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-rw-r--r--vendor/github.com/kballard/go-shellquote/LICENSE19
-rw-r--r--vendor/github.com/kballard/go-shellquote/README36
-rw-r--r--vendor/github.com/kballard/go-shellquote/doc.go3
-rw-r--r--vendor/github.com/kballard/go-shellquote/quote.go102
-rw-r--r--vendor/github.com/kballard/go-shellquote/unquote.go156
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/LICENSE27
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/README43
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_386.s36
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_amd64.s38
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_arm.s36
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_arm64.s36
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_decl.go16
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_mips64x.s40
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_mipsx.s40
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_ppc64x.s38
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_s390x.s37
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/fermat.go216
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/fft.go370
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/go.mod3
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/scan.go70
-rw-r--r--vendor/github.com/uptrace/bun/dialect/sqlitedialect/LICENSE24
-rw-r--r--vendor/github.com/uptrace/bun/dialect/sqlitedialect/dialect.go94
-rw-r--r--vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.mod7
-rw-r--r--vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.sum22
-rw-r--r--vendor/github.com/uptrace/bun/dialect/sqlitedialect/scan.go28
25 files changed, 1537 insertions, 0 deletions
diff --git a/vendor/github.com/kballard/go-shellquote/LICENSE b/vendor/github.com/kballard/go-shellquote/LICENSE
new file mode 100644
index 000000000..a6d77312e
--- /dev/null
+++ b/vendor/github.com/kballard/go-shellquote/LICENSE
@@ -0,0 +1,19 @@
+Copyright (C) 2014 Kevin Ballard
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the "Software"),
+to deal in the Software without restriction, including without limitation
+the rights to use, copy, modify, merge, publish, distribute, sublicense,
+and/or sell copies of the Software, and to permit persons to whom the
+Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included
+in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE
+OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/vendor/github.com/kballard/go-shellquote/README b/vendor/github.com/kballard/go-shellquote/README
new file mode 100644
index 000000000..4d34e87af
--- /dev/null
+++ b/vendor/github.com/kballard/go-shellquote/README
@@ -0,0 +1,36 @@
+PACKAGE
+
+package shellquote
+ import "github.com/kballard/go-shellquote"
+
+ Shellquote provides utilities for joining/splitting strings using sh's
+ word-splitting rules.
+
+VARIABLES
+
+var (
+ UnterminatedSingleQuoteError = errors.New("Unterminated single-quoted string")
+ UnterminatedDoubleQuoteError = errors.New("Unterminated double-quoted string")
+ UnterminatedEscapeError = errors.New("Unterminated backslash-escape")
+)
+
+
+FUNCTIONS
+
+func Join(args ...string) string
+ Join quotes each argument and joins them with a space. If passed to
+ /bin/sh, the resulting string will be split back into the original
+ arguments.
+
+func Split(input string) (words []string, err error)
+ Split splits a string according to /bin/sh's word-splitting rules. It
+ supports backslash-escapes, single-quotes, and double-quotes. Notably it
+ does not support the $'' style of quoting. It also doesn't attempt to
+ perform any other sort of expansion, including brace expansion, shell
+ expansion, or pathname expansion.
+
+ If the given input has an unterminated quoted string or ends in a
+ backslash-escape, one of UnterminatedSingleQuoteError,
+ UnterminatedDoubleQuoteError, or UnterminatedEscapeError is returned.
+
+
diff --git a/vendor/github.com/kballard/go-shellquote/doc.go b/vendor/github.com/kballard/go-shellquote/doc.go
new file mode 100644
index 000000000..9445fa4ad
--- /dev/null
+++ b/vendor/github.com/kballard/go-shellquote/doc.go
@@ -0,0 +1,3 @@
+// Shellquote provides utilities for joining/splitting strings using sh's
+// word-splitting rules.
+package shellquote
diff --git a/vendor/github.com/kballard/go-shellquote/quote.go b/vendor/github.com/kballard/go-shellquote/quote.go
new file mode 100644
index 000000000..72a8cb38b
--- /dev/null
+++ b/vendor/github.com/kballard/go-shellquote/quote.go
@@ -0,0 +1,102 @@
+package shellquote
+
+import (
+ "bytes"
+ "strings"
+ "unicode/utf8"
+)
+
+// Join quotes each argument and joins them with a space.
+// If passed to /bin/sh, the resulting string will be split back into the
+// original arguments.
+func Join(args ...string) string {
+ var buf bytes.Buffer
+ for i, arg := range args {
+ if i != 0 {
+ buf.WriteByte(' ')
+ }
+ quote(arg, &buf)
+ }
+ return buf.String()
+}
+
+const (
+ specialChars = "\\'\"`${[|&;<>()*?!"
+ extraSpecialChars = " \t\n"
+ prefixChars = "~"
+)
+
+func quote(word string, buf *bytes.Buffer) {
+ // We want to try to produce a "nice" output. As such, we will
+ // backslash-escape most characters, but if we encounter a space, or if we
+ // encounter an extra-special char (which doesn't work with
+ // backslash-escaping) we switch over to quoting the whole word. We do this
+ // with a space because it's typically easier for people to read multi-word
+ // arguments when quoted with a space rather than with ugly backslashes
+ // everywhere.
