| // Copyright 2019 The Wuffs Authors. |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // https://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| |
| //go:build ignore |
| // +build ignore |
| |
| package main |
| |
| // print-deflate-huff-table-size.go prints the worst-case number of elements in |
| // the std/deflate decoder's huffs tables. |
| // |
| // Usage: go run print-deflate-huff-table-size.go |
| // |
| // This program might take tens of seconds to run. |
| // |
| // It is algorithmically similar to examples/enough.c in the zlib C library. |
| // Much of the initial commentary in that file is also relevant for this |
| // program. Not all of it applies, though. For example, the Wuffs decoder |
| // implementation's primary (root) table length is fixed at compile time. It |
| // does not grow that at run-time, even if the shortest Huffman code is longer |
| // than that primary length. |
| // |
| // This program should print: |
| // |
| // ---------------- |
| // -------- Lit/Len (up to 286 symbols, 149142 combos) @1 @2 @3 @4 @5 @6 @7 @8 @9 @10 @11 @12 @13 @14 @15 |
| // primLen 3: 4376 entries = 8 prim + 4368 seco 1 0 0; 1 1 1 17 1 1 257 1 1 1 1 2 |
| // primLen 4: 2338 entries = 16 prim + 2322 seco 0 0 0 0; 3 1 1 177 97 1 1 1 1 1 2 |
| // primLen 5: 1330 entries = 32 prim + 1298 seco 1 0 0 0 0; 3 1 1 177 97 1 1 1 1 2 |
| // primLen 6: 852 entries = 64 prim + 788 seco 0 0 0 0 0 0; 1 229 49 1 1 1 1 1 2 |
| // primLen 7: 660 entries = 128 prim + 532 seco 1 0 0 0 0 0 0; 1 229 49 1 1 1 1 2 |
| // primLen 8: 660 entries = 256 prim + 404 seco 1 1 0 0 0 0 0 0; 1 229 49 1 1 1 2 |
| // primLen 9: 852 entries = 512 prim + 340 seco 1 1 1 0 0 0 0 0 0; 1 229 49 1 1 2 |
| // primLen 10: 1332 entries = 1024 prim + 308 seco 1 1 1 1 0 0 0 0 0 0; 1 229 49 1 2 |
| // primLen 11: 2340 entries = 2048 prim + 292 seco 1 1 1 1 1 0 0 0 0 0 0; 1 229 49 2 |
| // primLen 12: 4380 entries = 4096 prim + 284 seco 1 1 1 1 1 1 0 0 0 0 0 0; 1 229 50 |
| // primLen 13: 8472 entries = 8192 prim + 280 seco 1 1 1 1 1 1 0 1 0 0 0 0 0;105 174 |
| // primLen 14: 16658 entries = 16384 prim + 274 seco 1 1 1 1 1 1 0 1 1 1 0 1 1 1;274 |
| // primLen 15: 32768 entries = 32768 prim + 0 seco 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| // |
| // -------- Distance (up to 30 symbols, 1666 combos) @1 @2 @3 @4 @5 @6 @7 @8 @9 @10 @11 @12 @13 @14 @15 |
| // primLen 3: 4120 entries = 8 prim + 4112 seco 1 0 0; 1 9 9 1 1 1 1 1 1 1 1 2 |
| // primLen 4: 2080 entries = 16 prim + 2064 seco 1 1 0 0; 1 9 9 1 1 1 1 1 1 1 2 |
| // primLen 5: 1072 entries = 32 prim + 1040 seco 1 1 1 0 0; 1 9 9 1 1 1 1 1 1 2 |
| // primLen 6: 592 entries = 64 prim + 528 seco 1 1 1 1 0 0; 1 9 9 1 1 1 1 1 2 |
| // primLen 7: 400 entries = 128 prim + 272 seco 1 1 1 1 1 0 0; 1 9 9 1 1 1 1 2 |
| // primLen 8: 400 entries = 256 prim + 144 seco 1 1 1 1 1 1 0 0; 1 9 9 1 1 1 2 |
| // primLen 9: 592 entries = 512 prim + 80 seco 1 1 1 1 1 1 1 0 0; 1 9 9 1 1 2 |
| // primLen 10: 1072 entries = 1024 prim + 48 seco 1 1 1 1 1 1 1 1 0 0; 1 9 9 1 2 |
| // primLen 11: 2080 entries = 2048 prim + 32 seco 1 1 1 1 1 1 1 1 1 0 0; 1 9 9 2 |
| // primLen 12: 4120 entries = 4096 prim + 24 seco 1 1 1 1 1 1 1 1 1 1 0 0; 1 9 10 |
| // primLen 13: 8212 entries = 8192 prim + 20 seco 1 1 1 1 1 1 1 1 1 1 0 1 0; 5 14 |
| // primLen 14: 16400 entries = 16384 prim + 16 seco 1 1 1 1 1 1 1 1 1 1 1 0 0 0; 16 |
| // primLen 15: 32768 entries = 32768 prim + 0 seco 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| // ---------------- |
| // |
| // Deflate's canonical Huffman codes are up to 15 bits long, but the decoder |
