// Copyright 2019 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // Suffix array construction by induced sorting (SAIS). // See Ge Nong, Sen Zhang, and Wai Hong Chen, // "Two Efficient Algorithms for Linear Time Suffix Array Construction", // especially section 3 (https://ieeexplore.ieee.org/document/5582081). // See also http://zork.net/~st/jottings/sais.html. // // With optimizations inspired by Yuta Mori's sais-lite // (https://sites.google.com/site/yuta256/sais). // // And with other new optimizations. // Many of these functions are parameterized by the sizes of // the types they operate on. The generator gen.go makes // copies of these functions for use with other sizes. // Specifically: // // - A function with a name ending in _8_32 takes []byte and []int32 arguments // and is duplicated into _32_32, _8_64, and _64_64 forms. // The _32_32 and _64_64_ suffixes are shortened to plain _32 and _64. // Any lines in the function body that contain the text "byte-only" or "256" // are stripped when creating _32_32 and _64_64 forms. // (Those lines are typically 8-bit-specific optimizations.) // // - A function with a name ending only in _32 operates on []int32 // and is duplicated into a _64 form. (Note that it may still take a []byte, // but there is no need for a version of the function in which the []byte // is widened to a full integer array.) // The overall runtime of this code is linear in the input size: // it runs a sequence of linear passes to reduce the problem to // a subproblem at most half as big, invokes itself recursively, // and then runs a sequence of linear passes to turn the answer // for the subproblem into the answer for the original problem. // This gives T(N) = O(N) + T(N/2) = O(N) + O(N/2) + O(N/4) + ... = O(N). // // The outline of the code, with the forward and backward scans // through O(N)-sized arrays called out, is: // // sais_I_N // placeLMS_I_B // bucketMax_I_B // freq_I_B // (1) // (2) // (3) // induceSubL_I_B // bucketMin_I_B // freq_I_B // (4) // (5) // (6) // induceSubS_I_B // bucketMax_I_B // freq_I_B // (7) // (8) // (9) // assignID_I_B // (10) // map_B // (11) // recurse_B // (recursive call to sais_B_B for a subproblem of size at most 1/2 input, often much smaller) // unmap_I_B // (12) // (13) // expand_I_B // bucketMax_I_B // freq_I_B // (14) // (15) // (16) // induceL_I_B // bucketMin_I_B // freq_I_B // (17) // (18) // (19) // induceS_I_B // bucketMax_I_B // freq_I_B // (20) // (21) // (22) // // Here, _B indicates the suffix array size (_32 or _64) and _I the input size (_8 or _B). // // The outline shows there are in general 22 scans through // O(N)-sized arrays for a given level of the recursion. // In the top level, operating on 8-bit input text, // the six freq scans are fixed size (256) instead of potentially // input-sized. Also, the frequency is counted once and cached // whenever there is room to do so (there is nearly always room in general, // and always room at the top level), which eliminates all but // the first freq_I_B text scans (that is, 5 of the 6). // So the top level of the recursion only does 22 - 6 - 5 = 11 // input-sized scans and a typical level does 16 scans. // // The linear scans do not cost anywhere near as much as // the random accesses to the text made during a few of // the scans (specifically #6, #9, #16, #19, #22 marked above). // In real texts, there is not much but some locality to // the accesses, due to the repetitive structure of the text // (the same reason Burrows-Wheeler compression is so effective). // For random inputs, there is no locality, which makes those // accesses even more expensive, especially once the text // no longer fits in cache. // For example, running on 50 MB of Go source code, induceSubL_8_32 // (which runs only once, at the top level of the recursion) // takes 0.44s, while on 50 MB of random input, it takes 2.55s. // Nearly all the relative slowdown is explained by the text access: // // c0, c1 := text[k-1], text[k] // // That line runs for 0.23s on the Go text and 2.02s on random text. //go:generate go run gen.go package suffixarray // text_32 returns the suffix array for the input text. // It requires that len(text) fit in an int32 // and that the caller zero sa. func text_32(text []byte, sa []int32) { if int(int32(len(text))) != len(text) || len(text) != len(sa) { panic("suffixarray: misuse of text_32") } sais_8_32(text, 256, sa, make([]int32, 2*256)) } // sais_8_32 computes the suffix array of text. // The