````// Copyright (c) 2016 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 edwards25519`

`import (`
`	"crypto/subtle"`
`	"encoding/binary"`
`	"errors"`
`)`

`// A Scalar is an integer modulo`
`//`
`//     l = 2^252 + 27742317777372353535851937790883648493`
`//`
`// which is the prime order of the edwards25519 group.`
`//`
`// This type works similarly to math/big.Int, and all arguments and`
`// receivers are allowed to alias.`
`//`
`// The zero value is a valid zero element.`
`type Scalar struct {`
`	// s is the Scalar value in little-endian. The value is always reduced`
`	// between operations.`
`	s [32]byte`
`}`

`var (`
`	scZero = Scalar{[32]byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}`

`	scOne = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}`

`	scMinusOne = Scalar{[32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}}`
`)`

`// NewScalar returns a new zero Scalar.`
`func NewScalar() *Scalar {`
`	return &Scalar{}`
`}`

`// MultiplyAdd sets s = x * y + z mod l, and returns s.`
`func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar {`
`	scMulAdd(&s.s, &x.s, &y.s, &z.s)`
`	return s`
`}`

`// Add sets s = x + y mod l, and returns s.`
`func (s *Scalar) Add(x, y *Scalar) *Scalar {`
`	// s = 1 * x + y mod l`
`	scMulAdd(&s.s, &scOne.s, &x.s, &y.s)`
`	return s`
`}`

`// Subtract sets s = x - y mod l, and returns s.`
`func (s *Scalar) Subtract(x, y *Scalar) *Scalar {`
`	// s = -1 * y + x mod l`
`	scMulAdd(&s.s, &scMinusOne.s, &y.s, &x.s)`
`	return s`
`}`

`// Negate sets s = -x mod l, and returns s.`
`func (s *Scalar) Negate(x *Scalar) *Scalar {`
`	// s = -1 * x + 0 mod l`
`	scMulAdd(&s.s, &scMinusOne.s, &x.s, &scZero.s)`
`	return s`
`}`

`// Multiply sets s = x * y mod l, and returns s.`
`func (s *Scalar) Multiply(x, y *Scalar) *Scalar {`
`	// s = x * y + 0 mod l`
`	scMulAdd(&s.s, &x.s, &y.s, &scZero.s)`
`	return s`
`}`

`// Set sets s = x, and returns s.`
`func (s *Scalar) Set(x *Scalar) *Scalar {`
`	*s = *x`
`	return s`
`}`

`// SetUniformBytes sets s to an uniformly distributed value given 64 uniformly`
`// distributed random bytes.`
`func (s *Scalar) SetUniformBytes(x []byte) *Scalar {`
`	if len(x) != 64 {`
`		panic("edwards25519: invalid SetUniformBytes input length")`
`	}`
`	var wideBytes [64]byte`
`	copy(wideBytes[:], x[:])`
`	scReduce(&s.s, &wideBytes)`
`	return s`
`}`

`// SetCanonicalBytes sets s = x, where x is a 32-byte little-endian encoding of`
`// s, and returns s. If x is not a canonical encoding of s, SetCanonicalBytes`
`// returns nil and an error, and the receiver is unchanged.`
`func (s *Scalar) SetCanonicalBytes(x []byte) (*Scalar, error) {`
`	if len(x) != 32 {`
`		return nil, errors.New("invalid scalar length")`
`	}`
`	ss := &Scalar{}`
`	copy(ss.s[:], x)`
`	if !isReduced(ss) {`
`		return nil, errors.New("invalid scalar encoding")`
`	}`
`	s.s = ss.s`
`	return s, nil`
`}`

`// isReduced returns whether the given scalar is reduced modulo l.`
`func isReduced(s *Scalar) bool {`
`	for i := len(s.s) - 1; i >= 0; i-- {`
`		switch {`
`		case s.s[i] > scMinusOne.s[i]:`
`			return false`
`		case s.s[i] < scMinusOne.s[i]:`
`			return true`
`		}`
`	}`
`	return true`
`}`

`// SetBytesWithClamping applies the buffer pruning described in RFC 8032,`
`// Section 5.1.5 (also known as clamping) and sets s to the result. The input`
`// must be 32 bytes, and it is not modified.`
`//`
`// Note that since Scalar values are always reduced modulo the prime order of`