| // can use fewer than (1 << 15) entries in its look-up table, by splitting it |
| // into one primary table (of an at-compile-time fixed length <= 15) and zero |
| // or more secondary tables (of variable lengths, determined at-run-time). |
| // |
| // Symbols whose Huffman codes' length are less than or equal to the primary |
| // table length do not require any secondary tables. Longer codes are grouped |
| // by their primLen length prefix. Each group occupies one entry in the primary |
| // table, which redirects to a secondary table of size (1 << (N - primLen)), |
| // where N is the length of the longest code in that group. |
| // |
| // This program calculates that, for a primary table length of 9 bits, the |
| // worst case Huffman table size is 852 for the Literal/Length table (852 being |
| // a 512 entry primary table and the secondary tables totalling 340 further |
| // entries) and 592 (512 + 80) for the Distance table. |
| // |
| // Copy/pasting one row of that output (and the column headers): |
| // |
| // -------- Lit/Len (up to 286 symbols, 149142 combos) @1 @2 @3 @4 @5 @6 @7 @8 @9 @10 @11 @12 @13 @14 @15 |
| // primLen 9: 852 entries = 512 prim + 340 seco 1 1 1 0 0 0 0 0 0; 1 229 49 1 1 2 |
| // |
| // The "@1, @2, @3, ..." columns mean that one combination that hits that 852 |
| // worst case is having 1 1-length code, 1 2-length code, 1 3-length code, 0 |
| // 4-length codes, ..., 1 10-length code, 229 11-length codes, etc. There are a |
| // total of 286 (1 + 1 + 1 + 0 + ... + 49 + 1 + 1 + 2) codes, for 286 symbols. |
| // |
| // See test/data/artificial/deflate-huffman-primlen-9.deflate* for an actual |
| // example of valid Deflate-formatted data that exercises these worst-case code |
| // lengths (for a primary table length of 9 bits). |
| // |
| // Hypothetically, suppose that we used a primLen of 13 for the Distance table. |
| // Here is a code length assignment that produces 20 secondary table entries: |
| // |
| // -------- Distance (up to 30 symbols, 1666 combos) @1 @2 @3 @4 @5 @6 @7 @8 @9 @10 @11 @12 @13 @14 @15 |
| // primLen 13: 8212 entries = 8192 prim + 20 seco 1 1 1 1 1 1 1 1 1 1 0 1 0; 5 14 |
| // |
| // In detail: call the 14 length codes "e0", "e1", ..., "e4" and the 15 length |
| // codes "f00", "f01", "f02", ..., "f13". |
| // |
| // Recall that secondary tables' lengths are (1 << (N - primLen)), where N is |
| // the longest code for a given primLen length prefix. In this case, (N - |
| // primLen) is (15 - 13) if the secondary table contains a "f??" code, |
| // otherwise it N is (14 - 13). When the secondary table contains a mixture of |
| // lengths, some of the shorter codes' entries are duplicated. |
| // |
| // Also, for canonical Huffman codes, the codes (bitstrings) for 14-length |
| // codes are all assigned (sequentially) before any 15-length codes. There are |
| // therefore 6 secondary tables: |
| // |
| // - length 2: e0, e1. |
| // - length 2: e2, e3. |
| // - length 4: e4, e4, f00, f01. |
| // - length 4: f02, f03, f04, f05. |
| // - length 4: f06, f07, f08, f09. |
| // - length 4: f10, f11, f12, f13. |
| // |
| // The total size of the secondary tables is (2 + 2 + 4 + 4 + 4 + 4) = 20. |
| |
| import ( |
| "fmt" |
| "os" |
| "sort" |
| ) |
| |
| const ( |
| maxMaxNSyms = 286 // RFC 1951 lists 286 literal/length codes and 30 distance codes. |
| maxCodeLen = 15 // Each code's encoding is at most 15 bits. |
| ) |
| |
| func main() { |
| if err := main1(); err != nil { |
| os.Stderr.WriteString(err.Error() + "\n") |
| os.Exit(1) |
| } |
| } |
| |
| func main1() error { |
