# expansion: Improve double-word modulo by certain constant divisors [PR97459]

Message ID 20201128075452.GO3788@tucnak New show expansion: Improve double-word modulo by certain constant divisors [PR97459] | expand

## Commit Message

Jakub Jelinek Nov. 28, 2020, 7:54 a.m. UTC
```Hi!

As discussed in the PR, e.g. on x86_64 (both -m32 and -m64) there is no
double-word modulo and so we expand it to a __{,u}mod[dt]i3 call.
For certain constant divisors we can do better.  E.g. consider
32-bit word-size, 0x100000000ULL % 3 == 1, so we can use partly the Hacker's
delight modulo by summing digits approach and optimize
unsigned long long foo (unsigned long long x) { return x % 3; }
as
unsigned long long foo (unsigned long long x) {
unsigned int sum, carry;
carry = __builtin_add_overflow ((unsigned int) x, (unsigned int) (x >> 32), &sum);
sum += carry;
return sum % 3;
}
Similarly, 0x10000000ULL % 5 == 1 (note, 1 << 28), so
unsigned long long bar (unsigned long long x) { return x % 5; }
as
unsigned long long bar (unsigned long long x) {
unsigned int sum = x & ((1 << 28) - 1);
sum += (x >> 28) & ((1 << 28) - 1);
sum += (x >> 56);
return sum % 5;
}
etc.
And we can do also signed modulo,
long long baz (long long x) { return x % 5; }
as
long long baz (long long x) {
unsigned int sum = x & ((1 << 28) - 1);
sum += ((unsigned long long) x >> 28) & ((1 << 28) - 1);
sum += ((unsigned long long) x >> 56);
/* Sum adjustment for negative x.  */
sum += (x >> 63) & 3;
unsigned int rem = sum % 5;
/* And finally adjust it to the right interval for negative values.  */
return (int) (rem + ((x >> 63) & -4));
}

Bootstrapped/regtested on x86_64-linux and i686-linux, ok for trunk?

2020-11-28  Jakub Jelinek  <jakub@redhat.com>

PR rtl-optimization/97459
* internal-fn.c (expand_addsub_overflow): No longer static.
* optabs.c (expand_doubleword_mod): New function.
(expand_binop): Optimize double-word mod with constant divisor.

* gcc.dg/pr97459-1.c: New test.
* gcc.dg/pr97459-2.c: New test.

Jakub
```

Thomas Koenig Nov. 28, 2020, 2:55 p.m. UTC | #1
```Hello Jakub,

thanks a lot for taking this on!

As far as I can tell, the patch works very well, and really speeds up
things.

As (somewhat confusingly) discussed in the PR, there are a couple of
things that could still be done incrementally with this method.

Fist, it can be combined with, or even used for, the calulation
of the quotient.  Let a be a number for which your patch works,
for example 5.

If you want to calculate n / 5, you can do

rem = n % 5;  /* Fast, with your patch.  */
quot = (n - rem) * magic;

in a fast way, where magic is the multiplicative inverse of 5
modulo 2^128 (for a 128-bit number) or 2^64 (for a 64-bit number),
which can be calculated using gmp_invert. The multiplicative inverse
for division works because n - rem is divisible by 5.

Second, you can also use this for the quotient and/or remainder
by 2*a (for example 10), with a slight adjustment:

rem5 = n % 5;
quot5 = (n - rem5) * magic;
rem10 = (quot5 % 2) * 5 + rem5;
quot10 = quot5 / 2;

This would cover the important use case of getting the quotient and
remainder for division by 10.

However, a benchmark (source attached) indicates that this method
is much faster even when only one of quotient and remainder
of division by 10 is needed.  Numbers I got indicate that this
method is faster by about a factor of five than calling the
library version.

I hope this clears up the somewhat confusing string of comments
in the PR.

Best regards

Thomas
```
Richard Biener Nov. 30, 2020, 9:21 a.m. UTC | #2
```On Sat, 28 Nov 2020, Thomas Koenig wrote:

> Hello Jakub,
>
> thanks a lot for taking this on!
>
> As far as I can tell, the patch works very well, and really speeds up
> things.
>
> As (somewhat confusingly) discussed in the PR, there are a couple of
> things that could still be done incrementally with this method.
>
> Fist, it can be combined with, or even used for, the calulation
> of the quotient.  Let a be a number for which your patch works,
> for example 5.
>
> If you want to calculate n / 5, you can do
>
>   rem = n % 5;  /* Fast, with your patch.  */
>   quot = (n - rem) * magic;
>
> in a fast way, where magic is the multiplicative inverse of 5
> modulo 2^128 (for a 128-bit number) or 2^64 (for a 64-bit number),
> which can be calculated using gmp_invert. The multiplicative inverse
> for division works because n - rem is divisible by 5.
>
> Second, you can also use this for the quotient and/or remainder
> by 2*a (for example 10), with a slight adjustment:
>
>   rem5 = n % 5;
>   quot5 = (n - rem5) * magic;
>   rem10 = (quot5 % 2) * 5 + rem5;
>   quot10 = quot5 / 2;
>
> This would cover the important use case of getting the quotient and
> remainder for division by 10.
>
> However, a benchmark (source attached) indicates that this method
> is much faster even when only one of quotient and remainder
> of division by 10 is needed.  Numbers I got indicate that this
> method is faster by about a factor of five than calling the
> library version.

Hmm, the benchmark measures throughput of integer division/modulo
which is _much_ worse than just latency since division/modulo is
usually not pipelined so there can be only one division/modulo op
in-flight.

