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Diffstat (limited to 'tcl8.6/compat/zlib/examples/enough.c')
| -rw-r--r-- | tcl8.6/compat/zlib/examples/enough.c | 572 |
1 files changed, 0 insertions, 572 deletions
diff --git a/tcl8.6/compat/zlib/examples/enough.c b/tcl8.6/compat/zlib/examples/enough.c deleted file mode 100644 index b991144..0000000 --- a/tcl8.6/compat/zlib/examples/enough.c +++ /dev/null @@ -1,572 +0,0 @@ -/* enough.c -- determine the maximum size of inflate's Huffman code tables over - * all possible valid and complete Huffman codes, subject to a length limit. - * Copyright (C) 2007, 2008, 2012 Mark Adler - * Version 1.4 18 August 2012 Mark Adler - */ - -/* Version history: - 1.0 3 Jan 2007 First version (derived from codecount.c version 1.4) - 1.1 4 Jan 2007 Use faster incremental table usage computation - Prune examine() search on previously visited states - 1.2 5 Jan 2007 Comments clean up - As inflate does, decrease root for short codes - Refuse cases where inflate would increase root - 1.3 17 Feb 2008 Add argument for initial root table size - Fix bug for initial root table size == max - 1 - Use a macro to compute the history index - 1.4 18 Aug 2012 Avoid shifts more than bits in type (caused endless loop!) - Clean up comparisons of different types - Clean up code indentation - */ - -/* - Examine all possible Huffman codes for a given number of symbols and a - maximum code length in bits to determine the maximum table size for zilb's - inflate. Only complete Huffman codes are counted. - - Two codes are considered distinct if the vectors of the number of codes per - length are not identical. So permutations of the symbol assignments result - in the same code for the counting, as do permutations of the assignments of - the bit values to the codes (i.e. only canonical codes are counted). - - We build a code from shorter to longer lengths, determining how many symbols - are coded at each length. At each step, we have how many symbols remain to - be coded, what the last code length used was, and how many bit patterns of - that length remain unused. Then we add one to the code length and double the - number of unused patterns to graduate to the next code length. We then - assign all portions of the remaining symbols to that code length that - preserve the properties of a correct and eventually complete code. Those - properties are: we cannot use more bit patterns than are available; and when - all the symbols are used, there are exactly zero possible bit patterns - remaining. - - The inflate Huffman decoding algorithm uses two-level lookup tables for - speed. There is a single first-level table to decode codes up to root bits - in length (root == 9 in the current inflate implementation). The table - has 1 << root entries and is indexed by the next root bits of input. Codes - shorter than root bits have replicated table entries, so that the correct - entry is pointed to regardless of the bits that follow the short code. If - the code is longer than root bits, then the table entry points to a second- - level table. The size of that table is determined by the longest code with - that root-bit prefix. If that longest code has length len, then the table - has size 1 << (len - root), to index the remaining bits in that set of - codes. Each subsequent root-bit prefix then has its own sub-table. The - total number of table entries required by the code is calculated - incrementally as the number of codes at each bit length is populated. When - all of the codes are shorter than root bits, then root is reduced to the - longest code length, resulting in a single, smaller, one-level table. - - The inflate algorithm also provides for small values of root (relative to - the log2 of the number of symbols), where the shortest code has more bits - than root. In that case, root is increased to the length of the shortest - code. This program, by design, does not handle that case, so it is verified - that the number of symbols is less than 2^(root + 1). - - In order to speed up the examination (by about ten orders of magnitude for - the default arguments), the intermediate states in the build-up of a code - are remembered and previously visited branches are pruned. The memory - required for this will increase rapidly with the total number of symbols and - the maximum code length in bits. However this is a very small price to pay - for the vast speedup. - - First, all of the possible Huffman codes are counted, and reachable - intermediate states