| do("Lit/Len", 286) |
| do("Distance", 30) |
| return nil |
| } |
| |
| func do(name string, maxNSyms uint32) { |
| ftab := &feasibleTable{} |
| ftab.build(maxNSyms) |
| |
| // We can do the per-primLen computations concurrently, speeding up the |
| // overall wall time taken. |
| ch := make(chan string) |
| numPending := 0 |
| for primLen := uint32(3); primLen <= maxCodeLen; primLen++ { |
| go doPrimLen(ch, maxNSyms, ftab, primLen) |
| numPending++ |
| } |
| |
| // Gather, sort and print the results for each primLen. |
| results := make([]string, 0, numPending) |
| for ; numPending > 0; numPending-- { |
| results = append(results, <-ch) |
| } |
| sort.Strings(results) |
| fmt.Printf("\n-------- %8s (up to %3d symbols, %6d combos)"+ |
| " @1 @2 @3 @4 @5 @6 @7 @8 @9 @10 @11 @12 @13 @14 @15\n", |
| name, maxNSyms, ftab.count()) |
| for _, s := range results { |
| fmt.Println(s) |
| } |
| } |
| |
| type state struct { |
| ftab *feasibleTable |
| primLen uint32 |
| |
| currCase struct { |
| nAssignedCodes nAssignedCodes |
| } |
| |
| worstCase struct { |
| nAssignedCodes nAssignedCodes |
| nSecondary uint32 |
| } |
| |
| visited [maxCodeLen + 1][maxMaxNSyms + 1][maxMaxNSyms + 1]bitVector |
| } |
| |
| func doPrimLen(ch chan<- string, maxNSyms uint32, ftab *feasibleTable, primLen uint32) { |
| z := &state{ |
| ftab: ftab, |
| primLen: primLen, |
| } |
| |
| if z.primLen > maxCodeLen { |
| panic("unreachable") |
| |
| } else if z.primLen == maxCodeLen { |
| // There's only the primary table and no secondary tables. For an |
| // example that fills that primary table, create a trivial encoding of |
| // two symbols: one symbol's code is "0", the other's is "1". |
| z.worstCase.nAssignedCodes[1] = 2 |
| for n := uint32(2); n <= maxCodeLen; n++ { |
| z.worstCase.nAssignedCodes[n] = 0 |
| } |
| |
| } else { |
| // Brute force search the tree of possible code length assignments. |
| // |
| // nCodes is always even: the number of unassigned Huffman codes at |
| // length L is twice the number at length (L-1). At the start, there |
| // are two unassigned codes of length 1: "0" and "1". |
| // |
| // nSyms starts at nCodes, since (nCodes > nSyms) is infeasible: there |
| // will be unassigned codes. |
| for nCodes := uint32(2); nCodes <= maxNSyms; nCodes += 2 { |
| for nSyms := nCodes; nSyms <= maxNSyms; nSyms++ { |
| if z.ftab[z.primLen+1][nCodes][nSyms] { |
| z.visit(z.primLen+1, nCodes, nSyms, 0, 0) |
| } |
| } |
| } |
| |
| z.worstCase.nAssignedCodes.fillPrimaryValues(z.primLen) |
| } |
| |
| // Collect the details: the number of codes assigned to each length in the |
| // worst case. |
| details := "" |
| for n := uint32(1); n <= maxCodeLen; n++ { |
| if n == z.primLen+1 { |
| details += ";" |
| } else { |
| details += " " |
| } |
| details += fmt.Sprintf("%3d", z.worstCase.nAssignedCodes[n]) |
| } |
| |
| nPrimary := uint32(1) << z.primLen |
| nSecondary := z.worstCase.nSecondary |
| nEntries := nPrimary + nSecondary |
| |
| ch <- fmt.Sprintf("primLen %2d: %5d entries = %5d prim + %4d seco%s", |
| z.primLen, nEntries, nPrimary, nSecondary, details) |
| } |
| |
| // visit updates z.worstCase, starting with nCodes unassigned Huffman codes of |
| // length codeLen for nSyms symbols. nSecondary is the total size (number of |
| // entries) so far of all of the secondary tables. |
| // |
| // nRemain > 0 iff we have an incomplete secondary table, whose size was |
| // partially accounted for in nSecondary, by (1 << (codeLen - z.primLen)). If |
| // positive, nRemain is the number of unassigned entries in that incomplete |