`// the curve, the resulting value will not preserve any of the cofactor-clearing`
`// properties that clamping is meant to provide. It will however work as`
`// expected as long as it is applied to points on the prime order subgroup, like`
`// in Ed25519. In fact, it is lost to history why RFC 8032 adopted the`
`// irrelevant RFC 7748 clamping, but it is now required for compatibility.`
`func (s *Scalar) SetBytesWithClamping(x []byte) *Scalar {`
`	// The description above omits the purpose of the high bits of the clamping`
`	// for brevity, but those are also lost to reductions, and are also`
`	// irrelevant to edwards25519 as they protect against a specific`
`	// implementation bug that was once observed in a generic Montgomery ladder.`
`	if len(x) != 32 {`
`		panic("edwards25519: invalid SetBytesWithClamping input length")`
`	}`
`	var wideBytes [64]byte`
`	copy(wideBytes[:], x[:])`
`	wideBytes[0] &= 248`
`	wideBytes[31] &= 63`
`	wideBytes[31] |= 64`
`	scReduce(&s.s, &wideBytes)`
`	return s`
`}`

`// Bytes returns the canonical 32-byte little-endian encoding of s.`
`func (s *Scalar) Bytes() []byte {`
`	buf := make([]byte, 32)`
`	copy(buf, s.s[:])`
`	return buf`
`}`

`// Equal returns 1 if s and t are equal, and 0 otherwise.`
`func (s *Scalar) Equal(t *Scalar) int {`
`	return subtle.ConstantTimeCompare(s.s[:], t.s[:])`
`}`

`// scMulAdd and scReduce are ported from the public domain, “ref10”`
`// implementation of ed25519 from SUPERCOP.`

`func load3(in []byte) int64 {`
`	r := int64(in[0])`
`	r |= int64(in[1]) << 8`
`	r |= int64(in[2]) << 16`
`	return r`
`}`

`func load4(in []byte) int64 {`
`	r := int64(in[0])`
`	r |= int64(in[1]) << 8`
`	r |= int64(in[2]) << 16`
`	r |= int64(in[3]) << 24`
`	return r`
`}`

`// Input:`
`//   a[0]+256*a[1]+...+256^31*a[31] = a`
`//   b[0]+256*b[1]+...+256^31*b[31] = b`
`//   c[0]+256*c[1]+...+256^31*c[31] = c`
`//`
`// Output:`
`//   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l`
`//   where l = 2^252 + 27742317777372353535851937790883648493.`
`func scMulAdd(s, a, b, c *[32]byte) {`
`	a0 := 2097151 & load3(a[:])`
`	a1 := 2097151 & (load4(a[2:]) >> 5)`
`	a2 := 2097151 & (load3(a[5:]) >> 2)`
`	a3 := 2097151 & (load4(a[7:]) >> 7)`
`	a4 := 2097151 & (load4(a[10:]) >> 4)`
`	a5 := 2097151 & (load3(a[13:]) >> 1)`
`	a6 := 2097151 & (load4(a[15:]) >> 6)`
`	a7 := 2097151 & (load3(a[18:]) >> 3)`
`	a8 := 2097151 & load3(a[21:])`
`	a9 := 2097151 & (load4(a[23:]) >> 5)`
`	a10 := 2097151 & (load3(a[26:]) >> 2)`
`	a11 := (load4(a[28:]) >> 7)`
`	b0 := 2097151 & load3(b[:])`
`	b1 := 2097151 & (load4(b[2:]) >> 5)`
`	b2 := 2097151 & (load3(b[5:]) >> 2)`
`	b3 := 2097151 & (load4(b[7:]) >> 7)`
`	b4 := 2097151 & (load4(b[10:]) >> 4)`
`	b5 := 2097151 & (load3(b[13:]) >> 1)`
`	b6 := 2097151 & (load4(b[15:]) >> 6)`
`	b7 := 2097151 & (load3(b[18:]) >> 3)`
`	b8 := 2097151 & load3(b[21:])`
`	b9 := 2097151 & (load4(b[23:]) >> 5)`
`	b10 := 2097151 & (load3(b[26:]) >> 2)`
`	b11 := (load4(b[28:]) >> 7)`
`	c0 := 2097151 & load3(c[:])`
`	c1 := 2097151 & (load4(c[2:]) >> 5)`
`	c2 := 2097151 & (load3(c[5:]) >> 2)`
`	c3 := 2097151 & (load4(c[7:]) >> 7)`
`	c4 := 2097151 & (load4(c[10:]) >> 4)`
`	c5 := 2097151 & (load3(c[13:]) >> 1)`
`	c6 := 2097151 & (load4(c[15:]) >> 6)`
`	c7 := 2097151 & (load3(c[18:]) >> 3)`
`	c8 := 2097151 & load3(c[21:])`
`	c9 := 2097151 & (load4(c[23:]) >> 5)`
`	c10 := 2097151 & (load3(c[26:]) >> 2)`
`	c11 := (load4(c[28:]) >> 7)`
`	var carry [23]int64`

`	s0 := c0 + a0*b0`
`	s1 := c1 + a0*b1 + a1*b0`
`	s2 := c2 + a0*b2 + a1*b1 + a2*b0`
