blob: f1bf04901dc7b711ddf00e4b2ee59e9d0aa7eb11 [file] [log] [blame]
/*
* kmp_collapse.cpp -- loop collapse feature
*/
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "kmp.h"
#include "kmp_error.h"
#include "kmp_i18n.h"
#include "kmp_itt.h"
#include "kmp_stats.h"
#include "kmp_str.h"
#include "kmp_collapse.h"
#if OMPT_SUPPORT
#include "ompt-specific.h"
#endif
// OMPTODO: different style of comments (see kmp_sched)
// OMPTODO: OMPT/OMPD
// avoid inadevertently using a library based abs
template <typename T> T __kmp_abs(const T val) {
return (val < 0) ? -val : val;
}
kmp_uint32 __kmp_abs(const kmp_uint32 val) { return val; }
kmp_uint64 __kmp_abs(const kmp_uint64 val) { return val; }
//----------------------------------------------------------------------------
// Common functions for working with rectangular and non-rectangular loops
//----------------------------------------------------------------------------
template <typename T> int __kmp_sign(T val) {
return (T(0) < val) - (val < T(0));
}
template <typename T> class CollapseAllocator {
typedef T *pT;
private:
static const size_t allocaSize = 32; // size limit for stack allocations
// (8 bytes x 4 nested loops)
char stackAlloc[allocaSize];
static constexpr size_t maxElemCount = allocaSize / sizeof(T);
pT pTAlloc;
public:
CollapseAllocator(size_t n) : pTAlloc(reinterpret_cast<pT>(stackAlloc)) {
if (n > maxElemCount) {
pTAlloc = reinterpret_cast<pT>(__kmp_allocate(n * sizeof(T)));
}
}
~CollapseAllocator() {
if (pTAlloc != reinterpret_cast<pT>(stackAlloc)) {
__kmp_free(pTAlloc);
}
}
T &operator[](int index) { return pTAlloc[index]; }
operator const pT() { return pTAlloc; }
};
//----------Loop canonicalization---------------------------------------------
// For loop nest (any shape):
// convert != to < or >;
// switch from using < or > to <= or >=.
// "bounds" array has to be allocated per thread.
// All other internal functions will work only with canonicalized loops.
template <typename T>
void kmp_canonicalize_one_loop_XX(
ident_t *loc,
/*in/out*/ bounds_infoXX_template<T> *bounds) {
if (__kmp_env_consistency_check) {
if (bounds->step == 0) {
__kmp_error_construct(kmp_i18n_msg_CnsLoopIncrZeroProhibited, ct_pdo,
loc);
}
}
if (bounds->comparison == comparison_t::comp_not_eq) {
// We can convert this to < or >, depends on the sign of the step:
if (bounds->step > 0) {
bounds->comparison = comparison_t::comp_less;
} else {
bounds->comparison = comparison_t::comp_greater;
}
}
if (bounds->comparison == comparison_t::comp_less) {
// Note: ub0 can be unsigned. Should be Ok to hit overflow here,
// because ub0 + ub1*j should be still positive (otherwise loop was not
// well formed)
bounds->ub0 -= 1;
bounds->comparison = comparison_t::comp_less_or_eq;
} else if (bounds->comparison == comparison_t::comp_greater) {
bounds->ub0 += 1;
bounds->comparison = comparison_t::comp_greater_or_eq;
}
}
// Canonicalize loop nest. original_bounds_nest is an array of length n.
void kmp_canonicalize_loop_nest(ident_t *loc,
/*in/out*/ bounds_info_t *original_bounds_nest,
kmp_index_t n) {
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(original_bounds_nest[ind]);
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
kmp_canonicalize_one_loop_XX<kmp_int32>(
loc,
/*in/out*/ (bounds_infoXX_template<kmp_int32> *)(bounds));
break;
case loop_type_t::loop_type_uint32:
kmp_canonicalize_one_loop_XX<kmp_uint32>(
loc,
/*in/out*/ (bounds_infoXX_template<kmp_uint32> *)(bounds));
break;
case loop_type_t::loop_type_int64:
kmp_canonicalize_one_loop_XX<kmp_int64>(
loc,
/*in/out*/ (bounds_infoXX_template<kmp_int64> *)(bounds));
break;
case loop_type_t::loop_type_uint64:
kmp_canonicalize_one_loop_XX<kmp_uint64>(
loc,
/*in/out*/ (bounds_infoXX_template<kmp_uint64> *)(bounds));
break;
default:
KMP_ASSERT(false);
}
}
}
//----------Calculating trip count on one level-------------------------------
// Calculate trip count on this loop level.
// We do this either for a rectangular loop nest,
// or after an adjustment bringing the loops to a parallelepiped shape.
// This number should not depend on the value of outer IV
// even if the formular has lb1 and ub1.
// Note: for non-rectangular loops don't use span for this, it's too big.
template <typename T>
kmp_loop_nest_iv_t kmp_calculate_trip_count_XX(
/*in/out*/ bounds_infoXX_template<T> *bounds) {
if (bounds->comparison == comparison_t::comp_less_or_eq) {
if (bounds->ub0 < bounds->lb0) {
// Note: after this we don't need to calculate inner loops,
// but that should be an edge case:
bounds->trip_count = 0;
} else {
// ub - lb may exceed signed type range; we need to cast to
// kmp_loop_nest_iv_t anyway
bounds->trip_count =
static_cast<kmp_loop_nest_iv_t>(bounds->ub0 - bounds->lb0) /
__kmp_abs(bounds->step) +
1;
}
} else if (bounds->comparison == comparison_t::comp_greater_or_eq) {
if (bounds->lb0 < bounds->ub0) {
// Note: after this we don't need to calculate inner loops,
// but that should be an edge case:
bounds->trip_count = 0;
} else {
// lb - ub may exceed signed type range; we need to cast to
// kmp_loop_nest_iv_t anyway
bounds->trip_count =
static_cast<kmp_loop_nest_iv_t>(bounds->lb0 - bounds->ub0) /
__kmp_abs(bounds->step) +
1;
}
} else {
KMP_ASSERT(false);
}
return bounds->trip_count;
}
// Calculate trip count on this loop level.
kmp_loop_nest_iv_t kmp_calculate_trip_count(/*in/out*/ bounds_info_t *bounds) {
kmp_loop_nest_iv_t trip_count = 0;
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
trip_count = kmp_calculate_trip_count_XX<kmp_int32>(
/*in/out*/ (bounds_infoXX_template<kmp_int32> *)(bounds));
break;
case loop_type_t::loop_type_uint32:
trip_count = kmp_calculate_trip_count_XX<kmp_uint32>(
/*in/out*/ (bounds_infoXX_template<kmp_uint32> *)(bounds));
break;
case loop_type_t::loop_type_int64:
trip_count = kmp_calculate_trip_count_XX<kmp_int64>(
/*in/out*/ (bounds_infoXX_template<kmp_int64> *)(bounds));
break;
case loop_type_t::loop_type_uint64:
trip_count = kmp_calculate_trip_count_XX<kmp_uint64>(
/*in/out*/ (bounds_infoXX_template<kmp_uint64> *)(bounds));
break;
default:
KMP_ASSERT(false);
}
return trip_count;
}
//----------Trim original iv according to its type----------------------------
// Trim original iv according to its type.
// Return kmp_uint64 value which can be easily used in all internal calculations
// And can be statically cast back to original type in user code.