are noted by a non-zero count in a saved-results array. - Second, the intermediate states that lead to (root + 1) bit or longer codes - are used to look at all sub-codes from those junctures for their inflate - memory usage. (The amount of memory used is not affected by the number of - codes of root bits or less in length.) Third, the visited states in the - construction of those sub-codes and the associated calculation of the table - size is recalled in order to avoid recalculating from the same juncture. - Beginning the code examination at (root + 1) bit codes, which is enabled by - identifying the reachable nodes, accounts for about six of the orders of - magnitude of improvement for the default arguments. About another four - orders of magnitude come from not revisiting previous states. Out of - approximately 2x10^16 possible Huffman codes, only about 2x10^6 sub-codes - need to be examined to cover all of the possible table memory usage cases - for the default arguments of 286 symbols limited to 15-bit codes. - - Note that an unsigned long long type is used for counting. It is quite easy - to exceed the capacity of an eight-byte integer with a large number of - symbols and a large maximum code length, so multiple-precision arithmetic - would need to replace the unsigned long long arithmetic in that case. This - program will abort if an overflow occurs. The big_t type identifies where - the counting takes place. - - An unsigned long long type is also used for calculating the number of - possible codes remaining at the maximum length. This limits the maximum - code length to the number of bits in a long long minus the number of bits - needed to represent the symbols in a flat code. The code_t type identifies - where the bit pattern counting takes place. - */ - -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <assert.h> - -#define local static - -/* special data types */ -typedef unsigned long long big_t; /* type for code counting */ -typedef unsigned long long code_t; /* type for bit pattern counting */ -struct tab { /* type for been here check */ - size_t len; /* length of bit vector in char's */ - char *vec; /* allocated bit vector */ -}; - -/* The array for saving results, num[], is indexed with this triplet: - - syms: number of symbols remaining to code - left: number of available bit patterns at length len - len: number of bits in the codes currently being assigned - - Those indices are constrained thusly when saving results: - - syms: 3..totsym (totsym == total symbols to code) - left: 2..syms - 1, but only the evens (so syms == 8 -> 2, 4, 6) - len: 1..max - 1 (max == maximum code length in bits) - - syms == 2 is not saved since that immediately leads to a single code. left - must be even, since it represents the number of available bit patterns at - the current length, which is double the number at the previous length. - left ends at syms-1 since left == syms immediately results in a single code. - (left > sym is not allowed since that would result in an incomplete code.) - len is less than max, since the code completes immediately when len == max. - - The offset into the array is calculated for the three indices with the - first one (syms) being outermost, and the last one (len) being innermost. - We build the array with length max-1 lists for the len index, with syms-3 - of those for each symbol. There are totsym-2 of those, with each one - varying in length as a function of sym. See the calculation of index in - count() for the index, and the calculation of size in main() for the size - of the array. - - For the deflate example of 286 symbols limited to 15-bit codes, the array - has 284,284 entries, taking up 2.17 MB for an 8-byte big_t. More than - half of the space allocated for saved results is actually used -- not all - possible triplets are reached in the generation of valid Huffman codes. - */ - -/* The array for tracking visited states, done[], is itself indexed identically - to the num[] array as described above for the (syms, left, len) triplet. - Each element in the array is further indexed by the (mem, rem) doublet, - where mem is the amount of inflate table space used so far, and rem is the - remaining unused entries in the current inflate sub-table. Each indexed - element is simply one bit indicating whether the state has been visited or - not. Since the ranges for mem and rem are not known a priori, each bit - vector is of a variable size, and grows as needed to accommodate the visited - states. mem and rem are used