On Fri, 14 Jul 2023, Aldy Hernandez wrote: > I don't know what you're trying to accomplish here, as I haven't been > following the PR, but adding all these helper functions to the ranger header > file seems wrong, especially since there's only one use of them. I see you're > tweaking the irange API, adding helper functions to range-op (which is only > for code dealing with implementing range operators for tree codes), etc etc. > > If you need these helper functions, I suggest you put them closer to their > uses (i.e. wherever the match.pd support machinery goes).
Note I suggested the opposite beacuse I thought these kind of helpers are closer to value-range support than to match.pd. But I take away from your answer that there's nothing close in the value-range machinery that answers the question whether A op B may overflow? Richard. > Aldy > > On 7/11/23 11:04, Jiufu Guo wrote: > > 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-June/623028.html > > - The APIs for checking overflow of range operation are moved to > > other files: range-op and gimple-range. > > - Improve the patterns with '(X + C)' for unsigned type. > > > > 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: > > > > * gimple-range.cc (arith_without_overflow_p): New function. > > (same_sign_p): New function. > > * gimple-range.h (arith_without_overflow_p): New declare. > > (same_sign_p): New declare. > > * match.pd ((X - N * M) / N): New pattern. > > ((X + N * M) / N): New pattern. > > ((X + C) div_rshift N): New pattern. > > * range-op.cc (plus_without_overflow_p): New function. > > (minus_without_overflow_p): New function. > > (mult_without_overflow_p): New function. > > * range-op.h (plus_without_overflow_p): New declare. > > (minus_without_overflow_p): New declare. > > (mult_without_overflow_p): New declare. > > * value-query.h (get_range): New function > > * 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/testsuite/ChangeLog: > > > > * gcc.dg/pr108757-1.c: New test. > > * gcc.dg/pr108757-2.c: New test. > > * gcc.dg/pr108757.h: New test. > > > > --- > > gcc/gimple-range.cc | 50 +++++++ > > gcc/gimple-range.h | 2 + > > gcc/match.pd | 64 ++++++++ > > gcc/range-op.cc | 77 ++++++++++ > > gcc/range-op.h | 4 + > > gcc/value-query.h | 10 ++ > > gcc/value-range.cc | 12 ++ > > gcc/value-range.h | 2 + > > gcc/testsuite/gcc.dg/pr108757-1.c | 18 +++ > > gcc/testsuite/gcc.dg/pr108757-2.c | 19 +++ > > gcc/testsuite/gcc.dg/pr108757.h | 233 ++++++++++++++++++++++++++++++ > > 11 files changed, 491 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-range.cc b/gcc/gimple-range.cc > > index > > 01e62d3ff3901143bde33dc73c0debf41d0c0fdd..620fe32e85e5fe3847a933554fc656b2939cf02d > > 100644 > > --- a/gcc/gimple-range.cc > > +++ b/gcc/gimple-range.cc > > @@ -926,3 +926,53 @@ assume_query::dump (FILE *f) > > } > > fprintf (f, "------------------------------\n"); > > } > > + > > +/* Return true if the operation "X CODE Y" in type does not overflow > > + underflow or wrap with value range info, otherwise return false. */ > > + > > +bool > > +arith_without_overflow_p (tree_code code, tree x, tree y, tree type) > > +{ > > + gcc_assert (INTEGRAL_TYPE_P (type)); > > + > > + if (TYPE_OVERFLOW_UNDEFINED (type)) > > + return true; > > + > > + value_range vr0; > > + value_range vr1; > > + if (!