kmp_uint64 kmp_fix_iv(loop_type_t loop_iv_type, kmp_uint64 original_iv) {
kmp_uint64 res = 0;
switch (loop_iv_type) {
case loop_type_t::loop_type_int8:
res = static_cast<kmp_uint64>(static_cast<kmp_int8>(original_iv));
break;
case loop_type_t::loop_type_uint8:
res = static_cast<kmp_uint64>(static_cast<kmp_uint8>(original_iv));
break;
case loop_type_t::loop_type_int16:
res = static_cast<kmp_uint64>(static_cast<kmp_int16>(original_iv));
break;
case loop_type_t::loop_type_uint16:
res = static_cast<kmp_uint64>(static_cast<kmp_uint16>(original_iv));
break;
case loop_type_t::loop_type_int32:
res = static_cast<kmp_uint64>(static_cast<kmp_int32>(original_iv));
break;
case loop_type_t::loop_type_uint32:
res = static_cast<kmp_uint64>(static_cast<kmp_uint32>(original_iv));
break;
case loop_type_t::loop_type_int64:
res = static_cast<kmp_uint64>(static_cast<kmp_int64>(original_iv));
break;
case loop_type_t::loop_type_uint64:
res = static_cast<kmp_uint64>(original_iv);
break;
default:
KMP_ASSERT(false);
}
return res;
}
//----------Compare two IVs (remember they have a type)-----------------------
bool kmp_ivs_eq(loop_type_t loop_iv_type, kmp_uint64 original_iv1,
kmp_uint64 original_iv2) {
bool res = false;
switch (loop_iv_type) {
case loop_type_t::loop_type_int8:
res = static_cast<kmp_int8>(original_iv1) ==
static_cast<kmp_int8>(original_iv2);
break;
case loop_type_t::loop_type_uint8:
res = static_cast<kmp_uint8>(original_iv1) ==
static_cast<kmp_uint8>(original_iv2);
break;
case loop_type_t::loop_type_int16:
res = static_cast<kmp_int16>(original_iv1) ==
static_cast<kmp_int16>(original_iv2);
break;
case loop_type_t::loop_type_uint16:
res = static_cast<kmp_uint16>(original_iv1) ==
static_cast<kmp_uint16>(original_iv2);
break;
case loop_type_t::loop_type_int32:
res = static_cast<kmp_int32>(original_iv1) ==
static_cast<kmp_int32>(original_iv2);
break;
case loop_type_t::loop_type_uint32:
res = static_cast<kmp_uint32>(original_iv1) ==
static_cast<kmp_uint32>(original_iv2);
break;
case loop_type_t::loop_type_int64:
res = static_cast<kmp_int64>(original_iv1) ==
static_cast<kmp_int64>(original_iv2);
break;
case loop_type_t::loop_type_uint64:
res = static_cast<kmp_uint64>(original_iv1) ==
static_cast<kmp_uint64>(original_iv2);
break;
default:
KMP_ASSERT(false);
}
return res;
}
//----------Calculate original iv on one level--------------------------------
// Return true if the point fits into upper bounds on this level,
// false otherwise
template <typename T>
bool kmp_iv_is_in_upper_bound_XX(const bounds_infoXX_template<T> *bounds,
const kmp_point_t original_ivs,
kmp_index_t ind) {
T iv = static_cast<T>(original_ivs[ind]);
T outer_iv = static_cast<T>(original_ivs[bounds->outer_iv]);
if (((bounds->comparison == comparison_t::comp_less_or_eq) &&
(iv > (bounds->ub0 + bounds->ub1 * outer_iv))) ||
((bounds->comparison == comparison_t::comp_greater_or_eq) &&
(iv < (bounds->ub0 + bounds->ub1 * outer_iv)))) {
// The calculated point is outside of loop upper boundary:
return false;
}
return true;
}
// Calculate one iv corresponding to iteration on the level ind.
// Return true if it fits into lower-upper bounds on this level
// (if not, we need to re-calculate)
template <typename T>
bool kmp_calc_one_iv_XX(const bounds_infoXX_template<T> *bounds,
/*in/out*/ kmp_point_t original_ivs,
const kmp_iterations_t iterations, kmp_index_t ind,
bool start_with_lower_bound, bool checkBounds) {
kmp_uint64 temp = 0;
T outer_iv = static_cast<T>(original_ivs[bounds->outer_iv]);
if (start_with_lower_bound) {
// we moved to the next iteration on one of outer loops, should start
// with the lower bound here:
temp = bounds->lb0 + bounds->lb1 * outer_iv;
} else {
auto iteration = iterations[ind];
temp = bounds->lb0 + bounds->lb1 * outer_iv + iteration * bounds->step;
}
// Now trim original iv according to its type:
original_ivs[ind] = kmp_fix_iv(bounds->loop_iv_type, temp);
if (checkBounds) {
return kmp_iv_is_in_upper_bound_XX(bounds, original_ivs, ind);
} else {
return true;
}
}
bool kmp_calc_one_iv(const bounds_info_t *bounds,
/*in/out*/ kmp_point_t original_ivs,
const kmp_iterations_t iterations, kmp_index_t ind,
bool start_with_lower_bound, bool checkBounds) {
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
return kmp_calc_one_iv_XX<kmp_int32>(
(bounds_infoXX_template<kmp_int32> *)(bounds),
/*in/out*/ original_ivs, iterations, ind, start_with_lower_bound,
checkBounds);
break;
case loop_type_t::loop_type_uint32:
return kmp_calc_one_iv_XX<kmp_uint32>(
(bounds_infoXX_template<kmp_uint32> *)(bounds),
/*in/out*/ original_ivs, iterations, ind, start_with_lower_bound,
checkBounds);
break;
case loop_type_t::loop_type_int64:
return kmp_calc_one_iv_XX<kmp_int64>(
(bounds_infoXX_template<kmp_int64> *)(bounds),
/*in/out*/ original_ivs, iterations, ind, start_with_lower_bound,
checkBounds);
break;
case loop_type_t::loop_type_uint64:
return kmp_calc_one_iv_XX<kmp_uint64>(
(bounds_infoXX_template<kmp_uint64> *)(bounds),
/*in/out*/ original_ivs, iterations, ind, start_with_lower_bound,
checkBounds);
break;
default:
KMP_ASSERT(false);
return false;
}
}
//----------Calculate original iv on one level for rectangular loop nest------
// Calculate one iv corresponding to iteration on the level ind.
// Return true if it fits into lower-upper bounds on this level
// (if not, we need to re-calculate)
template <typename T>
void kmp_calc_one_iv_rectang_XX(const bounds_infoXX_template<T> *bounds,
/*in/out*/ kmp_uint64 *original_ivs,
const kmp_iterations_t iterations,
kmp_index_t ind) {
auto iteration = iterations[ind];
kmp_uint64 temp =
bounds->lb0 +
bounds->lb1 * static_cast<T>(original_ivs[bounds->outer_iv]) +
iteration * bounds->step;
// Now trim original iv according to its type:
original_ivs[ind] = kmp_fix_iv(bounds->loop_iv_type, temp);
}
void kmp_calc_one_iv_rectang(const bounds_info_t *bounds,
/*in/out*/ kmp_uint64 *original_ivs,
const kmp_iterations_t iterations,
kmp_index_t ind) {
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
kmp_calc_one_iv_rectang_XX<kmp_int32>(
(bounds_infoXX_template<kmp_int32> *)(bounds),
/*in/out*/ original_ivs, iterations, ind);
break;
case loop_type_t::loop_type_uint32:
kmp_calc_one_iv_rectang_XX<kmp_uint32>(
(bounds_infoXX_template<kmp_uint32> *)(bounds),
/*in/out*/ original_ivs, iterations, ind);
break;
case loop_type_t::loop_type_int64:
kmp_calc_one_iv_rectang_XX<kmp_int64>(
(bounds_infoXX_template<kmp_int64> *)(bounds),
/*in/out*/ original_ivs, iterations, ind);
break;
case loop_type_t::loop_type_uint64:
kmp_calc_one_iv_rectang_XX<kmp_uint64>(
(bounds_infoXX_template<kmp_uint64> *)(bounds),
/*in/out*/ original_ivs, iterations, ind);
break;
default:
KMP_ASSERT(false);
}
}
//----------------------------------------------------------------------------
// Rectangular loop nest
//----------------------------------------------------------------------------
//----------Canonicalize loop nest and calculate trip count-------------------
// Canonicalize loop nest and calculate overall trip count.
// "bounds_nest" has to be allocated per thread.
// API will modify original bounds_nest array to bring it to a canonical form
// (only <= and >=, no !=, <, >). If the original loop nest was already in a
// canonical form there will be no changes to bounds in bounds_nest array
// (only trip counts will be calculated).
// Returns trip count of overall space.
extern "C" kmp_loop_nest_iv_t
__kmpc_process_loop_nest_rectang(ident_t *loc, kmp_int32 gtid,
/*in/out*/ bounds_info_t *original_bounds_nest,
kmp_index_t n) {
kmp_canonicalize_loop_nest(loc, /*in/out*/ original_bounds_nest, n);
kmp_loop_nest_iv_t total = 1;
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(original_bounds_nest[ind]);
kmp_loop_nest_iv_t trip_count = kmp_calculate_trip_count(/*in/out*/ bounds);
total *= trip_count;
}
return total;
}
//----------Calculate old induction variables---------------------------------
// Calculate old induction variables corresponding to overall new_iv.
// Note: original IV will be returned as if it had kmp_uint64 type,
// will have to be converted to original type in user code.
// Note: trip counts should be already calculated by
// __kmpc_process_loop_nest_rectang.