| // secondary table. |
| // |
| // visit can recursively call itself with longer codeLen values. As it does so, |
| // it temporarily sets z.currCase.nAssignedCodes[codeLen], restoring that to |
| // zero before it returns. |
| func (z *state) visit(codeLen uint32, nCodes uint32, nSyms uint32, nSecondary uint32, nRemain uint32) { |
| if z.alreadyVisited(codeLen, nCodes, nSyms, nSecondary, nRemain) { |
| // No-op. |
| |
| } else if nCodes > nSyms { |
| // Infeasible: there will be unassigned codes. |
| |
| } else if nCodes == nSyms { |
| // Fill in the incomplete secondary table (if present) and any new |
| // secondary tables (if necessary) to assign the nCodes codes to the |
| // nSyms symbols. At the end, we should have no remaining entries. |
| n := nCodes |
| for n > nRemain { |
| n -= nRemain |
| nRemain = 1 << (codeLen - z.primLen) |
| nSecondary += nRemain |
| } |
| if n != nRemain { |
| panic("inconsistent secondary table size") |
| } |
| |
| // Update z.worstCase if we have a new record for nSecondary. |
| if z.worstCase.nSecondary < nSecondary { |
| z.worstCase.nSecondary = nSecondary |
| z.worstCase.nAssignedCodes = z.currCase.nAssignedCodes |
| z.worstCase.nAssignedCodes[codeLen] = nCodes |
| } |
| |
| } else { // nCodes < nSyms. |
| codeLen1 := codeLen + 1 |
| // Brute force assigning n codes of this codeLen. The other (nCodes - |
| // n) codes will have longer codes. |
| for n := uint32(0); n < nCodes; n++ { |
| nCodes1 := (nCodes - n) * 2 |
| nSyms1 := nSyms - n |
| |
| if nCodes1 > nSyms1 { |
| // Infeasible: there will be unassigned codes. |
| |
| } else if z.ftab[codeLen1][nCodes1][nSyms1] { |
| nSecondary1 := nSecondary |
| nRemain1 := nRemain * 2 |
| |
| if nRemain1 > 0 { |
| // We have an incomplete secondary table, which has been |
| // partially accounted for: nSecondary has previously been |
| // incremented by X, where X equals (1 << (codeLen - |
| // z.primLen)). |
| // |
| // As we recursively call visit, with codeLen increased by |
| // 1, then we need to double the accounted size of that |
| // secondary table to 2*X. Since X out of that 2*X has |
| // already been added, we need to increment nSecondary1 by |
| // just the difference, which is also X. |
| nSecondary1 += 1 << (codeLen - z.primLen) |
| } |
| |
| z.currCase.nAssignedCodes[codeLen] = n |
| z.visit(codeLen1, nCodes1, nSyms1, nSecondary1, nRemain1) |
| z.currCase.nAssignedCodes[codeLen] = 0 |
| } |
| |
| // Open a new secondary table if necessary: one whose size is (1 << |
| // (codeLen - z.primLen)). |
| if nRemain == 0 { |
| nRemain = 1 << (codeLen - z.primLen) |
| nSecondary += nRemain |
| } |
| |
| // Assign one of the incomplete secondary table's entries. |
| nRemain-- |
| } |
| } |
| } |
| |
| // alreadyVisited returns whether z has already visited the (nSecondary, |
| // nRemain) pair. As a side effect, it also marks that pair as visited. |
| func (z *state) alreadyVisited(codeLen uint32, nCodes uint32, nSyms uint32, nSecondary uint32, nRemain uint32) bool { |
| // Use the zig re-numbering to minimize the memory requirements for the |
| // visited slice. There's an additional 8-fold memory reduction by using 1 |
| // bit per element, not 1 bool (1 byte) per element. |
| i := zig(nSecondary/8, nRemain) |
| mask := uint8(1) << (nSecondary & 7) |
| |
| visited := z.visited[codeLen][nCodes][nSyms] |
| if uint64(i) < uint64(len(visited)) { |
| x := visited[i] |
| visited[i] = x | mask |
| return x&mask != 0 |
| } |
| |
| oldDone := visited |
| visited = make(bitVector, i+1) |
| copy(visited, oldDone) |
| visited[i] = mask |
| |