(get_range (vr0, x) && get_range (vr1, y))) > > + return false; > > + > > + switch (code) > > + { > > + case PLUS_EXPR: > > + return plus_without_overflow_p (vr0, vr1, type); > > + case MINUS_EXPR: > > + return minus_without_overflow_p (vr0, vr1, type); > > + case MULT_EXPR: > > + return mult_without_overflow_p (vr0, vr1, type); > > + default: > > + gcc_unreachable (); > > + } > > + > > + return false; > > +} > > + > > +/* Return true if "X" and "Y" have the same sign or zero. */ > > + > > +bool > > +same_sign_p (tree x, tree y, tree type) > > +{ > > + gcc_assert (INTEGRAL_TYPE_P (type)); > > + > > + if (TYPE_UNSIGNED (type)) > > + return true; > > + > > + value_range vr0; > > + value_range vr1; > > + if (!(get_range (vr0, x) && get_range (vr1, y))) > > + return false; > > + > > + return (vr0.nonnegative_p () && vr1.nonnegative_p ()) > > + || (vr0.nonpositive_p () && vr1.nonpositive_p ()); > > +} > > diff --git a/gcc/gimple-range.h b/gcc/gimple-range.h > > index > > 6587e4923ff44e10826a697ecced237a0ad23c88..84eac87392b642ed3305011415c804f5b319e09f > > 100644 > > --- a/gcc/gimple-range.h > > +++ b/gcc/gimple-range.h > > @@ -101,5 +101,7 @@ protected: > > gori_compute m_gori; > > }; > > > > +bool arith_without_overflow_p (tree_code code, tree x, tree y, tree type); > > +bool same_sign_p (tree x, tree y, tree type); > > > > #endif // GCC_GIMPLE_RANGE_H > > diff --git a/gcc/match.pd b/gcc/match.pd > > index > > 8543f777a28e4f39b2b2a40d0702aed88786bbb3..87e990c5b1ebbd116d7d7efdba62347d3a967cdd > > 100644 > > --- a/gcc/match.pd > > +++ b/gcc/match.pd > > @@ -942,6 +942,70 @@ 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) > > + (if (INTEGRAL_TYPE_P (type) > > + && arith_without_overflow_p (MULT_EXPR, @1, @2, type) > > + && arith_without_overflow_p (PLUS_EXPR, @0, @3, type) > > + && same_sign_p (@0, @4, type)) > > + (plus (div @0 @2) @1))) > > + > > + /* Simplify (t - M*N) / N -> t / N - M. */ > > + (simplify > > + (div (minus@4 @0 (mult:c@3 @1 @2)) @2) > > + (if (INTEGRAL_TYPE_P (type) > > + && arith_without_overflow_p (MULT_EXPR, @1, @2, type) > > + && arith_without_overflow_p (MINUS_EXPR, @0, @3, type) > > + && same_sign_p (@0, @4, type)) > > + (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; > > + if (INTEGRAL_TYPE_P (type)) > > + { > > + ok = is_rshift ? wi::ctz (c) >= n.to_shwi () > > + : wi::multiple_of_p (c, n, TYPE_SIGN (type)); > > + ok = ok && arith_without_overflow_p (PLUS_EXPR, @0, @1, type) > > + && same_sign_p (@0, @3, type); > > + > > + /* 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); > > + value_range vr; > > + ok = ok && get_range (vr, @0) > > + && wi::geu_p (vr.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/range-op.cc b/gcc/range-op.cc > > index > > cb584314f4cfc93aeec50c7f888829997a7dc8eb..487e781a0cdfa39416589983a246327957c14d54 > > 100644 > > --- a/gcc/range-op.cc > > +++ b/gcc/range-op.cc > > @@ -4311,6 +4311,83 @@ range_op_table::initialize_integral_ops () > > > > } > > > > +bool > > +plus_without_overflow_p (value_range &vr0, value_range &vr1, tree type) > > +{ > > + wi::overflow_type ovf; > > + signop sgn = TYPE_SIGN (type); > > + wide_int wmax0 = vr0.upper_bound (); > > + wide_int wmax1 = vr1.upper_bound (); > > + wi::add (wmax0, wmax1, sgn, &ovf); > > + if (ovf != wi::OVF_NONE) > > + return false; > > + > > + if (TYPE_UNSIGNED (type)) > > + return true; > > + > > + wide_int wmin0 = vr0.lower_bound (); > > + wide_int wmin1 = vr1.lower_bound (); > > + wi::add (wmin0, wmin1, sgn, &ovf); > > + if (ovf != wi::OVF_NONE) > > + return false; > > + > > + return true; > > +} > > + > > +bool > > +minus_without_overflow_p (value_range &vr0, value_range &vr1, tree type) > > +{ > > + wi::overflow_type ovf; > > + signop sgn = TYPE_SIGN (type); > > + wide_int wmin0 = vr0.lower_bound (); > > + wide_int wmax1 = vr1.upper_bound (); > > + wi::sub (wmin0, wmax1, sgn, &ovf); > > + if (ovf != wi::OVF_NONE) > > + return