| Message ID | 20231003122251.3325435-6-adhemerval.zanella@linaro.org |
|---|---|
| State | Accepted |
| Commit | 274a46c9b25ab733a1fb9fb1497f1beecae30193 |
| Headers | show |
| Series | Use introsort for qsort | expand |
On Tue, Oct 3, 2023 at 7:23 AM Adhemerval Zanella <adhemerval.zanella@linaro.org> wrote: > > This patch makes the quicksort implementation to acts as introsort, to > avoid worse-case performance (and thus making it O(nlog n)). It switch > to heapsort when the depth level reaches 2*log2(total elements). The > heapsort is a textbook implementation. > > Checked on x86_64-linux-gnu and aarch64-linux-gnu. > --- > stdlib/qsort.c | 89 ++++++++++++++++++++++++++++++++++++++++++++++---- > 1 file changed, 82 insertions(+), 7 deletions(-) > > diff --git a/stdlib/qsort.c b/stdlib/qsort.c > index 80706b3357..d5f205affc 100644 > --- a/stdlib/qsort.c > +++ b/stdlib/qsort.c > @@ -98,6 +98,7 @@ typedef struct > { > char *lo; > char *hi; > + size_t depth; > } stack_node; > > /* The stack needs log (total_elements) entries (we could even subtract > @@ -107,22 +108,85 @@ typedef struct > enum { STACK_SIZE = CHAR_BIT * sizeof (size_t) }; > > static inline stack_node * > -push (stack_node *top, char *lo, char *hi) > +push (stack_node *top, char *lo, char *hi, size_t depth) > { > top->lo = lo; > top->hi = hi; > + top->depth = depth; > return ++top; > } > > static inline stack_node * > -pop (stack_node *top, char **lo, char **hi) > +pop (stack_node *top, char **lo, char **hi, size_t *depth) > { > --top; > *lo = top->lo; > *hi = top->hi; > + *depth = top->depth; > return top; > } > > +/* NB: N is inclusive bound for BASE. */ > +static inline void > +siftdown (void *base, size_t size, size_t k, size_t n, > + enum swap_type_t swap_type, __compar_d_fn_t cmp, void *arg) > +{ > + while (k <= n / 2) > + { > + size_t j = 2 * k; > + if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0) > + j++; > + > + if (cmp (base + (k * size), base + (j * size), arg) >= 0) > + break; > + > + do_swap (base + (size * j), base + (k * size), size, swap_type); > + k = j; > + } > +} > + > +static inline void > +heapify (void *base, size_t size, size_t n, enum swap_type_t swap_type, > + __compar_d_fn_t cmp, void *arg) > +{ > + size_t k = n / 2; > + while (1) > + { > + siftdown (base, size, k, n, swap_type, cmp, arg); > + if (k-- == 0) > + break; > + } > +} > + > +/* A non-recursive heapsort, used on introsort implementation as a fallback > + routine with worst-case performance of O(nlog n) and worst-case space > + complexity of O(1). It sorts the array starting at BASE and ending at > + END, with each element of SIZE bytes. The SWAP_TYPE is the callback > + function used to swap elements, and CMP is the function used to compare > + elements. */ > +static void > +heapsort_r (void *base, void *end, size_t size, enum swap_type_t swap_type, > + __compar_d_fn_t cmp, void *arg) > +{ > + const size_t count = ((uintptr_t) end - (uintptr_t) base) / size; > + > + if (count < 2) > + return; > + > + size_t n = count - 1; > + > + /* Build the binary heap, largest value at the base[0]. */ > + heapify (base, size, n, swap_type, cmp, arg); > + > + /* On each iteration base[0:n] is the binary heap, while base[n:count] > + is sorted. */ > + while (n > 0) > + { > + do_swap (base, base + (n * size), size, swap_type); > + n--; > + siftdown (base, size, 0, n, swap_type, cmp, arg); > + } > +} > > static inline void > insertion_sort_qsort_partitions (void *const pbase, size_t total_elems, > @@ -208,7 +272,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, > > const size_t max_thresh = MAX_THRESH * size; > > - if (total_elems == 0) > + if (total_elems <= 1) > /* Avoid lossage with unsigned arithmetic below. */ > return; > > @@ -220,15 +284,26 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, > else > swap_type = SWAP_BYTES; > > + /* Maximum depth before quicksort switches to heapsort. */ > + size_t depth = 2 * (sizeof (size_t) * CHAR_BIT - 1 > + - __builtin_clzl (total_elems)); > + > if (total_elems > MAX_THRESH) > { > char *lo = base_ptr; > char *hi = &lo[size * (total_elems - 1)]; > stack_node stack[STACK_SIZE]; > - stack_node *top = stack + 1; > + stack_node *top = push (stack, NULL, NULL, depth); > > while (stack < top) > { > + if (depth == 0) > + { > + heapsort_r (lo, hi, size, swap_type, cmp, arg); > + top = pop (top, &lo, &hi, &depth); > + continue; > + } > + > char *left_ptr; > char *right_ptr; > > @@ -292,7 +367,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, > { > if ((size_t) (hi - left_ptr) <= max_thresh) > /* Ignore both small partitions. */ > - top = pop (top, &lo, &hi); > + top = pop (top, &lo, &hi, &depth); > else > /* Ignore small left partition. */ > lo = left_ptr; > @@ -303,13 +378,13 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, > else if ((right_ptr - lo) > (hi - left_ptr)) > { > /* Push larger left partition indices. */ > - top = push (top, lo, right_ptr); > + top = push (top, lo, right_ptr, depth - 1); > lo = left_ptr; > } > else > { > /* Push larger right partition indices. */ > - top = push (top, left_ptr, hi); > + top = push (top, left_ptr, hi, depth - 1); > hi = right_ptr; > } > } > -- > 2.34.1 > LGTM Reviewed-by: Noah Goldstein <goldstein.w.n@gmail.com>
