>> n)
>> +{
>> +  l = 32;
>> +  while (--l < n)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +
>> +int a[3200], b[3200];
>> +int fail;
>> +
>> +int
>> +main ()
>> +{
>> +  unsigned l, n;
>> +  unsigned res;
>> +  /* l > n*/
>> +  n = UINT_MAX - 64;
>> +  l = n + 32;
>> +  res = foo (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n;
>> +  res = foo (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n - 1;
>> +  res = foo (a, b, l, n);
>> +  if (res != l + 1)
>> +    fail++;
>> +
>> +  l = n - 32;
>> +  res = foo (a, b, l, n);
>> +  if (res != l + 1)
>> +    fail++;
>> +
>> +  l = UINT_MAX;
>> +  res = foo (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n + 32;
>> +  res = foo_1 (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n + 32;
>> +  res = foo_2 (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n;
>> +  res = foo_3 (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n - 1;
>> +  res = foo_3 (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n - 2;
>> +  res = foo_3 (a, b, l, n);
>> +  if (res != l + 1)
>> +    fail++;
>> +
>> +  res = foo_5 (a, b, l, n);
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  n = 64;
>> +  l = n - 32;
>> +  res = bar (a, b, l, n);
>> +  res++;
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n;
>> +  res = bar (a, b, l, n);
>> +  res++;
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  l = n + 1;
>> +  res = bar (a, b, l, n);
>> +  res++;
>> +  if (res != l)
>> +    fail++;
>> +
>> +  l = 0;
>> +  res = bar (a, b, l, n);
>> +  res++;
>> +  if (res != l)
>> +    fail++;
>> +
>> +  l = 32;
>> +  res = bar_1 (a, b, l, n);
>> +  res++;
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  res = bar_1 (a, b, l, n);
>> +  res++;
>> +  if (res != 0)
>> +    fail++;
>> +
>> +  if (fail)
>> +    __builtin_abort ();
>> +  return 0;
>> +}
>> +
>> +/* { dg-final { scan-tree-dump-times "vectorized 1 loops" 7 "vect" } 
>> } */
>> diff --git a/gcc/testsuite/gcc.dg/vect/pr101145.inc 
>> b/gcc/testsuite/gcc.dg/vect/pr101145.inc
>> new file mode 100644
>> index 00000000000..6eed3fa8aca
>> --- /dev/null
>> +++ b/gcc/testsuite/gcc.dg/vect/pr101145.inc
>> @@ -0,0 +1,63 @@
>> +TYPE __attribute__ ((noinline))
>> +foo_sign (int *__restrict__ a, int *__restrict__ b, TYPE l, TYPE n)
>> +{
>> +  for (l = L_BASE; n < l; l += C)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +TYPE __attribute__ ((noinline))
>> +bar_sign (int *__restrict__ a, int *__restrict__ b, TYPE l, TYPE n)
>> +{
>> +  for (l = L_BASE_DOWN; l < n; l -= C)
>> +    *a++ = *b++ + 1;
>> +  return l;
>> +}
>> +
>> +int __attribute__ ((noinline)) neq (int a, int b) { return a != b; }
>> +
>> +int a[1000], b[1000];
>> +int fail;
>> +
>> +int
>> +main ()
>> +{
>> +  TYPE res;
>> +  TYPE l;
>> +  TYPE n;
>> +  n = N_BASE;
>> +  l = n - C;
>> +  res = foo_sign (a, b, l, n);
>> +  if (res != l)
>> +    fail++;
>> +
>> +  l = n;
>> +  res = foo_sign (a, b, l, n);
>> +  if (res != l)
>> +    fail++;
>> +
>> +  l = n + C;
>> +  res = foo_sign (a, b, l, n);
>> +  if (neq ((res - MIN) / C, 0))
>> +    fail++;
>> +
>> +  n = N_BASE_DOWN;
>> +  l = n - C;
>> +  res = bar_sign (a, b, l, n);
>> +  if (neq ((MAX - res) / C, 0))
>> +    fail++;
>> +
>> +  l = n;
>> +  res = bar_sign (a, b, l, n);
>> +  if (res != l)
>> +    fail++;
>> +
>> +  l = n + C;
>> +  res = bar_sign (a, b, l, n);