| z.visited[codeLen][nCodes][nSyms] = visited |
| return false |
| } |
| |
| type bitVector []uint8 |
| |
| // zig packs a pair of non-negative integers (i, j) into a single unique |
| // non-negative integer, in a zig-zagging pattern: |
| // |
| // i=0 i=1 i=2 i=3 i=4 etc |
| // j=0: 0 1 3 6 10 ... |
| // j=1: 2 4 7 11 16 ... |
| // j=2: 5 8 12 17 23 ... |
| // j=3: 9 13 18 24 31 ... |
| // j=4: 14 19 25 32 40 ... |
| // etc: ... ... ... ... ... ... |
| // |
| // The closed from expression relies on the fact that the sum (0 + 1 + ... + n) |
| // equals ((n * (n + 1)) / 2). |
| // |
| // This lets us minimize the memory requirements of a triangular array: one for |
| // which a[i][j] is only accessed when ((i+j) < someBound). |
| func zig(i uint32, j uint32) uint32 { |
| if (i > 0x4000) || (j > 0x4000) { |
| panic("overflow") |
| } |
| n := i + j |
| return ((n * (n + 1)) / 2) + j |
| } |
| |
| // nAssignedCodes[i] holds the number of codes of length i. |
| type nAssignedCodes [maxCodeLen + 1]uint32 |
| |
| // fillPrimaryValues fills in feasible a[n] values for n <= primLen. It assumes |
| // that the caller has already filled in a[n] for n > primLen. |
| func (a *nAssignedCodes) fillPrimaryValues(primLen uint32) { |
| // Looping backwards from the maxCodeLen, figure out how many unassigned |
| // primLen length codes there were. |
| // |
| // For example, if there were 10 assigned 15 length codes, then there must |
| // have been (10 / 2 = 5) unassigned 14 length codes. If there were also 7 |
| // 14 length codes, then there must have been ((5 + 7) / 2 = 6) unassigned |
| // 13 length codes. Etcetera. |
| nUnassignedPrimLen := uint32(0) |
| for n := uint32(maxCodeLen); n > primLen; n-- { |
| nUnassignedPrimLen += a[n] |
| if nUnassignedPrimLen%2 != 0 { |
| panic("cannot undo Huffman code split") |
| } |
| nUnassignedPrimLen /= 2 |
| } |
| if nUnassignedPrimLen < 1 { |
| panic("not enough unassigned primLen length codes") |
| } |
| |
| // Pick a combination of assigning shorter length codes (i.e. setting a[n] |
| // values) to reach that nUnassignedPrimLen target. There are many possible |
| // ways to do so, but only one unique way with the additional constraint |
| // that each value is either 0 or 1: unique because every positive number |
| // has a unique binary representation. |
| // |
| // For example, suppose we need to have 12 unassigned primLen length codes. |
| // With that additional constraint, the way to do this is: |
| // |
| // - 12 unassigned code of length primLen-0. |
| // - 6 unassigned code of length primLen-1. |
| // - 3 unassigned code of length primLen-2. |
| // - 2 unassigned code of length primLen-3. |
| // - 1 unassigned code of length primLen-4. |
| // - 1 unassigned code of length primLen-5. |
| // - 1 unassigned code of length primLen-6. |
| // - etc |
| // |
| // Each left hand column value is either ((2*b)-0) or ((2*b)-1), where b is |
| // the the number below. Subtracting 0 or 1 means that we assign 0 or 1 |
| // codes of that row's length: |
| // |
| // - 0 assigned code of length primLen-0. |
| // - 0 assigned code of length primLen-1. |
| // - 1 assigned code of length primLen-2. |
| // - 0 assigned code of length primLen-3. |
| // - 1 assigned code of length primLen-4. |
| // - 1 assigned code of length primLen-5. |
| // - 1 assigned code of length primLen-6. |
| // - etc |
| // |
| // Reading upwards, this is the binary string "...1110100", which is the |
| // two's complement representation of the decimal number -12: the negative |
| // of nUnassignedPrimLen. |
| bits := -int32(nUnassignedPrimLen) |