to calculate a single index in a triangular - array. Since the range of mem is expected in the default case to be about - ten times larger than the range of rem, the array is skewed to reduce the - memory usage, with eight times the range for mem than for rem. See the - calculations for offset and bit in beenhere() for the details. - - For the deflate example of 286 symbols limited to 15-bit codes, the bit - vectors grow to total approximately 21 MB, in addition to the 4.3 MB done[] - array itself. - */ - -/* Globals to avoid propagating constants or constant pointers recursively */ -local int max; /* maximum allowed bit length for the codes */ -local int root; /* size of base code table in bits */ -local int large; /* largest code table so far */ -local size_t size; /* number of elements in num and done */ -local int *code; /* number of symbols assigned to each bit length */ -local big_t *num; /* saved results array for code counting */ -local struct tab *done; /* states already evaluated array */ - -/* Index function for num[] and done[] */ -#define INDEX(i,j,k) (((size_t)((i-1)>>1)*((i-2)>>1)+(j>>1)-1)*(max-1)+k-1) - -/* Free allocated space. Uses globals code, num, and done. */ -local void cleanup(void) -{ - size_t n; - - if (done != NULL) { - for (n = 0; n < size; n++) - if (done[n].len) - free(done[n].vec); - free(done); - } - if (num != NULL) - free(num); - if (code != NULL) - free(code); -} - -/* Return the number of possible Huffman codes using bit patterns of lengths - len through max inclusive, coding syms symbols, with left bit patterns of - length len unused -- return -1 if there is an overflow in the counting. - Keep a record of previous results in num to prevent repeating the same - calculation. Uses the globals max and num. */ -local big_t count(int syms, int len, int left) -{ - big_t sum; /* number of possible codes from this juncture */ - big_t got; /* value returned from count() */ - int least; /* least number of syms to use at this juncture */ - int most; /* most number of syms to use at this juncture */ - int use; /* number of bit patterns to use in next call */ - size_t index; /* index of this case in *num */ - - /* see if only one possible code */ - if (syms == left) - return 1; - - /* note and verify the expected state */ - assert(syms > left && left > 0 && len < max); - - /* see if we've done this one already */ - index = INDEX(syms, left, len); - got = num[index]; - if (got) - return got; /* we have -- return the saved result */ - - /* we need to use at least this many bit patterns so that the code won't be - incomplete at the next length (more bit patterns than symbols) */ - least = (left << 1) - syms; - if (least < 0) - least = 0; - - /* we can use at most this many bit patterns, lest there not be enough - available for the remaining symbols at the maximum length (if there were - no limit to the code length, this would become: most = left - 1) */ - most = (((code_t)left << (max - len)) - syms) / - (((code_t)1 << (max - len)) - 1); - - /* count all possible codes from this juncture and add them up */ - sum = 0; - for (use = least; use <= most; use++) { - got = count(syms - use, len + 1, (left - use) << 1); - sum += got; - if (got == (big_t)0 - 1 || sum < got) /* overflow */ - return (big_t)0 - 1; - } - - /* verify that all recursive calls are productive */ - assert(sum != 0); - - /* save the result and return it */ - num[index] = sum; - return sum; -} - -/* Return true if we've been here before, set to true if not. Set a bit in a - bit vector to indicate visiting this state. Each (syms,len,left) state - has a variable size bit vector indexed by (mem,rem). The bit vector is - lengthened if needed to allow setting the (mem,rem) bit. */ -local int beenhere(int syms, int len, int left, int mem, int rem) -{ - size_t index; /* index for this state's bit vector */ - size_t offset; /* offset in this state's bit vector */ - int bit; /* mask for this state's bit */ - size_t length; /* length of the bit vector in bytes */ - char *vector; /* new or enlarged bit vector */ - - /* point to vector for (syms,left,len), bit in vector for (mem,rem) */ - index = INDEX(syms, left, len); - mem -= 1 << root; - offset = (mem >> 3) + rem; - offset = ((offset * (offset + 1)) >> 1) + rem; - bit = 1 << (mem & 7); - - /* see if we've been here */ - length = done[index].len; - if (offset < length && (done[index].vec[offset] & bit) != 0) - return 1; /* done this! */ - - /* we haven't been here before -- set the bit to show we have now */ - - /* see