Hi,
Richard Biener <rguent...@suse.de> writes: > On Wed, 7 Jun 2023, Jiufu Guo wrote: > >> Hi, >> >> This patch tries to optimize "(X - N * M) / N" to "X / N - M". >> For C code, "/" towards zero (trunc_div), and "X - N * M" maybe >> wrap/overflow/underflow. So, it is valid that "X - N * M" does >> not cross zero and does not wrap/overflow/underflow. >> >> Compare with previous version: >> https://gcc.gnu.org/pipermail/gcc-patches/2023-May/618796.html >> >> This patch 1. adds the patterns for variable N or M, >> 2. uses simpler form "(X - N * M) / N" for patterns, >> 3. adds functions to gimle-fold.h/cc (not gimple-match-head.cc) >> 4. updates testcases >> >> Bootstrap & regtest pass on ppc64{,le} and x86_64. >> Is this patch ok for trunk? > > Comments below. > >> >> BR, >> Jeff (Jiufu Guo) >> >> PR tree-optimization/108757 >> >> gcc/ChangeLog: >> >> * gimple-fold.cc (maybe_mult_overflow): New function. >> (maybe_plus_overflow): New function. >> (maybe_minus_overflow): New function. >> (plus_mult_no_ovf_and_keep_sign): New function. >> (plus_no_ovf_and_keep_sign): New function. >> * gimple-fold.h (maybe_mult_overflow): New declare. >> (plus_mult_no_ovf_and_keep_sign): New declare. >> (plus_no_ovf_and_keep_sign): New declare. >> * match.pd ((X - N * M) / N): New pattern. >> ((X + N * M) / N): New pattern. >> ((X + C) / N): New pattern. >> ((X + C) >> 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/gimple-fold.cc | 161 ++++++++++++++++++++ >> gcc/gimple-fold.h | 3 + >> gcc/match.pd | 58 +++++++ >> gcc/testsuite/gcc.dg/pr108757-1.c | 18 +++ >> gcc/testsuite/gcc.dg/pr108757-2.c | 19 +++ >> gcc/testsuite/gcc.dg/pr108757.h | 244 ++++++++++++++++++++++++++++++ >> 6 files changed, 503 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/gimple-fold.cc b/gcc/gimple-fold.cc >> index 581575b65ec..bb833ae17b3 100644 >> --- a/gcc/gimple-fold.cc >> +++ b/gcc/gimple-fold.cc >> @@ -9349,3 +9349,164 @@ gimple_stmt_integer_valued_real_p (gimple *stmt, int >> depth) >> return false; >> } >> } >> + >> +/* Return true if "X * Y" may be overflow. */ >> + >> +bool >> +maybe_mult_overflow (value_range &x, value_range &y, signop sgn) > > These functions look like some "basic" functionality that should > be (or maybe already is? Andrew?) provided by the value-range > framework. That means it should not reside in gimple-fold.{cc,h} > but elsehwere and possibly with an API close to the existing > value-range stuff. > > Andrew? It would be great to get the overflow info directly from VR :) Now, in range-op.cc, there is aleady value_range_with_overflow and value_range_from_overflowed_bounds which checks OVFs. While this information seems not recorded. Maybe, it is helpful adding a field in VR and adding API to query it. > >> +{ >> + wide_int wmin0 = x.lower_bound (); >> + wide_int wmax0 = x.upper_bound (); >> + wide_int wmin1 = y.lower_bound (); >> + wide_int wmax1 = y.upper_bound (); >> + >> + wi::overflow_type min_ovf, max_ovf; >> + wi::mul (wmin0, wmin1, sgn, &min_ovf); >> + wi::mul (wmax0, wmax1, sgn, &max_ovf); >> + if (min_ovf == wi::OVF_NONE && max_ovf == wi::OVF_NONE) >> + { >> + wi::mul (wmin0, wmax1, sgn, &min_ovf); >> + wi::mul (wmax0, wmin1, sgn, &max_ovf); >> + if (min_ovf == wi::OVF_NONE && max_ovf == wi::OVF_NONE) >> + return false; >> + } >> + return true; >> +} >> + >> +/* Return true if "X + Y" may be overflow. */ >> + >> +static bool >> +maybe_plus_overflow (value_range &x, value_range &y, signop sgn) >> +{ >> + wide_int wmin0 = x.lower_bound (); >> + wide_int wmax0 = x.upper_bound (); >> + wide_int wmin1 = y.lower_bound (); >> + wide_int wmax1 = y.upper_bound (); >> + >> + wi::overflow_type min_ovf, max_ovf; >> + wi::add (wmax0, wmax1, sgn, &min_ovf); >> + wi::add (wmin0, wmin1, sgn, &max_ovf); >> + if (min_ovf == wi::OVF_NONE && max_ovf == wi::OVF_NONE) >> + return false; >> + >> + return true; >> +} >> + >> +/* Return true if "X - Y" may be overflow. */ >> + >> +static bool >> +maybe_minus_overflow (value_range &x, value_range &y, signop sgn) >> +{ >> + wide_int wmin0 = x.lower_bound (); >> + wide_int wmax0 = x.upper_bound (); >> + wide_int wmin1 = y.lower_bound (); >> + wide_int wmax1 = y.upper_bound (); >> + >> + wi::overflow_type min_ovf, max_ovf; >> + wi::sub (wmin0, wmax1, sgn, &min_ovf); >> + wi::sub (wmax0, wmin1, sgn, &max_ovf); >> + if (min_ovf == wi::OVF_NONE && max_ovf == wi::OVF_NONE) >> + return false; >> + >> + return true; >> +} >> + >> +/* Return true if there is no overflow in the expression. >> + And no sign change on the plus/minus for X. > > What does the second sentence mean? sign(X) == sign (X + N*M)? > I suppose zero has positive sign? Right! This is useful for signed int. If "X" and "X + N*M" are both negative, this transformation would be also valid. Would use "sign(X) == sign (X + N*M)" clearly. > >> + CODE is PLUS_EXPR, if the expression is "X + N * M". >> + CODE is MINUS_EXPR, if the expression is "X - N * M". >> + TYPE is the integer type of the expressions. */ >> + >> +bool >> +plus_mult_no_ovf_and_keep_sign (tree x, tree m, tree n, tree_code code, >> + tree type) >> +{ >> + value_range vr0; >> + value_range vr1; >> + value_range vr2; >> + >> + if (get_range_query (cfun)->range_of_expr (vr0, x) >> + && get_range_query (cfun)->range_of_expr (vr1, n) >> + && get_range_query (cfun)->range_of_expr (vr2, m) && !vr0.varying_p () >> + && !vr0.undefined_p () && !vr1.varying_p () && !vr1.undefined_p () >> + && !vr2.varying_p () && !vr2.undefined_p ()) >> + { >> + signop sgn = TYPE_SIGN (type); >> + if (!TYPE_OVERFLOW_UNDEFINED (type)) >> + { >> + if (maybe_mult_overflow (vr1, vr2, sgn)) >> + { >> + m = fold_build1 (NEGATE_EXPR, type, m); > > How's this valid? 'm' might wrap here? IMHO this special-case > needs a comment. Maybe you try to handle only constant 'm' here > since we tend to canonicalize X - N * 4u to X + N * -4u? Thanks! A comment should be added. This would be useful for "unsigned" (for signed, OVF info for 'n*m' would be same with 'n*-m'). Like a prepared test case for this: opt_u7 (UINT x, UINT n, UINT m) { if (n > N || m <= UMAX - M) return 0; if (x > UMAX - (M*N) + GAP) return 0; UINT a = x - (m * n); UINT b = a / n; Here, m is "-M to -1u", then "n*m" overflows, but "n*-m" does not overflow. And "x - (m * n)" can be treated as "x + (-m) * n". > >> + if (get_range_query (cfun)->range_of_expr (vr2, m) >> + && !vr2.varying_p () && !vr2.undefined_p () >> + && !maybe_mult_overflow (vr1, vr2, sgn)) >> + code = (code == MINUS_EXPR) ? PLUS_EXPR : MINUS_EXPR; >> + else >> + return false; >> + } >> + >> + /* Get range of N*M */ >> + tree mult = fold_build2 (MULT_EXPR, type, n, m); > > Since you are working on GIMPLE 'mult' has an SSA name associated > which should also possibly get you more precise ranges (just capture > it, no need to re-generate a GENERIC expression here). Great idea! > >> + value_range vr3; >> + bool r = get_range_query (cfun)->range_of_expr (vr3, mult); >> + gcc_assert (r && !vr3.varying_p () && !vr3.undefined_p ()); >> + >> + bool overflow = code == MINUS_EXPR >> + ? maybe_minus_overflow (vr0, vr3, sgn) >> + : maybe_plus_overflow (vr0, vr3, sgn); >> + if (overflow) >> + return false; >> + } >> + >> + /* The value cross "0" is also a concern. */ >> + if (sgn == UNSIGNED) >> + return true; >> + tree op >> + = fold_build2 (code, type, x, fold_build2 (MULT_EXPR, type, n, m)); >> + value_range vr4; > > Again please use the captured representative here. Thanks! > >> + if (get_range_query (cfun)->range_of_expr (vr4, op) && !vr4.varying_p >> () >> + && !vr4.undefined_p ()) >> + { >> + /* X and (X +- N*M) are both positive (or both negtive). */ >> + if ((wi::ge_p (vr0.lower_bound (), 0, sgn) >> + && wi::ge_p (vr4.lower_bound (), 0, sgn)) >> + || (wi::le_p (vr0.upper_bound (), 0, sgn) >> + && wi::le_p (vr4.upper_bound (), 0, sgn))) > > As noted above I was hoping there's a value-range API for this. We > seem to have set_nonnegative, set_zero, etc. but no way to query > a known sign for integer ranges. FP ranges have signbit_p, > I guess that would work here, too, no? Thanks for pointing out this! I will check these APIs! > > Andrew? > > Seeing the repeated check for !varying && !undefined I wonder if > we can somehow avoid the repetition with a higher level API? The VR info for x,n,m are checked. If OVF info for "X", "N*M", are checked too, ranges for combined expressions ("N*M", "X-N*M") may not be needed, but verifying the final OVF infor may still be required. Thanks for any comments!! > >> + return true; >> + } >> + } >> + >> +return false; >> +} >> + >> +/* Return true if there is no overflow and no sign change in "X + C". >> + C is a constant integer. */ >> + >> +bool >> +plus_no_ovf_and_keep_sign (tree x, tree c, tree type) > > Pass 'c' as const wide_int& here. Yeap, while "tree_int_cst_sign_bit (c)" can be used on "tree c" :) Using wide_int should be also ok, tree_int_cst_sign_bit is also based on wide_int. > >> +{ >> + value_range vr; >> + if (get_range_query (cfun)->range_of_expr (vr, x) && !vr.varying_p () >> + && !vr.undefined_p ()) >> + { >> + wi::overflow_type ovf = wi::OVF_NONE; >> + wide_int min = vr.lower_bound (); >> + wide_int max = vr.upper_bound (); >> + wide_int wc = wi::to_wide (c); >> + if (!TYPE_OVERFLOW_UNDEFINED (type)) >> + { >> + if (tree_int_cst_sign_bit (c)) >> + wi::sub (min, -wc, TYPE_SIGN (type), &ovf); >> + else >> + wi::add (max, wc, TYPE_SIGN (type), &ovf); >> + } >> + if (ovf == wi::OVF_NONE) >> + /* unsigned, or 't' and 't + C' are both positive/negative. */ >> + if (TYPE_UNSIGNED (type) >> + || (wi::ge_p (min, 0, SIGNED) && wi::ge_p (min + wc, 0, SIGNED)) > > the second compare should be the same as wi::ge_p (min, -wc, SIGNED) or > are you implicitely checking for overflow here? "wi::ge_p (min + wc, 0, SIGNED)" is used just because it may more readable as: "'min + wc' is positive". > >> + || (wi::le_p (max, 0, SIGNED) && wi::le_p (max + wc, 0, SIGNED))) >> + return true; >> + } >> + >> + return false; >> +} >> diff --git a/gcc/gimple-fold.h b/gcc/gimple-fold.h >> index 2fd58db9a2e..45df86a433e 100644 >> --- a/gcc/gimple-fold.h >> +++ b/gcc/gimple-fold.h >> @@ -64,6 +64,9 @@ extern gimple_seq rewrite_to_defined_overflow (gimple *, >> bool = false); >> extern void replace_call_with_value (gimple_stmt_iterator *, tree); >> extern tree tree_vec_extract (gimple_stmt_iterator *, tree, tree, tree, >> tree); >> extern void gsi_replace_with_seq_vops (gimple_stmt_iterator *, gimple_seq); >> +extern bool maybe_mult_overflow (tree, tree, tree); >> +extern bool plus_mult_no_ovf_and_keep_sign (tree, tree, tree, tree_code, >> tree); >> +extern bool plus_no_ovf_and_keep_sign (tree, tree, tree); >> >> /* gimple_build, functionally matching fold_buildN, outputs stmts >> int the provided sequence, matching and simplifying them on-the-fly. >> diff --git a/gcc/match.pd b/gcc/match.pd >> index 16482b741ea..6f7a6afdca8 100644 >> --- a/gcc/match.pd >> +++ b/gcc/match.pd >> @@ -942,6 +942,64 @@ 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 @0 (mult:c @1 @2)) @2) >> + (if (INTEGRAL_TYPE_P (type) >> + && plus_mult_no_ovf_and_keep_sign (@0, @1, @2, PLUS_EXPR, type)) >> + (plus (div @0 @2) @1))) >> + >> + /* Simplify (t - M*N) / N -> t / N - M. */ >> + (simplify >> + (div (minus @0 (mult:c @1 @2)) @2) >> + (if (INTEGRAL_TYPE_P (type) >> + && plus_mult_no_ovf_and_keep_sign (@0, @1, @2, MINUS_EXPR, type)) >> + (minus (div @0 @2) @1))) >> + >> + /* Simplify (t + C) / N -> t / N + C / N where C is multiple of N */ >> + (simplify >> + (div (plus @0 INTEGER_CST@1) INTEGER_CST@2) >> + (with >> + { tree repaired_c = @1; >> + if (TYPE_UNSIGNED (type) && tree_int_cst_sign_bit (@1)) >> + repaired_c = fold_build1 (NEGATE_EXPR, type, @1); > > What if @1 is 0x80000000? Please consider re-doing this with > wide_int from the start. Thanks for the great catch here! This is a special value, while NEGATE would not break it here. OK, wide_int would be preferred. Thanks again for your quick and helpful comments! BR, Jeff (Jiufu Guo) > >> + } >> + (if (INTEGRAL_TYPE_P (type) >> + && multiple_of_p (type, repaired_c, @2) >> + && plus_no_ovf_and_keep_sign (@0, @1, type)) >> + (with >> + { wide_int m; >> + wide_int c = wi::to_wide (@1); >> + wide_int n = wi::to_wide (@2); >> + wi::overflow_type ovf; >> + if (TYPE_UNSIGNED (type) && tree_int_cst_sign_bit (@1)) >> + m = -wi::div_trunc (-c, n, TYPE_SIGN (type), &ovf); >> + else >> + m = wi::div_trunc (c, n, TYPE_SIGN (type), &ovf); >> + gcc_assert (ovf == wi::OVF_NONE); >> + } >> + (plus (div @0 @2) { wide_int_to_tree(type, m); })))))) >> + >> +/* Simplify (t + C) >> N -> t >> N + C>>N if low N bits of C is 0. */ >> +(simplify >> + (rshift (plus @0 INTEGER_CST@1) INTEGER_CST@2) >> + (if (INTEGRAL_TYPE_P (type) && !tree_int_cst_sign_bit (@2) >> + && wi::ctz (wi::to_wide (@1)) >= wi::to_wide (@2).to_shwi () >> + && plus_no_ovf_and_keep_sign (@0, @1, type)) >> + (with >> + { wide_int m; >> + wide_int c = wi::to_wide (@1); >> + wide_int n = wi::to_wide (@2); >> + if (TYPE_UNSIGNED (type) && tree_int_cst_sign_bit (@1)) >> + m = -wi::rshift (-c, n, TYPE_SIGN (type)); >> + else >> + m = wi::rshift (c, n, TYPE_SIGN (type)); >> + } >> + (plus (rshift @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..7e7b60c756d >> --- /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 <limits.h> >> +#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..2a9ad234e68 >> --- /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 <limits.h> >> +#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\\) \\- " 4 >> "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..9dfa527f533 >> --- /dev/null >> +++ b/gcc/testsuite/gcc.dg/pr108757.h >> @@ -0,0 +1,244 @@ >> +#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; >> +} >> + >> +UINT NOINLINE >> +opt_u7 (UINT x, UINT n, UINT m) >> +{ >> + if (n > N || m <= UMAX - M) >> + return 0; >> + if (x > UMAX - (M*N) + GAP) >> + return 0; >> + UINT a = x - (m * n); >> + UINT b = a / n; >> + return b + m; >> +} >>