text must contain only values in [0, textMax). // The suffix array is stored in sa, which the caller // must ensure is already zeroed. // The caller must also provide temporary space tmp // with len(tmp) ≥ textMax. If len(tmp) ≥ 2*textMax // then the algorithm runs a little faster. // If sais_8_32 modifies tmp, it sets tmp[0] = -1 on return. func sais_8_32(text []byte, textMax int, sa, tmp []int32) { if len(sa) != len(text) || len(tmp) < int(textMax) { panic("suffixarray: misuse of sais_8_32") } // Trivial base cases. Sorting 0 or 1 things is easy. if len(text) == 0 { return } if len(text) == 1 { sa[0] = 0 return } // Establish slices indexed by text character // holding character frequency and bucket-sort offsets. // If there's only enough tmp for one slice, // we make it the bucket offsets and recompute // the character frequency each time we need it. var freq, bucket []int32 if len(tmp) >= 2*textMax { freq, bucket = tmp[:textMax], tmp[textMax:2*textMax] freq[0] = -1 // mark as uninitialized } else { freq, bucket = nil, tmp[:textMax] } // The SAIS algorithm. // Each of these calls makes one scan through sa. // See the individual functions for documentation // about each's role in the algorithm. numLMS := placeLMS_8_32(text, sa, freq, bucket) if numLMS <= 1 { // 0 or 1 items are already sorted. Do nothing. } else { induceSubL_8_32(text, sa, freq, bucket) induceSubS_8_32(text, sa, freq, bucket) length_8_32(text, sa, numLMS) maxID := assignID_8_32(text, sa, numLMS) if maxID < numLMS { map_32(sa, numLMS) recurse_32(sa, tmp, numLMS, maxID) unmap_8_32(text, sa, numLMS) } else { // If maxID == numLMS, then each LMS-substring // is unique, so the relative ordering of two LMS-suffixes // is determined by just the leading LMS-substring. // That is, the LMS-suffix sort order matches the // (simpler) LMS-substring sort order. // Copy the original LMS-substring order into the // suffix array destination. copy(sa, sa[len(sa)-numLMS:]) } expand_8_32(text, freq, bucket, sa, numLMS) } induceL_8_32(text, sa, freq, bucket) induceS_8_32(text, sa, freq, bucket) // Mark for caller that we overwrote tmp. tmp[0] = -1 } // freq_8_32 returns the character frequencies // for text, as a slice indexed by character value. // If freq is nil, freq_8_32 uses and returns bucket. // If freq is non-nil, freq_8_32 assumes that freq[0] >= 0 // means the frequencies are already computed. // If the frequency data is overwritten or uninitialized, // the caller must set freq[0] = -1 to force recomputation // the next time it is needed. func freq_8_32(text []byte, freq, bucket []int32) []int32 { if freq != nil && freq[0] >= 0 { return freq // already computed } if freq == nil { freq = bucket } freq = freq[:256] // eliminate bounds check for freq[c] below for i := range freq { freq[i] = 0 } for _, c := range text { freq[c]++ } return freq } // bucketMin_8_32 stores into bucket[c] the minimum index // in the bucket for character c in a bucket-sort of text. func bucketMin_8_32(text []byte, freq, bucket []int32) { freq = freq_8_32(text, freq, bucket) freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below bucket = bucket[:256] // eliminate bounds check for bucket[i] below total := int32(0) for i, n := range freq { bucket[i] = total total += n } } // bucketMax_8_32 stores into bucket[c] the maximum index // in the bucket for character c in a bucket-sort of text. // The bucket indexes for c are [min, max). // That is, max is one past the final index in that bucket. func bucketMax_8_32(text []byte, freq, bucket []int32) { freq = freq_8_32(text, freq, bucket) freq = freq[:256] // establish len(freq) = 256, so 0 ≤ i < 256 below bucket = bucket[:256] // eliminate bounds check for bucket[i] below total := int32(0) for i, n := range freq { total += n bucket[i] = total } } // The SAIS algorithm proceeds in a sequence of scans through sa. // Each of the following functions implements one scan, // and the functions appear here in the order they execute in the algorithm. // placeLMS_8_32 places into sa the indexes of the // final characters of the LMS substrings of text, // sorted into the rightmost ends of their correct buckets // in the suffix array. // // The imaginary sentinel character at the end of the text // is the final character of the final LMS substring, but there // is no bucket for the imaginary sentinel character, // which has a smaller value than any real character. // The caller must therefore pretend that sa[-1] == len(text). // // The text