// OMPTODO: special case 2, 3 nested loops: either do different
// interface without array or possibly template this over n
extern "C" void
__kmpc_calc_original_ivs_rectang(ident_t *loc, kmp_loop_nest_iv_t new_iv,
const bounds_info_t *original_bounds_nest,
/*out*/ kmp_uint64 *original_ivs,
kmp_index_t n) {
CollapseAllocator<kmp_loop_nest_iv_t> iterations(n);
// First, calc corresponding iteration in every original loop:
for (kmp_index_t ind = n; ind > 0;) {
--ind;
auto bounds = &(original_bounds_nest[ind]);
// should be optimized to OPDIVREM:
auto temp = new_iv / bounds->trip_count;
auto iteration = new_iv % bounds->trip_count;
new_iv = temp;
iterations[ind] = iteration;
}
KMP_ASSERT(new_iv == 0);
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(original_bounds_nest[ind]);
kmp_calc_one_iv_rectang(bounds, /*in/out*/ original_ivs, iterations, ind);
}
}
//----------------------------------------------------------------------------
// Non-rectangular loop nest
//----------------------------------------------------------------------------
//----------Calculate maximum possible span of iv values on one level---------
// Calculate span for IV on this loop level for "<=" case.
// Note: it's for <= on this loop nest level, so lower bound should be smallest
// value, upper bound should be the biggest value. If the loop won't execute,
// 'smallest' may be bigger than 'biggest', but we'd better not switch them
// around.
template <typename T>
void kmp_calc_span_lessoreq_XX(
/* in/out*/ bounds_info_internalXX_template<T> *bounds,
/* in/out*/ bounds_info_internal_t *bounds_nest) {
typedef typename traits_t<T>::unsigned_t UT;
// typedef typename traits_t<T>::signed_t ST;
// typedef typename big_span_t span_t;
typedef T span_t;
auto &bbounds = bounds->b;
if ((bbounds.lb1 != 0) || (bbounds.ub1 != 0)) {
// This dimention depends on one of previous ones; can't be the outermost
// one.
bounds_info_internalXX_template<T> *previous =
reinterpret_cast<bounds_info_internalXX_template<T> *>(
&(bounds_nest[bbounds.outer_iv]));
// OMPTODO: assert that T is compatible with loop variable type on
// 'previous' loop
{
span_t bound_candidate1 =
bbounds.lb0 + bbounds.lb1 * previous->span_smallest;
span_t bound_candidate2 =
bbounds.lb0 + bbounds.lb1 * previous->span_biggest;
if (bound_candidate1 < bound_candidate2) {
bounds->span_smallest = bound_candidate1;
} else {
bounds->span_smallest = bound_candidate2;
}
}
{
// We can't adjust the upper bound with respect to step, because
// lower bound might be off after adjustments
span_t bound_candidate1 =
bbounds.ub0 + bbounds.ub1 * previous->span_smallest;
span_t bound_candidate2 =
bbounds.ub0 + bbounds.ub1 * previous->span_biggest;
if (bound_candidate1 < bound_candidate2) {
bounds->span_biggest = bound_candidate2;
} else {
bounds->span_biggest = bound_candidate1;
}
}
} else {
// Rectangular:
bounds->span_smallest = bbounds.lb0;
bounds->span_biggest = bbounds.ub0;
}
if (!bounds->loop_bounds_adjusted) {
// Here it's safe to reduce the space to the multiply of step.
// OMPTODO: check if the formular is correct.
// Also check if it would be safe to do this if we didn't adjust left side.
bounds->span_biggest -=
(static_cast<UT>(bbounds.ub0 - bbounds.lb0)) % bbounds.step; // abs?
}
}
// Calculate span for IV on this loop level for ">=" case.
template <typename T>
void kmp_calc_span_greateroreq_XX(
/* in/out*/ bounds_info_internalXX_template<T> *bounds,
/* in/out*/ bounds_info_internal_t *bounds_nest) {
typedef typename traits_t<T>::unsigned_t UT;
// typedef typename traits_t<T>::signed_t ST;
// typedef typename big_span_t span_t;
typedef T span_t;
auto &bbounds = bounds->b;
if ((bbounds.lb1 != 0) || (bbounds.ub1 != 0)) {
// This dimention depends on one of previous ones; can't be the outermost
// one.
bounds_info_internalXX_template<T> *previous =
reinterpret_cast<bounds_info_internalXX_template<T> *>(
&(bounds_nest[bbounds.outer_iv]));
// OMPTODO: assert that T is compatible with loop variable type on
// 'previous' loop
{
span_t bound_candidate1 =
bbounds.lb0 + bbounds.lb1 * previous->span_smallest;
span_t bound_candidate2 =
bbounds.lb0 + bbounds.lb1 * previous->span_biggest;
if (bound_candidate1 >= bound_candidate2) {
bounds->span_smallest = bound_candidate1;
} else {
bounds->span_smallest = bound_candidate2;
}
}
{
// We can't adjust the upper bound with respect to step, because
// lower bound might be off after adjustments
span_t bound_candidate1 =
bbounds.ub0 + bbounds.ub1 * previous->span_smallest;
span_t bound_candidate2 =
bbounds.ub0 + bbounds.ub1 * previous->span_biggest;
if (bound_candidate1 >= bound_candidate2) {
bounds->span_biggest = bound_candidate2;
} else {
bounds->span_biggest = bound_candidate1;
}
}
} else {
// Rectangular:
bounds->span_biggest = bbounds.lb0;
bounds->span_smallest = bbounds.ub0;
}
if (!bounds->loop_bounds_adjusted) {
// Here it's safe to reduce the space to the multiply of step.
// OMPTODO: check if the formular is correct.
// Also check if it would be safe to do this if we didn't adjust left side.
bounds->span_biggest -=
(static_cast<UT>(bbounds.ub0 - bbounds.lb0)) % bbounds.step; // abs?
}
}
// Calculate maximum possible span for IV on this loop level.
template <typename T>
void kmp_calc_span_XX(
/* in/out*/ bounds_info_internalXX_template<T> *bounds,
/* in/out*/ bounds_info_internal_t *bounds_nest) {
if (bounds->b.comparison == comparison_t::comp_less_or_eq) {
kmp_calc_span_lessoreq_XX(/* in/out*/ bounds, /* in/out*/ bounds_nest);
} else {
KMP_ASSERT(bounds->b.comparison == comparison_t::comp_greater_or_eq);
kmp_calc_span_greateroreq_XX(/* in/out*/ bounds, /* in/out*/ bounds_nest);
}
}
//----------All initial processing of the loop nest---------------------------
// Calculate new bounds for this loop level.
// To be able to work with the nest we need to get it to a parallelepiped shape.
// We need to stay in the original range of values, so that there will be no
// overflow, for that we'll adjust both upper and lower bounds as needed.
template <typename T>
void kmp_calc_new_bounds_XX(
/* in/out*/ bounds_info_internalXX_template<T> *bounds,
/* in/out*/ bounds_info_internal_t *bounds_nest) {
auto &bbounds = bounds->b;
if (bbounds.lb1 == bbounds.ub1) {
// Already parallel, no need to adjust:
bounds->loop_bounds_adjusted = false;
} else {
bounds->loop_bounds_adjusted = true;
T old_lb1 = bbounds.lb1;
T old_ub1 = bbounds.ub1;
if (__kmp_sign(old_lb1) != __kmp_sign(old_ub1)) {
// With this shape we can adjust to a rectangle:
bbounds.lb1 = 0;
bbounds.ub1 = 0;
} else {
// get upper and lower bounds to be parallel
// with values in the old range.
// Note: abs didn't work here.
if (((old_lb1 < 0) && (old_lb1 < old_ub1)) ||
((old_lb1 > 0) && (old_lb1 > old_ub1))) {
bbounds.lb1 = old_ub1;
} else {
bbounds.ub1 = old_lb1;
}
}
// Now need to adjust lb0, ub0, otherwise in some cases space will shrink.
// The idea here that for this IV we are now getting the same span
// irrespective of the previous IV value.
bounds_info_internalXX_template<T> *previous =
reinterpret_cast<bounds_info_internalXX_template<T> *>(
&bounds_nest[bbounds.outer_iv]);
if (bbounds.comparison == comparison_t::comp_less_or_eq) {
if (old_lb1 < bbounds.lb1) {
KMP_ASSERT(old_lb1 < 0);
// The length is good on outer_iv biggest number,
// can use it to find where to move the lower bound:
T sub = (bbounds.lb1 - old_lb1) * previous->span_biggest;
bbounds.lb0 -= sub; // OMPTODO: what if it'll go out of unsigned space?