>> +  if (res != l)
>> +    fail++;
>> +
>> +  if (fail)
>> +    __builtin_abort ();
>> +  return 0;
>> +}
>> diff --git a/gcc/testsuite/gcc.dg/vect/pr101145_1.c 
>> b/gcc/testsuite/gcc.dg/vect/pr101145_1.c
>> new file mode 100644
>> index 00000000000..94f6b99b893
>> --- /dev/null
>> +++ b/gcc/testsuite/gcc.dg/vect/pr101145_1.c
>> @@ -0,0 +1,15 @@
>> +/* { dg-require-effective-target vect_int } */
>> +/* { dg-options "-O3 -fdump-tree-vect-details" } */
>> +#define TYPE signed char
>> +#define MIN -128
>> +#define MAX 127
>> +#define N_BASE (MAX - 32)
>> +#define N_BASE_DOWN (MIN + 32)
>> +
>> +#define C 3
>> +#define L_BASE l
>> +#define L_BASE_DOWN l
>> +
>> +#include "pr101145.inc"
>> +
>> +/* { dg-final { scan-tree-dump-times "vectorized 1 loops" 2 "vect" } 
>> } */
>> diff --git a/gcc/testsuite/gcc.dg/vect/pr101145_2.c 
>> b/gcc/testsuite/gcc.dg/vect/pr101145_2.c
>> new file mode 100644
>> index 00000000000..d3cfc9e01e1
>> --- /dev/null
>> +++ b/gcc/testsuite/gcc.dg/vect/pr101145_2.c
>> @@ -0,0 +1,15 @@
>> +/* { dg-require-effective-target vect_int } */
>> +/* { dg-options "-O3 -fdump-tree-vect-details" } */
>> +#define TYPE unsigned char
>> +#define MIN 0
>> +#define MAX 255
>> +#define N_BASE (MAX - 32 + 1)
>> +#define N_BASE_DOWN (MIN + 32)
>> +
>> +#define C 2
>> +#define L_BASE l
>> +#define L_BASE_DOWN l
>> +
>> +#include "pr101145.inc"
>> +
>> +/* { dg-final { scan-tree-dump-times "vectorized 1 loops" 2 "vect" } 
>> } */
>> diff --git a/gcc/testsuite/gcc.dg/vect/pr101145_3.c 
>> b/gcc/testsuite/gcc.dg/vect/pr101145_3.c
>> new file mode 100644
>> index 00000000000..e2cf9b1f7e6
>> --- /dev/null
>> +++ b/gcc/testsuite/gcc.dg/vect/pr101145_3.c
>> @@ -0,0 +1,15 @@
>> +/* { dg-require-effective-target vect_int } */
>> +/* { dg-options "-O3 -fdump-tree-vect-details" } */
>> +#define TYPE int *
>> +#define MIN ((TYPE)0)
>> +#define MAX ((TYPE)((long long)-1))
>> +#define N_BASE ((TYPE) (-32))
>> +#define N_BASE_DOWN (MIN + 32)
>> +
>> +#define C 1
>> +#define L_BASE l
>> +#define L_BASE_DOWN l
>> +
>> +#include "pr101145.inc"
>> +
>> +/* { dg-final { scan-tree-dump-times "vectorized 1 loops" 2 "vect" } 
>> } */
>> diff --git a/gcc/tree-ssa-loop-niter.c b/gcc/tree-ssa-loop-niter.c
>> index b5add827018..06db6a36ef8 100644
>> --- a/gcc/tree-ssa-loop-niter.c
>> +++ b/gcc/tree-ssa-loop-niter.c
>> @@ -1473,6 +1473,86 @@ assert_loop_rolls_lt (tree type, affine_iv 
>> *iv0, affine_iv *iv1,
>>      }
>>  }
>> 
>> +/* Determines number of iterations of loop whose ending condition
>> +   is IV0 < IV1 which likes:  {base, -C} < n,  or n < {base, C}.
>> +   The number of iterations is stored to NITER.  */
>> +
>> +static bool
>> +number_of_iterations_until_wrap (class loop *, tree type, affine_iv 
>> *iv0,
>> +				 affine_iv *iv1, class tree_niter_desc *niter)
>> +{
>> +  tree niter_type = unsigned_type_for (type);
>> +  tree max, min;
>> +
>> +  if (POINTER_TYPE_P (type))
>> +    {
>> +      max = fold_convert (type, TYPE_MAX_VALUE (niter_type));
>> +      min = fold_convert (type, TYPE_MIN_VALUE (niter_type));
>> +    }
>> +  else
>> +    {
>> +      max = TYPE_MAX_VALUE (type);
>> +      min = TYPE_MIN_VALUE (type);
>> +    }
> 
> It would be cheaper to use wide_int here - wi::min/max_value
> (TYPE_PRECISION (...), TYPE_SIGN (...)) and in the simplification
> code below.