So not sure how relevant the benchmark is - a benchmark measuring
only the latency difference would be more useful, but that's of
course harder to get at.  Maybe add a data dependence on each of
the loop iteration computations.

Richard.

> I hope this clears up the somewhat confusing string of comments
> in the PR.
>
> Best regards
>
> 	Thomas
>
```
Richard Biener Nov. 30, 2020, 9:24 a.m. UTC | #3
```On Sat, 28 Nov 2020, Jakub Jelinek wrote:

> Hi!
>
> As discussed in the PR, e.g. on x86_64 (both -m32 and -m64) there is no
> double-word modulo and so we expand it to a __{,u}mod[dt]i3 call.
> For certain constant divisors we can do better.  E.g. consider
> 32-bit word-size, 0x100000000ULL % 3 == 1, so we can use partly the Hacker's
> delight modulo by summing digits approach and optimize
> unsigned long long foo (unsigned long long x) { return x % 3; }
> as
> unsigned long long foo (unsigned long long x) {
>   unsigned int sum, carry;
>   carry = __builtin_add_overflow ((unsigned int) x, (unsigned int) (x >> 32), &sum);
>   sum += carry;
>   return sum % 3;
> }
> Similarly, 0x10000000ULL % 5 == 1 (note, 1 << 28), so
> unsigned long long bar (unsigned long long x) { return x % 5; }
> as
> unsigned long long bar (unsigned long long x) {
>   unsigned int sum = x & ((1 << 28) - 1);
>   sum += (x >> 28) & ((1 << 28) - 1);
>   sum += (x >> 56);
>   return sum % 5;
> }
> etc.
> And we can do also signed modulo,
> long long baz (long long x) { return x % 5; }
> as
> long long baz (long long x) {
>   unsigned int sum = x & ((1 << 28) - 1);
>   sum += ((unsigned long long) x >> 28) & ((1 << 28) - 1);
>   sum += ((unsigned long long) x >> 56);
>   /* Sum adjustment for negative x.  */
>   sum += (x >> 63) & 3;
>   unsigned int rem = sum % 5;
>   /* And finally adjust it to the right interval for negative values.  */
>   return (int) (rem + ((x >> 63) & -4));
> }
>
> Bootstrapped/regtested on x86_64-linux and i686-linux, ok for trunk?

OK.

Thanks,
Richard.

> 2020-11-28  Jakub Jelinek  <jakub@redhat.com>
>
> 	PR rtl-optimization/97459
> 	* internal-fn.c (expand_addsub_overflow): No longer static.
> 	* optabs.c (expand_doubleword_mod): New function.
> 	(expand_binop): Optimize double-word mod with constant divisor.
>
> 	* gcc.dg/pr97459-1.c: New test.
> 	* gcc.dg/pr97459-2.c: New test.
>
> --- gcc/internal-fn.h.jj	2020-11-27 11:19:37.950190425 +0100
> +++ gcc/internal-fn.h	2020-11-27 13:18:13.116798464 +0100
> @@ -224,6 +224,8 @@ extern bool internal_gather_scatter_fn_s
>  extern bool internal_check_ptrs_fn_supported_p (internal_fn, tree,
>  						poly_uint64, unsigned int);
>
> +extern void expand_addsub_overflow (location_t, tree_code, tree, tree, tree,
> +				    bool, bool, bool, bool, tree *);
>  extern void expand_internal_call (gcall *);
>  extern void expand_internal_call (internal_fn, gcall *);
>  extern void expand_PHI (internal_fn, gcall *);
> --- gcc/internal-fn.c.jj	2020-11-27 11:19:37.950190425 +0100
> +++ gcc/internal-fn.c	2020-11-27 13:18:13.117798453 +0100
> @@ -798,7 +798,7 @@ expand_ubsan_result_store (rtx target, r
>     CODE says whether the operation is +, or -.  */
>
> -static void
> +void
>  expand_addsub_overflow (location_t loc, tree_code code, tree lhs,
>  			tree arg0, tree arg1, bool unsr_p, bool uns0_p,
>  			bool uns1_p, bool is_ubsan, tree *datap)
> --- gcc/optabs.c.jj	2020-11-27 11:19:38.000189859 +0100
> +++ gcc/optabs.c	2020-11-27 16:06:30.971435747 +0100
> @@ -44,6 +44,8 @@ along with GCC; see the file COPYING3.