if we need to lengthen the vector in order to set the bit */ - if (length <= offset) { - /* if we have one already, enlarge it, zero out the appended space */ - if (length) { - do { - length <<= 1; - } while (length <= offset); - vector = realloc(done[index].vec, length); - if (vector != NULL) - memset(vector + done[index].len, 0, length - done[index].len); - } - - /* otherwise we need to make a new vector and zero it out */ - else { - length = 1 << (len - root); - while (length <= offset) - length <<= 1; - vector = calloc(length, sizeof(char)); - } - - /* in either case, bail if we can't get the memory */ - if (vector == NULL) { - fputs("abort: unable to allocate enough memory\n", stderr); - cleanup(); - exit(1); - } - - /* install the new vector */ - done[index].len = length; - done[index].vec = vector; - } - - /* set the bit */ - done[index].vec[offset] |= bit; - return 0; -} - -/* Examine all possible codes from the given node (syms, len, left). Compute - the amount of memory required to build inflate's decoding tables, where the - number of code structures used so far is mem, and the number remaining in - the current sub-table is rem. Uses the globals max, code, root, large, and - done. */ -local void examine(int syms, int len, int left, int mem, int rem) -{ - int least; /* least number of syms to use at this juncture */ - int most; /* most number of syms to use at this juncture */ - int use; /* number of bit patterns to use in next call */ - - /* see if we have a complete code */ - if (syms == left) { - /* set the last code entry */ - code[len] = left; - - /* complete computation of memory used by this code */ - while (rem < left) { - left -= rem; - rem = 1 << (len - root); - mem += rem; - } - assert(rem == left); - - /* if this is a new maximum, show the entries used and the sub-code */ - if (mem > large) { - large = mem; - printf("max %d: ", mem); - for (use = root + 1; use <= max; use++) - if (code[use]) - printf("%d[%d] ", code[use], use); - putchar('\n'); - fflush(stdout); - } - - /* remove entries as we drop back down in the recursion */ - code[len] = 0; - return; - } - - /* prune the tree if we can */ - if (beenhere(syms, len, left, mem, rem)) - return; - - /* we need to use at least this many bit patterns so that the code won't be - incomplete at the next length (more bit patterns than symbols) */ - least = (left << 1) - syms; - if (least < 0) - least = 0; - - /* we can use at most this many bit patterns, lest there not be enough - available for the remaining symbols at the maximum length (if there were - no limit to the code length, this would become: most = left - 1) */ - most = (((code_t)left << (max - len)) - syms) / - (((code_t)1 << (max - len)) - 1); - - /* occupy least table spaces, creating new sub-tables as needed */ - use = least; - while (rem < use) { - use -= rem; - rem = 1 << (len - root); - mem += rem; - } - rem -= use; - - /* examine codes from here, updating table space as we go */ - for (use = least; use <= most; use++) { - code[len] = use; - examine(syms - use, len + 1, (left - use) << 1, - mem + (rem ? 1 << (len - root) : 0), rem << 1); - if (rem == 0) { - rem = 1 << (len - root); - mem += rem; - } - rem--; - } - - /* remove entries as we drop back down in the recursion */ - code[len] = 0; -} - -/* Look at all sub-codes starting with root + 1 bits. Look at only the valid - intermediate code states (syms, left, len). For each completed code, - calculate the amount of memory required by inflate to build the decoding - tables. Find the maximum amount of memory required and show the code that - requires that maximum. Uses the globals max, root, and num. */ -local void enough(int syms) -{ - int n; /* number of remaing symbols for this node */ - int left; /* number of unused bit patterns at this length */ - size_t index; /* index of this case in *num */ - - /* clear code */ - for (n = 0; n <= max; n++) - code[n] = 0; - - /* look at all (root + 1) bit and longer codes */ - large = 1 << root; /* base table */ - if (root < max) /* otherwise, there's only a base table */ - for (n = 3; n <= syms; n++) - for (left = 2; left < n; left += 2) - { - /* look at all reachable (root + 1) bit nodes, and the - resulting codes (complete at root + 2 or more) */ - index = INDEX(n, left, root + 1); - if (root + 1 < max && num[index]) /* reachable node */ - examine(n, root + 1, left, 1 << root, 0); - - /* also look at root bit codes with completions at root + 1 - bits (not saved in num, since complete), just in case */ - if (num[index - 