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authorLibravatar Terin Stock <terinjokes@gmail.com>2025-03-09 17:47:56 +0100
committerLibravatar Terin Stock <terinjokes@gmail.com>2025-03-10 01:59:49 +0100
commit3ac1ee16f377d31a0fb80c8dae28b6239ac4229e (patch)
treef61faa581feaaeaba2542b9f2b8234a590684413 /vendor/github.com/remyoudompheng/bigfft
parent[chore] update URLs to forked source (diff)
downloadgotosocial-3ac1ee16f377d31a0fb80c8dae28b6239ac4229e.tar.xz
[chore] remove vendor
Diffstat (limited to 'vendor/github.com/remyoudompheng/bigfft')
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/LICENSE27
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/README54
-rw-r--r--vendor/github.com/remyoudompheng/bigfft/arith_decl.go33
-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/scan.go70
6 files changed, 0 insertions, 770 deletions
diff --git a/vendor/github.com/remyoudompheng/bigfft/LICENSE b/vendor/github.com/remyoudompheng/bigfft/LICENSE
deleted file mode 100644
index 744875676..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/LICENSE
+++ /dev/null
@@ -1,27 +0,0 @@
-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
deleted file mode 100644
index 0fcd39d96..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/README
+++ /dev/null
@@ -1,54 +0,0 @@
-This library is a toy proof-of-concept implementation of the
-well-known Schonhage-Strassen method for multiplying integers.
-It is not expected to have a real life usecase outside number
-theory computations, nor is it expected to be used in any production
-system.
-
-If you are using it in your project, you may want to carefully
-examine the actual requirement or problem you are trying to solve.
-
-# Comparison with the standard library and GMP
-
-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_decl.go b/vendor/github.com/remyoudompheng/bigfft/arith_decl.go
deleted file mode 100644
index 96937dff8..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/arith_decl.go
+++ /dev/null
@@ -1,33 +0,0 @@
-// 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"
- _ "unsafe"
-)
-
-type Word = big.Word
-
-//go:linkname addVV math/big.addVV
-func addVV(z, x, y []Word) (c Word)
-
-//go:linkname subVV math/big.subVV
-func subVV(z, x, y []Word) (c Word)
-
-//go:linkname addVW math/big.addVW
-func addVW(z, x []Word, y Word) (c Word)
-
-//go:linkname subVW math/big.subVW
-func subVW(z, x []Word, y Word) (c Word)
-
-//go:linkname shlVU math/big.shlVU
-func shlVU(z, x []Word, s uint) (c Word)
-
-//go:linkname mulAddVWW math/big.mulAddVWW
-func mulAddVWW(z, x []Word, y, r Word) (c Word)
-
-//go:linkname addMulVVW math/big.addMulVVW
-func addMulVVW(z, x []Word, y Word) (c Word)
diff --git a/vendor/github.com/remyoudompheng/bigfft/fermat.go b/vendor/github.com/remyoudompheng/bigfft/fermat.go
deleted file mode 100644
index 200ee5732..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/fermat.go
+++ /dev/null
@@ -1,216 +0,0 @@
-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
deleted file mode 100644
index 2d4c1e7a9..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/fft.go
+++ /dev/null
@@ -1,370 +0,0 @@
-// 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/scan.go b/vendor/github.com/remyoudompheng/bigfft/scan.go
deleted file mode 100644
index dd3f2679e..000000000
--- a/vendor/github.com/remyoudompheng/bigfft/scan.go
+++ /dev/null
@@ -1,70 +0,0 @@
-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