>  #include "expr.h"
>  #include "optabs-tree.h"
>  #include "libfuncs.h"
> +#include "internal-fn.h"
> +#include "langhooks.h"
>
>  static void prepare_float_lib_cmp (rtx, rtx, enum rtx_code, rtx *,
>  				   machine_mode *);
> @@ -926,6 +928,196 @@ expand_doubleword_mult (machine_mode mod
>    return product;
>  }
> +
> +/* Subroutine of expand_binop.  Optimize unsigned double-word OP0 % OP1 for
> +   constant OP1.  If for some bit in [BITS_PER_WORD / 2, BITS_PER_WORD] range
> +   (prefer higher bits) ((1w << bit) % OP1) == 1, then the modulo can be
> +   computed in word-mode as ((OP0 & (bit - 1)) + ((OP0 >> bit) & (bit - 1))
> +   + (OP0 >> (2 * bit))) % OP1.  Whether we need to sum 2, 3 or 4 values
> +   depends on the bit value, if 2, then carry from the addition needs to be
> +   added too, i.e. like:
> +   sum += __builtin_add_overflow (low, high, &sum)
> +
> +   Optimize signed double-word OP0 % OP1 similarly, just apply some correction
> +   factor to the sum before doing unsigned remainder, in the form of
> +   sum += (((signed) OP0 >> (2 * BITS_PER_WORD - 1)) & const);
> +   then perform unsigned
> +   remainder = sum % OP1;
> +   and finally
> +   remainder += ((signed) OP0 >> (2 * BITS_PER_WORD - 1)) & (1 - OP1);  */
> +
> +static rtx
> +expand_doubleword_mod (machine_mode mode, rtx op0, rtx op1, bool unsignedp)
> +{
> +  if (INTVAL (op1) <= 1)
> +    return NULL_RTX;
> +
> +  rtx_insn *last = get_last_insn ();
> +  for (int bit = BITS_PER_WORD; bit >= BITS_PER_WORD / 2; bit--)
> +    {
> +      wide_int w = wi::shifted_mask (bit, 1, false, 2 * BITS_PER_WORD);
> +      if (wi::ne_p (wi::umod_trunc (w, INTVAL (op1)), 1))
> +	continue;
> +      rtx sum = NULL_RTX, mask = NULL_RTX;
> +      if (bit == BITS_PER_WORD)
> +	{
> +	  /* For signed modulo we need to add correction to the sum
> +	     and that might again overflow.  */
> +	  if (!unsignedp)
> +	    continue;
> +	  if (optab_handler (uaddv4_optab, word_mode) == CODE_FOR_nothing)
> +	    continue;
> +	  tree wtype = lang_hooks.types.type_for_mode (word_mode, 1);
> +	  if (wtype == NULL_TREE)
> +	    continue;
> +	  tree ctype = build_complex_type (wtype);
> +	  if (TYPE_MODE (ctype) != GET_MODE_COMPLEX_MODE (word_mode))
> +	    continue;
> +	  machine_mode cmode = TYPE_MODE (ctype);
> +	  rtx op00 = operand_subword_force (op0, 0, mode);
> +	  rtx op01 = operand_subword_force (op0, 1, mode);
> +	  rtx cres = gen_rtx_CONCAT (cmode, gen_reg_rtx (word_mode),
> +				     gen_reg_rtx (word_mode));
> +	  tree lhs = make_tree (ctype, cres);
> +	  tree arg0 = make_tree (wtype, op00);
> +	  tree arg1 = make_tree (wtype, op01);
> +	  expand_addsub_overflow (UNKNOWN_LOCATION, PLUS_EXPR, lhs, arg0,
> +				  arg1, true, true, true, false, NULL);
> +	  sum = expand_simple_binop (word_mode, PLUS, XEXP (cres, 0),
> +				     XEXP (cres, 1), NULL_RTX, 1,
> +				     OPTAB_DIRECT);
> +	  if (sum == NULL_RTX)
> +	    return NULL_RTX;
> +	}
> +      else
> +	{
> +	  /* Code below uses GEN_INT, so we need the masks to be representable
> +	     in HOST_WIDE_INTs.  */
> +	  if (bit >= HOST_BITS_PER_WIDE_INT)
> +	    continue;
> +	  /* If op0 is e.g. -1 or -2 unsigned, then the 2 additions might
> +	     overflow.  Consider 64-bit -1ULL for word size 32, if we add
> +	     0x7fffffffU + 0x7fffffffU + 3U, it wraps around to 1.  */
> +	  if (bit == BITS_PER_WORD - 1)
> +	    continue;
> +
> +	  int count = (2 * BITS_PER_WORD + bit - 1) / bit;
> +	  rtx sum_corr = NULL_RTX;
> +
> +	  if (!unsignedp)
> +	    {
> +	      /* For signed modulo, compute it as unsigned modulo of
> +		 sum with a correction added to it if OP0 is negative,
> +		 such that the result can be computed as unsigned
> +		 remainder + ((OP1 >> (2 * BITS_PER_WORD - 1)) & (1 - OP1).  */
> +	      w = wi::min_value (2 * BITS_PER_WORD, SIGNED);
> +	      wide_int wmod1 = wi::umod_trunc (w, INTVAL (op1));
> +	      wide_int wmod2 = wi::smod_trunc (w, INTVAL (op1));
> +	      /* wmod2 == -wmod1.  */
> +	      wmod2 = wmod2 + (INTVAL (op1) - 1);
> +	      if (wi::ne_p (wmod1, wmod2))
> +		{
> +		  wide_int wcorr = wmod2 - wmod1;
> +		  if (wi::neg_p (w))
> +		    wcorr = wcorr + INTVAL (op1);
> +		  /* Now verify if the count sums can't overflow, and punt