indexes of LMS-substring characters are always ≥ 1 // (the first LMS-substring must be preceded by one or more L-type // characters that are not part of any LMS-substring), // so using 0 as a “not present” suffix array entry is safe, // both in this function and in most later functions // (until induceL_8_32 below). func placeLMS_8_32(text []byte, sa, freq, bucket []int32) int { bucketMax_8_32(text, freq, bucket) numLMS := 0 lastB := int32(-1) bucket = bucket[:256] // eliminate bounds check for bucket[c1] below // The next stanza of code (until the blank line) loop backward // over text, stopping to execute a code body at each position i // such that text[i] is an L-character and text[i+1] is an S-character. // That is, i+1 is the position of the start of an LMS-substring. // These could be hoisted out into a function with a callback, // but at a significant speed cost. Instead, we just write these // seven lines a few times in this source file. The copies below // refer back to the pattern established by this original as the // "LMS-substring iterator". // // In every scan through the text, c0, c1 are successive characters of text. // In this backward scan, c0 == text[i] and c1 == text[i+1]. // By scanning backward, we can keep track of whether the current // position is type-S or type-L according to the usual definition: // // - position len(text) is type S with text[len(text)] == -1 (the sentinel) // - position i is type S if text[i] < text[i+1], or if text[i] == text[i+1] && i+1 is type S. // - position i is type L if text[i] > text[i+1], or if text[i] == text[i+1] && i+1 is type L. // // The backward scan lets us maintain the current type, // update it when we see c0 != c1, and otherwise leave it alone. // We want to identify all S positions with a preceding L. // Position len(text) is one such position by definition, but we have // nowhere to write it down, so we eliminate it by untruthfully // setting isTypeS = false at the start of the loop. c0, c1, isTypeS := byte(0), byte(0), false for i := len(text) - 1; i >= 0; i-- { c0, c1 = text[i], c0 if c0 < c1 { isTypeS = true } else if c0 > c1 && isTypeS { isTypeS = false // Bucket the index i+1 for the start of an LMS-substring. b := bucket[c1] - 1 bucket[c1] = b sa[b] = int32(i + 1) lastB = b numLMS++ } } // We recorded the LMS-substring starts but really want the ends. // Luckily, with two differences, the start indexes and the end indexes are the same. // The first difference is that the rightmost LMS-substring's end index is len(text), // so the caller must pretend that sa[-1] == len(text), as noted above. // The second difference is that the first leftmost LMS-substring start index // does not end an earlier LMS-substring, so as an optimization we can omit // that leftmost LMS-substring start index (the last one we wrote). // // Exception: if numLMS <= 1, the caller is not going to bother with // the recursion at all and will treat the result as containing LMS-substring starts. // In that case, we don't remove the final entry. if numLMS > 1 { sa[lastB] = 0 } return numLMS } // induceSubL_8_32 inserts the L-type text indexes of LMS-substrings // into sa, assuming that the final characters of the LMS-substrings // are already inserted into sa, sorted by final character, and at the // right (not left) end of the corresponding character bucket. // Each LMS-substring has the form (as a regexp) /S+L+S/: // one or more S-type, one or more L-type, final S-type. // induceSubL_8_32 leaves behind only the leftmost L-type text // index for each LMS-substring. That is, it removes the final S-type // indexes that are present on entry, and it inserts but then removes // the interior L-type indexes too. // (Only the leftmost L-type index is needed by induceSubS_8_32.) func induceSubL_8_32(text []byte, sa, freq, bucket []int32) { // Initialize positions for left side of character buckets. bucketMin_8_32(text, freq, bucket) bucket = bucket[:256] // eliminate bounds check for bucket[cB] below // As we scan the array left-to-right, each sa[i] = j > 0 is a correctly // sorted suffix array entry (for text[j:]) for which we know that j-1 is type L. // Because j-1 is type L, inserting it into sa now will sort it correctly. // But we want to distinguish a j-1 with j-2 of type L from type S. // We can process the former but want to leave the latter for the caller. // We record the difference by negating j-1 if it is preceded by type S. // Either way, the insertion (into the