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Tue, 18 Jul 2023 14:05:47 GMT Received: from smtpav04.fra02v.mail.ibm.com (unknown [127.0.0.1]) by IMSVA (Postfix) with ESMTP id 7D86E2004E; Tue, 18 Jul 2023 14:05:47 +0000 (GMT) Received: from smtpav04.fra02v.mail.ibm.com (unknown [127.0.0.1]) by IMSVA (Postfix) with ESMTP id A42422004B; Tue, 18 Jul 2023 14:05:45 +0000 (GMT) Received: from ltcden2-lp1.aus.stglabs.ibm.com (unknown [9.3.90.43]) by smtpav04.fra02v.mail.ibm.com (Postfix) with ESMTP; Tue, 18 Jul 2023 14:05:45 +0000 (GMT) To: gcc-patches@gcc.gnu.org Cc: amacleod@redhat.com, aldyh@redhat.com, rguenther@suse.de, jeffreyalaw@gmail.com, richard.sandiford@arm.com, segher@kernel.crashing.org, dje.gcc@gmail.com, linkw@gcc.gnu.org, bergner@linux.ibm.com, guojiufu@linux.ibm.com Subject: [PATCH V5 1/2] Add overflow API for plus minus mult on range Date: Tue, 18 Jul 2023 22:05:43 +0800 Message-Id: <20230718140544.3497370-1-guojiufu@linux.ibm.com> X-Mailer: git-send-email 2.39.3 X-TM-AS-GCONF: 00 X-Proofpoint-ORIG-GUID: nyw-a6hVlvHCmVeuxmf3BOmXZ0IvGrrA X-Proofpoint-GUID: q0XPFlshVUBzS8uR3oLPPobqBloqhwgR X-Proofpoint-UnRewURL: 0 URL was un-rewritten MIME-Version: 1.0 X-Proofpoint-Virus-Version: vendor=baseguard engine=ICAP:2.0.254,Aquarius:18.0.957,Hydra:6.0.591,FMLib:17.11.176.26 definitions=2023-07-18_10,2023-07-18_01,2023-05-22_02 X-Proofpoint-Spam-Details: rule=outbound_notspam policy=outbound score=0 priorityscore=1501 impostorscore=0 suspectscore=0 mlxscore=0 adultscore=0 bulkscore=0 phishscore=0 malwarescore=0 spamscore=0 clxscore=1015 mlxlogscore=999 lowpriorityscore=0 classifier=spam adjust=0 reason=mlx scancount=1 engine=8.12.0-2306200000 definitions=main-2307180129 X-Spam-Status: No, score=-10.8 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_EF, GIT_PATCH_0, KAM_SHORT, RCVD_IN_MSPIKE_H5, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_PASS, TXREP, T_SCC_BODY_TEXT_LINE autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Jiufu Guo via Gcc-patches From: Jiufu Guo Reply-To: Jiufu Guo Errors-To: gcc-patches-bounces+ouuuleilei=gmail.com@gcc.gnu.org Sender: "Gcc-patches" X-getmail-retrieved-from-mailbox: INBOX X-GMAIL-THRID: 1771767911023640105 X-GMAIL-MSGID: 1771767911023640105 Hi, As discussed in previous reviews, adding overflow APIs to range-op would be useful. Those APIs could help to check if overflow happens when operating between two 'range's, like: plus, minus, and mult. Previous discussions are here: https://gcc.gnu.org/pipermail/gcc-patches/2023-July/624067.html https://gcc.gnu.org/pipermail/gcc-patches/2023-July/624701.html Bootstrap & regtest pass on ppc64{,le} and x86_64. Is this patch ok for trunk? BR, Jeff (Jiufu Guo) gcc/ChangeLog: * range-op-mixed.h (operator_plus::overflow_free_p): New declare. (operator_minus::overflow_free_p): New declare. (operator_mult::overflow_free_p): New declare. * range-op.cc (range_op_handler::overflow_free_p): New function. (range_operator::overflow_free_p): New default function. (operator_plus::overflow_free_p): New function. (operator_minus::overflow_free_p): New