> +		     if they could.  */
> +		  w = wi::mask (bit, false, 2 * BITS_PER_WORD);
> +		  w = w * (count - 1);
> +		  w = w + wi::mask (2 * BITS_PER_WORD - (count - 1) * bit,
> +				    false, 2 * BITS_PER_WORD);
> +		  w = w + wcorr;
> +		  w = wi::lrshift (w, BITS_PER_WORD);
> +		  if (wi::ne_p (w, 0))
> +		    continue;
> +
> +		  mask = operand_subword_force (op0, WORDS_BIG_ENDIAN ? 0 : 1,
> +						mode);
> +					      GEN_INT (BITS_PER_WORD - 1),
> +					      NULL_RTX, 0, OPTAB_DIRECT);
> +		  if (mask == NULL_RTX)
> +		    return NULL_RTX;
> +		  sum_corr = immed_wide_int_const (wcorr, word_mode);
> +		  sum_corr = expand_simple_binop (word_mode, AND, mask,
> +						  sum_corr, NULL_RTX, 1,
> +						  OPTAB_DIRECT);
> +		  if (sum_corr == NULL_RTX)
> +		    return NULL_RTX;
> +		}
> +	    }
> +
> +	  for (int i = 0; i < count; i++)
> +	    {
> +	      rtx v = op0;
> +	      if (i)
> +		v = expand_simple_binop (mode, LSHIFTRT, v, GEN_INT (i * bit),
> +					 NULL_RTX, 1, OPTAB_DIRECT);
> +	      if (v == NULL_RTX)
> +		return NULL_RTX;
> +	      v = lowpart_subreg (word_mode, v, mode);
> +	      if (v == NULL_RTX)
> +		return NULL_RTX;
> +	      if (i != count - 1)
> +		v = expand_simple_binop (word_mode, AND, v,
> +					 GEN_INT ((HOST_WIDE_INT_1U << bit)
> +						  - 1), NULL_RTX, 1,
> +					 OPTAB_DIRECT);
> +	      if (v == NULL_RTX)
> +		return NULL_RTX;
> +	      if (sum == NULL_RTX)
> +		sum = v;
> +	      else
> +		sum = expand_simple_binop (word_mode, PLUS, sum, v, NULL_RTX,
> +					   1, OPTAB_DIRECT);
> +	      if (sum == NULL_RTX)
> +		return NULL_RTX;
> +	    }
> +	  if (sum_corr)
> +	    {
> +	      sum = expand_simple_binop (word_mode, PLUS, sum, sum_corr,
> +					 NULL_RTX, 1, OPTAB_DIRECT);
> +	      if (sum == NULL_RTX)
> +		return NULL_RTX;
> +	    }
> +	}
> +      rtx remainder = expand_divmod (1, TRUNC_MOD_EXPR, word_mode, sum, op1,
> +				     NULL_RTX, 1);
> +      if (remainder == NULL_RTX)
> +	return NULL_RTX;
> +
> +      if (!unsignedp)
> +	{
> +	  if (mask == NULL_RTX)
> +	    {
> +	      mask = operand_subword_force (op0, WORDS_BIG_ENDIAN ? 0 : 1,
> +					    mode);
> +					  GEN_INT (BITS_PER_WORD - 1),
> +					  NULL_RTX, 0, OPTAB_DIRECT);
> +	      if (mask == NULL_RTX)
> +		return NULL_RTX;
> +	    }
> +				      GEN_INT (1 - INTVAL (op1)),
> +				      NULL_RTX, 1, OPTAB_DIRECT);
> +	  if (mask == NULL_RTX)
> +	    return NULL_RTX;
> +	  remainder = expand_simple_binop (word_mode, PLUS, remainder,
> +					   mask, NULL_RTX, 1, OPTAB_DIRECT);
> +	  if (remainder == NULL_RTX)
> +	    return NULL_RTX;
> +	}
> +
> +      remainder = convert_modes (mode, word_mode, remainder, unsignedp);
> +      /* Punt if we need any library calls.  */
> +      for (; last; last = NEXT_INSN (last))
> +	if (CALL_P (last))
> +	  return NULL_RTX;
> +      return remainder;
> +    }
> +  return NULL_RTX;
> +}
>
>  /* Wrapper around expand_binop which takes an rtx code to specify
>     the operation to perform, not an optab pointer.  All other
> @@ -1806,6 +1998,37 @@ expand_binop (machine_mode mode, optab b
>  	}
>      }
>
> +  /* Attempt to synthetize double word modulo by constant divisor.  */
> +  if ((binoptab == umod_optab || binoptab == smod_optab)
> +      && optimize
> +      && CONST_INT_P (op1)
> +      && is_int_mode (mode, &int_mode)
> +      && GET_MODE_SIZE (int_mode) == 2 * UNITS_PER_WORD
> +      && optab_handler (lshr_optab, int_mode) != CODE_FOR_nothing
> +      && optab_handler (and_optab, word_mode) != CODE_FOR_nothing
> +      && optab_handler (add_optab, word_mode) != CODE_FOR_nothing
> +      && optimize_insn_for_speed_p ())
> +    {
> +      rtx remainder = expand_doubleword_mod (int_mode, op0, op1,
> +					     binoptab == umod_optab);
> +      if (remainder != NULL_RTX)
> +	{
> +	  if (optab_handler (mov_optab, int_mode) != CODE_FOR_nothing)
> +	    {
> +	      rtx_insn *move = emit_move_insn (target ? target : remainder,
> +					       remainder);
> +	      set_dst_reg_note (move,
> +				REG_EQUAL,
> +				gen_rtx_fmt_ee (UMOD, int_mode,
> +						copy_rtx (op0), op1),
> +				target ? target : remainder);
> +	    }
> +	  return remainder;
> +	}
> +      else
> +	delete_insns_since (last);
> +    }
> +
>    /* It can't be open-coded in this mode.