1] && n <= left << 1) - examine((n - left) << 1, root + 1, (n - left) << 1, - 1 << root, 0); - } - - /* done */ - printf("done: maximum of %d table entries\n", large); -} - -/* - Examine and show the total number of possible Huffman codes for a given - maximum number of symbols, initial root table size, and maximum code length - in bits -- those are the command arguments in that order. The default - values are 286, 9, and 15 respectively, for the deflate literal/length code. - The possible codes are counted for each number of coded symbols from two to - the maximum. The counts for each of those and the total number of codes are - shown. The maximum number of inflate table entires is then calculated - across all possible codes. Each new maximum number of table entries and the - associated sub-code (starting at root + 1 == 10 bits) is shown. - - To count and examine Huffman codes that are not length-limited, provide a - maximum length equal to the number of symbols minus one. - - For the deflate literal/length code, use "enough". For the deflate distance - code, use "enough 30 6". - - This uses the %llu printf format to print big_t numbers, which assumes that - big_t is an unsigned long long. If the big_t type is changed (for example - to a multiple precision type), the method of printing will also need to be - updated. - */ -int main(int argc, char **argv) -{ - int syms; /* total number of symbols to code */ - int n; /* number of symbols to code for this run */ - big_t got; /* return value of count() */ - big_t sum; /* accumulated number of codes over n */ - code_t word; /* for counting bits in code_t */ - - /* set up globals for cleanup() */ - code = NULL; - num = NULL; - done = NULL; - - /* get arguments -- default to the deflate literal/length code */ - syms = 286; - root = 9; - max = 15; - if (argc > 1) { - syms = atoi(argv[1]); - if (argc > 2) { - root = atoi(argv[2]); - if (argc > 3) - max = atoi(argv[3]); - } - } - if (argc > 4 || syms < 2 || root < 1 || max < 1) { - fputs("invalid arguments, need: [sym >= 2 [root >= 1 [max >= 1]]]\n", - stderr); - return 1; - } - - /* if not restricting the code length, the longest is syms - 1 */ - if (max > syms - 1) - max = syms - 1; - - /* determine the number of bits in a code_t */ - for (n = 0, word = 1; word; n++, word <<= 1) - ; - - /* make sure that the calculation of most will not overflow */ - if (max > n || (code_t)(syms - 2) >= (((code_t)0 - 1) >> (max - 1))) { - fputs("abort: code length too long for internal types\n", stderr); - return 1; - } - - /* reject impossible code requests */ - if ((code_t)(syms - 1) > ((code_t)1 << max) - 1) { - fprintf(stderr, "%d symbols cannot be coded in %d bits\n", - syms, max); - return 1; - } - - /* allocate code vector */ - code = calloc(max + 1, sizeof(int)); - if (code == NULL) { - fputs("abort: unable to allocate enough memory\n", stderr); - return 1; - } - - /* determine size of saved results array, checking for overflows, - allocate and clear the array (set all to zero with calloc()) */ - if (syms == 2) /* iff max == 1 */ - num = NULL; /* won't be saving any results */ - else { - size = syms >> 1; - if (size > ((size_t)0 - 1) / (n = (syms - 1) >> 1) || - (size *= n, size > ((size_t)0 - 1) / (n = max - 1)) || - (size *= n, size > ((size_t)0 - 1) / sizeof(big_t)) || - (num = calloc(size, sizeof(big_t))) == NULL) { - fputs("abort: unable to allocate enough memory\n", stderr); - cleanup(); - return 1; - } - } - - /* count possible codes for all numbers of symbols, add up counts */ - sum = 0; - for (n = 2; n <= syms; n++) { - got = count(n, 1, 2); - sum += got; - if (got == (big_t)0 - 1 || sum < got) { /* overflow */ - fputs("abort: can't count that high!\n", stderr); - cleanup(); - return 1; - } - printf("%llu %d-codes\n", got, n); - } - printf("%llu total codes for 2 to %d symbols", sum, syms); - if (max < syms - 1) - printf(" (%d-bit length limit)\n", max); - else - puts(" (no length limit)"); - - /* allocate and clear done array for beenhere() */ - if (syms == 2) - done = NULL; - else if (size > ((size_t)0 - 1) / sizeof(struct tab) || - (done = calloc(size, sizeof(struct tab))) == NULL) { - fputs("abort: unable to allocate enough memory\n", stderr); - cleanup(); - return 1; - } - - /* find and show maximum inflate table usage */ - if (root > max) /* reduce root to max length */ - root = max; - if ((code_t)syms < ((code_t)1 << (root + 1))) - enough(syms); - else - puts("cannot handle minimum code lengths > root"); - - /* done */ - cleanup(); - return 0; -} |