// e.g. it was 0?? (same below)
} else if (old_lb1 > bbounds.lb1) {
// still need to move lower bound:
T add = (old_lb1 - bbounds.lb1) * previous->span_smallest;
bbounds.lb0 += add;
}
if (old_ub1 > bbounds.ub1) {
KMP_ASSERT(old_ub1 > 0);
// The length is good on outer_iv biggest number,
// can use it to find where to move upper bound:
T add = (old_ub1 - bbounds.ub1) * previous->span_biggest;
bbounds.ub0 += add;
} else if (old_ub1 < bbounds.ub1) {
// still need to move upper bound:
T sub = (bbounds.ub1 - old_ub1) * previous->span_smallest;
bbounds.ub0 -= sub;
}
} else {
KMP_ASSERT(bbounds.comparison == comparison_t::comp_greater_or_eq);
if (old_lb1 < bbounds.lb1) {
KMP_ASSERT(old_lb1 < 0);
T sub = (bbounds.lb1 - old_lb1) * previous->span_smallest;
bbounds.lb0 -= sub;
} else if (old_lb1 > bbounds.lb1) {
T add = (old_lb1 - bbounds.lb1) * previous->span_biggest;
bbounds.lb0 += add;
}
if (old_ub1 > bbounds.ub1) {
KMP_ASSERT(old_ub1 > 0);
T add = (old_ub1 - bbounds.ub1) * previous->span_smallest;
bbounds.ub0 += add;
} else if (old_ub1 < bbounds.ub1) {
T sub = (bbounds.ub1 - old_ub1) * previous->span_biggest;
bbounds.ub0 -= sub;
}
}
}
}
// Do all processing for one canonicalized loop in the nest
// (assuming that outer loops already were processed):
template <typename T>
kmp_loop_nest_iv_t kmp_process_one_loop_XX(
/* in/out*/ bounds_info_internalXX_template<T> *bounds,
/*in/out*/ bounds_info_internal_t *bounds_nest) {
kmp_calc_new_bounds_XX(/* in/out*/ bounds, /* in/out*/ bounds_nest);
kmp_calc_span_XX(/* in/out*/ bounds, /* in/out*/ bounds_nest);
return kmp_calculate_trip_count_XX(/*in/out*/ &(bounds->b));
}
// Non-rectangular loop nest, canonicalized to use <= or >=.
// Process loop nest to have a parallelepiped shape,
// calculate biggest spans for IV's on all levels and calculate overall trip
// count. "bounds_nest" has to be allocated per thread.
// Returns overall trip count (for adjusted space).
kmp_loop_nest_iv_t kmp_process_loop_nest(
/*in/out*/ bounds_info_internal_t *bounds_nest, kmp_index_t n) {
kmp_loop_nest_iv_t total = 1;
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(bounds_nest[ind]);
kmp_loop_nest_iv_t trip_count = 0;
switch (bounds->b.loop_type) {
case loop_type_t::loop_type_int32:
trip_count = kmp_process_one_loop_XX<kmp_int32>(
/*in/out*/ (bounds_info_internalXX_template<kmp_int32> *)(bounds),
/*in/out*/ bounds_nest);
break;
case loop_type_t::loop_type_uint32:
trip_count = kmp_process_one_loop_XX<kmp_uint32>(
/*in/out*/ (bounds_info_internalXX_template<kmp_uint32> *)(bounds),
/*in/out*/ bounds_nest);
break;
case loop_type_t::loop_type_int64:
trip_count = kmp_process_one_loop_XX<kmp_int64>(
/*in/out*/ (bounds_info_internalXX_template<kmp_int64> *)(bounds),
/*in/out*/ bounds_nest);
break;
case loop_type_t::loop_type_uint64:
trip_count = kmp_process_one_loop_XX<kmp_uint64>(
/*in/out*/ (bounds_info_internalXX_template<kmp_uint64> *)(bounds),
/*in/out*/ bounds_nest);
break;
default:
KMP_ASSERT(false);
}
total *= trip_count;
}
return total;
}
//----------Calculate iterations (in the original or updated space)-----------
// Calculate number of iterations in original or updated space resulting in
// original_ivs[ind] (only on this level, non-negative)
// (not counting initial iteration)
template <typename T>
kmp_loop_nest_iv_t
kmp_calc_number_of_iterations_XX(const bounds_infoXX_template<T> *bounds,
const kmp_point_t original_ivs,
kmp_index_t ind) {
kmp_loop_nest_iv_t iterations = 0;
if (bounds->comparison == comparison_t::comp_less_or_eq) {
iterations =
(static_cast<T>(original_ivs[ind]) - bounds->lb0 -
bounds->lb1 * static_cast<T>(original_ivs[bounds->outer_iv])) /
__kmp_abs(bounds->step);
} else {
KMP_DEBUG_ASSERT(bounds->comparison == comparison_t::comp_greater_or_eq);
iterations = (bounds->lb0 +
bounds->lb1 * static_cast<T>(original_ivs[bounds->outer_iv]) -
static_cast<T>(original_ivs[ind])) /
__kmp_abs(bounds->step);
}
return iterations;
}
// Calculate number of iterations in the original or updated space resulting in
// original_ivs[ind] (only on this level, non-negative)
kmp_loop_nest_iv_t kmp_calc_number_of_iterations(const bounds_info_t *bounds,
const kmp_point_t original_ivs,
kmp_index_t ind) {
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
return kmp_calc_number_of_iterations_XX<kmp_int32>(
(bounds_infoXX_template<kmp_int32> *)(bounds), original_ivs, ind);
break;
case loop_type_t::loop_type_uint32:
return kmp_calc_number_of_iterations_XX<kmp_uint32>(
(bounds_infoXX_template<kmp_uint32> *)(bounds), original_ivs, ind);
break;
case loop_type_t::loop_type_int64:
return kmp_calc_number_of_iterations_XX<kmp_int64>(
(bounds_infoXX_template<kmp_int64> *)(bounds), original_ivs, ind);
break;
case loop_type_t::loop_type_uint64:
return kmp_calc_number_of_iterations_XX<kmp_uint64>(
(bounds_infoXX_template<kmp_uint64> *)(bounds), original_ivs, ind);
break;
default:
KMP_ASSERT(false);
return 0;
}
}
//----------Calculate new iv corresponding to original ivs--------------------
// We got a point in the original loop nest.
// Take updated bounds and calculate what new_iv will correspond to this point.
// When we are getting original IVs from new_iv, we have to adjust to fit into
// original loops bounds. Getting new_iv for the adjusted original IVs will help
// with making more chunks non-empty.
kmp_loop_nest_iv_t
kmp_calc_new_iv_from_original_ivs(const bounds_info_internal_t *bounds_nest,
const kmp_point_t original_ivs,
kmp_index_t n) {
kmp_loop_nest_iv_t new_iv = 0;
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(bounds_nest[ind].b);
new_iv = new_iv * bounds->trip_count +
kmp_calc_number_of_iterations(bounds, original_ivs, ind);
}
return new_iv;
}
//----------Calculate original ivs for provided iterations--------------------
// Calculate original IVs for provided iterations, assuming iterations are
// calculated in the original space.
// Loop nest is in canonical form (with <= / >=).
bool kmp_calc_original_ivs_from_iterations(
const bounds_info_t *original_bounds_nest, kmp_index_t n,
/*in/out*/ kmp_point_t original_ivs,
/*in/out*/ kmp_iterations_t iterations, kmp_index_t ind) {
kmp_index_t lengthened_ind = n;
for (; ind < n;) {
auto bounds = &(original_bounds_nest[ind]);
bool good = kmp_calc_one_iv(bounds, /*in/out*/ original_ivs, iterations,
ind, (lengthened_ind < ind), true);
if (!good) {
// The calculated iv value is too big (or too small for >=):
if (ind == 0) {
// Space is empty:
return false;
} else {
// Go to next iteration on the outer loop:
--ind;
++iterations[ind];
lengthened_ind = ind;
for (kmp_index_t i = ind + 1; i < n; ++i) {
iterations[i] = 0;
}
continue;
}
}
++ind;
}
return true;
}
//----------Calculate original ivs for the beginning of the loop nest---------
// Calculate IVs for the beginning of the loop nest.
// Note: lower bounds of all loops may not work -
// if on some of the iterations of the outer loops inner loops are empty.
// Loop nest is in canonical form (with <= / >=).
bool kmp_calc_original_ivs_for_start(const bounds_info_t *original_bounds_nest,
kmp_index_t n,
/*out*/ kmp_point_t original_ivs) {
// Iterations in the original space, multiplied by step:
CollapseAllocator<kmp_loop_nest_iv_t> iterations(n);
for (kmp_index_t ind = n; ind > 0;) {
--ind;
iterations[ind] = 0;
}
// Now calculate the point:
bool b = kmp_calc_original_ivs_from_iterations(original_bounds_nest, n,
/*in/out*/ original_ivs,
/*in/out*/ iterations, 0);
return b;
}
//----------Calculate next point in the original loop space-------------------
// From current set of original IVs calculate next point.