>       Use a library call if one is available and caller says that's ok.  */
>
> --- gcc/testsuite/gcc.dg/pr97459-1.c.jj	2020-11-27 14:16:50.735828637 +0100
> +++ gcc/testsuite/gcc.dg/pr97459-1.c	2020-11-27 14:16:12.212259188 +0100
> @@ -0,0 +1,54 @@
> +/* PR rtl-optimization/97459 */
> +/* { dg-do run } */
> +/* { dg-options "-O2" } */
> +/* { dg-additional-options "-DEXPENSIVE" { target run_expensive_tests } } */
> +
> +#ifdef __SIZEOF_INT128__
> +typedef __uint128_t T;
> +#else
> +typedef unsigned long long T;
> +#endif
> +
> +T __attribute__((noipa)) foo (T x, T n) { return x % n; }
> +#define C(n) T __attribute__((noipa)) foo##n (T x) { return x % (n - 10000); }
> +
> +#define C1(n) C(n##1) C(n##3) C(n##5) C(n##7) C(n##9)
> +#define C2(n) C1(n##0) C1(n##1) C1(n##2) C1(n##3) C1(n##4) \
> +	      C1(n##5) C1(n##6) C1(n##7) C1(n##8) C1(n##9)
> +#ifdef EXPENSIVE
> +#define C3(n) C2(n##0) C2(n##1) C2(n##2) C2(n##3) C2(n##4) \
> +	      C2(n##5) C2(n##6) C2(n##7) C2(n##8) C2(n##9)
> +#define C4(n) C3(n##0) C3(n##1) C3(n##2) C3(n##3) C3(n##4) \
> +	      C3(n##5) C3(n##6) C3(n##7) C3(n##8) C3(n##9)
> +#else
> +#define C3(n) C2(n##0) C2(n##4) C2(n##9)
> +#define C4(n) C3(n##0) C3(n##3) C3(n##7)
> +#endif
> +#define TESTS C4(1)
> +
> +TESTS
> +
> +struct S { T x; T (*foo) (T); };
> +
> +#undef C
> +#define C(n) { n - 10000, foo##n },
> +
> +struct S tests[] = {
> +TESTS
> +  { 0, 0 }
> +};
> +
> +int
> +main ()
> +{
> +  int i, j, k;
> +  for (k = 0; tests[k].x; k++)
> +    for (i = 0; i < sizeof (T) * __CHAR_BIT__; i++)
> +      for (j = -5; j <= 5; j++)
> +	{
> +	  T x = ((T) 1 << i) + j;
> +	  if (foo (x, tests[k].x) != tests[k].foo (x))
> +	    __builtin_abort ();
> +	}
> +  return 0;
> +}
> --- gcc/testsuite/gcc.dg/pr97459-2.c.jj	2020-11-27 15:53:36.831080388 +0100
> +++ gcc/testsuite/gcc.dg/pr97459-2.c	2020-11-27 15:50:20.763269826 +0100
> @@ -0,0 +1,57 @@
> +/* PR rtl-optimization/97459 */
> +/* { dg-do run } */
> +/* { dg-options "-O2" } */
> +/* { dg-additional-options "-DEXPENSIVE" { target run_expensive_tests } } */
> +
> +#ifdef __SIZEOF_INT128__
> +typedef __int128_t T;
> +typedef __uint128_t U;
> +#else
> +typedef long long T;
> +typedef unsigned long long U;
> +#endif
> +
> +T __attribute__((noipa)) foo (T x, T n) { return x % n; }
> +#define C(n) T __attribute__((noipa)) foo##n (T x) { return x % (n - 10000); }
> +
> +#define C1(n) C(n##1) C(n##3) C(n##5) C(n##7) C(n##9)
> +#define C2(n) C1(n##0) C1(n##1) C1(n##2) C1(n##3) C1(n##4) \
> +	      C1(n##5) C1(n##6) C1(n##7) C1(n##8) C1(n##9)
> +#ifdef EXPENSIVE
> +#define C3(n) C2(n##0) C2(n##1) C2(n##2) C2(n##3) C2(n##4) \
> +	      C2(n##5) C2(n##6) C2(n##7) C2(n##8) C2(n##9)
> +#define C4(n) C3(n##0) C3(n##1) C3(n##2) C3(n##3) C3(n##4) \
> +	      C3(n##5) C3(n##6) C3(n##7) C3(n##8) C3(n##9)
> +#else
> +#define C3(n) C2(n##0) C2(n##4) C2(n##9)
> +#define C4(n) C3(n##0) C3(n##3) C3(n##7)
> +#endif
> +#define TESTS C4(1)
> +
> +TESTS
> +
> +struct S { T x; T (*foo) (T); };
> +
> +#undef C
> +#define C(n) { n - 10000, foo##n },
> +
> +struct S tests[] = {
> +TESTS
> +  { 0, 0 }
> +};
> +
> +int
> +main ()
> +{
> +  int i, j, k;
> +  for (k = 0; tests[k].x; k++)
> +    for (i = 0; i < sizeof (T) * __CHAR_BIT__; i++)
> +      for (j = -5; j <= 5; j++)
> +	{
> +	  U x = ((U) 1 << i) + j;
> +	  if (foo ((T) x, tests[k].x) != tests[k].foo ((T) x)
> +	      || foo ((T) -x, tests[k].x) != tests[k].foo ((T) -x))
> +	    __builtin_abort ();
> +	}
> +  return 0;
> +}
>
> 	Jakub
>
>
```

## Patch

```--- gcc/internal-fn.h.jj	2020-11-27 11:19:37.950190425 +0100
+++ gcc/internal-fn.h	2020-11-27 13:18:13.116798464 +0100
@@ -224,6 +224,8 @@  extern bool internal_gather_scatter_fn_s
extern bool internal_check_ptrs_fn_supported_p (internal_fn, tree,
poly_uint64, unsigned int);

+extern void expand_addsub_overflow (location_t, tree_code, tree, tree, tree,
+				    bool, bool, bool, bool, tree *);
extern void expand_internal_call (gcall *);
extern void expand_internal_call (internal_fn, gcall *);
extern void expand_PHI (internal_fn, gcall *);
--- gcc/internal-fn.c.jj	2020-11-27 11:19:37.950190425 +0100
+++ gcc/internal-fn.c	2020-11-27 13:18:13.117798453 +0100
@@ -798,7 +798,7 @@  expand_ubsan_result_store (rtx target, r
CODE says whether the operation is +, or -.  */

-static void
+void
expand_addsub_overflow (location_t loc, tree_code code, tree lhs,
tree arg0, tree arg1, bool unsr_p, bool uns0_p,
bool uns1_p, bool is_ubsan, tree *datap)
--- gcc/optabs.c.jj	2020-11-27 11:19:38.000189859 +0100
+++ gcc/optabs.c	2020-11-27 16:06:30.971435747 +0100
@@ -44,6 +44,8 @@  along with GCC; see the file COPYING3.