| for n := primLen; n >= 1; n-- { |
| a[n] = uint32(bits & 1) |
| bits >>= 1 |
| } |
| if bits != -1 { |
| panic("did not finish with one unassigned zero-length code") |
| } |
| |
| // As a coherence check of the "negative two's complement" theory, loop |
| // forwards to calculate the number of unassigned primLen length codes, |
| // which should match nUnassignedPrimLen. |
| nUnassigned := uint32(1) |
| for n := uint32(1); n <= primLen; n++ { |
| nUnassigned *= 2 |
| if nUnassigned <= a[n] { |
| panic("not enough unassigned codes") |
| } |
| nUnassigned -= a[n] |
| } |
| if nUnassigned != nUnassignedPrimLen { |
| panic("inconsistent unassigned codes") |
| } |
| } |
| |
| // feasibleTable[codeLen][nCodes][nSyms] is whether it is feasible to assign |
| // Huffman codes (of length at least codeLen) to nSyms symbols, given nCodes |
| // unassigned codes of length codeLen. Each unassigned code of length L can be |
| // split into 2 codes of length L+1, 4 codes of length L+2, etc, up to a |
| // maximum code length of maxCodeLen. A feasible assignment ends with zero |
| // unassigned codes, no more and no less. |
| type feasibleTable [maxCodeLen + 1][maxMaxNSyms + 1][maxMaxNSyms + 1]bool |
| |
| func (f *feasibleTable) count() (ret uint64) { |
| for i := range *f { |
| for j := range f[i] { |
| for k := range f[i][j] { |
| if f[i][j][k] { |
| ret++ |
| } |
| } |
| } |
| } |
| return ret |
| } |
| |
| func (f *feasibleTable) build(maxNSyms uint32) { |
| for nSyms := uint32(2); nSyms <= maxNSyms; nSyms++ { |
| if f.buildMore(1, 2, nSyms) != bmResultOK { |
| panic("infeasible [codeLen][nCodes][nSyms] combination") |
| } |
| } |
| } |
| |
| const ( |
| bmResultOK = 0 |
| bmResultUseFewerCodes = 1 |
| bmResultUseMoreCodes = 2 |
| bmResultUnsatisfiable = 3 |
| ) |
| |
| func (f *feasibleTable) buildMore(codeLen uint32, nCodes uint32, nSyms uint32) uint32 { |
| if nCodes == nSyms { |
| if nCodes%2 == 1 { |
| panic("odd nCodes declared feasible") |
| } |
| // This is trivial: assign every symbol a code of length codeLen. |
| f[codeLen][nCodes][nSyms] = true |
| return bmResultOK |
| } else if nCodes > nSyms { |
| // Infeasible: there will be unassigned codes. |
| return bmResultUseMoreCodes |
| } |
| // From here onwards, we have (nCodes < nSyms). |
| |
| if (nCodes << (maxCodeLen - codeLen)) < nSyms { |
| // Infeasible: there will be unassigned symbols, even if we extend the |
| // codes out to maxCodeLen. |
| return bmResultUseFewerCodes |
| } |
| |
| // If we've already visited this [codeLen][nCodes][nSyms] combination, |
| // there's no need to re-do the computation. |
| if f[codeLen][nCodes][nSyms] { |
| return bmResultOK |
| } |
| |
| // Try assigning n out of the nCodes codes 1-to-1 to a symbol, remembering |
| // that we have checked above that (nCodes < nSyms). The remaining (nCodes |
| // - n) codes are lengthened by 1, doubling the number of them, and try to |
| // assign those longer codes to the remaining (nSyms - n) symbols. |
| ok := false |
| codeLen1 := codeLen + 1 |
| for n := uint32(0); n < nCodes; n++ { |
| nCodes1 := (nCodes - n) * 2 |
| nSyms1 := nSyms - n |
| |
| if x := f.buildMore(codeLen1, nCodes1, nSyms1); x == bmResultOK { |
| ok = true |
| } else if x == bmResultUseFewerCodes { |
| // This value of n didn't succeed, but also any larger n also won't |
| // succeed, so we can break the loop early. |
| break |
| } |
| } |
| |
| if !ok { |
| return bmResultUnsatisfiable |
| } |
| if nCodes%2 == 1 { |
| panic("odd nCodes declared feasible") |
| } |
| f[codeLen][nCodes][nSyms] = true |
| return bmResultOK |
| } |
