zlib 1.2.3.4v1.2.3.4

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+/* 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 Mark Adler
+ * Version 1.3  17 February 2008  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
+ */
+
+/*
+   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 == -1 || sum < got)         /* overflow */
+            return -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 */
+
+    /* 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 */
+    n = 0;
+    while (((code_t)1 << n) != 0)
+        n++;
+
+    /* make sure that the calculation of most will not overflow */
+    if (max > n || 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 (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 == -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 (syms < ((code_t)1 << (root + 1)))
+        enough(syms);
+    else
+        puts("cannot handle minimum code lengths > root");
+
+    /* done */
+    cleanup();
+    return 0;
+}