diff --git a/stdlib/qsort.c b/stdlib/qsort.c index 80706b3357..d5f205affc 100644 --- a/stdlib/qsort.c +++ b/stdlib/qsort.c @@ -98,6 +98,7 @@ typedef struct { char *lo; char *hi; + size_t depth; } stack_node; /* The stack needs log (total_elements) entries (we could even subtract @@ -107,22 +108,85 @@ typedef struct enum { STACK_SIZE = CHAR_BIT * sizeof (size_t) }; static inline stack_node * -push (stack_node *top, char *lo, char *hi) +push (stack_node *top, char *lo, char *hi, size_t depth) { top->lo = lo; top->hi = hi; + top->depth = depth; return ++top; } static inline stack_node * -pop (stack_node *top, char **lo, char **hi) +pop (stack_node *top, char **lo, char **hi, size_t *depth) { --top; *lo = top->lo; *hi = top->hi; + *depth = top->depth; return top; } +/* NB: N is inclusive bound for BASE. */ +static inline void +siftdown (void *base, size_t size, size_t k, size_t n, + enum swap_type_t swap_type, __compar_d_fn_t cmp, void *arg) +{ + while (k <= n / 2) + { + size_t j = 2 * k; + if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0) + j++; + + if (cmp (base + (k * size), base + (j * size), arg) >= 0) + break; + + do_swap (base + (size * j), base + (k * size), size, swap_type); + k = j; + } +} + +static inline void +heapify (void *base, size_t size, size_t n, enum swap_type_t swap_type, + __compar_d_fn_t cmp, void *arg) +{ + size_t k = n / 2; + while (1) + { + siftdown (base, size, k, n, swap_type, cmp, arg); + if (k-- == 0) + break; + } +} + +/* A non-recursive heapsort, used on introsort implementation as a fallback + routine with worst-case performance of O(nlog n) and worst-case space + complexity of O(1). It sorts the array starting at BASE and ending at + END, with each element of SIZE bytes. The SWAP_TYPE is the callback + function used to swap elements, and CMP is the function used to compare + elements. */ +static void +heapsort_r (void *base, void *end, size_t size, enum swap_type_t swap_type, + __compar_d_fn_t cmp, void *arg) +{ + const size_t count = ((uintptr_t) end - (uintptr_t) base) / size; + + if (count < 2) + return; + + size_t n = count - 1; + + /* Build the binary heap, largest value at the base[0]. */ + heapify (base, size, n, swap_type, cmp, arg); + + /* On each iteration base[0:n] is the binary heap, while base[n:count] + is sorted. */ + while (n > 0) + { + do_swap (base, base + (n * size), size, swap_type); + n--; + siftdown (base, size, 0, n, swap_type, cmp, arg); + } +} static inline void insertion_sort_qsort_partitions (void *const pbase, size_t total_elems, @@ -208,7 +272,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, const size_t max_thresh = MAX_THRESH * size; - if (total_elems == 0) + if (total_elems <= 1) /* Avoid lossage with unsigned arithmetic below. */ return; @@ -220,15 +284,26 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, else swap_type = SWAP_BYTES; + /* Maximum depth before quicksort switches to heapsort. */ + size_t depth = 2 * (sizeof (size_t) * CHAR_BIT - 1 + - __builtin_clzl (total_elems)); + if (total_elems > MAX_THRESH) { char *lo = base_ptr; char *hi = &lo[size * (total_elems - 1)]; stack_node stack[STACK_SIZE]; - stack_node *top = stack + 1; + stack_node *top = push (stack, NULL, NULL, depth); while (stack < top) { + if (depth == 0) + { + heapsort_r (lo, hi, size, swap_type, cmp, arg); + top = pop (top, &lo, &hi, &depth); + continue; + } + char *left_ptr; char *right_ptr; @@ -292,7 +367,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, { if ((size_t) (hi - left_ptr) <= max_thresh) /* Ignore both small partitions. */ - top = pop (top, &lo, &hi); + top = pop (top, &lo, &hi, &depth); else /* Ignore small left partition. */ lo = left_ptr; @@ -303,13 +378,13 @@ _quicksort (void *const pbase, size_t total_elems, size_t size, else if ((right_ptr - lo) > (hi - left_ptr)) { /* Push larger left partition indices. */ - top = push (top, lo, right_ptr); + top = push (top, lo, right_ptr, depth - 1); lo = left_ptr; } else { /* Push larger right partition indices. */ - top = push (top, left_ptr, hi); + top = push (top, left_ptr, hi, depth - 1); hi = right_ptr; } }