+ origLen := buf.Len()
+
+ if len(word) == 0 {
+ // oops, no content
+ buf.WriteString("''")
+ return
+ }
+
+ cur, prev := word, word
+ atStart := true
+ for len(cur) > 0 {
+ c, l := utf8.DecodeRuneInString(cur)
+ cur = cur[l:]
+ if strings.ContainsRune(specialChars, c) || (atStart && strings.ContainsRune(prefixChars, c)) {
+ // copy the non-special chars up to this point
+ if len(cur) < len(prev) {
+ buf.WriteString(prev[0 : len(prev)-len(cur)-l])
+ }
+ buf.WriteByte('\\')
+ buf.WriteRune(c)
+ prev = cur
+ } else if strings.ContainsRune(extraSpecialChars, c) {
+ // start over in quote mode
+ buf.Truncate(origLen)
+ goto quote
+ }
+ atStart = false
+ }
+ if len(prev) > 0 {
+ buf.WriteString(prev)
+ }
+ return
+
+quote:
+ // quote mode
+ // Use single-quotes, but if we find a single-quote in the word, we need
+ // to terminate the string, emit an escaped quote, and start the string up
+ // again
+ inQuote := false
+ for len(word) > 0 {
+ i := strings.IndexRune(word, '\'')
+ if i == -1 {
+ break
+ }
+ if i > 0 {
+ if !inQuote {
+ buf.WriteByte('\'')
+ inQuote = true
+ }
+ buf.WriteString(word[0:i])
+ }
+ word = word[i+1:]
+ if inQuote {
+ buf.WriteByte('\'')
+ inQuote = false
+ }
+ buf.WriteString("\\'")
+ }
+ if len(word) > 0 {
+ if !inQuote {
+ buf.WriteByte('\'')
+ }
+ buf.WriteString(word)
+ buf.WriteByte('\'')
+ }
+}
diff --git a/vendor/github.com/kballard/go-shellquote/unquote.go b/vendor/github.com/kballard/go-shellquote/unquote.go
new file mode 100644
index 000000000..b1b13da93
--- /dev/null
+++ b/vendor/github.com/kballard/go-shellquote/unquote.go
@@ -0,0 +1,156 @@
+package shellquote
+
+import (
+ "bytes"
+ "errors"
+ "strings"
+ "unicode/utf8"
+)
+
+var (
+ UnterminatedSingleQuoteError = errors.New("Unterminated single-quoted string")
+ UnterminatedDoubleQuoteError = errors.New("Unterminated double-quoted string")
+ UnterminatedEscapeError = errors.New("Unterminated backslash-escape")
+)
+
+var (
+ splitChars = " \n\t"
+ singleChar = '\''
+ doubleChar = '"'
+ escapeChar = '\\'
+ doubleEscapeChars = "$`\"\n\\"
+)
+
+// Split splits a string according to /bin/sh's word-splitting rules. It
+// supports backslash-escapes, single-quotes, and double-quotes. Notably it does
+// not support the $'' style of quoting. It also doesn't attempt to perform any
+// other sort of expansion, including brace expansion, shell expansion, or
+// pathname expansion.
+//
+// If the given input has an unterminated quoted string or ends in a
+// backslash-escape, one of UnterminatedSingleQuoteError,
+// UnterminatedDoubleQuoteError, or UnterminatedEscapeError is returned.
+func Split(input string) (words []string, err error) {
+ var buf bytes.Buffer
+ words = make([]string, 0)
+
+ for len(input) > 0 {
+ // skip any splitChars at the start
+ c, l := utf8.DecodeRuneInString(input)
+ if strings.ContainsRune(splitChars, c) {
+ input = input[l:]
+ continue
+ } else if c == escapeChar {
+ // Look ahead for escaped newline so we can skip over it
+ next := input[l:]
+ if len(next) == 0 {
+ err = UnterminatedEscapeError
+ return
+ }
+ c2, l2 := utf8.DecodeRuneInString(next)
+ if c2 == '\n' {
+ input = next[l2:]
+ continue
+ }
+ }
+
+ var word string
+ word, input, err = splitWord(input, &buf)
+ if err != nil {
+ return
+ }
+ words = append(words, word)
+ }
+ return
+}
+
+func splitWord(input string, buf *bytes.Buffer) (word string, remainder string, err error) {
+ buf.Reset()
+
+raw:
+ {
+ cur := input
+ for len(cur) > 0 {
+ c, l := utf8.DecodeRuneInString(cur)
+ cur = cur[l:]
+ if c == singleChar {
+ buf.WriteString(input[0 : len(input)-len(cur)-l])
+ input = cur
+ goto single
+ } else if c == doubleChar {
+ buf.WriteString(input[0 : len(input)-len(cur)-l])
+ input = cur
+ goto double
+ } else if c == escapeChar {
+ buf.WriteString(input[0 : len(input)-len(cur)-l])
+ input = cur
+ goto escape
+ } else if strings.ContainsRune(splitChars, c) {
+ buf.WriteString(input[0 : len(input)-len(cur)-l])
+ return buf.String(), cur, nil
+ }
+ }
+ if len(input) > 0 {
+ buf.WriteString(input)
+ input = ""
+ }
+ goto done
+ }
+
+escape:
+ {
+ if len(input) == 0 {
+ return "", "", UnterminatedEscapeError
+ }
+ c, l := utf8.DecodeRuneInString(input)
+ if c == '\n' {
+ // a backslash-escaped newline is elided from the output entirely
+ } else {
+ buf.WriteString(input[:l])
+ }
+ input = input[l:]
+ }
+ goto raw
+
+single:
+ {
+ i := strings.IndexRune(input, singleChar)
+ if i == -1 {
+ return "", "", UnterminatedSingleQuoteError
+ }
+ buf.WriteString(input[0:i])
+ input = input[i+1:]
+ goto raw
+ }
+
+double:
+ {
+ cur := input
+ for len(cur) > 0 {
+ c, l := utf8.DecodeRuneInString(cur)
+ cur = cur[l:]
+ if c == doubleChar {
+ buf.WriteString(input[0 : len(input)-len(cur)-l])
+ input = cur
+ goto raw
+ } else if c == escapeChar {
+ // bash only supports certain escapes in double-quoted strings
+ c2, l2 := utf8.DecodeRuneInString(cur)
+ cur = cur[l2:]
+ if strings.ContainsRune(doubleEscapeChars, c2) {
+ buf.WriteString(input[0 : len(input)-len(cur)-l-l2])
+ if c2 == '\n' {
+ // newline is special, skip the backslash entirely
+ } else {
+ buf.WriteRune(c2)
+ }
+ input = cur
+ }
+ }
+ }
+ return "", "", UnterminatedDoubleQuoteError
+ }
+
+done:
+ return buf.String(), input, nil
+}
diff --git a/vendor/github.com/remyoudompheng/bigfft/LICENSE b/vendor/github.com/remyoudompheng/bigfft/LICENSE
new file mode 100644
index 000000000..744875676
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/LICENSE
@@ -0,0 +1,27 @@
+Copyright (c) 2012 The Go Authors. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+ * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+ * Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/vendor/github.com/remyoudompheng/bigfft/README b/vendor/github.com/remyoudompheng/bigfft/README
new file mode 100644
index 000000000..303c61772
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/README
@@ -0,0 +1,43 @@
+Benchmarking math/big vs. bigfft
+
+Number size old ns/op new ns/op delta
+ 1kb 1599 1640 +2.56%
+ 10kb 61533 62170 +1.04%
+ 50kb 833693 831051 -0.32%
+100kb 2567995 2693864 +4.90%
+ 1Mb 105237800 28446400 -72.97%
+ 5Mb 1272947000 168554600 -86.76%
+ 10Mb 3834354000 405120200 -89.43%
+ 20Mb 11514488000 845081600 -92.66%
+ 50Mb 49199945000 2893950000 -94.12%
+100Mb 147599836000 5921594000 -95.99%
+
+Benchmarking GMP vs bigfft
+
+Number size GMP ns/op Go ns/op delta
+ 1kb 536 1500 +179.85%
+ 10kb 26669 50777 +90.40%
+ 50kb 252270 658534 +161.04%
+100kb 686813 2127534 +209.77%
+ 1Mb 12100000 22391830 +85.06%
+ 5Mb 111731843 133550600 +19.53%
+ 10Mb 212314000 318595800 +50.06%
+ 20Mb 490196000 671512800 +36.99%
+ 50Mb 1280000000 2451476000 +91.52%
+100Mb 2673000000 5228991000 +95.62%
+
+Benchmarks were run on a Core 2 Quad Q8200 (2.33GHz).