> 
>> +  tree high = max, low = min, one = build_int_cst (niter_type, 1);
>> +  tree step;
>> +
>> +  /* n < {base, C}. */
>> +  if (integer_zerop (iv0->step) && TREE_CODE (iv1->step) == 
>> INTEGER_CST
>> +      && !tree_int_cst_sign_bit (iv1->step))
>> +    {
>> +      step = iv1->step;
>> +      niter->niter = fold_build2 (MINUS_EXPR, niter_type, max, 
>> iv1->base);
>> +      if (TREE_CODE (iv1->base) == INTEGER_CST)
>> +	low = fold_build2 (MINUS_EXPR, type, iv1->base, one);
>> +      else if (TREE_CODE (iv0->base) == INTEGER_CST)
>> +	low = iv0->base;
>> +    }
>> +  /* {base, -C} < n. */
>> +  else if (TREE_CODE (iv0->step) == INTEGER_CST
>> +	   && tree_int_cst_sign_bit (iv0->step) && integer_zerop 
>> (iv1->step))
>> +    {
>> +      step = fold_build1 (NEGATE_EXPR, TREE_TYPE (iv0->step), 
>> iv0->step);
>> +      niter->niter = fold_build2 (MINUS_EXPR, niter_type, iv0->base, 
>> min);
>> +      if (TREE_CODE (iv0->base) == INTEGER_CST)
>> +	high = fold_build2 (PLUS_EXPR, type, iv0->base, one);
>> +      else if (TREE_CODE (iv1->base) == INTEGER_CST)
>> +	high = iv1->base;
>> +    }
>> +  else
>> +    return false;
>> +
>> +  /* (delta + step - 1) / step */
>> +  step = fold_convert (niter_type, step);
>> +  niter->niter = fold_convert (niter_type, niter->niter);
>> +  niter->niter = fold_build2 (PLUS_EXPR, niter_type, niter->niter, 
>> step);
>> +  niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, 
>> niter->niter, step);
>> +
>> +  tree m = fold_build2 (MINUS_EXPR, niter_type, high, low);
>> +  m = fold_convert (niter_type, m);
>> +  mpz_t mstep, tmp, mmax;
>> +  mpz_init (mstep);
>> +  mpz_init (tmp);
>> +  mpz_init (mmax);
>> +  wi::to_mpz (wi::to_wide (step), mstep, UNSIGNED);
>> +  wi::to_mpz (wi::to_wide (m), mmax, UNSIGNED);
>> +  mpz_add (tmp, mmax, mstep);
>> +  mpz_sub_ui (tmp, tmp, 1);
>> +  mpz_fdiv_q (tmp, tmp, mstep);
>> +  niter->max = widest_int::from (wi::from_mpz (niter_type, tmp, 
>> false),
>> +				 TYPE_SIGN (niter_type));
>> +  mpz_clear (mstep);
>> +  mpz_clear (tmp);
> 
> You forget to clear mmax?  I wonder why you need to involve GMP here
> at all since this is just add/sub/divide - you could use
> widest_int directly I think.  At least the back-and-forth between
> trees, wide-int and mpz looks odd.
> 
> Richard.