text[j-1] bucket) is guaranteed to // happen at sa[i´] for some i´ > i, that is, in the portion of sa we have // yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3, // and so on, in sorted but not necessarily adjacent order, until it finds // one preceded by an index of type S, at which point it must stop. // // As we scan through the array, we clear the worked entries (sa[i] > 0) to zero, // and we flip sa[i] < 0 to -sa[i], so that the loop finishes with sa containing // only the indexes of the leftmost L-type indexes for each LMS-substring. // // The suffix array sa therefore serves simultaneously as input, output, // and a miraculously well-tailored work queue. // placeLMS_8_32 left out the implicit entry sa[-1] == len(text), // corresponding to the identified type-L index len(text)-1. // Process it before the left-to-right scan of sa proper. // See body in loop for commentary. k := len(text) - 1 c0, c1 := text[k-1], text[k] if c0 < c1 { k = -k } // Cache recently used bucket index: // we're processing suffixes in sorted order // and accessing buckets indexed by the // byte before the sorted order, which still // has very good locality. // Invariant: b is cached, possibly dirty copy of bucket[cB]. cB := c1 b := bucket[cB] sa[b] = int32(k) b++ for i := 0; i < len(sa); i++ { j := int(sa[i]) if j == 0 { // Skip empty entry. continue } if j < 0 { // Leave discovered type-S index for caller. sa[i] = int32(-j) continue } sa[i] = 0 // Index j was on work queue, meaning k := j-1 is L-type, // so we can now place k correctly into sa. // If k-1 is L-type, queue k for processing later in this loop. // If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller. k := j - 1 c0, c1 := text[k-1], text[k] if c0 < c1 { k = -k } if cB != c1 { bucket[cB] = b cB = c1 b = bucket[cB] } sa[b] = int32(k) b++ } } // induceSubS_8_32 inserts the S-type text indexes of LMS-substrings // into sa, assuming that the leftmost L-type text indexes are already // inserted into sa, sorted by LMS-substring suffix, and at the // left end of the corresponding character bucket. // Each LMS-substring has the form (as a regexp) /S+L+S/: // one or more S-type, one or more L-type, final S-type. // induceSubS_8_32 leaves behind only the leftmost S-type text // index for each LMS-substring, in sorted order, at the right end of sa. // That is, it removes the L-type indexes that are present on entry, // and it inserts but then removes the interior S-type indexes too, // leaving the LMS-substring start indexes packed into sa[len(sa)-numLMS:]. // (Only the LMS-substring start indexes are processed by the recursion.) func induceSubS_8_32(text []byte, sa, freq, bucket []int32) { // Initialize positions for right side of character buckets. bucketMax_8_32(text, freq, bucket) bucket = bucket[:256] // eliminate bounds check for bucket[cB] below // Analogous to induceSubL_8_32 above, // as we scan the array right-to-left, each sa[i] = j > 0 is a correctly // sorted suffix array entry (for text[j:]) for which we know that j-1 is type S. // Because j-1 is type S, inserting it into sa now will sort it correctly. // But we want to distinguish a j-1 with j-2 of type S from type L. // We can process the former but want to leave the latter for the caller. // We record the difference by negating j-1 if it is preceded by type L. // Either way, the insertion (into the text[j-1] bucket) is guaranteed to // happen at sa[i´] for some i´ < i, that is, in the portion of sa we have // yet to scan. A single pass therefore sees indexes j, j-1, j-2, j-3, // and so on, in sorted but not necessarily adjacent order, until it finds // one preceded by an index of type L, at which point it must stop. // That index (preceded by one of type L) is an LMS-substring start. // // As we scan through the array, we clear the worked entries (sa[i] > 0) to zero, // and we flip sa[i] < 0 to -sa[i] and compact into the top of sa, // so that the loop finishes with the top of sa containing exactly // the LMS-substring start indexes, sorted by LMS-substring. // Cache recently used bucket index: cB := byte(0) b := bucket[cB] top := len(sa) for i := len(sa) - 1; i >= 0; i-- { j := int(sa[i]) if j == 0 { // Skip empty entry. continue } sa[i] = 0 if j < 0 { // Leave discovered LMS-substring start index for caller. top-- sa[top] = int32(-j) continue } // Index j was on work queue, meaning k := j-1 is S-type, // so we can now place k correctly into sa. // If k-1 is S-type, queue k for processing later in this