// Return false if there is no next point in the loop bounds.
bool kmp_calc_next_original_ivs(const bounds_info_t *original_bounds_nest,
kmp_index_t n, const kmp_point_t original_ivs,
/*out*/ kmp_point_t next_original_ivs) {
// Iterations in the original space, multiplied by step (so can be negative):
CollapseAllocator<kmp_loop_nest_iv_t> iterations(n);
// First, calc corresponding iteration in every original loop:
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(original_bounds_nest[ind]);
iterations[ind] = kmp_calc_number_of_iterations(bounds, original_ivs, ind);
}
for (kmp_index_t ind = 0; ind < n; ++ind) {
next_original_ivs[ind] = original_ivs[ind];
}
// Next add one step to the iterations on the inner-most level, and see if we
// need to move up the nest:
kmp_index_t ind = n - 1;
++iterations[ind];
bool b = kmp_calc_original_ivs_from_iterations(
original_bounds_nest, n, /*in/out*/ next_original_ivs, iterations, ind);
return b;
}
//----------Calculate chunk end in the original loop space--------------------
// For one level calculate old induction variable corresponding to overall
// new_iv for the chunk end.
// Return true if it fits into upper bound on this level
// (if not, we need to re-calculate)
template <typename T>
bool kmp_calc_one_iv_for_chunk_end_XX(
const bounds_infoXX_template<T> *bounds,
const bounds_infoXX_template<T> *updated_bounds,
/*in/out*/ kmp_point_t original_ivs, const kmp_iterations_t iterations,
kmp_index_t ind, bool start_with_lower_bound, bool compare_with_start,
const kmp_point_t original_ivs_start) {
// typedef std::conditional<std::is_signed<T>::value, kmp_int64, kmp_uint64>
// big_span_t;
// OMPTODO: is it good enough, or do we need ST or do we need big_span_t?
T temp = 0;
T outer_iv = static_cast<T>(original_ivs[bounds->outer_iv]);
if (start_with_lower_bound) {
// we moved to the next iteration on one of outer loops, may as well use
// the lower bound here:
temp = bounds->lb0 + bounds->lb1 * outer_iv;
} else {
// Start in expanded space, but:
// - we need to hit original space lower bound, so need to account for
// that
// - we have to go into original space, even if that means adding more
// iterations than was planned
// - we have to go past (or equal to) previous point (which is the chunk
// starting point)
auto iteration = iterations[ind];
auto step = bounds->step;
// In case of >= it's negative:
auto accountForStep =
((bounds->lb0 + bounds->lb1 * outer_iv) -
(updated_bounds->lb0 + updated_bounds->lb1 * outer_iv)) %
step;
temp = updated_bounds->lb0 + updated_bounds->lb1 * outer_iv +
accountForStep + iteration * step;
if (((bounds->comparison == comparison_t::comp_less_or_eq) &&
(temp < (bounds->lb0 + bounds->lb1 * outer_iv))) ||
((bounds->comparison == comparison_t::comp_greater_or_eq) &&
(temp > (bounds->lb0 + bounds->lb1 * outer_iv)))) {
// Too small (or too big), didn't reach the original lower bound. Use
// heuristic:
temp = bounds->lb0 + bounds->lb1 * outer_iv + iteration / 2 * step;
}
if (compare_with_start) {
T start = static_cast<T>(original_ivs_start[ind]);
temp = kmp_fix_iv(bounds->loop_iv_type, temp);
// On all previous levels start of the chunk is same as the end, need to
// be really careful here:
if (((bounds->comparison == comparison_t::comp_less_or_eq) &&
(temp < start)) ||
((bounds->comparison == comparison_t::comp_greater_or_eq) &&
(temp > start))) {
// End of the chunk can't be smaller (for >= bigger) than it's start.
// Use heuristic:
temp = start + iteration / 4 * step;
}
}
}
original_ivs[ind] = temp = kmp_fix_iv(bounds->loop_iv_type, temp);
if (((bounds->comparison == comparison_t::comp_less_or_eq) &&
(temp > (bounds->ub0 + bounds->ub1 * outer_iv))) ||
((bounds->comparison == comparison_t::comp_greater_or_eq) &&
(temp < (bounds->ub0 + bounds->ub1 * outer_iv)))) {
// Too big (or too small for >=).
return false;
}
return true;
}
// For one level calculate old induction variable corresponding to overall
// new_iv for the chunk end.
bool kmp_calc_one_iv_for_chunk_end(const bounds_info_t *bounds,
const bounds_info_t *updated_bounds,
/*in/out*/ kmp_point_t original_ivs,
const kmp_iterations_t iterations,
kmp_index_t ind, bool start_with_lower_bound,
bool compare_with_start,
const kmp_point_t original_ivs_start) {
switch (bounds->loop_type) {
case loop_type_t::loop_type_int32:
return kmp_calc_one_iv_for_chunk_end_XX<kmp_int32>(
(bounds_infoXX_template<kmp_int32> *)(bounds),
(bounds_infoXX_template<kmp_int32> *)(updated_bounds),
/*in/out*/
original_ivs, iterations, ind, start_with_lower_bound,
compare_with_start, original_ivs_start);
break;
case loop_type_t::loop_type_uint32:
return kmp_calc_one_iv_for_chunk_end_XX<kmp_uint32>(
(bounds_infoXX_template<kmp_uint32> *)(bounds),
(bounds_infoXX_template<kmp_uint32> *)(updated_bounds),
/*in/out*/
original_ivs, iterations, ind, start_with_lower_bound,
compare_with_start, original_ivs_start);
break;
case loop_type_t::loop_type_int64:
return kmp_calc_one_iv_for_chunk_end_XX<kmp_int64>(
(bounds_infoXX_template<kmp_int64> *)(bounds),
(bounds_infoXX_template<kmp_int64> *)(updated_bounds),
/*in/out*/
original_ivs, iterations, ind, start_with_lower_bound,
compare_with_start, original_ivs_start);
break;
case loop_type_t::loop_type_uint64:
return kmp_calc_one_iv_for_chunk_end_XX<kmp_uint64>(
(bounds_infoXX_template<kmp_uint64> *)(bounds),
(bounds_infoXX_template<kmp_uint64> *)(updated_bounds),
/*in/out*/
original_ivs, iterations, ind, start_with_lower_bound,
compare_with_start, original_ivs_start);
break;
default:
KMP_ASSERT(false);
return false;
}
}
// Calculate old induction variables corresponding to overall new_iv for the
// chunk end. If due to space extension we are getting old IVs outside of the
// boundaries, bring them into the boundaries. Need to do this in the runtime,
// esp. on the lower bounds side. When getting result need to make sure that the
// new chunk starts at next position to old chunk, not overlaps with it (this is
// done elsewhere), and need to make sure end of the chunk is further than the
// beginning of the chunk. We don't need an exact ending point here, just
// something more-or-less close to the desired chunk length, bigger is fine
// (smaller would be fine, but we risk going into infinite loop, so do smaller
// only at the very end of the space). result: false if could not find the
// ending point in the original loop space. In this case the caller can use
// original upper bounds as the end of the chunk. Chunk won't be empty, because
// it'll have at least the starting point, which is by construction in the
// original space.
bool kmp_calc_original_ivs_for_chunk_end(
const bounds_info_t *original_bounds_nest, kmp_index_t n,
const bounds_info_internal_t *updated_bounds_nest,
const kmp_point_t original_ivs_start, kmp_loop_nest_iv_t new_iv,
/*out*/ kmp_point_t original_ivs) {
// Iterations in the expanded space:
CollapseAllocator<kmp_loop_nest_iv_t> iterations(n);
// First, calc corresponding iteration in every modified loop:
for (kmp_index_t ind = n; ind > 0;) {
--ind;
auto &updated_bounds = updated_bounds_nest[ind];
// should be optimized to OPDIVREM:
auto new_ind = new_iv / updated_bounds.b.trip_count;
auto iteration = new_iv % updated_bounds.b.trip_count;
new_iv = new_ind;
iterations[ind] = iteration;
}
KMP_DEBUG_ASSERT(new_iv == 0);
kmp_index_t lengthened_ind = n;
kmp_index_t equal_ind = -1;
// Next calculate the point, but in original loop nest.
for (kmp_index_t ind = 0; ind < n;) {
auto bounds = &(original_bounds_nest[ind]);
auto updated_bounds = &(updated_bounds_nest[ind].b);
bool good = kmp_calc_one_iv_for_chunk_end(
bounds, updated_bounds,
/*in/out*/ original_ivs, iterations, ind, (lengthened_ind < ind),
(equal_ind >= ind - 1), original_ivs_start);
if (!good) {
// Too big (or too small for >=).