+FFT is enabled when input numbers are over 200kbits.
+
+Scanning large decimal number from strings.
+(math/big [n^2 complexity] vs bigfft [n^1.6 complexity], Core i5-4590)
+
+Digits old ns/op new ns/op delta
+1e3 9995 10876 +8.81%
+1e4 175356 243806 +39.03%
+1e5 9427422 6780545 -28.08%
+1e6 1776707489 144867502 -91.85%
+2e6 6865499995 346540778 -94.95%
+5e6 42641034189 1069878799 -97.49%
+10e6 151975273589 2693328580 -98.23%
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_386.s b/vendor/github.com/remyoudompheng/bigfft/arith_386.s
new file mode 100644
index 000000000..cc50a0172
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_386.s
@@ -0,0 +1,36 @@
+// Trampolines to math/big assembly implementations.
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ JMP math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+TEXT ·subVV(SB),NOSPLIT,$0
+ JMP math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ JMP math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+TEXT ·subVW(SB),NOSPLIT,$0
+ JMP math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ JMP math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ JMP math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ JMP math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ JMP math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_amd64.s b/vendor/github.com/remyoudompheng/bigfft/arith_amd64.s
new file mode 100644
index 000000000..0b79335fc
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_amd64.s
@@ -0,0 +1,38 @@
+// Trampolines to math/big assembly implementations.
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ JMP math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+// (same as addVV except for SBBQ instead of ADCQ and label names)
+TEXT ·subVV(SB),NOSPLIT,$0
+ JMP math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ JMP math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
+TEXT ·subVW(SB),NOSPLIT,$0
+ JMP math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ JMP math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ JMP math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ JMP math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ JMP math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_arm.s b/vendor/github.com/remyoudompheng/bigfft/arith_arm.s
new file mode 100644
index 000000000..0ed60f5ca
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_arm.s
@@ -0,0 +1,36 @@
+// Trampolines to math/big assembly implementations.
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ B math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+TEXT ·subVV(SB),NOSPLIT,$0
+ B math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ B math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+TEXT ·subVW(SB),NOSPLIT,$0
+ B math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ B math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ B math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ B math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ B math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_arm64.s b/vendor/github.com/remyoudompheng/bigfft/arith_arm64.s
new file mode 100644
index 000000000..0ed60f5ca
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_arm64.s
@@ -0,0 +1,36 @@
+// Trampolines to math/big assembly implementations.
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ B math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+TEXT ·subVV(SB),NOSPLIT,$0
+ B math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ B math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+TEXT ·subVW(SB),NOSPLIT,$0
+ B math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ B math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ B math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ B math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ B math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_decl.go b/vendor/github.com/remyoudompheng/bigfft/arith_decl.go
new file mode 100644
index 000000000..7659b0192
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_decl.go
@@ -0,0 +1,16 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package bigfft
+
+import . "math/big"
+
+// implemented in arith_$GOARCH.s
+func addVV(z, x, y []Word) (c Word)
+func subVV(z, x, y []Word) (c Word)
+func addVW(z, x []Word, y Word) (c Word)
+func subVW(z, x []Word, y Word) (c Word)
+func shlVU(z, x []Word, s uint) (c Word)
+func mulAddVWW(z, x []Word, y, r Word) (c Word)
+func addMulVVW(z, x []Word, y Word) (c Word)
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_mips64x.s b/vendor/github.com/remyoudompheng/bigfft/arith_mips64x.s
new file mode 100644
index 000000000..824438826
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_mips64x.s
@@ -0,0 +1,40 @@
+// Trampolines to math/big assembly implementations.
+
+// +build mips64 mips64le
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ JMP math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+// (same as addVV except for SBBQ instead of ADCQ and label names)
+TEXT ·subVV(SB),NOSPLIT,$0
+ JMP math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ JMP math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
+TEXT ·subVW(SB),NOSPLIT,$0
+ JMP math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ JMP math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ JMP math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ JMP math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ JMP math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_mipsx.s b/vendor/github.com/remyoudompheng/bigfft/arith_mipsx.s
new file mode 100644
index 000000000..6c0e92e57
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_mipsx.s
@@ -0,0 +1,40 @@
+// Trampolines to math/big assembly implementations.
+
+// +build mips mipsle
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ JMP math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+// (same as addVV except for SBBQ instead of ADCQ and label names)
+TEXT ·subVV(SB),NOSPLIT,$0
+ JMP math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ JMP math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
+TEXT ·subVW(SB),NOSPLIT,$0
+ JMP math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ JMP math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ JMP math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ JMP math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ JMP math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_ppc64x.s b/vendor/github.com/remyoudompheng/bigfft/arith_ppc64x.s
new file mode 100644
index 000000000..16c7f1535
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_ppc64x.s
@@ -0,0 +1,38 @@
+// Trampolines to math/big assembly implementations.
+
+// +build ppc64 ppc64le
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ BR math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+TEXT ·subVV(SB),NOSPLIT,$0
+ BR math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ BR math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+TEXT ·subVW(SB),NOSPLIT,$0
+ BR math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ BR math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ BR math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ BR math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ BR math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/arith_s390x.s b/vendor/github.com/remyoudompheng/bigfft/arith_s390x.s
new file mode 100644
index 000000000..f72ab0533
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/arith_s390x.s
@@ -0,0 +1,37 @@
+
+// Trampolines to math/big assembly implementations.