loop. // If k-1 is L-type (text[k-1] > text[k]), queue -k to save for the caller. k := j - 1 c1 := text[k] c0 := text[k-1] if c0 > c1 { k = -k } if cB != c1 { bucket[cB] = b cB = c1 b = bucket[cB] } b-- sa[b] = int32(k) } } // length_8_32 computes and records the length of each LMS-substring in text. // The length of the LMS-substring at index j is stored at sa[j/2], // avoiding the LMS-substring indexes already stored in the top half of sa. // (If index j is an LMS-substring start, then index j-1 is type L and cannot be.) // There are two exceptions, made for optimizations in name_8_32 below. // // First, the final LMS-substring is recorded as having length 0, which is otherwise // impossible, instead of giving it a length that includes the implicit sentinel. // This ensures the final LMS-substring has length unequal to all others // and therefore can be detected as different without text comparison // (it is unequal because it is the only one that ends in the implicit sentinel, // and the text comparison would be problematic since the implicit sentinel // is not actually present at text[len(text)]). // // Second, to avoid text comparison entirely, if an LMS-substring is very short, // sa[j/2] records its actual text instead of its length, so that if two such // substrings have matching “length,” the text need not be read at all. // The definition of “very short” is that the text bytes must pack into an uint32, // and the unsigned encoding e must be ≥ len(text), so that it can be // distinguished from a valid length. func length_8_32(text []byte, sa []int32, numLMS int) { end := 0 // index of current LMS-substring end (0 indicates final LMS-substring) // The encoding of N text bytes into a “length” word // adds 1 to each byte, packs them into the bottom // N*8 bits of a word, and then bitwise inverts the result. // That is, the text sequence A B C (hex 41 42 43) // encodes as ^uint32(0x42_43_44). // LMS-substrings can never start or end with 0xFF. // Adding 1 ensures the encoded byte sequence never // starts or ends with 0x00, so that present bytes can be // distinguished from zero-padding in the top bits, // so the length need not be separately encoded. // Inverting the bytes increases the chance that a // 4-byte encoding will still be ≥ len(text). // In particular, if the first byte is ASCII (<= 0x7E, so +1 <= 0x7F) // then the high bit of the inversion will be set, // making it clearly not a valid length (it would be a negative one). // // cx holds the pre-inverted encoding (the packed incremented bytes). cx := uint32(0) // byte-only // This stanza (until the blank line) is the "LMS-substring iterator", // described in placeLMS_8_32 above, with one line added to maintain cx. c0, c1, isTypeS := byte(0), byte(0), false for i := len(text) - 1; i >= 0; i-- { c0, c1 = text[i], c0 cx = cx<<8 | uint32(c1+1) // byte-only if c0 < c1 { isTypeS = true } else if c0 > c1 && isTypeS { isTypeS = false // Index j = i+1 is the start of an LMS-substring. // Compute length or encoded text to store in sa[j/2]. j := i + 1 var code int32 if end == 0 { code = 0 } else { code = int32(end - j) if code <= 32/8 && ^cx >= uint32(len(text)) { // byte-only code = int32(^cx) // byte-only } // byte-only } sa[j>>1] = code end = j + 1 cx = uint32(c1 + 1) // byte-only } } } // assignID_8_32 assigns a dense ID numbering to the // set of LMS-substrings respecting string ordering and equality, // returning the maximum assigned ID. // For example given the input "ababab", the LMS-substrings // are "aba", "aba", and "ab", renumbered as 2 2 1. // sa[len(sa)-numLMS:] holds the LMS-substring indexes // sorted in string order, so to assign numbers we can // consider each in turn, removing adjacent duplicates. // The new ID for the LMS-substring at index j is written to sa[j/2], // overwriting the length previously stored there (by length_8_32 above). func assignID_8_32(text []byte, sa []int32, numLMS int) int { id := 0 lastLen := int32(-1) // impossible lastPos := int32(0) for _, j := range sa[len(sa)-numLMS:] { // Is the LMS-substring at index j new, or is it the same as the last one we saw? n := sa[j/2] if n != lastLen { goto New } if uint32(n) >= uint32(len(text)) { // “Length” is really encoded full text, and they match. goto Same } { // Compare actual texts. n := int(n) this := text[j:][:n] last := text[lastPos:][:n] for i := 0; i < n; i++ { if this[i] != last[i] { goto New } } goto Same } New: id++ lastPos = j lastLen = n Same: sa[j/2] = int32(id) } return