#include "expr.h"
#include "optabs-tree.h"
#include "libfuncs.h"
+#include "internal-fn.h"
+#include "langhooks.h"

static void prepare_float_lib_cmp (rtx, rtx, enum rtx_code, rtx *,
machine_mode *);
@@ -926,6 +928,196 @@  expand_doubleword_mult (machine_mode mod
return product;
}
+
+/* Subroutine of expand_binop.  Optimize unsigned double-word OP0 % OP1 for
+   constant OP1.  If for some bit in [BITS_PER_WORD / 2, BITS_PER_WORD] range
+   (prefer higher bits) ((1w << bit) % OP1) == 1, then the modulo can be
+   computed in word-mode as ((OP0 & (bit - 1)) + ((OP0 >> bit) & (bit - 1))
+   + (OP0 >> (2 * bit))) % OP1.  Whether we need to sum 2, 3 or 4 values
+   depends on the bit value, if 2, then carry from the addition needs to be
+   sum += __builtin_add_overflow (low, high, &sum)
+
+   Optimize signed double-word OP0 % OP1 similarly, just apply some correction
+   factor to the sum before doing unsigned remainder, in the form of
+   sum += (((signed) OP0 >> (2 * BITS_PER_WORD - 1)) & const);
+   then perform unsigned
+   remainder = sum % OP1;
+   and finally
+   remainder += ((signed) OP0 >> (2 * BITS_PER_WORD - 1)) & (1 - OP1);  */
+
+static rtx
+expand_doubleword_mod (machine_mode mode, rtx op0, rtx op1, bool unsignedp)
+{
+  if (INTVAL (op1) <= 1)
+    return NULL_RTX;
+
+  rtx_insn *last = get_last_insn ();
+  for (int bit = BITS_PER_WORD; bit >= BITS_PER_WORD / 2; bit--)
+    {
+      wide_int w = wi::shifted_mask (bit, 1, false, 2 * BITS_PER_WORD);
+      if (wi::ne_p (wi::umod_trunc (w, INTVAL (op1)), 1))
+	continue;
+      rtx sum = NULL_RTX, mask = NULL_RTX;
+      if (bit == BITS_PER_WORD)
+	{
+	  /* For signed modulo we need to add correction to the sum
+	     and that might again overflow.  */
+	  if (!unsignedp)
+	    continue;
+	  if (optab_handler (uaddv4_optab, word_mode) == CODE_FOR_nothing)
+	    continue;
+	  tree wtype = lang_hooks.types.type_for_mode (word_mode, 1);
+	  if (wtype == NULL_TREE)
+	    continue;
+	  tree ctype = build_complex_type (wtype);
+	  if (TYPE_MODE (ctype) != GET_MODE_COMPLEX_MODE (word_mode))
+	    continue;
+	  machine_mode cmode = TYPE_MODE (ctype);
+	  rtx op00 = operand_subword_force (op0, 0, mode);
+	  rtx op01 = operand_subword_force (op0, 1, mode);
+	  rtx cres = gen_rtx_CONCAT (cmode, gen_reg_rtx (word_mode),
+				     gen_reg_rtx (word_mode));
+	  tree lhs = make_tree (ctype, cres);
+	  tree arg0 = make_tree (wtype, op00);
+	  tree arg1 = make_tree (wtype, op01);
+	  expand_addsub_overflow (UNKNOWN_LOCATION, PLUS_EXPR, lhs, arg0,
+				  arg1, true, true, true, false, NULL);
+	  sum = expand_simple_binop (word_mode, PLUS, XEXP (cres, 0),
+				     XEXP (cres, 1), NULL_RTX, 1,
+				     OPTAB_DIRECT);
+	  if (sum == NULL_RTX)
+	    return NULL_RTX;
+	}
+      else
+	{
+	  /* Code below uses GEN_INT, so we need the masks to be representable
+	     in HOST_WIDE_INTs.  */
+	  if (bit >= HOST_BITS_PER_WIDE_INT)
+	    continue;
+	  /* If op0 is e.g. -1 or -2 unsigned, then the 2 additions might
+	     overflow.  Consider 64-bit -1ULL for word size 32, if we add
+	     0x7fffffffU + 0x7fffffffU + 3U, it wraps around to 1.  */
+	  if (bit == BITS_PER_WORD - 1)
+	    continue;
+
+	  int count = (2 * BITS_PER_WORD + bit - 1) / bit;
+	  rtx sum_corr = NULL_RTX;
+
+	  if (!unsignedp)
+	    {
+	      /* For signed modulo, compute it as unsigned modulo of
+		 sum with a correction added to it if OP0 is negative,
+		 such that the result can be computed as unsigned
+		 remainder + ((OP1 >> (2 * BITS_PER_WORD - 1)) & (1 - OP1).  */
+	      w = wi::min_value (2 * BITS_PER_WORD, SIGNED);
+	      wide_int wmod1 = wi::umod_trunc (w, INTVAL (op1));
+	      wide_int wmod2 = wi::smod_trunc (w, INTVAL (op1));
+	      /* wmod2 == -wmod1.  */
+	      wmod2 = wmod2 + (INTVAL (op1) - 1);
+	      if (wi::ne_p (wmod1, wmod2))
+		{
+		  wide_int wcorr = wmod2 - wmod1;
+		  if (wi::neg_p (w))
+		    wcorr = wcorr + INTVAL (op1);
