/* Copyright (C) 1991,1992,1996,1997,1999,2004 Free Software Foundation, Inc. Copyright (C) 2006 Vincent Fourmond. This file is taken from the GNU C Library. Written by Douglas C. Schmidt (schmidt@ics.uci.edu), modified by Vincent Fourmond to specialize for joint sort of double arrays. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. */ /* If you consider tuning this algorithm, you should consult first: Engineering a sort function; Jon Bentley and M. Douglas McIlroy; Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */ #include #include #include #include /* SWAP has to be completely redefined to take care of swapping *both* arrays */ inline static void swap_one(double * a, double * b) { double tmp; tmp = *a; *a = *b; *b = tmp; } #define SWAP(a,b) \ do {swap_one(a,b);\ swap_one((a - x_values + y_values), (b - x_values + y_values));}\ while(0) /* Discontinue quicksort algorithm when partition gets below this size. This particular magic number was chosen to work best on a Sun 4/260. */ #define MAX_THRESH 4 /* Stack node declarations used to store unfulfilled partition obligations. */ typedef struct { double *lo; double *hi; } stack_node; /* The next 4 #defines implement a very fast in-line stack abstraction. */ /* The stack needs log (total_elements) entries (we could even subtract log(MAX_THRESH)). Since total_elements has type size_t, we get as upper bound for log (total_elements): bits per byte (CHAR_BIT) * sizeof(size_t). */ #define STACK_SIZE (CHAR_BIT * sizeof(size_t)) #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top)) #define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi))) #define STACK_NOT_EMPTY (stack < top) /* Order size using quicksort. This implementation incorporates four optimizations discussed in Sedgewick: 1. Non-recursive, using an explicit stack of pointer that store the next array partition to sort. To save time, this maximum amount of space required to store an array of SIZE_MAX is allocated on the stack. Assuming a 32-bit (64 bit) integer for size_t, this needs only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes). Pretty cheap, actually. 2. Chose the pivot element using a median-of-three decision tree. This reduces the probability of selecting a bad pivot value and eliminates certain extraneous comparisons. 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving insertion sort to order the MAX_THRESH items within each partition. This is a big win, since insertion sort is faster for small, mostly sorted array segments. 4. The larger of the two sub-partitions is always pushed onto the stack first, with the algorithm then concentrating on the smaller partition. This *guarantees* no more than log (total_elems) stack size is needed (actually O(1) in this case)! */ INTERN void joint_quicksort (double *const x_values, double * const y_values, size_t total_elems) { double * const base_ptr = x_values; if (total_elems == 0) /* Avoid lossage with unsigned arithmetic below. */ return; if (total_elems > MAX_THRESH) { double *lo = base_ptr; double *hi = lo + (total_elems - 1); stack_node stack[STACK_SIZE]; stack_node *top = stack; PUSH (NULL, NULL); while (STACK_NOT_EMPTY) { double *left_ptr; double *right_ptr; /* Select median value from among LO, MID, and HI. Rearrange LO and HI so the three values are sorted. This lowers the probability of picking a pathological pivot value and skips a comparison for both the LEFT_PTR and RIGHT_PTR in the while loops. */ double *mid = lo + ((hi - lo) >> 1); if (*mid < *lo) SWAP (mid, lo); if (*hi < *mid) SWAP (mid, hi); else goto jump_over; if (*mid < *lo) SWAP (mid, lo); jump_over:; left_ptr = lo + 1; right_ptr = hi - 1; /* Here's the famous ``collapse the walls'' section of quicksort. Gotta like those tight inner loops! They are the main reason that this algorithm runs much faster than others. */ do { while (*left_ptr < *mid) left_ptr ++; while (*mid < *right_ptr) right_ptr --; if (left_ptr < right_ptr) { SWAP (left_ptr, right_ptr); if (mid == left_ptr) mid = right_ptr; else if (mid == right_ptr) mid = left_ptr; left_ptr ++; right_ptr --; } else if (left_ptr == right_ptr) { left_ptr ++; right_ptr --; break; } } while (left_ptr <= right_ptr); /* Set up pointers for next iteration. First determine whether left and right partitions are below the threshold size. If so, ignore one or both. Otherwise, push the larger partition's bounds on the stack and continue sorting the smaller one. */ if ((size_t) (right_ptr - lo) <= MAX_THRESH) { if ((size_t) (hi - left_ptr) <= MAX_THRESH) /* Ignore both small partitions. */ POP (lo, hi); else /* Ignore small left partition. */ lo = left_ptr; } else if ((size_t) (hi - left_ptr) <= MAX_THRESH) /* Ignore small right partition. */ hi = right_ptr; else if ((right_ptr - lo) > (hi - left_ptr)) { /* Push larger left partition indices. */ PUSH (lo, right_ptr); lo = left_ptr; } else { /* Push larger right partition indices. */ PUSH (left_ptr, hi); hi = right_ptr; } } } /* Once the BASE_PTR array is partially sorted by quicksort the rest is completely sorted using insertion sort, since this is efficient for partitions below MAX_THRESH size. BASE_PTR points to the beginning of the array to sort, and END_PTR points at the very last element in the array (*not* one beyond it!). */ #define min(x, y) ((x) < (y) ? (x) : (y)) { double *const end_ptr = base_ptr + (total_elems - 1); double *tmp_ptr = base_ptr; double *thresh = min(end_ptr, base_ptr + MAX_THRESH); double *run_ptr; /* Find smallest element in first threshold and place it at the array's beginning. This is the smallest array element, and the operation speeds up insertion sort's inner loop. */ for (run_ptr = tmp_ptr + 1; run_ptr <= thresh; run_ptr ++) if (*run_ptr < *tmp_ptr) tmp_ptr = run_ptr; if (tmp_ptr != base_ptr) SWAP (tmp_ptr, base_ptr); /* Insertion sort, running from left-hand-side up to right-hand-side. */ run_ptr = base_ptr + 1; while ((run_ptr ++) < end_ptr) { tmp_ptr = run_ptr - 1; while (*run_ptr < *tmp_ptr) tmp_ptr --; tmp_ptr ++; if (tmp_ptr != run_ptr) { double tmp = *run_ptr; double tmp_y = *(run_ptr - x_values + y_values); double * trav = run_ptr; while(--trav >= tmp_ptr) { *(trav + 1) = *trav; *(trav + 1 - x_values + y_values) = *(trav - x_values + y_values); } *tmp_ptr = tmp; *(tmp_ptr - x_values + y_values) = tmp_y; } } } } /* Hey, it miraculously looks like I got it right... */