From 3ac1ee16f377d31a0fb80c8dae28b6239ac4229e Mon Sep 17 00:00:00 2001
From: Terin Stock <terinjokes@gmail.com>
Date: Sun, 9 Mar 2025 17:47:56 +0100
Subject: [chore] remove vendor

---
 vendor/github.com/remyoudompheng/bigfft/fft.go | 370 -------------------------
 1 file changed, 370 deletions(-)
 delete mode 100644 vendor/github.com/remyoudompheng/bigfft/fft.go

(limited to 'vendor/github.com/remyoudompheng/bigfft/fft.go')

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
-}
-- 
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