false; > > + > > + if (TYPE_UNSIGNED (type)) > > + return true; > > + > > + wide_int wmax0 = vr0.upper_bound (); > > + wide_int wmin1 = vr1.lower_bound (); > > + wi::sub (wmax0, wmin1, sgn, &ovf); > > + if (ovf != wi::OVF_NONE) > > + return false; > > + > > + return true; > > +} > > + > > +bool > > +mult_without_overflow_p (value_range &vr0, value_range &vr1, tree type) > > +{ > > + wi::overflow_type ovf; > > + signop sgn = TYPE_SIGN (type); > > + wide_int wmax0 = vr0.upper_bound (); > > + wide_int wmax1 = vr1.upper_bound (); > > + wi::mul (wmax0, wmax1, sgn, &ovf); > > + if (ovf != wi::OVF_NONE) > > + return false; > > + > > + if (TYPE_UNSIGNED (type)) > > + return true; > > + > > + wide_int wmin0 = vr0.lower_bound (); > > + wide_int wmin1 = vr1.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 > > af94c2756a74f710aa50aec1ac3b3de5eeb43a8e..1697ce5464c0cc8fbfb86234137ba7cc23e10979 > > 100644 > > --- a/gcc/range-op.h > > +++ b/gcc/range-op.h > > @@ -220,6 +220,10 @@ protected: > > range_operator *m_operator; > > }; > > > > +extern bool plus_without_overflow_p (value_range &, value_range &, tree); > > +extern bool minus_without_overflow_p (value_range &, value_range &, tree); > > +extern bool mult_without_overflow_p (value_range &, value_range &, tree); > > + > > // Cast the range in R to TYPE if R supports TYPE. > > > > inline bool > > diff --git a/gcc/value-query.h b/gcc/value-query.h > > index > > d10c3eac1e2e6c477cbab026942a45b4fcc2ddce..cf488c7ea9bfc423fd3de9d2c743f71175804ae2 > > 100644 > > --- a/gcc/value-query.h > > +++ b/gcc/value-query.h > > @@ -137,6 +137,16 @@ get_range_query (const struct function *fun) > > return (fun && fun->x_range_query) ? fun->x_range_query : > > &global_ranges; > > } > > > > +/* Return true if there is range for "X" expression at "S" statement, > > + and the range is not varying and not undefined. */ > > + > > +inline bool > > +get_range (vrange &r, tree x, gimple *s = NULL) > > +{ > > + return get_range_query (cfun)->range_of_expr (r, x, s) && !r.varying_p () > > + && !r.undefined_p (); > > +} > > + > > // Query the global range of NAME in function F. Default to cfun. > > extern void gimple_range_global (vrange &v, tree name, > > struct function *f = cfun); > > diff --git a/gcc/value-range.cc b/gcc/value-range.cc > > index > > 011bdbdeae62845b5627a8dfa0d261370df7e5db..5ae4e044194326c24aab6babf8e0df3e4b313e98 > > 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 > > 0170188201bc9b1c4e117661c9a62819dc1547c5..a12dea514e48cdd04a3cee5dc6304637e501d399 > > 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; > > + bool nonnegative_p () const; > > + bool nonpositive_p () const; > > > > // In-place operators. > > virtual bool union_ (const vrange &) override; > > diff --git a/gcc/testsuite/gcc.dg/pr108757-1.c > > b/gcc/testsuite/gcc.dg/pr108757-1.c > > new file mode 100644 > > index > > 0000000000000000000000000000000000000000..7908f4bdcb8e225fe311b668efbe8f6db525b4d5 > > --- /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 > > 0000000000000000000000000000000000000000..82bebd09944f0be2e0690c604723bfe6182acec3 > > --- /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\\) \\- " 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 > > 0000000000000000000000000000000000000000..5550199c1ef952f54eaa83087cec25e992057c34 > > --- /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; > > +} > > + > > > -- Richard Biener <rguent...@suse.de> SUSE Software Solutions Germany GmbH, Frankenstrasse 146, 90461 Nuernberg, Germany; GF: Ivo Totev, Andrew Myers, Andrew McDonald, Boudien Moerman; HRB 36809 (AG Nuernberg)