+
+#include "textflag.h"
+
+// func addVV(z, x, y []Word) (c Word)
+TEXT ·addVV(SB),NOSPLIT,$0
+ BR math∕big·addVV(SB)
+
+// func subVV(z, x, y []Word) (c Word)
+TEXT ·subVV(SB),NOSPLIT,$0
+ BR math∕big·subVV(SB)
+
+// func addVW(z, x []Word, y Word) (c Word)
+TEXT ·addVW(SB),NOSPLIT,$0
+ BR math∕big·addVW(SB)
+
+// func subVW(z, x []Word, y Word) (c Word)
+TEXT ·subVW(SB),NOSPLIT,$0
+ BR math∕big·subVW(SB)
+
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),NOSPLIT,$0
+ BR math∕big·shlVU(SB)
+
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),NOSPLIT,$0
+ BR math∕big·shrVU(SB)
+
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
+TEXT ·mulAddVWW(SB),NOSPLIT,$0
+ BR math∕big·mulAddVWW(SB)
+
+// func addMulVVW(z, x []Word, y Word) (c Word)
+TEXT ·addMulVVW(SB),NOSPLIT,$0
+ BR math∕big·addMulVVW(SB)
+
diff --git a/vendor/github.com/remyoudompheng/bigfft/fermat.go b/vendor/github.com/remyoudompheng/bigfft/fermat.go
new file mode 100644
index 000000000..200ee5732
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/fermat.go
@@ -0,0 +1,216 @@
+package bigfft
+
+import (
+ "math/big"
+)
+
+// Arithmetic modulo 2^n+1.
+
+// A fermat of length w+1 represents a number modulo 2^(w*_W) + 1. The last
+// word is zero or one. A number has at most two representatives satisfying the
+// 0-1 last word constraint.
+type fermat nat
+
+func (n fermat) String() string { return nat(n).String() }
+
+func (z fermat) norm() {
+ n := len(z) - 1
+ c := z[n]
+ if c == 0 {
+ return
+ }
+ if z[0] >= c {
+ z[n] = 0
+ z[0] -= c
+ return
+ }
+ // z[0] < z[n].
+ subVW(z, z, c) // Substract c
+ if c > 1 {
+ z[n] -= c - 1
+ c = 1
+ }
+ // Add back c.
+ if z[n] == 1 {
+ z[n] = 0
+ return
+ } else {
+ addVW(z, z, 1)
+ }
+}
+
+// Shift computes (x << k) mod (2^n+1).
+func (z fermat) Shift(x fermat, k int) {
+ if len(z) != len(x) {
+ panic("len(z) != len(x) in Shift")
+ }
+ n := len(x) - 1
+ // Shift by n*_W is taking the opposite.
+ k %= 2 * n * _W
+ if k < 0 {
+ k += 2 * n * _W
+ }
+ neg := false
+ if k >= n*_W {
+ k -= n * _W
+ neg = true
+ }
+
+ kw, kb := k/_W, k%_W
+
+ z[n] = 1 // Add (-1)
+ if !neg {
+ for i := 0; i < kw; i++ {
+ z[i] = 0
+ }
+ // Shift left by kw words.
+ // x = a·2^(n-k) + b
+ // x<<k = (b<<k) - a
+ copy(z[kw:], x[:n-kw])
+ b := subVV(z[:kw+1], z[:kw+1], x[n-kw:])
+ if z[kw+1] > 0 {
+ z[kw+1] -= b
+ } else {
+ subVW(z[kw+1:], z[kw+1:], b)
+ }
+ } else {
+ for i := kw + 1; i < n; i++ {
+ z[i] = 0
+ }
+ // Shift left and negate, by kw words.
+ copy(z[:kw+1], x[n-kw:n+1]) // z_low = x_high
+ b := subVV(z[kw:n], z[kw:n], x[:n-kw]) // z_high -= x_low
+ z[n] -= b
+ }
+ // Add back 1.
+ if z[n] > 0 {
+ z[n]--
+ } else if z[0] < ^big.Word(0) {
+ z[0]++
+ } else {
+ addVW(z, z, 1)
+ }
+ // Shift left by kb bits
+ shlVU(z, z, uint(kb))
+ z.norm()
+}
+
+// ShiftHalf shifts x by k/2 bits the left. Shifting by 1/2 bit
+// is multiplication by sqrt(2) mod 2^n+1 which is 2^(3n/4) - 2^(n/4).
+// A temporary buffer must be provided in tmp.
+func (z fermat) ShiftHalf(x fermat, k int, tmp fermat) {
+ n := len(z) - 1
+ if k%2 == 0 {
+ z.Shift(x, k/2)
+ return
+ }
+ u := (k - 1) / 2
+ a := u + (3*_W/4)*n
+ b := u + (_W/4)*n
+ z.Shift(x, a)
+ tmp.Shift(x, b)
+ z.Sub(z, tmp)
+}
+
+// Add computes addition mod 2^n+1.
+func (z fermat) Add(x, y fermat) fermat {
+ if len(z) != len(x) {
+ panic("Add: len(z) != len(x)")
+ }
+ addVV(z, x, y) // there cannot be a carry here.
+ z.norm()
+ return z
+}
+
+// Sub computes substraction mod 2^n+1.
+func (z fermat) Sub(x, y fermat) fermat {
+ if len(z) != len(x) {
+ panic("Add: len(z) != len(x)")
+ }
+ n := len(y) - 1
+ b := subVV(z[:n], x[:n], y[:n])
+ b += y[n]
+ // If b > 0, we need to subtract b<<n, which is the same as adding b.
+ z[n] = x[n]
+ if z[0] <= ^big.Word(0)-b {
+ z[0] += b
+ } else {
+ addVW(z, z, b)
+ }
+ z.norm()
+ return z
+}
+
+func (z fermat) Mul(x, y fermat) fermat {
+ if len(x) != len(y) {
+ panic("Mul: len(x) != len(y)")
+ }
+ n := len(x) - 1
+ if n < 30 {
+ z = z[:2*n+2]
+ basicMul(z, x, y)
+ z = z[:2*n+1]
+ } else {
+ var xi, yi, zi big.Int
+ xi.SetBits(x)
+ yi.SetBits(y)
+ zi.SetBits(z)
+ zb := zi.Mul(&xi, &yi).Bits()
+ if len(zb) <= n {
+ // Short product.
+ copy(z, zb)
+ for i := len(zb); i < len(z); i++ {
+ z[i] = 0
+ }
+ return z
+ }
+ z = zb
+ }
+ // len(z) is at most 2n+1.