if (ind == 0) {
// Need to reduce to the end.
return false;
} else {
// Go to next iteration on outer loop:
--ind;
++(iterations[ind]);
lengthened_ind = ind;
if (equal_ind >= lengthened_ind) {
// We've changed the number of iterations here,
// can't be same anymore:
equal_ind = lengthened_ind - 1;
}
for (kmp_index_t i = ind + 1; i < n; ++i) {
iterations[i] = 0;
}
continue;
}
}
if ((equal_ind == ind - 1) &&
(kmp_ivs_eq(bounds->loop_iv_type, original_ivs[ind],
original_ivs_start[ind]))) {
equal_ind = ind;
} else if ((equal_ind > ind - 1) &&
!(kmp_ivs_eq(bounds->loop_iv_type, original_ivs[ind],
original_ivs_start[ind]))) {
equal_ind = ind - 1;
}
++ind;
}
return true;
}
//----------Calculate upper bounds for the last chunk-------------------------
// Calculate one upper bound for the end.
template <typename T>
void kmp_calc_one_iv_end_XX(const bounds_infoXX_template<T> *bounds,
/*in/out*/ kmp_point_t original_ivs,
kmp_index_t ind) {
T temp = bounds->ub0 +
bounds->ub1 * static_cast<T>(original_ivs[bounds->outer_iv]);
original_ivs[ind] = kmp_fix_iv(bounds->loop_iv_type, temp);
}
void kmp_calc_one_iv_end(const bounds_info_t *bounds,
/*in/out*/ kmp_point_t original_ivs, kmp_index_t ind) {
switch (bounds->loop_type) {
default:
KMP_ASSERT(false);
break;
case loop_type_t::loop_type_int32:
kmp_calc_one_iv_end_XX<kmp_int32>(
(bounds_infoXX_template<kmp_int32> *)(bounds),
/*in/out*/ original_ivs, ind);
break;
case loop_type_t::loop_type_uint32:
kmp_calc_one_iv_end_XX<kmp_uint32>(
(bounds_infoXX_template<kmp_uint32> *)(bounds),
/*in/out*/ original_ivs, ind);
break;
case loop_type_t::loop_type_int64:
kmp_calc_one_iv_end_XX<kmp_int64>(
(bounds_infoXX_template<kmp_int64> *)(bounds),
/*in/out*/ original_ivs, ind);
break;
case loop_type_t::loop_type_uint64:
kmp_calc_one_iv_end_XX<kmp_uint64>(
(bounds_infoXX_template<kmp_uint64> *)(bounds),
/*in/out*/ original_ivs, ind);
break;
}
}
// Calculate upper bounds for the last loop iteration. Just use original upper
// bounds (adjusted when canonicalized to use <= / >=). No need to check that
// this point is in the original space (it's likely not)
void kmp_calc_original_ivs_for_end(
const bounds_info_t *const original_bounds_nest, kmp_index_t n,
/*out*/ kmp_point_t original_ivs) {
for (kmp_index_t ind = 0; ind < n; ++ind) {
auto bounds = &(original_bounds_nest[ind]);
kmp_calc_one_iv_end(bounds, /*in/out*/ original_ivs, ind);
}
}
/**************************************************************************
* Identify nested loop structure - loops come in the canonical form
* Lower triangle matrix: i = 0; i <= N; i++ {0,0}:{N,0}
* j = 0; j <= 0/-1+1*i; j++ {0,0}:{0/-1,1}
* Upper Triangle matrix
* i = 0; i <= N; i++ {0,0}:{N,0}
* j = 0+1*i; j <= N; j++ {0,1}:{N,0}
* ************************************************************************/
nested_loop_type_t
kmp_identify_nested_loop_structure(/*in*/ bounds_info_t *original_bounds_nest,
/*in*/ kmp_index_t n) {
// only 2-level nested loops are supported
if (n != 2) {
return nested_loop_type_unkown;
}
// loops must be canonical
KMP_ASSERT(
(original_bounds_nest[0].comparison == comparison_t::comp_less_or_eq) &&
(original_bounds_nest[1].comparison == comparison_t::comp_less_or_eq));
// check outer loop bounds: for triangular need to be {0,0}:{N,0}
kmp_uint64 outer_lb0_u64 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].lb0_u64);
kmp_uint64 outer_ub0_u64 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].ub0_u64);
kmp_uint64 outer_lb1_u64 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].lb1_u64);
kmp_uint64 outer_ub1_u64 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].ub1_u64);
if (outer_lb0_u64 != 0 || outer_lb1_u64 != 0 || outer_ub1_u64 != 0) {
return nested_loop_type_unkown;
}
// check inner bounds to determine triangle type
kmp_uint64 inner_lb0_u64 = kmp_fix_iv(original_bounds_nest[1].loop_iv_type,
original_bounds_nest[1].lb0_u64);
kmp_uint64 inner_ub0_u64 = kmp_fix_iv(original_bounds_nest[1].loop_iv_type,
original_bounds_nest[1].ub0_u64);
kmp_uint64 inner_lb1_u64 = kmp_fix_iv(original_bounds_nest[1].loop_iv_type,
original_bounds_nest[1].lb1_u64);
kmp_uint64 inner_ub1_u64 = kmp_fix_iv(original_bounds_nest[1].loop_iv_type,
original_bounds_nest[1].ub1_u64);
// lower triangle loop inner bounds need to be {0,0}:{0/-1,1}
if (inner_lb0_u64 == 0 && inner_lb1_u64 == 0 &&
(inner_ub0_u64 == 0 || inner_ub0_u64 == -1) && inner_ub1_u64 == 1) {
return nested_loop_type_lower_triangular_matrix;
}
// upper triangle loop inner bounds need to be {0,1}:{N,0}
if (inner_lb0_u64 == 0 && inner_lb1_u64 == 1 &&
inner_ub0_u64 == outer_ub0_u64 && inner_ub1_u64 == 0) {
return nested_loop_type_upper_triangular_matrix;
}
return nested_loop_type_unkown;
}
/**************************************************************************
* SQRT Approximation: https://math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
* Start point is x so the result is always > sqrt(x)
* The method has uniform convergence, PRECISION is set to 0.1
* ************************************************************************/
#define level_of_precision 0.1
double sqrt_newton_approx(/*in*/ kmp_uint64 x) {
double sqrt_old = 0.;
double sqrt_new = (double)x;
do {
sqrt_old = sqrt_new;
sqrt_new = (sqrt_old + x / sqrt_old) / 2;
} while ((sqrt_old - sqrt_new) > level_of_precision);
return sqrt_new;
}
/**************************************************************************
* Handle lower triangle matrix in the canonical form
* i = 0; i <= N; i++ {0,0}:{N,0}
* j = 0; j <= 0/-1 + 1*i; j++ {0,0}:{0/-1,1}
* ************************************************************************/
void kmp_handle_lower_triangle_matrix(
/*in*/ kmp_uint32 nth,
/*in*/ kmp_uint32 tid,
/*in */ kmp_index_t n,
/*in/out*/ bounds_info_t *original_bounds_nest,
/*out*/ bounds_info_t *chunk_bounds_nest) {
// transfer loop types from the original loop to the chunks
for (kmp_index_t i = 0; i < n; ++i) {
chunk_bounds_nest[i] = original_bounds_nest[i];
}
// cleanup iv variables
kmp_uint64 outer_ub0 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].ub0_u64);
kmp_uint64 outer_lb0 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].lb0_u64);
kmp_uint64 inner_ub0 = kmp_fix_iv(original_bounds_nest[1].loop_iv_type,
original_bounds_nest[1].ub0_u64);
// calculate the chunk's lower and upper bounds
// the total number of iterations in the loop is the sum of the arithmetic
// progression from the outer lower to outer upper bound (inclusive since the
// loop is canonical) note that less_than inner loops (inner_ub0 = -1)
// effectively make the progression 1-based making N = (outer_ub0 - inner_lb0
// + 1) -> N - 1
kmp_uint64 outer_iters = (outer_ub0 - outer_lb0 + 1) + inner_ub0;
kmp_uint64 iter_total = outer_iters * (outer_iters + 1) / 2;
// the current thread's number of iterations:
// each thread gets an equal number of iterations: total number of iterations
// divided by the number of threads plus, if there's a remainder,
// the first threads with the number up to the remainder get an additional
// iteration each to cover it
kmp_uint64 iter_current =
iter_total / nth + ((tid < (iter_total % nth)) ? 1 : 0);
// cumulative number of iterations executed by all the previous threads:
// threads with the tid below the remainder will have (iter_total/nth+1)
// elements, and so will all threads before them so the cumulative number of
// iterations executed by the all previous will be the current thread's number
// of iterations multiplied by the number of previous threads which is equal
// to the current thread's tid; threads with the number equal or above the
// remainder will have (iter_total/nth) elements so the cumulative number of
// iterations previously executed is its number of iterations multipled by the
// number of previous threads which is again equal to the current thread's tid
// PLUS all the remainder iterations that will have been executed by the
// previous threads
kmp_uint64 iter_before_current =
tid * iter_current + ((tid < iter_total % nth) ? 0 : (iter_total % nth));
// cumulative number of iterations executed with the current thread is
// the cumulative number executed before it plus its own
kmp_uint64 iter_with_current = iter_before_current + iter_current;
// calculate the outer loop lower bound (lbo) which is the max outer iv value
// that gives the number of iterations that is equal or just below the total
// number of iterations executed by the previous threads, for less_than
// (1-based) inner loops (inner_ub0 == -1) it will be i.e.