+		  /* Now verify if the count sums can't overflow, and punt
+		     if they could.  */
+		  w = wi::mask (bit, false, 2 * BITS_PER_WORD);
+		  w = w * (count - 1);
+		  w = w + wi::mask (2 * BITS_PER_WORD - (count - 1) * bit,
+				    false, 2 * BITS_PER_WORD);
+		  w = w + wcorr;
+		  w = wi::lrshift (w, BITS_PER_WORD);
+		  if (wi::ne_p (w, 0))
+		    continue;
+
+		  mask = operand_subword_force (op0, WORDS_BIG_ENDIAN ? 0 : 1,
+						mode);
+					      GEN_INT (BITS_PER_WORD - 1),
+					      NULL_RTX, 0, OPTAB_DIRECT);
+		    return NULL_RTX;
+		  sum_corr = immed_wide_int_const (wcorr, word_mode);
+		  sum_corr = expand_simple_binop (word_mode, AND, mask,
+						  sum_corr, NULL_RTX, 1,
+						  OPTAB_DIRECT);
+		  if (sum_corr == NULL_RTX)
+		    return NULL_RTX;
+		}
+	    }
+
+	  for (int i = 0; i < count; i++)
+	    {
+	      rtx v = op0;
+	      if (i)
+		v = expand_simple_binop (mode, LSHIFTRT, v, GEN_INT (i * bit),
+					 NULL_RTX, 1, OPTAB_DIRECT);
+	      if (v == NULL_RTX)
+		return NULL_RTX;
+	      v = lowpart_subreg (word_mode, v, mode);
+	      if (v == NULL_RTX)
+		return NULL_RTX;
+	      if (i != count - 1)
+		v = expand_simple_binop (word_mode, AND, v,
+					 GEN_INT ((HOST_WIDE_INT_1U << bit)
+						  - 1), NULL_RTX, 1,
+					 OPTAB_DIRECT);
+	      if (v == NULL_RTX)
+		return NULL_RTX;
+	      if (sum == NULL_RTX)
+		sum = v;
+	      else
+		sum = expand_simple_binop (word_mode, PLUS, sum, v, NULL_RTX,
+					   1, OPTAB_DIRECT);
+	      if (sum == NULL_RTX)
+		return NULL_RTX;
+	    }
+	  if (sum_corr)
+	    {
+	      sum = expand_simple_binop (word_mode, PLUS, sum, sum_corr,
+					 NULL_RTX, 1, OPTAB_DIRECT);
+	      if (sum == NULL_RTX)
+		return NULL_RTX;
+	    }
+	}
+      rtx remainder = expand_divmod (1, TRUNC_MOD_EXPR, word_mode, sum, op1,
+				     NULL_RTX, 1);
+      if (remainder == NULL_RTX)
+	return NULL_RTX;
+
+      if (!unsignedp)
+	{
+	    {
+	      mask = operand_subword_force (op0, WORDS_BIG_ENDIAN ? 0 : 1,
+					    mode);
+					  GEN_INT (BITS_PER_WORD - 1),
+					  NULL_RTX, 0, OPTAB_DIRECT);
+		return NULL_RTX;
+	    }
+				      GEN_INT (1 - INTVAL (op1)),
+				      NULL_RTX, 1, OPTAB_DIRECT);
+	    return NULL_RTX;
+	  remainder = expand_simple_binop (word_mode, PLUS, remainder,
+	  if (remainder == NULL_RTX)
+	    return NULL_RTX;
+	}
+
+      remainder = convert_modes (mode, word_mode, remainder, unsignedp);
+      /* Punt if we need any library calls.  */
+      for (; last; last = NEXT_INSN (last))
+	if (CALL_P (last))
+	  return NULL_RTX;
+      return remainder;
+    }
+  return NULL_RTX;
+}

/* Wrapper around expand_binop which takes an rtx code to specify
the operation to perform, not an optab pointer.  All other
@@ -1806,6 +1998,37 @@  expand_binop (machine_mode mode, optab b
}
}

+  /* Attempt to synthetize double word modulo by constant divisor.  */
+  if ((binoptab == umod_optab || binoptab == smod_optab)
+      && optimize
+      && CONST_INT_P (op1)
+      && is_int_mode (mode, &int_mode)
+      && GET_MODE_SIZE (int_mode) == 2 * UNITS_PER_WORD
+      && optab_handler (lshr_optab, int_mode) != CODE_FOR_nothing
+      && optab_handler (and_optab, word_mode) != CODE_FOR_nothing
+      && optab_handler (add_optab, word_mode) != CODE_FOR_nothing
+      && optimize_insn_for_speed_p ())
+    {
+      rtx remainder = expand_doubleword_mod (int_mode, op0, op1,
+					     binoptab == umod_optab);
+      if (remainder != NULL_RTX)
+	{
+	  if (optab_handler (mov_optab, int_mode) != CODE_FOR_nothing)
+	    {
+	      rtx_insn *move = emit_move_insn (target ? target : remainder,
+					       remainder);
+	      set_dst_reg_note (move,
+				REG_EQUAL,
+				gen_rtx_fmt_ee (UMOD, int_mode,
+						copy_rtx (op0), op1),
+				target ? target : remainder);
+	    }
+	  return remainder;
+	}
+      else
+	delete_insns_since (last);
+    }
+
/* It can't be open-coded in this mode.