+ if len(z) > 2*n+1 {
+ panic("len(z) > 2n+1")
+ }
+ // We now have
+ // z = z[:n] + 1<<(n*W) * z[n:2n+1]
+ // which normalizes to:
+ // z = z[:n] - z[n:2n] + z[2n]
+ c1 := big.Word(0)
+ if len(z) > 2*n {
+ c1 = addVW(z[:n], z[:n], z[2*n])
+ }
+ c2 := big.Word(0)
+ if len(z) >= 2*n {
+ c2 = subVV(z[:n], z[:n], z[n:2*n])
+ } else {
+ m := len(z) - n
+ c2 = subVV(z[:m], z[:m], z[n:])
+ c2 = subVW(z[m:n], z[m:n], c2)
+ }
+ // Restore carries.
+ // Substracting z[n] -= c2 is the same
+ // as z[0] += c2
+ z = z[:n+1]
+ z[n] = c1
+ c := addVW(z, z, c2)
+ if c != 0 {
+ panic("impossible")
+ }
+ z.norm()
+ return z
+}
+
+// copied from math/big
+//
+// basicMul multiplies x and y and leaves the result in z.
+// The (non-normalized) result is placed in z[0 : len(x) + len(y)].
+func basicMul(z, x, y fermat) {
+ // initialize z
+ for i := 0; i < len(z); i++ {
+ z[i] = 0
+ }
+ for i, d := range y {
+ if d != 0 {
+ z[len(x)+i] = addMulVVW(z[i:i+len(x)], x, d)
+ }
+ }
+}
diff --git a/vendor/github.com/remyoudompheng/bigfft/fft.go b/vendor/github.com/remyoudompheng/bigfft/fft.go
new file mode 100644
index 000000000..2d4c1e7a9
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/fft.go
@@ -0,0 +1,370 @@
+// Package bigfft implements multiplication of big.Int using FFT.
+//
+// The implementation is based on the Schönhage-Strassen method
+// using integer FFT modulo 2^n+1.
+package bigfft
+
+import (
+ "math/big"
+ "unsafe"
+)
+
+const _W = int(unsafe.Sizeof(big.Word(0)) * 8)
+
+type nat []big.Word
+
+func (n nat) String() string {
+ v := new(big.Int)
+ v.SetBits(n)
+ return v.String()
+}
+
+// fftThreshold is the size (in words) above which FFT is used over
+// Karatsuba from math/big.
+//
+// TestCalibrate seems to indicate a threshold of 60kbits on 32-bit
+// arches and 110kbits on 64-bit arches.
+var fftThreshold = 1800
+
+// Mul computes the product x*y and returns z.
+// It can be used instead of the Mul method of
+// *big.Int from math/big package.
+func Mul(x, y *big.Int) *big.Int {
+ xwords := len(x.Bits())
+ ywords := len(y.Bits())
+ if xwords > fftThreshold && ywords > fftThreshold {
+ return mulFFT(x, y)
+ }
+ return new(big.Int).Mul(x, y)
+}
+
+func mulFFT(x, y *big.Int) *big.Int {
+ var xb, yb nat = x.Bits(), y.Bits()
+ zb := fftmul(xb, yb)
+ z := new(big.Int)
+ z.SetBits(zb)
+ if x.Sign()*y.Sign() < 0 {
+ z.Neg(z)
+ }
+ return z
+}
+
+// A FFT size of K=1<<k is adequate when K is about 2*sqrt(N) where
+// N = x.Bitlen() + y.Bitlen().
+
+func fftmul(x, y nat) nat {
+ k, m := fftSize(x, y)
+ xp := polyFromNat(x, k, m)
+ yp := polyFromNat(y, k, m)
+ rp := xp.Mul(&yp)
+ return rp.Int()
+}
+
+// fftSizeThreshold[i] is the maximal size (in bits) where we should use
+// fft size i.
+var fftSizeThreshold = [...]int64{0, 0, 0,
+ 4 << 10, 8 << 10, 16 << 10, // 5
+ 32 << 10, 64 << 10, 1 << 18, 1 << 20, 3 << 20, // 10
+ 8 << 20, 30 << 20, 100 << 20, 300 << 20, 600 << 20,
+}
+
+// returns the FFT length k, m the number of words per chunk
+// such that m << k is larger than the number of words
+// in x*y.
+func fftSize(x, y nat) (k uint, m int) {
+ words := len(x) + len(y)
+ bits := int64(words) * int64(_W)
+ k = uint(len(fftSizeThreshold))
+ for i := range fftSizeThreshold {
+ if fftSizeThreshold[i] > bits {
+ k = uint(i)
+ break
+ }
+ }
+ // The 1<<k chunks of m words must have N bits so that
+ // 2^N-1 is larger than x*y. That is, m<<k > words
+ m = words>>k + 1
+ return
+}
+
+// valueSize returns the length (in words) to use for polynomial
+// coefficients, to compute a correct product of polynomials P*Q
+// where deg(P*Q) < K (== 1<<k) and where coefficients of P and Q are
+// less than b^m (== 1 << (m*_W)).
+// The chosen length (in bits) must be a multiple of 1 << (k-extra).
+func valueSize(k uint, m int, extra uint) int {
+ // The coefficients of P*Q are less than b^(2m)*K
+ // so we need W * valueSize >= 2*m*W+K
+ n := 2*m*_W + int(k) // necessary bits
+ K := 1 << (k - extra)
+ if K < _W {
+ K = _W
+ }
+ n = ((n / K) + 1) * K // round to a multiple of K
+ return n / _W
+}
+
+// poly represents an integer via a polynomial in Z[x]/(x^K+1)
+// where K is the FFT length and b^m is the computation basis 1<<(m*_W).
+// If P = a[0] + a[1] x + ... a[n] x^(K-1), the associated natural number
+// is P(b^m).
+type poly struct {
+ k uint // k is such that K = 1<<k.
+ m int // the m such that P(b^m) is the original number.
+ a []nat // a slice of at most K m-word coefficients.
+}
+
+// polyFromNat slices the number x into a polynomial
+// with 1<<k coefficients made of m words.
+func polyFromNat(x nat, k uint, m int) poly {
+ p := poly{k: k, m: m}
+ length := len(x)/m + 1
+ p.a = make([]nat, length)
+ for i := range p.a {
+ if len(x) < m {
+ p.a[i] = make(nat, m)
+ copy(p.a[i], x)
+ break
+ }
+ p.a[i] = x[:m]
+ x = x[m:]
+ }
+ return p
+}
+
+// Int evaluates back a poly to its integer value.