// lbo*(lbo-1)/2<=iter_before_current => lbo^2-lbo-2*iter_before_current<=0
// for less_than_equal (0-based) inner loops (inner_ub == 0) it will be:
// i.e. lbo*(lbo+1)/2<=iter_before_current =>
// lbo^2+lbo-2*iter_before_current<=0 both cases can be handled similarily
// using a parameter to control the equation sign
kmp_int64 inner_adjustment = 1 + 2 * inner_ub0;
kmp_uint64 lower_bound_outer =
(kmp_uint64)(sqrt_newton_approx(inner_adjustment * inner_adjustment +
8 * iter_before_current) +
inner_adjustment) /
2 -
inner_adjustment;
// calculate the inner loop lower bound which is the remaining number of
// iterations required to hit the total number of iterations executed by the
// previous threads giving the starting point of this thread
kmp_uint64 lower_bound_inner =
iter_before_current -
((lower_bound_outer + inner_adjustment) * lower_bound_outer) / 2;
// calculate the outer loop upper bound using the same approach as for the
// inner bound except using the total number of iterations executed with the
// current thread
kmp_uint64 upper_bound_outer =
(kmp_uint64)(sqrt_newton_approx(inner_adjustment * inner_adjustment +
8 * iter_with_current) +
inner_adjustment) /
2 -
inner_adjustment;
// calculate the inner loop upper bound which is the remaining number of
// iterations required to hit the total number of iterations executed after
// the current thread giving the starting point of the next thread
kmp_uint64 upper_bound_inner =
iter_with_current -
((upper_bound_outer + inner_adjustment) * upper_bound_outer) / 2;
// adjust the upper bounds down by 1 element to point at the last iteration of
// the current thread the first iteration of the next thread
if (upper_bound_inner == 0) {
// {n,0} => {n-1,n-1}
upper_bound_outer -= 1;
upper_bound_inner = upper_bound_outer;
} else {
// {n,m} => {n,m-1} (m!=0)
upper_bound_inner -= 1;
}
// assign the values, zeroing out lb1 and ub1 values since the iteration space
// is now one-dimensional
chunk_bounds_nest[0].lb0_u64 = lower_bound_outer;
chunk_bounds_nest[1].lb0_u64 = lower_bound_inner;
chunk_bounds_nest[0].ub0_u64 = upper_bound_outer;
chunk_bounds_nest[1].ub0_u64 = upper_bound_inner;
chunk_bounds_nest[0].lb1_u64 = 0;
chunk_bounds_nest[0].ub1_u64 = 0;
chunk_bounds_nest[1].lb1_u64 = 0;
chunk_bounds_nest[1].ub1_u64 = 0;
#if 0
printf("tid/nth = %d/%d : From [%llu, %llu] To [%llu, %llu] : Chunks %llu/%llu\n",
tid, nth, chunk_bounds_nest[0].lb0_u64, chunk_bounds_nest[1].lb0_u64,
chunk_bounds_nest[0].ub0_u64, chunk_bounds_nest[1].ub0_u64, iter_current, iter_total);
#endif
}
/**************************************************************************
* Handle upper triangle matrix in the canonical form
* i = 0; i <= N; i++ {0,0}:{N,0}
* j = 0+1*i; j <= N; j++ {0,1}:{N,0}
* ************************************************************************/
void kmp_handle_upper_triangle_matrix(
/*in*/ kmp_uint32 nth,
/*in*/ kmp_uint32 tid,
/*in */ kmp_index_t n,
/*in/out*/ bounds_info_t *original_bounds_nest,
/*out*/ bounds_info_t *chunk_bounds_nest) {
// transfer loop types from the original loop to the chunks
for (kmp_index_t i = 0; i < n; ++i) {
chunk_bounds_nest[i] = original_bounds_nest[i];
}
// cleanup iv variables
kmp_uint64 outer_ub0 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].ub0_u64);
kmp_uint64 outer_lb0 = kmp_fix_iv(original_bounds_nest[0].loop_iv_type,
original_bounds_nest[0].lb0_u64);
[[maybe_unused]] kmp_uint64 inner_ub0 = kmp_fix_iv(
original_bounds_nest[1].loop_iv_type, original_bounds_nest[1].ub0_u64);
// calculate the chunk's lower and upper bounds
// the total number of iterations in the loop is the sum of the arithmetic
// progression from the outer lower to outer upper bound (inclusive since the
// loop is canonical) note that less_than inner loops (inner_ub0 = -1)
// effectively make the progression 1-based making N = (outer_ub0 - inner_lb0
// + 1) -> N - 1
kmp_uint64 outer_iters = (outer_ub0 - outer_lb0 + 1);
kmp_uint64 iter_total = outer_iters * (outer_iters + 1) / 2;
// the current thread's number of iterations:
// each thread gets an equal number of iterations: total number of iterations
// divided by the number of threads plus, if there's a remainder,
// the first threads with the number up to the remainder get an additional
// iteration each to cover it
kmp_uint64 iter_current =
iter_total / nth + ((tid < (iter_total % nth)) ? 1 : 0);
// cumulative number of iterations executed by all the previous threads:
// threads with the tid below the remainder will have (iter_total/nth+1)
// elements, and so will all threads before them so the cumulative number of
// iterations executed by the all previous will be the current thread's number
// of iterations multiplied by the number of previous threads which is equal
// to the current thread's tid; threads with the number equal or above the
// remainder will have (iter_total/nth) elements so the cumulative number of
// iterations previously executed is its number of iterations multipled by the
// number of previous threads which is again equal to the current thread's tid
// PLUS all the remainder iterations that will have been executed by the
// previous threads
kmp_uint64 iter_before_current =
tid * iter_current + ((tid < iter_total % nth) ? 0 : (iter_total % nth));
// cumulative number of iterations executed with the current thread is
// the cumulative number executed before it plus its own
kmp_uint64 iter_with_current = iter_before_current + iter_current;
// calculate the outer loop lower bound (lbo) which is the max outer iv value
// that gives the number of iterations that is equal or just below the total
// number of iterations executed by the previous threads:
// lbo*(lbo+1)/2<=iter_before_current =>
// lbo^2+lbo-2*iter_before_current<=0
kmp_uint64 lower_bound_outer =
(kmp_uint64)(sqrt_newton_approx(1 + 8 * iter_before_current) + 1) / 2 - 1;
// calculate the inner loop lower bound which is the remaining number of
// iterations required to hit the total number of iterations executed by the
// previous threads giving the starting point of this thread
kmp_uint64 lower_bound_inner =
iter_before_current - ((lower_bound_outer + 1) * lower_bound_outer) / 2;
// calculate the outer loop upper bound using the same approach as for the
// inner bound except using the total number of iterations executed with the
// current thread
kmp_uint64 upper_bound_outer =
(kmp_uint64)(sqrt_newton_approx(1 + 8 * iter_with_current) + 1) / 2 - 1;
// calculate the inner loop upper bound which is the remaining number of
// iterations required to hit the total number of iterations executed after
// the current thread giving the starting point of the next thread
kmp_uint64 upper_bound_inner =
iter_with_current - ((upper_bound_outer + 1) * upper_bound_outer) / 2;
// adjust the upper bounds down by 1 element to point at the last iteration of
// the current thread the first iteration of the next thread
if (upper_bound_inner == 0) {
// {n,0} => {n-1,n-1}
upper_bound_outer -= 1;
upper_bound_inner = upper_bound_outer;
} else {
// {n,m} => {n,m-1} (m!=0)
upper_bound_inner -= 1;
}
// assign the values, zeroing out lb1 and ub1 values since the iteration space
// is now one-dimensional
chunk_bounds_nest[0].lb0_u64 = (outer_iters - 1) - upper_bound_outer;
chunk_bounds_nest[1].lb0_u64 = (outer_iters - 1) - upper_bound_inner;
chunk_bounds_nest[0].ub0_u64 = (outer_iters - 1) - lower_bound_outer;
chunk_bounds_nest[1].ub0_u64 = (outer_iters - 1) - lower_bound_inner;
chunk_bounds_nest[0].lb1_u64 = 0;
chunk_bounds_nest[0].ub1_u64 = 0;
chunk_bounds_nest[1].lb1_u64 = 0;
chunk_bounds_nest[1].ub1_u64 = 0;
#if 0
printf("tid/nth = %d/%d : From [%llu, %llu] To [%llu, %llu] : Chunks %llu/%llu\n",
tid, nth, chunk_bounds_nest[0].lb0_u64, chunk_bounds_nest[1].lb0_u64,
chunk_bounds_nest[0].ub0_u64, chunk_bounds_nest[1].ub0_u64, iter_current, iter_total);
#endif
}
//----------Init API for non-rectangular loops--------------------------------
// Init API for collapsed loops (static, no chunks defined).