Use a library call if one is available and caller says that's ok.  */

--- gcc/testsuite/gcc.dg/pr97459-1.c.jj	2020-11-27 14:16:50.735828637 +0100
+++ gcc/testsuite/gcc.dg/pr97459-1.c	2020-11-27 14:16:12.212259188 +0100
@@ -0,0 +1,54 @@
+/* PR rtl-optimization/97459 */
+/* { dg-do run } */
+/* { dg-options "-O2" } */
+/* { dg-additional-options "-DEXPENSIVE" { target run_expensive_tests } } */
+
+#ifdef __SIZEOF_INT128__
+typedef __uint128_t T;
+#else
+typedef unsigned long long T;
+#endif
+
+T __attribute__((noipa)) foo (T x, T n) { return x % n; }
+#define C(n) T __attribute__((noipa)) foo##n (T x) { return x % (n - 10000); }
+
+#define C1(n) C(n##1) C(n##3) C(n##5) C(n##7) C(n##9)
+#define C2(n) C1(n##0) C1(n##1) C1(n##2) C1(n##3) C1(n##4) \
+	      C1(n##5) C1(n##6) C1(n##7) C1(n##8) C1(n##9)
+#ifdef EXPENSIVE
+#define C3(n) C2(n##0) C2(n##1) C2(n##2) C2(n##3) C2(n##4) \
+	      C2(n##5) C2(n##6) C2(n##7) C2(n##8) C2(n##9)
+#define C4(n) C3(n##0) C3(n##1) C3(n##2) C3(n##3) C3(n##4) \
+	      C3(n##5) C3(n##6) C3(n##7) C3(n##8) C3(n##9)
+#else
+#define C3(n) C2(n##0) C2(n##4) C2(n##9)
+#define C4(n) C3(n##0) C3(n##3) C3(n##7)
+#endif
+#define TESTS C4(1)
+
+TESTS
+
+struct S { T x; T (*foo) (T); };
+
+#undef C
+#define C(n) { n - 10000, foo##n },
+
+struct S tests[] = {
+TESTS
+  { 0, 0 }
+};
+
+int
+main ()
+{
+  int i, j, k;
+  for (k = 0; tests[k].x; k++)
+    for (i = 0; i < sizeof (T) * __CHAR_BIT__; i++)
+      for (j = -5; j <= 5; j++)
+	{
+	  T x = ((T) 1 << i) + j;
+	  if (foo (x, tests[k].x) != tests[k].foo (x))
+	    __builtin_abort ();
+	}
+  return 0;
+}
--- gcc/testsuite/gcc.dg/pr97459-2.c.jj	2020-11-27 15:53:36.831080388 +0100
+++ gcc/testsuite/gcc.dg/pr97459-2.c	2020-11-27 15:50:20.763269826 +0100
@@ -0,0 +1,57 @@
+/* PR rtl-optimization/97459 */
+/* { dg-do run } */
+/* { dg-options "-O2" } */
+/* { dg-additional-options "-DEXPENSIVE" { target run_expensive_tests } } */
+
+#ifdef __SIZEOF_INT128__
+typedef __int128_t T;
+typedef __uint128_t U;
+#else
+typedef long long T;
+typedef unsigned long long U;
+#endif
+
+T __attribute__((noipa)) foo (T x, T n) { return x % n; }
+#define C(n) T __attribute__((noipa)) foo##n (T x) { return x % (n - 10000); }
+
+#define C1(n) C(n##1) C(n##3) C(n##5) C(n##7) C(n##9)
+#define C2(n) C1(n##0) C1(n##1) C1(n##2) C1(n##3) C1(n##4) \
+	      C1(n##5) C1(n##6) C1(n##7) C1(n##8) C1(n##9)
+#ifdef EXPENSIVE
+#define C3(n) C2(n##0) C2(n##1) C2(n##2) C2(n##3) C2(n##4) \
+	      C2(n##5) C2(n##6) C2(n##7) C2(n##8) C2(n##9)
+#define C4(n) C3(n##0) C3(n##1) C3(n##2) C3(n##3) C3(n##4) \
+	      C3(n##5) C3(n##6) C3(n##7) C3(n##8) C3(n##9)
+#else
+#define C3(n) C2(n##0) C2(n##4) C2(n##9)
+#define C4(n) C3(n##0) C3(n##3) C3(n##7)
+#endif
+#define TESTS C4(1)
+
+TESTS
+
+struct S { T x; T (*foo) (T); };
+
+#undef C
+#define C(n) { n - 10000, foo##n },
+
+struct S tests[] = {
+TESTS
+  { 0, 0 }
+};
+
+int
+main ()
+{
+  int i, j, k;
+  for (k = 0; tests[k].x; k++)
+    for (i = 0; i < sizeof (T) * __CHAR_BIT__; i++)
+      for (j = -5; j <= 5; j++)
+	{
+	  U x = ((U) 1 << i) + j;
+	  if (foo ((T) x, tests[k].x) != tests[k].foo ((T) x)
+	      || foo ((T) -x, tests[k].x) != tests[k].foo ((T) -x))
+	    __builtin_abort ();
+	}
+  return 0;
+}

```