> 
>> +  niter->may_be_zero
>> +    = fold_build2 (LE_EXPR, boolean_type_node, iv1->base, iv0->base);
>> +
>> +  niter->control.no_overflow = false;
>> +
>> +  return true;
>> +}
>> +
>>  /* Determines number of iterations of loop whose ending condition
>>     is IV0 < IV1.  TYPE is the type of the iv.  The number of
>>     iterations is stored to NITER.  BNDS bounds the difference
>> @@ -1501,6 +1581,11 @@ number_of_iterations_lt (class loop *loop, tree 
>> type, affine_iv *iv0,
>>        niter->bound = iv0->base;
>>      }
>> 
>> +  /* {base, -C} < n,  or n < {base, C} */
>> +  if (tree_int_cst_sign_bit (iv0->step)
>> +      || (!integer_zerop (iv1->step) && !tree_int_cst_sign_bit 
>> (iv1->step)))
>> +    return number_of_iterations_until_wrap (loop, type, iv0, iv1, 
>> niter);
>> +
>>    delta = fold_build2 (MINUS_EXPR, niter_type,
>>  		       fold_convert (niter_type, iv1->base),
>>  		       fold_convert (niter_type, iv0->base));
>> @@ -1665,62 +1750,6 @@ dump_affine_iv (FILE *file, affine_iv *iv)
>>      }
>>  }
>> 
>> -/* Given exit condition IV0 CODE IV1 in TYPE, this function adjusts
>> -   the condition for loop-until-wrap cases.  For example:
>> -     (unsigned){8, -1}_loop < 10        => {0, 1} != 9
>> -     10 < (unsigned){0, max - 7}_loop   => {0, 1} != 8
>> -   Return true if condition is successfully adjusted.  */
>> -
>> -static bool
>> -adjust_cond_for_loop_until_wrap (tree type, affine_iv *iv0, tree_code 
>> *code,
>> -				 affine_iv *iv1)
>> -{
>> -  /* Only support simple cases for the moment.  */
>> -  if (TREE_CODE (iv0->base) != INTEGER_CST
>> -      || TREE_CODE (iv1->base) != INTEGER_CST)
>> -    return false;
>> -
>> -  tree niter_type = unsigned_type_for (type), high, low;
>> -  /* Case: i-- < 10.  */
>> -  if (integer_zerop (iv1->step))
>> -    {
>> -      /* TODO: Should handle case in which abs(step) != 1.  */
>> -      if (!integer_minus_onep (iv0->step))
>> -	return false;
>> -      /* Give up on infinite loop.  */
>> -      if (*code == LE_EXPR
>> -	  && tree_int_cst_equal (iv1->base, TYPE_MAX_VALUE (type)))
>> -	return false;
>> -      high = fold_build2 (PLUS_EXPR, niter_type,
>> -			  fold_convert (niter_type, iv0->base),
>> -			  build_int_cst (niter_type, 1));
>> -      low = fold_convert (niter_type, TYPE_MIN_VALUE (type));
>> -    }
>> -  else if (integer_zerop (iv0->step))
>> -    {
>> -      /* TODO: Should handle case in which abs(step) != 1.  */
>> -      if (!integer_onep (iv1->step))
>> -	return false;
>> -      /* Give up on infinite loop.  */
>> -      if (*code == LE_EXPR
>> -	  && tree_int_cst_equal (iv0->base, TYPE_MIN_VALUE (type)))
>> -	return false;
>> -      high = fold_convert (niter_type, TYPE_MAX_VALUE (type));
>> -      low = fold_build2 (MINUS_EXPR, niter_type,
>> -			 fold_convert (niter_type, iv1->base),
>> -			 build_int_cst (niter_type, 1));
>> -    }
>> -  else
>> -    gcc_unreachable ();
>> -
>> -  iv0->base = low;
>> -  iv0->step = fold_convert (niter_type, integer_one_node);
>> -  iv1->base = high;
>> -  iv1->step = build_int_cst (niter_type, 0);
>> -  *code = NE_EXPR;
>> -  return true;
>> -}
>> -
>>  /* Determine the number of iterations according to condition (for 
>> staying
>>     inside loop) which compares two induction variables using 
>> comparison
>>     operator CODE.  The induction variable on left side of the 
>> comparison
>> @@ -1855,15 +1884,6 @@ number_of_iterations_cond (class loop *loop,
>>        return true;
>>      }
>> 
>> -  /* Handle special case loops: while (i-- < 10) and while (10 < i++) 
>> by
>> -     adjusting iv0, iv1 and code.  */
>> -  if (code != NE_EXPR
>> -      && (tree_int_cst_sign_bit (iv0->step)
>> -	  || (!integer_zerop (iv1->step)
>> -	      && !tree_int_cst_sign_bit (iv1->step)))
>> -      && !adjust_cond_for_loop_until_wrap (type, iv0, &code, iv1))
>> -    return false;
>> -
>>    /* OK, now we know we have a senseful loop.  Handle several cases, 
>> depending
>>       on what comparison operator is used.  */
>>    bound_difference (loop, iv1->base, iv0->base, &bnds);
>> 


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