+func (p *poly) Int() nat {
+ length := len(p.a)*p.m + 1
+ if na := len(p.a); na > 0 {
+ length += len(p.a[na-1])
+ }
+ n := make(nat, length)
+ m := p.m
+ np := n
+ for i := range p.a {
+ l := len(p.a[i])
+ c := addVV(np[:l], np[:l], p.a[i])
+ if np[l] < ^big.Word(0) {
+ np[l] += c
+ } else {
+ addVW(np[l:], np[l:], c)
+ }
+ np = np[m:]
+ }
+ n = trim(n)
+ return n
+}
+
+func trim(n nat) nat {
+ for i := range n {
+ if n[len(n)-1-i] != 0 {
+ return n[:len(n)-i]
+ }
+ }
+ return nil
+}
+
+// Mul multiplies p and q modulo X^K-1, where K = 1<<p.k.
+// The product is done via a Fourier transform.
+func (p *poly) Mul(q *poly) poly {
+ // extra=2 because:
+ // * some power of 2 is a K-th root of unity when n is a multiple of K/2.
+ // * 2 itself is a square (see fermat.ShiftHalf)
+ n := valueSize(p.k, p.m, 2)
+
+ pv, qv := p.Transform(n), q.Transform(n)
+ rv := pv.Mul(&qv)
+ r := rv.InvTransform()
+ r.m = p.m
+ return r
+}
+
+// A polValues represents the value of a poly at the powers of a
+// K-th root of unity θ=2^(l/2) in Z/(b^n+1)Z, where b^n = 2^(K/4*l).
+type polValues struct {
+ k uint // k is such that K = 1<<k.
+ n int // the length of coefficients, n*_W a multiple of K/4.
+ values []fermat // a slice of K (n+1)-word values
+}
+
+// Transform evaluates p at θ^i for i = 0...K-1, where
+// θ is a K-th primitive root of unity in Z/(b^n+1)Z.
+func (p *poly) Transform(n int) polValues {
+ k := p.k
+ inputbits := make([]big.Word, (n+1)<<k)
+ input := make([]fermat, 1<<k)
+ // Now computed q(ω^i) for i = 0 ... K-1
+ valbits := make([]big.Word, (n+1)<<k)
+ values := make([]fermat, 1<<k)
+ for i := range values {
+ input[i] = inputbits[i*(n+1) : (i+1)*(n+1)]
+ if i < len(p.a) {
+ copy(input[i], p.a[i])
+ }
+ values[i] = fermat(valbits[i*(n+1) : (i+1)*(n+1)])
+ }
+ fourier(values, input, false, n, k)
+ return polValues{k, n, values}
+}
+
+// InvTransform reconstructs p (modulo X^K - 1) from its
+// values at θ^i for i = 0..K-1.
+func (v *polValues) InvTransform() poly {
+ k, n := v.k, v.n
+
+ // Perform an inverse Fourier transform to recover p.
+ pbits := make([]big.Word, (n+1)<<k)
+ p := make([]fermat, 1<<k)
+ for i := range p {
+ p[i] = fermat(pbits[i*(n+1) : (i+1)*(n+1)])
+ }
+ fourier(p, v.values, true, n, k)
+ // Divide by K, and untwist q to recover p.
+ u := make(fermat, n+1)
+ a := make([]nat, 1<<k)
+ for i := range p {
+ u.Shift(p[i], -int(k))
+ copy(p[i], u)
+ a[i] = nat(p[i])
+ }
+ return poly{k: k, m: 0, a: a}
+}
+
+// NTransform evaluates p at θω^i for i = 0...K-1, where
+// θ is a (2K)-th primitive root of unity in Z/(b^n+1)Z
+// and ω = θ².
+func (p *poly) NTransform(n int) polValues {
+ k := p.k
+ if len(p.a) >= 1<<k {
+ panic("Transform: len(p.a) >= 1<<k")
+ }
+ // θ is represented as a shift.
+ θshift := (n * _W) >> k
+ // p(x) = a_0 + a_1 x + ... + a_{K-1} x^(K-1)
+ // p(θx) = q(x) where
+ // q(x) = a_0 + θa_1 x + ... + θ^(K-1) a_{K-1} x^(K-1)
+ //
+ // Twist p by θ to obtain q.
+ tbits := make([]big.Word, (n+1)<<k)
+ twisted := make([]fermat, 1<<k)
+ src := make(fermat, n+1)
+ for i := range twisted {
+ twisted[i] = fermat(tbits[i*(n+1) : (i+1)*(n+1)])
+ if i < len(p.a) {
+ for i := range src {
+ src[i] = 0
+ }
+ copy(src, p.a[i])
+ twisted[i].Shift(src, θshift*i)
+ }
+ }
+
+ // Now computed q(ω^i) for i = 0 ... K-1
+ valbits := make([]big.Word, (n+1)<<k)
+ values := make([]fermat, 1<<k)
+ for i := range values {
+ values[i] = fermat(valbits[i*(n+1) : (i+1)*(n+1)])
+ }
+ fourier(values, twisted, false, n, k)
+ return polValues{k, n, values}
+}
+
+// InvTransform reconstructs a polynomial from its values at
+// roots of x^K+1. The m field of the returned polynomial
+// is unspecified.
+func (v *polValues) InvNTransform() poly {
+ k := v.k
+ n := v.n
+ θshift := (n * _W) >> k
+
+ // Perform an inverse Fourier transform to recover q.
+ qbits := make([]big.Word, (n+1)<<k)
+ q := make([]fermat, 1<<k)
+ for i := range q {
+ q[i] = fermat(qbits[i*(n+1) : (i+1)*(n+1)])
+ }
+ fourier(q, v.values, true, n, k)
+
+ // Divide by K, and untwist q to recover p.
+ u := make(fermat, n+1)
+ a := make([]nat, 1<<k)
+ for i := range q {
+ u.Shift(q[i], -int(k)-i*θshift)
+ copy(q[i], u)
+ a[i] = nat(q[i])
+ }
+ return poly{k: k, m: 0, a: a}
+}
+
+// fourier performs an unnormalized Fourier transform
+// of src, a length 1<<k vector of numbers modulo b^n+1
+// where b = 1<<_W.
+func fourier(dst []fermat, src []fermat, backward bool, n int, k uint) {
+ var rec func(dst, src []fermat, size uint)
+ tmp := make(fermat, n+1) // pre-allocate temporary variables.
+ tmp2 := make(fermat, n+1) // pre-allocate temporary variables.
+
+ // The recursion function of the FFT.
+ // The root of unity used in the transform is ω=1<<(ω2shift/2).
+ // The source array may use shifted indices (i.e. the i-th
+ // element is src[i << idxShift]).
+ rec = func(dst, src []fermat, size uint) {
+ idxShift := k - size
+ ω2shift := (4 * n * _W) >> size
+ if backward {
+ ω2shift = -ω2shift
+ }
+
+ // Easy cases.