id } // map_32 maps the LMS-substrings in text to their new IDs, // producing the subproblem for the recursion. // The mapping itself was mostly applied by assignID_8_32: // sa[i] is either 0, the ID for the LMS-substring at index 2*i, // or the ID for the LMS-substring at index 2*i+1. // To produce the subproblem we need only remove the zeros // and change ID into ID-1 (our IDs start at 1, but text chars start at 0). // // map_32 packs the result, which is the input to the recursion, // into the top of sa, so that the recursion result can be stored // in the bottom of sa, which sets up for expand_8_32 well. func map_32(sa []int32, numLMS int) { w := len(sa) for i := len(sa) / 2; i >= 0; i-- { j := sa[i] if j > 0 { w-- sa[w] = j - 1 } } } // recurse_32 calls sais_32 recursively to solve the subproblem we've built. // The subproblem is at the right end of sa, the suffix array result will be // written at the left end of sa, and the middle of sa is available for use as // temporary frequency and bucket storage. func recurse_32(sa, oldTmp []int32, numLMS, maxID int) { dst, saTmp, text := sa[:numLMS], sa[numLMS:len(sa)-numLMS], sa[len(sa)-numLMS:] // Set up temporary space for recursive call. // We must pass sais_32 a tmp buffer with at least maxID entries. // // The subproblem is guaranteed to have length at most len(sa)/2, // so that sa can hold both the subproblem and its suffix array. // Nearly all the time, however, the subproblem has length < len(sa)/3, // in which case there is a subproblem-sized middle of sa that // we can reuse for temporary space (saTmp). // When recurse_32 is called from sais_8_32, oldTmp is length 512 // (from text_32), and saTmp will typically be much larger, so we'll use saTmp. // When deeper recursions come back to recurse_32, now oldTmp is // the saTmp from the top-most recursion, it is typically larger than // the current saTmp (because the current sa gets smaller and smaller // as the recursion gets deeper), and we keep reusing that top-most // large saTmp instead of the offered smaller ones. // // Why is the subproblem length so often just under len(sa)/3? // See Nong, Zhang, and Chen, section 3.6 for a plausible explanation. // In brief, the len(sa)/2 case would correspond to an SLSLSLSLSLSL pattern // in the input, perfect alternation of larger and smaller input bytes. // Real text doesn't do that. If each L-type index is randomly followed // by either an L-type or S-type index, then half the substrings will // be of the form SLS, but the other half will be longer. Of that half, // half (a quarter overall) will be SLLS; an eighth will be SLLLS, and so on. // Not counting the final S in each (which overlaps the first S in the next), // This works out to an average length 2×½ + 3×¼ + 4×⅛ + ... = 3. // The space we need is further reduced by the fact that many of the // short patterns like SLS will often be the same character sequences // repeated throughout the text, reducing maxID relative to numLMS. // // For short inputs, the averages may not run in our favor, but then we // can often fall back to using the length-512 tmp available in the // top-most call. (Also a short allocation would not be a big deal.) // // For pathological inputs, we fall back to allocating a new tmp of length // max(maxID, numLMS/2). This level of the recursion needs maxID, // and all deeper levels of the recursion will need no more than numLMS/2, // so this one allocation is guaranteed to suffice for the entire stack // of recursive calls. tmp := oldTmp if len(tmp) < len(saTmp) { tmp = saTmp } if len(tmp) < numLMS { // TestSAIS/forcealloc reaches this code. n := maxID if n < numLMS/2 { n = numLMS / 2 } tmp = make([]int32, n) } // sais_32 requires that the caller arrange to clear dst, // because in general the caller may know dst is // freshly-allocated and already cleared. But this one is not. for i := range dst { dst[i] = 0 } sais_32(text, maxID, dst, tmp) } // unmap_8_32 unmaps the subproblem back to the original. // sa[:numLMS] is the LMS-substring numbers, which don't matter much anymore. // sa[len(sa)-numLMS:] is the sorted list of those LMS-substring numbers. // The key part is that if the list says K that means the K'th substring. // We can replace sa[:numLMS] with the indexes of the LMS-substrings. // Then if the list says K it really means sa[K]. // Having mapped the list back to LMS-substring indexes, // we can place those into the right buckets. func unmap_8_32(text []byte, sa []int32, numLMS