// "bounds_nest" has to be allocated per thread.
// API will modify original bounds_nest array to bring it to a canonical form
// (only <= and >=, no !=, <, >). If the original loop nest was already in a
// canonical form there will be no changes to bounds in bounds_nest array
// (only trip counts will be calculated). Internally API will expand the space
// to parallelogram/parallelepiped, calculate total, calculate bounds for the
// chunks in terms of the new IV, re-calc them in terms of old IVs (especially
// important on the left side, to hit the lower bounds and not step over), and
// pick the correct chunk for this thread (so it will calculate chunks up to the
// needed one). It could be optimized to calculate just this chunk, potentially
// a bit less well distributed among threads. It is designed to make sure that
// threads will receive predictable chunks, deterministically (so that next nest
// of loops with similar characteristics will get exactly same chunks on same
// threads).
// Current contract: chunk_bounds_nest has only lb0 and ub0,
// lb1 and ub1 are set to 0 and can be ignored. (This may change in the future).
extern "C" kmp_int32
__kmpc_for_collapsed_init(ident_t *loc, kmp_int32 gtid,
/*in/out*/ bounds_info_t *original_bounds_nest,
/*out*/ bounds_info_t *chunk_bounds_nest,
kmp_index_t n, /*out*/ kmp_int32 *plastiter) {
KMP_DEBUG_ASSERT(plastiter && original_bounds_nest);
KE_TRACE(10, ("__kmpc_for_collapsed_init called (%d)\n", gtid));
if (__kmp_env_consistency_check) {
__kmp_push_workshare(gtid, ct_pdo, loc);
}
kmp_canonicalize_loop_nest(loc, /*in/out*/ original_bounds_nest, n);
CollapseAllocator<bounds_info_internal_t> updated_bounds_nest(n);
for (kmp_index_t i = 0; i < n; ++i) {
updated_bounds_nest[i].b = original_bounds_nest[i];
}
kmp_loop_nest_iv_t total =
kmp_process_loop_nest(/*in/out*/ updated_bounds_nest, n);
if (plastiter != NULL) {
*plastiter = FALSE;
}
if (total == 0) {
// Loop won't execute:
return FALSE;
}
// OMPTODO: DISTRIBUTE is not supported yet
__kmp_assert_valid_gtid(gtid);
kmp_uint32 tid = __kmp_tid_from_gtid(gtid);
kmp_info_t *th = __kmp_threads[gtid];
kmp_team_t *team = th->th.th_team;
kmp_uint32 nth = team->t.t_nproc; // Number of threads
KMP_DEBUG_ASSERT(tid < nth);
// Handle special cases
nested_loop_type_t loop_type =
kmp_identify_nested_loop_structure(original_bounds_nest, n);
if (loop_type == nested_loop_type_lower_triangular_matrix) {
kmp_handle_lower_triangle_matrix(nth, tid, n, original_bounds_nest,
chunk_bounds_nest);
return TRUE;
} else if (loop_type == nested_loop_type_upper_triangular_matrix) {
kmp_handle_upper_triangle_matrix(nth, tid, n, original_bounds_nest,
chunk_bounds_nest);
return TRUE;
}
CollapseAllocator<kmp_uint64> original_ivs_start(n);
if (!kmp_calc_original_ivs_for_start(original_bounds_nest, n,
/*out*/ original_ivs_start)) {
// Loop won't execute:
return FALSE;
}
// Not doing this optimization for one thread:
// (1) more to test
// (2) without it current contract that chunk_bounds_nest has only lb0 and
// ub0, lb1 and ub1 are set to 0 and can be ignored.
// if (nth == 1) {
// // One thread:
// // Copy all info from original_bounds_nest, it'll be good enough.
// for (kmp_index_t i = 0; i < n; ++i) {
// chunk_bounds_nest[i] = original_bounds_nest[i];
// }
// if (plastiter != NULL) {
// *plastiter = TRUE;
// }
// return TRUE;
//}
kmp_loop_nest_iv_t new_iv = kmp_calc_new_iv_from_original_ivs(
updated_bounds_nest, original_ivs_start, n);
bool last_iter = false;
for (; nth > 0;) {
// We could calculate chunk size once, but this is to compensate that the
// original space is not parallelepiped and some threads can be left
// without work:
KMP_DEBUG_ASSERT(total >= new_iv);
kmp_loop_nest_iv_t total_left = total - new_iv;
kmp_loop_nest_iv_t chunk_size = total_left / nth;
kmp_loop_nest_iv_t remainder = total_left % nth;
kmp_loop_nest_iv_t curr_chunk_size = chunk_size;
if (remainder > 0) {
++curr_chunk_size;
--remainder;
}
#if defined(KMP_DEBUG)
kmp_loop_nest_iv_t new_iv_for_start = new_iv;
#endif
if (curr_chunk_size > 1) {
new_iv += curr_chunk_size - 1;
}
CollapseAllocator<kmp_uint64> original_ivs_end(n);
if ((nth == 1) || (new_iv >= total - 1)) {
// Do this one till the end - just in case we miscalculated
// and either too much is left to process or new_iv is a bit too big:
kmp_calc_original_ivs_for_end(original_bounds_nest, n,
/*out*/ original_ivs_end);
last_iter = true;
} else {
// Note: here we make sure it's past (or equal to) the previous point.
if (!kmp_calc_original_ivs_for_chunk_end(original_bounds_nest, n,
updated_bounds_nest,
original_ivs_start, new_iv,
/*out*/ original_ivs_end)) {
// We could not find the ending point, use the original upper bounds:
kmp_calc_original_ivs_for_end(original_bounds_nest, n,
/*out*/ original_ivs_end);
last_iter = true;
}
}
#if defined(KMP_DEBUG)
auto new_iv_for_end = kmp_calc_new_iv_from_original_ivs(
updated_bounds_nest, original_ivs_end, n);
KMP_DEBUG_ASSERT(new_iv_for_end >= new_iv_for_start);
#endif
if (last_iter && (tid != 0)) {
// We are done, this was last chunk, but no chunk for current thread was
// found:
return FALSE;
}
if (tid == 0) {
// We found the chunk for this thread, now we need to check if it's the
// last chunk or not:
CollapseAllocator<kmp_uint64> original_ivs_next_start(n);
if (last_iter ||
!kmp_calc_next_original_ivs(original_bounds_nest, n, original_ivs_end,
/*out*/ original_ivs_next_start)) {
// no more loop iterations left to process,
// this means that currently found chunk is the last chunk:
if (plastiter != NULL) {
*plastiter = TRUE;
}
}
// Fill in chunk bounds:
for (kmp_index_t i = 0; i < n; ++i) {
chunk_bounds_nest[i] =
original_bounds_nest[i]; // To fill in types, etc. - optional
chunk_bounds_nest[i].lb0_u64 = original_ivs_start[i];
chunk_bounds_nest[i].lb1_u64 = 0;
chunk_bounds_nest[i].ub0_u64 = original_ivs_end[i];
chunk_bounds_nest[i].ub1_u64 = 0;
}
return TRUE;
}
--tid;
--nth;
bool next_chunk = kmp_calc_next_original_ivs(
original_bounds_nest, n, original_ivs_end, /*out*/ original_ivs_start);
if (!next_chunk) {
// no more loop iterations to process,
// the prevoius chunk was the last chunk
break;
}
// original_ivs_start is next to previous chunk original_ivs_end,
// we need to start new chunk here, so chunks will be one after another
// without any gap or overlap:
new_iv = kmp_calc_new_iv_from_original_ivs(updated_bounds_nest,
original_ivs_start, n);
}
return FALSE;
}