+ if len(src[0]) != n+1 || len(dst[0]) != n+1 {
+ panic("len(src[0]) != n+1 || len(dst[0]) != n+1")
+ }
+ switch size {
+ case 0:
+ copy(dst[0], src[0])
+ return
+ case 1:
+ dst[0].Add(src[0], src[1<<idxShift]) // dst[0] = src[0] + src[1]
+ dst[1].Sub(src[0], src[1<<idxShift]) // dst[1] = src[0] - src[1]
+ return
+ }
+
+ // Let P(x) = src[0] + src[1<<idxShift] * x + ... + src[K-1 << idxShift] * x^(K-1)
+ // The P(x) = Q1(x²) + x*Q2(x²)
+ // where Q1's coefficients are src with indices shifted by 1
+ // where Q2's coefficients are src[1<<idxShift:] with indices shifted by 1
+
+ // Split destination vectors in halves.
+ dst1 := dst[:1<<(size-1)]
+ dst2 := dst[1<<(size-1):]
+ // Transform Q1 and Q2 in the halves.
+ rec(dst1, src, size-1)
+ rec(dst2, src[1<<idxShift:], size-1)
+
+ // Reconstruct P's transform from transforms of Q1 and Q2.
+ // dst[i] is dst1[i] + ω^i * dst2[i]
+ // dst[i + 1<<(k-1)] is dst1[i] + ω^(i+K/2) * dst2[i]
+ //
+ for i := range dst1 {
+ tmp.ShiftHalf(dst2[i], i*ω2shift, tmp2) // ω^i * dst2[i]
+ dst2[i].Sub(dst1[i], tmp)
+ dst1[i].Add(dst1[i], tmp)
+ }
+ }
+ rec(dst, src, k)
+}
+
+// Mul returns the pointwise product of p and q.
+func (p *polValues) Mul(q *polValues) (r polValues) {
+ n := p.n
+ r.k, r.n = p.k, p.n
+ r.values = make([]fermat, len(p.values))
+ bits := make([]big.Word, len(p.values)*(n+1))
+ buf := make(fermat, 8*n)
+ for i := range r.values {
+ r.values[i] = bits[i*(n+1) : (i+1)*(n+1)]
+ z := buf.Mul(p.values[i], q.values[i])
+ copy(r.values[i], z)
+ }
+ return
+}
diff --git a/vendor/github.com/remyoudompheng/bigfft/go.mod b/vendor/github.com/remyoudompheng/bigfft/go.mod
new file mode 100644
index 000000000..e621735f7
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/go.mod
@@ -0,0 +1,3 @@
+module github.com/remyoudompheng/bigfft
+
+go 1.12
diff --git a/vendor/github.com/remyoudompheng/bigfft/scan.go b/vendor/github.com/remyoudompheng/bigfft/scan.go
new file mode 100644
index 000000000..dd3f2679e
--- /dev/null
+++ b/vendor/github.com/remyoudompheng/bigfft/scan.go
@@ -0,0 +1,70 @@
+package bigfft
+
+import (
+ "math/big"
+)
+
+// FromDecimalString converts the base 10 string
+// representation of a natural (non-negative) number
+// into a *big.Int.
+// Its asymptotic complexity is less than quadratic.
+func FromDecimalString(s string) *big.Int {
+ var sc scanner
+ z := new(big.Int)
+ sc.scan(z, s)
+ return z
+}
+
+type scanner struct {
+ // powers[i] is 10^(2^i * quadraticScanThreshold).
+ powers []*big.Int
+}
+
+func (s *scanner) chunkSize(size int) (int, *big.Int) {
+ if size <= quadraticScanThreshold {
+ panic("size < quadraticScanThreshold")
+ }
+ pow := uint(0)
+ for n := size; n > quadraticScanThreshold; n /= 2 {
+ pow++
+ }
+ // threshold * 2^(pow-1) <= size < threshold * 2^pow
+ return quadraticScanThreshold << (pow - 1), s.power(pow - 1)
+}
+
+func (s *scanner) power(k uint) *big.Int {
+ for i := len(s.powers); i <= int(k); i++ {
+ z := new(big.Int)
+ if i == 0 {
+ if quadraticScanThreshold%14 != 0 {
+ panic("quadraticScanThreshold % 14 != 0")
+ }
+ z.Exp(big.NewInt(1e14), big.NewInt(quadraticScanThreshold/14), nil)
+ } else {
+ z.Mul(s.powers[i-1], s.powers[i-1])
+ }
+ s.powers = append(s.powers, z)
+ }
+ return s.powers[k]
+}
+
+func (s *scanner) scan(z *big.Int, str string) {
+ if len(str) <= quadraticScanThreshold {
+ z.SetString(str, 10)
+ return
+ }
+ sz, pow := s.chunkSize(len(str))
+ // Scan the left half.
+ s.scan(z, str[:len(str)-sz])
+ // FIXME: reuse temporaries.
+ left := Mul(z, pow)
+ // Scan the right half
+ s.scan(z, str[len(str)-sz:])
+ z.Add(z, left)
+}
+
+// quadraticScanThreshold is the number of digits
+// below which big.Int.SetString is more efficient
+// than subquadratic algorithms.
+// 1232 digits fit in 4096 bits.
+const quadraticScanThreshold = 1232
diff --git a/vendor/github.com/uptrace/bun/dialect/sqlitedialect/LICENSE b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/LICENSE
new file mode 100644
index 000000000..7ec81810c
--- /dev/null
+++ b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/LICENSE
@@ -0,0 +1,24 @@
+Copyright (c) 2021 Vladimir Mihailenco. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+ * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/vendor/github.com/uptrace/bun/dialect/sqlitedialect/dialect.go b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/dialect.go
new file mode 100644
index 000000000..33d25f2d1
--- /dev/null
+++ b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/dialect.go
@@ -0,0 +1,94 @@
+package sqlitedialect
+
+import (
+ "database/sql"
+ "reflect"
+ "sync"
+
+ "github.com/uptrace/bun/dialect"
+ "github.com/uptrace/bun/dialect/feature"
+ "github.com/uptrace/bun/dialect/sqltype"
+ "github.com/uptrace/bun/schema"
+)
+
+type Dialect struct {
+ tables *schema.Tables
+ features feature.Feature
+
+ appenderMap sync.Map
+ scannerMap sync.Map
+}
+
+func New() *Dialect {
+ d := new(Dialect)
+ d.tables = schema.NewTables(d)
+ d.features = feature.Returning | feature.InsertTableAlias | feature.DeleteTableAlias
+ return d
+}
+
+func (d *Dialect) Init(*sql.DB) {}
+
+func (d *Dialect) Name() dialect.Name {
+ return dialect.SQLite
+}
+
+func (d *Dialect) Features() feature.Feature {
+ return d.features
+}
+
+func (d *Dialect) Tables() *schema.Tables {
+ return d.tables
+}
+
+func (d *Dialect) OnTable(table *schema.Table) {
+ for _, field := range table.FieldMap {
+ d.onField(field)
+ }
+}
+
+func (d *Dialect) onField(field *schema.Field) {
+ // INTEGER PRIMARY KEY is an alias for the ROWID.
