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author | 2025-03-09 17:47:56 +0100 | |
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committer | 2025-03-10 01:59:49 +0100 | |
commit | 3ac1ee16f377d31a0fb80c8dae28b6239ac4229e (patch) | |
tree | f61faa581feaaeaba2542b9f2b8234a590684413 /vendor/github.com/remyoudompheng/bigfft | |
parent | [chore] update URLs to forked source (diff) | |
download | gotosocial-3ac1ee16f377d31a0fb80c8dae28b6239ac4229e.tar.xz |
[chore] remove vendor
Diffstat (limited to 'vendor/github.com/remyoudompheng/bigfft')
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/LICENSE | 27 | ||||
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/README | 54 | ||||
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/arith_decl.go | 33 | ||||
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/fermat.go | 216 | ||||
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/fft.go | 370 | ||||
-rw-r--r-- | vendor/github.com/remyoudompheng/bigfft/scan.go | 70 |
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 |