function. (operator_mult::overflow_free_p): New function. * range-op.h (range_op_handler::overflow_free_p): New declare. (range_operator::overflow_free_p): New declare. * value-range.cc (irange::nonnegative_p): New function. (irange::nonpositive_p): New function. * value-range.h (irange::nonnegative_p): New declare. (irange::nonpositive_p): New declare. --- gcc/range-op-mixed.h | 11 ++++ gcc/range-op.cc | 124 +++++++++++++++++++++++++++++++++++++++++++ gcc/range-op.h | 5 ++ gcc/value-range.cc | 12 +++++ gcc/value-range.h | 2 + 5 files changed, 154 insertions(+) diff --git a/gcc/range-op-mixed.h b/gcc/range-op-mixed.h index 6944742ecbc..42157ed9061 100644 --- a/gcc/range-op-mixed.h +++ b/gcc/range-op-mixed.h @@ -383,6 +383,10 @@ public: relation_kind rel) const final override; void update_bitmask (irange &r, const irange &lh, const irange &rh) const final override; + + virtual bool overflow_free_p (const irange &lh, const irange &rh, + relation_trio = TRIO_VARYING) const; + private: void wi_fold (irange &r, tree type, const wide_int &lh_lb, const wide_int &lh_ub, const wide_int &rh_lb, @@ -446,6 +450,10 @@ public: relation_kind rel) const final override; void update_bitmask (irange &r, const irange &lh, const irange &rh) const final override; + + virtual bool overflow_free_p (const irange &lh, const irange &rh, + relation_trio = TRIO_VARYING) const; + private: void wi_fold (irange &r, tree type, const wide_int &lh_lb, const wide_int &lh_ub, const wide_int &rh_lb, @@ -525,6 +533,9 @@ public: const REAL_VALUE_TYPE &lh_lb, const REAL_VALUE_TYPE &lh_ub, const REAL_VALUE_TYPE &rh_lb, const REAL_VALUE_TYPE &rh_ub, relation_kind kind) const final override; + virtual bool overflow_free_p (const irange &lh, const irange &rh, + relation_trio = TRIO_VARYING) const; + }; class operator_addr_expr : public range_operator diff --git a/gcc/range-op.cc b/gcc/range-op.cc index cb584314f4c..632b044331b 100644 --- a/gcc/range-op.cc +++ b/gcc/range-op.cc @@ -366,6 +366,22 @@ range_op_handler::op1_op2_relation (const vrange &lhs) const } } +bool +range_op_handler::overflow_free_p (const vrange &lh, + const vrange &rh, + relation_trio rel) const +{ + gcc_checking_assert (m_operator); + switch (dispatch_kind (lh, lh, rh)) + { + case RO_III: + return m_operator->overflow_free_p(as_a (lh), + as_a (rh), + rel); + default: + return false; + } +} // Convert irange bitmasks into a VALUE MASK pair suitable for calling CCP. @@ -688,6 +704,13 @@ range_operator::op1_op2_relation_effect (irange &lhs_range ATTRIBUTE_UNUSED, return false; } +bool +range_operator::overflow_free_p (const irange &, const irange &, + relation_trio) const +{ + return false; +} + // Apply any known bitmask updates based on this operator. void @@ -4311,6 +4334,107 @@ range_op_table::initialize_integral_ops () } +bool +operator_plus::overflow_free_p (const irange &lh, const irange &rh, + relation_trio) const +{ + if (lh.undefined_p () || rh.undefined_p ()) + return false; + + tree type = lh.type (); + if (TYPE_OVERFLOW_UNDEFINED (type)) + return true; + + wi::overflow_type ovf; + signop sgn = TYPE_SIGN (type); + wide_int