+ // It is safe to convert all ints to INTEGER, because SQLite types don't have size.
+ switch field.DiscoveredSQLType {
+ case sqltype.SmallInt, sqltype.BigInt:
+ field.DiscoveredSQLType = sqltype.Integer
+ }
+}
+
+func (d *Dialect) IdentQuote() byte {
+ return '"'
+}
+
+func (d *Dialect) Append(fmter schema.Formatter, b []byte, v interface{}) []byte {
+ return schema.Append(fmter, b, v, nil)
+}
+
+func (d *Dialect) Appender(typ reflect.Type) schema.AppenderFunc {
+ if v, ok := d.appenderMap.Load(typ); ok {
+ return v.(schema.AppenderFunc)
+ }
+
+ fn := schema.Appender(typ, nil)
+
+ if v, ok := d.appenderMap.LoadOrStore(typ, fn); ok {
+ return v.(schema.AppenderFunc)
+ }
+ return fn
+}
+
+func (d *Dialect) FieldAppender(field *schema.Field) schema.AppenderFunc {
+ return schema.FieldAppender(d, field)
+}
+
+func (d *Dialect) Scanner(typ reflect.Type) schema.ScannerFunc {
+ if v, ok := d.scannerMap.Load(typ); ok {
+ return v.(schema.ScannerFunc)
+ }
+
+ fn := scanner(typ)
+
+ if v, ok := d.scannerMap.LoadOrStore(typ, fn); ok {
+ return v.(schema.ScannerFunc)
+ }
+ return fn
+}
diff --git a/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.mod b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.mod
new file mode 100644
index 000000000..1fb9b7ab1
--- /dev/null
+++ b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.mod
@@ -0,0 +1,7 @@
+module github.com/uptrace/bun/dialect/sqlitedialect
+
+go 1.16
+
+replace github.com/uptrace/bun => ../..
+
+require github.com/uptrace/bun v0.4.3
diff --git a/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.sum b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.sum
new file mode 100644
index 000000000..4d0f1c1bb
--- /dev/null
+++ b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/go.sum
@@ -0,0 +1,22 @@
+github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
+github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
+github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
+github.com/jinzhu/inflection v1.0.0 h1:K317FqzuhWc8YvSVlFMCCUb36O/S9MCKRDI7QkRKD/E=
+github.com/jinzhu/inflection v1.0.0/go.mod h1:h+uFLlag+Qp1Va5pdKtLDYj+kHp5pxUVkryuEj+Srlc=
+github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
+github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
+github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
+github.com/stretchr/testify v1.6.1/go.mod h1:6Fq8oRcR53rry900zMqJjRRixrwX3KX962/h/Wwjteg=
+github.com/stretchr/testify v1.7.0 h1:nwc3DEeHmmLAfoZucVR881uASk0Mfjw8xYJ99tb5CcY=
+github.com/stretchr/testify v1.7.0/go.mod h1:6Fq8oRcR53rry900zMqJjRRixrwX3KX962/h/Wwjteg=
+github.com/tmthrgd/go-hex v0.0.0-20190904060850-447a3041c3bc h1:9lRDQMhESg+zvGYmW5DyG0UqvY96Bu5QYsTLvCHdrgo=
+github.com/tmthrgd/go-hex v0.0.0-20190904060850-447a3041c3bc/go.mod h1:bciPuU6GHm1iF1pBvUfxfsH0Wmnc2VbpgvbI9ZWuIRs=
+github.com/vmihailenco/msgpack/v5 v5.3.4 h1:qMKAwOV+meBw2Y8k9cVwAy7qErtYCwBzZ2ellBfvnqc=
+github.com/vmihailenco/msgpack/v5 v5.3.4/go.mod h1:7xyJ9e+0+9SaZT0Wt1RGleJXzli6Q/V5KbhBonMG9jc=
+github.com/vmihailenco/tagparser/v2 v2.0.0 h1:y09buUbR+b5aycVFQs/g70pqKVZNBmxwAhO7/IwNM9g=
+github.com/vmihailenco/tagparser/v2 v2.0.0/go.mod h1:Wri+At7QHww0WTrCBeu4J6bNtoV6mEfg5OIWRZA9qds=
+golang.org/x/sys v0.0.0-20210616094352-59db8d763f22 h1:RqytpXGR1iVNX7psjB3ff8y7sNFinVFvkx1c8SjBkio=
+golang.org/x/sys v0.0.0-20210616094352-59db8d763f22/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
+gopkg.in/yaml.v3 v3.0.0-20200313102051-9f266ea9e77c h1:dUUwHk2QECo/6vqA44rthZ8ie2QXMNeKRTHCNY2nXvo=
+gopkg.in/yaml.v3 v3.0.0-20200313102051-9f266ea9e77c/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
diff --git a/vendor/github.com/uptrace/bun/dialect/sqlitedialect/scan.go b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/scan.go
new file mode 100644
index 000000000..44c50c2e9
--- /dev/null
+++ b/vendor/github.com/uptrace/bun/dialect/sqlitedialect/scan.go
@@ -0,0 +1,28 @@
+package sqlitedialect
+
+import (
+ "fmt"
+ "reflect"
+
+ "github.com/uptrace/bun/schema"
+)
+
+func scanner(typ reflect.Type) schema.ScannerFunc {
+ if typ.Kind() == reflect.Interface {
+ return scanInterface
+ }
+ return schema.Scanner(typ)
+}
+
+func scanInterface(dest reflect.Value, src interface{}) error {
+ if dest.IsNil() {
+ dest.Set(reflect.ValueOf(src))
+ return nil
+ }
+
+ dest = dest.Elem()
+ if fn := scanner(dest.Type()); fn != nil {
+ return fn(dest, src)
+ }
+ return fmt.Errorf("bun: can't scan %#v into %s", src, dest.Type())
+}