int) { unmap := sa[len(sa)-numLMS:] j := len(unmap) // "LMS-substring iterator" (see placeLMS_8_32 above). c0, c1, isTypeS := byte(0), byte(0), false for i := len(text) - 1; i >= 0; i-- { c0, c1 = text[i], c0 if c0 < c1 { isTypeS = true } else if c0 > c1 && isTypeS { isTypeS = false // Populate inverse map. j-- unmap[j] = int32(i + 1) } } // Apply inverse map to subproblem suffix array. sa = sa[:numLMS] for i := 0; i < len(sa); i++ { sa[i] = unmap[sa[i]] } } // expand_8_32 distributes the compacted, sorted LMS-suffix indexes // from sa[:numLMS] into the tops of the appropriate buckets in sa, // preserving the sorted order and making room for the L-type indexes // to be slotted into the sorted sequence by induceL_8_32. func expand_8_32(text []byte, freq, bucket, sa []int32, numLMS int) { bucketMax_8_32(text, freq, bucket) bucket = bucket[:256] // eliminate bound check for bucket[c] below // Loop backward through sa, always tracking // the next index to populate from sa[:numLMS]. // When we get to one, populate it. // Zero the rest of the slots; they have dead values in them. x := numLMS - 1 saX := sa[x] c := text[saX] b := bucket[c] - 1 bucket[c] = b for i := len(sa) - 1; i >= 0; i-- { if i != int(b) { sa[i] = 0 continue } sa[i] = saX // Load next entry to put down (if any). if x > 0 { x-- saX = sa[x] // TODO bounds check c = text[saX] b = bucket[c] - 1 bucket[c] = b } } } // induceL_8_32 inserts L-type text indexes into sa, // assuming that the leftmost S-type indexes are inserted // into sa, in sorted order, in the right bucket halves. // It leaves all the L-type indexes in sa, but the // leftmost L-type indexes are negated, to mark them // for processing by induceS_8_32. func induceL_8_32(text []byte, sa, freq, bucket []int32) { // Initialize positions for left side of character buckets. bucketMin_8_32(text, freq, bucket) bucket = bucket[:256] // eliminate bounds check for bucket[cB] below // This scan is similar to the one in induceSubL_8_32 above. // That one arranges to clear all but the leftmost L-type indexes. // This scan leaves all the L-type indexes and the original S-type // indexes, but it negates the positive leftmost L-type indexes // (the ones that induceS_8_32 needs to process). // expand_8_32 left out the implicit entry sa[-1] == len(text), // corresponding to the identified type-L index len(text)-1. // Process it before the left-to-right scan of sa proper. // See body in loop for commentary. k := len(text) - 1 c0, c1 := text[k-1], text[k] if c0 < c1 { k = -k } // Cache recently used bucket index. cB := c1 b := bucket[cB] sa[b] = int32(k) b++ for i := 0; i < len(sa); i++ { j := int(sa[i]) if j <= 0 { // Skip empty or negated entry (including negated zero). continue } // Index j was on work queue, meaning k := j-1 is L-type, // so we can now place k correctly into sa. // If k-1 is L-type, queue k for processing later in this loop. // If k-1 is S-type (text[k-1] < text[k]), queue -k to save for the caller. // If k is zero, k-1 doesn't exist, so we only need to leave it // for the caller. The caller can't tell the difference between // an empty slot and a non-empty zero, but there's no need // to distinguish them anyway: the final suffix array will end up // with one zero somewhere, and that will be a real zero. k := j - 1 c1 := text[k] if k > 0 { if c0 := text[k-1]; c0 < c1 { k = -k } } if cB != c1 { bucket[cB] = b cB = c1 b = bucket[cB] } sa[b] = int32(k) b++ } } func induceS_8_32(text []byte, sa, freq, bucket []int32) { // Initialize positions for right side of character buckets. bucketMax_8_32(text, freq, bucket) bucket = bucket[:256] // eliminate bounds check for bucket[cB] below cB := byte(0) b := bucket[cB] for i := len(sa) - 1; i >= 0; i-- { j := int(sa[i]) if j >= 0 { // Skip non-flagged entry. // (This loop can't see an empty entry; 0 means the real zero index.) continue } // Negative j is a work queue entry; rewrite to positive j for final suffix array. j = -j sa[i] = int32(j) // Index j was on work queue (encoded as -j but now decoded), // meaning k := j-1 is L-type, // so we can now place k correctly into sa. // If k-1 is S-type, queue -k for processing later in this loop. // If k-1 is L-type (text[k-1] > text[k]), queue k to save for the caller. // If k is zero, k-1 doesn't exist, so we only need to leave it // for the caller. k := j - 1 c1 := text[k] if k > 0 { if c0 := text[k-1]; c0 <= c1 { k = -k } } if cB != c1 { bucket[cB] = b cB = c1 b = bucket[cB] } b-- sa[b] = int32(k) } }