wmax0 = lh.upper_bound (); + wide_int wmax1 = rh.upper_bound (); + wi::add (wmax0, wmax1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + if (TYPE_UNSIGNED (type)) + return true; + + wide_int wmin0 = lh.lower_bound (); + wide_int wmin1 = rh.lower_bound (); + wi::add (wmin0, wmin1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + return true; +} + +bool +operator_minus::overflow_free_p (const irange &lh, const irange &rh, + relation_trio) const +{ + if (lh.undefined_p () || rh.undefined_p ()) + return false; + + tree type = lh.type (); + if (TYPE_OVERFLOW_UNDEFINED (type)) + return true; + + wi::overflow_type ovf; + signop sgn = TYPE_SIGN (type); + wide_int wmin0 = lh.lower_bound (); + wide_int wmax1 = rh.upper_bound (); + wi::sub (wmin0, wmax1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + if (TYPE_UNSIGNED (type)) + return true; + + wide_int wmax0 = lh.upper_bound (); + wide_int wmin1 = rh.lower_bound (); + wi::sub (wmax0, wmin1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + return true; +} + +bool +operator_mult::overflow_free_p (const irange &lh, const irange &rh, + relation_trio) const +{ + if (lh.undefined_p () || rh.undefined_p ()) + return false; + + tree type = lh.type (); + if (TYPE_OVERFLOW_UNDEFINED (type)) + return true; + + wi::overflow_type ovf; + signop sgn = TYPE_SIGN (type); + wide_int wmax0 = lh.upper_bound (); + wide_int wmax1 = rh.upper_bound (); + wi::mul (wmax0, wmax1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + if (TYPE_UNSIGNED (type)) + return true; + + wide_int wmin0 = lh.lower_bound (); + wide_int wmin1 = rh.lower_bound (); + wi::mul (wmin0, wmin1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + wi::mul (wmin0, wmax1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + wi::mul (wmax0, wmin1, sgn, &ovf); + if (ovf != wi::OVF_NONE) + return false; + + return true; +} + #if CHECKING_P #include "selftest.h" diff --git a/gcc/range-op.h b/gcc/range-op.h index af94c2756a7..db3b03f28a5 100644 --- a/gcc/range-op.h +++ b/gcc/range-op.h @@ -147,6 +147,9 @@ public: virtual relation_kind op1_op2_relation (const irange &lhs) const; virtual relation_kind op1_op2_relation (const frange &lhs) const; + + virtual bool overflow_free_p (const irange &lh, const irange &rh, + relation_trio = TRIO_VARYING) const; protected: // Perform an integral operation between 2 sub-ranges and return it. virtual void wi_fold (irange &r, tree type, @@ -214,6 +217,8 @@ public: const vrange &op2, relation_kind = VREL_VARYING) const; relation_kind op1_op2_relation (const vrange &lhs) const; + bool overflow_free_p (const vrange &lh, const vrange &rh, + relation_trio = TRIO_VARYING) const; protected: unsigned dispatch_kind (const vrange &lhs, const vrange &op1, const vrange& op2) const; diff --git a/gcc/value-range.cc b/gcc/value-range.cc index 011bdbdeae6..5ae4e044194 100644 --- a/gcc/value-range.cc +++ b/gcc/value-range.cc @@ -313,6 +313,18 @@ add_vrange (const vrange &v, inchash::hash &hstate, } //namespace inchash +bool +irange::nonnegative_p () const +{ + return wi::ge_p (lower_bound (), 0, TYPE_SIGN (type ())); +} + +bool +irange::nonpositive_p () const +{ + return wi::le_p (upper_bound (), 0, TYPE_SIGN (type ())); +} + bool irange::supports_type_p (const_tree type) const { diff --git a/gcc/value-range.h b/gcc/value-range.h index 0170188201b..a12dea514e4 100644 --- a/gcc/value-range.h +++ b/gcc/value-range.h @@ -280,6 +280,8 @@ public: virtual bool singleton_p (tree *result = NULL) const override; bool singleton_p (wide_int &) const; bool contains_p (const wide_int &) const; 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Tue, 18 Jul 2023 14:05:49 GMT Received: from smtpav04.fra02v.mail.ibm.com (unknown [127.0.0.1]) by IMSVA (Postfix) with ESMTP id 965B42004D; Tue, 18 Jul 2023 14:05:49 +0000 (GMT) Received: from smtpav04.fra02v.mail.ibm.com (unknown [127.0.0.1]) by IMSVA (Postfix) with ESMTP id BF3D02004B; Tue, 18 Jul 2023 14:05:47 +0000 (GMT) Received: from ltcden2-lp1.aus.stglabs.ibm.com (unknown [9.3.90.43]) by smtpav04.fra02v.mail.ibm.com (Postfix) with ESMTP; Tue, 18 Jul 2023 14:05:47 +0000 (GMT) To: gcc-patches@gcc.gnu.org Cc: amacleod@redhat.com, aldyh@redhat.com, rguenther@suse.de, jeffreyalaw@gmail.com, richard.sandiford@arm.com, segher@kernel.crashing.org, dje.gcc@gmail.com, linkw@gcc.gnu.org, bergner@linux.ibm.com, guojiufu@linux.ibm.com Subject: [PATCH V5 2/2] Optimize '(X - N * M) / N' to 'X / N - M' if valid Date: Tue, 18 Jul 2023 22:05:44 +0800 Message-Id: <20230718140544.3497370-2-guojiufu@linux.ibm.com> X-Mailer: git-send-email 2.39.3 In-Reply-To: <20230718140544.3497370-1-guojiufu@linux.ibm.com> References: <20230718140544.3497370-1-guojiufu@linux.ibm.com> X-TM-AS-GCONF: 00 X-Proofpoint-ORIG-GUID: 4cF84sD_QePIPOH7yGB5-nv3FvDlgLfb X-Proofpoint-GUID: jdIp0iSEaIQfEamHS1n5GYw-AFJ-r2cd X-Proofpoint-UnRewURL: 0 URL was un-rewritten MIME-Version: 1.0 X-Proofpoint-Virus-Version: vendor=baseguard engine=ICAP:2.0.254,Aquarius:18.0.957,Hydra:6.0.591,FMLib:17.11.176.26 definitions=2023-07-18_10,2023-07-18_01,2023-05-22_02 X-Proofpoint-Spam-Details: rule=outbound_notspam policy=outbound score=0 impostorscore=0 suspectscore=0 lowpriorityscore=0 priorityscore=1501 malwarescore=0 adultscore=0 clxscore=1015 mlxlogscore=920 mlxscore=0 spamscore=0 bulkscore=0 phishscore=0 classifier=spam adjust=0 reason=mlx scancount=1 engine=8.12.0-2306200000 definitions=main-2307180129 X-Spam-Status: No, score=-10.8 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_EF, GIT_PATCH_0, KAM_SHORT, RCVD_IN_MSPIKE_H5, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_PASS, TXREP, T_SCC_BODY_TEXT_LINE autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Jiufu Guo via Gcc-patches From: Jiufu Guo Reply-To: Jiufu Guo Errors-To: gcc-patches-bounces+ouuuleilei=gmail.com@gcc.gnu.org Sender: "Gcc-patches" X-getmail-retrieved-from-mailbox: INBOX X-GMAIL-THRID: 1771767571613780249 X-GMAIL-MSGID: 1771767571613780249 Hi, Integer expression "(X - N * M) / N" can be optimized to "X / N - M" if there is no wrap/overflow/underflow and "X - N * M" has the same sign with "X". Compare the previous version: https://gcc.gnu.org/pipermail/gcc-patches/2023-July/624067.html - APIs: overflow, nonnegative_p and nonpositive_p are moved close to value range. - Use above APIs in match.pd. Bootstrap & regtest pass on ppc64{,le} and x86_64. Is this patch ok for trunk? BR, Jeff (Jiufu Guo) PR tree-optimization/108757 gcc/ChangeLog: * match.pd ((X - N * M) / N): New pattern. ((X + N * M) / N): New pattern. ((X + C) div_rshift N): New pattern. gcc/testsuite/ChangeLog: * gcc.dg/pr108757-1.c: New test. * gcc.dg/pr108757-2.c: New test. * gcc.dg/pr108757.h: New test. --- gcc/match.pd | 85 +++++++++++ gcc/testsuite/gcc.dg/pr108757-1.c | 18 +++ gcc/testsuite/gcc.dg/pr108757-2.c | 19 +++ gcc/testsuite/gcc.dg/pr108757.h | 233 ++++++++++++++++++++++++++++++ 4 files changed, 355 insertions(+) create mode 100644 gcc/testsuite/gcc.dg/pr108757-1.c create mode 100644 gcc/testsuite/gcc.dg/pr108757-2.c create mode 100644 gcc/testsuite/gcc.dg/pr108757.h diff --git a/gcc/match.pd b/gcc/match.pd index 8543f777a28..39dbb0567dc 100644 --- a/gcc/match.pd +++ b/gcc/match.pd @@ -942,6 +942,91 @@ DEFINE_INT_AND_FLOAT_ROUND_FN (RINT) #endif )))) +#if GIMPLE +(for div (trunc_div exact_div) + /* Simplify (t + M*N) / N -> t / N + M. */ + (simplify + (div (plus:c@4 @0 (mult:c@3 @1 @2)) @2) + (with {value_range vr0, vr1, vr2, vr3, vr4;} + (if (INTEGRAL_TYPE_P (type) + && get_range_query (cfun)->range_of_expr (vr1, @1) + && get_range_query (cfun)->range_of_expr (vr2, @2) + && range_op_handler (MULT_EXPR).overflow_free_p (vr1, vr2) + && get_range_query (cfun)->range_of_expr (vr0, @0) + && get_range_query (cfun)->range_of_expr (vr3, @3) + && range_op_handler (PLUS_EXPR).overflow_free_p (vr0, vr3) + && get_range_query (cfun)->range_of_expr (vr4, @4) + && (TYPE_UNSIGNED (type) + || (vr0.nonnegative_p () && vr4.nonnegative_p ()) + || (vr0.nonpositive_p () && vr4.nonpositive_p ()))) + (plus (div @0 @2) @1)))) + + /* Simplify (t - M*N) / N -> t / N - M. */ + (simplify + (div (minus@4 @0 (mult:c@3 @1 @2)) @2) + (with {value_range vr0, vr1, vr2, vr3, vr4;} + (if (INTEGRAL_TYPE_P (type) + && get_range_query (cfun)->range_of_expr (vr1, @1) + && get_range_query (cfun)->range_of_expr (vr2, @2) + && range_op_handler (MULT_EXPR).overflow_free_p (vr1, vr2) + && get_range_query (cfun)->range_of_expr (vr0, @0) + && get_range_query (cfun)->range_of_expr (vr3, @3) + && range_op_handler (MINUS_EXPR).overflow_free_p (vr0, vr3) + && get_range_query (cfun)->range_of_expr (vr4, @4) + && (TYPE_UNSIGNED (type) + || (vr0.nonnegative_p () && vr4.nonnegative_p ()) + || (vr0.nonpositive_p () && vr4.nonpositive_p ()))) + (minus (div @0 @2) @1))))) + +/* Simplify + (t + C) / N -> t / N + C / N where C is multiple of N. + (t + C) >> N -> t >> N + C>>N if low N bits of C is 0. */ +(for op (trunc_div exact_div rshift) + (simplify + (op (plus@3 @0 INTEGER_CST@1) INTEGER_CST@2) + (with + { + wide_int c = wi::to_wide (@1); + wide_int n = wi::to_wide (@2); + bool is_rshift = op == RSHIFT_EXPR; + bool neg_c = false; + bool ok = false; + value_range vr0; + if (INTEGRAL_TYPE_P (type) + && get_range_query (cfun)->range_of_expr (vr0, @0)) + { + ok = is_rshift ? wi::ctz (c) >= n.to_shwi () + : wi::multiple_of_p (c, n, TYPE_SIGN (type)); + value_range vr1, vr3; + ok = ok && get_range_query (cfun)->range_of_expr (vr1, @1) + && range_op_handler (PLUS_EXPR).overflow_free_p (vr0, vr1) + && get_range_query (cfun)->range_of_expr (vr3, @3) + && (TYPE_UNSIGNED (type) + || (vr0.nonnegative_p () && vr3.nonnegative_p ()) + || (vr0.nonpositive_p () && vr3.nonpositive_p ())); + + /* Try check 'X + C' as 'X - -C' for unsigned. */ + if (!ok && TYPE_UNSIGNED (type) && c.sign_mask () < 0) + { + neg_c = true; + c = -c; + ok = is_rshift ? wi::ctz (c) >= n.to_shwi () + : wi::multiple_of_p (c, n, UNSIGNED); + ok = ok && wi::geu_p (vr0.lower_bound (), c); + } + } + } + (if (ok) + (with + { + wide_int m; + m = is_rshift ? wi::rshift (c, n, TYPE_SIGN (type)) + : wi::div_trunc (c, n, TYPE_SIGN (type)); + m = neg_c ? -m : m; + } + (plus (op @0 @2) { wide_int_to_tree(type, m); })))))) +#endif + (for op (negate abs) /* Simplify cos(-x) and cos(|x|) -> cos(x). Similarly for cosh. */ (for coss (COS COSH) diff --git a/gcc/testsuite/gcc.dg/pr108757-1.c b/gcc/testsuite/gcc.dg/pr108757-1.c new file mode 100644 index 00000000000..7908f4bdcb8 --- /dev/null +++ b/gcc/testsuite/gcc.dg/pr108757-1.c @@ -0,0 +1,18 @@ +/* PR tree-optimization/108757 */ +/* { dg-do compile } */ +/* { dg-options "-O2 -fdump-tree-optimized" } */ + +#include +#define N 5 +#define M 3 +#define GAP 0 +typedef unsigned int UINT; +typedef int INT; +#define UMAX UINT_MAX +#define IMAX INT_MAX +#define IMIN INT_MIN +#include "pr108757.h" + +/* { dg-final { scan-tree-dump-not " = x_\[0-9\]+\\(D\\) \\+ " "optimized" } } * +/* { dg-final { scan-tree-dump-not " = x_\[0-9\]+\\(D\\) \\- " "optimized" } } */ +/* { dg-final { scan-tree-dump-not " = b_\[0-9\]+ \\+ " "optimized" } } */ diff --git a/gcc/testsuite/gcc.dg/pr108757-2.c b/gcc/testsuite/gcc.dg/pr108757-2.c new file mode 100644 index 00000000000..82bebd09944 --- /dev/null +++ b/gcc/testsuite/gcc.dg/pr108757-2.c @@ -0,0 +1,19 @@ +/* PR tree-optimization/108757 */ +/* { dg-do compile } */ +/* { dg-options "-O2 -fdump-tree-optimized -fwrapv" } */ + +#include +#define N 4 +#define M 3 +#define GAP 2 +typedef unsigned int UINT; +typedef int INT; +#define UMAX UINT_MAX +#define IMAX INT_MAX +#define IMIN INT_MIN +#include "pr108757.h" + +/* { dg-final { scan-tree-dump-times " = x_\[0-9\]+\\(D\\) \\+ " 16 "optimized" } } */ +/* { dg-final { scan-tree-dump-times " = x_\[0-9\]+\\(D\\) \\- " 3 "optimized" } } */ +/* { dg-final { scan-tree-dump-times " \\+ x_\[0-9\]+\\(D\\)" 3 "optimized" } } */ + diff --git a/gcc/testsuite/gcc.dg/pr108757.h b/gcc/testsuite/gcc.dg/pr108757.h new file mode 100644 index 00000000000..5550199c1ef --- /dev/null +++ b/gcc/testsuite/gcc.dg/pr108757.h @@ -0,0 +1,233 @@ +#define NOINLINE __attribute__ ((noinline)) +UINT NOINLINE +opt_u1 (UINT x) +{ + if (x < (M * N) - GAP) + return 0; + UINT a = x - (M * N); + UINT b = a / N; + return b + M; +} + +UINT NOINLINE +opt_u2 (UINT x) +{ + if (x > (UMAX - (M * N) + GAP)) + return 0; + UINT a = x + (M * N); + UINT b = a / N; + return b - M; +} + +INT NOINLINE +opt_s1 (INT x) +{ + if (x < (M * N) - GAP) + return 0; + INT a = x - (M * N); + INT b = a / N; + return b + M; +} + +INT NOINLINE +opt_s2 (INT x) +{ + if (x < IMIN + (M * N) - GAP || x > 0) + return 0; + INT a = x - (M * N); + INT b = a / N; + return b + M; +} + +INT NOINLINE +opt_s3 (INT x) +{ + if (x < (M * N) - GAP) + return 0; + INT a = x - (M * N); + INT b = a / -N; + return b + -M; +} + +INT NOINLINE +opt_s4 (INT x) +{ + if (x < IMIN + (M * N) - GAP || x > 0) + return 0; + INT a = x - (M * N); + INT b = a / -N; + return b + -M; +} + +INT NOINLINE +opt_s5 (INT x) +{ + if (x > (-M * N) + GAP) + return 0; + INT a = x - (-M * N); + INT b = a / N; + return b + -M; +} + +INT NOINLINE +opt_s6 (INT x) +{ + if (x > IMAX - (M * N) + GAP || x < 0) + return 0; + INT a = x - (-M * N); + INT b = a / N; + return b + -M; +} + +INT NOINLINE +opt_s7 (INT x) +{ + if (x > (M * -N) + GAP) + return 0; + INT a = x - (M * -N); + INT b = a / -N; + return b + M; +} + +INT NOINLINE +opt_s8 (INT x) +{ + if (x > IMAX - (M * N) + GAP || x < 0) + return 0; + INT a = x - (M * -N); + INT b = a / -N; + return b + M; +} + +UINT NOINLINE +opt_u3 (UINT x) +{ + if (x < (M << N) - GAP) + return 0; + UINT a = x - (M << N); + UINT b = a >> N; + return b + M; +} + +UINT NOINLINE +opt_u4 (UINT x) +{ + if (x > (UMAX - (M << N)) + GAP) + return 0; + UINT a = x + (M << N); + UINT b = a >> N; + return b - M; +} + +INT NOINLINE +opt_s9 (INT x) +{ + if (x < (M << N) - GAP) + return 0; + INT a = x - (M << N); + INT b = a >> N; + return b + M; +} + +INT NOINLINE +opt_s10 (INT x) +{ + if (x < IMIN + (M << N) - GAP || x > 0) + return 0; + INT a = x - (M << N); + INT b = a >> N; + return b + M; +} + +INT NOINLINE +opt_s11 (INT x) +{ + if (x > (-M << N) + GAP) + return 0; + INT a = x - (-M << N); + INT b = a >> N; + return b + -M; +} + +INT NOINLINE +opt_s12 (INT x) +{ + if (x > IMAX - (M << N) + GAP || x < 0) + return 0; + INT a = x - (-M << N); + INT b = a >> N; + return b + -M; +} + +UINT NOINLINE +opt_u5 (UINT x, UINT n, UINT m) +{ + if (n > N || m > M) + return 0; + if (x < (M*N) - GAP) + return 0; + UINT a = x - (m * n); + UINT b = a / n; + return b + m; +} + +UINT NOINLINE +opt_u6 (UINT x, UINT n, UINT m) +{ + if (n > N || m > M) + return 0; + if (x > (UMAX - M*N) + GAP) + return 0; + UINT a = x + (m * n); + UINT b = a / n; + return b - m; +} + +INT NOINLINE +opt_s13 (INT x, INT n, INT m) +{ + if (n > N || m > M || n < 0 || m < 0) + return 0; + if (x < (M*N) - GAP) + return 0; + INT a = x - (m * n); + INT b = a / n; + return b + m; +} + +INT NOINLINE +opt_s14 (INT x, INT n, INT m) +{ + if (n > N || m > M || n < 0 || m < 0) + return 0; + if (x > -M*N + GAP) + return 0; + INT a = x + (m * n); + INT b = a / n; + return b - m; +} + +INT +opt_s15 (INT x, INT n, INT m) +{ + if (n > 0 || m > 0 || n < -N || m < -M) + return 0; + if (x < (M*N) - GAP) + return 0; + INT a = x - (m * n); + INT b = a / n; + return b + m; +} + +INT NOINLINE +opt_s16 (INT x, INT n, INT m) +{ + if (n > 0 || m > 0 || n < -N || m < -M) + return 0; + if (x < 0 || x > (IMAX - M*N) + GAP) + return 0; + INT a = x + (m * n); + INT b = a / n; + return b - m; +} +