`	s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0`
`	s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0`
`	s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0`
`	s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0`
`	s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0`
`	s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0`
`	s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0`
`	s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0`
`	s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0`
`	s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1`
`	s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2`
`	s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3`
`	s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4`
`	s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5`
`	s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6`
`	s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7`
`	s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8`
`	s20 := a9*b11 + a10*b10 + a11*b9`
`	s21 := a10*b11 + a11*b10`
`	s22 := a11 * b11`
`	s23 := int64(0)`

`	carry[0] = (s0 + (1 << 20)) >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[2] = (s2 + (1 << 20)) >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[4] = (s4 + (1 << 20)) >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[6] = (s6 + (1 << 20)) >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[8] = (s8 + (1 << 20)) >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[10] = (s10 + (1 << 20)) >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`
`	carry[12] = (s12 + (1 << 20)) >> 21`
`	s13 += carry[12]`
`	s12 -= carry[12] << 21`
`	carry[14] = (s14 + (1 << 20)) >> 21`
`	s15 += carry[14]`
`	s14 -= carry[14] << 21`
`	carry[16] = (s16 + (1 << 20)) >> 21`
`	s17 += carry[16]`
`	s16 -= carry[16] << 21`
`	carry[18] = (s18 + (1 << 20)) >> 21`
`	s19 += carry[18]`
`	s18 -= carry[18] << 21`
`	carry[20] = (s20 + (1 << 20)) >> 21`
`	s21 += carry[20]`
`	s20 -= carry[20] << 21`
`	carry[22] = (s22 + (1 << 20)) >> 21`
`	s23 += carry[22]`
`	s22 -= carry[22] << 21`

`	carry[1] = (s1 + (1 << 20)) >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[3] = (s3 + (1 << 20)) >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[5] = (s5 + (1 << 20)) >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[7] = (s7 + (1 << 20)) >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[9] = (s9 + (1 << 20)) >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[11] = (s11 + (1 << 20)) >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`
`	carry[13] = (s13 + (1 << 20)) >> 21`
`	s14 += carry[13]`
`	s13 -= carry[13] << 21`
`	carry[15] = (s15 + (1 << 20)) >> 21`
`	s16 += carry[15]`
`	s15 -= carry[15] << 21`
`	carry[17] = (s17 + (1 << 20)) >> 21`
`	s18 += carry[17]`
`	s17 -= carry[17] << 21`
`	carry[19] = (s19 + (1 << 20)) >> 21`
`	s20 += carry[19]`
`	s19 -= carry[19] << 21`
`	carry[21] = (s21 + (1 << 20)) >> 21`
`	s22 += carry[21]`
`	s21 -= carry[21] << 21`

`	s11 += s23 * 666643`
`	s12 += s23 * 470296`
`	s13 += s23 * 654183`
`	s14 -= s23 * 997805`
`	s15 += s23 * 136657`
`	s16 -= s23 * 683901`
`	s23 = 0`

`	s10 += s22 * 666643`
`	s11 += s22 * 470296`
`	s12 += s22 * 654183`
`	s13 -= s22 * 997805`
`	s14 += s22 * 136657`
`	s15 -= s22 * 683901`
`	s22 = 0`

`	s9 += s21 * 666643`
`	s10 += s21 * 470296`
`	s11 += s21 * 654183`
`	s12 -= s21 * 997805`
`	s13 += s21 * 136657`
`	s14 -= s21 * 683901`
`	s21 = 0`

`	s8 += s20 * 666643`
`	s9 += s20 * 470296`
`	s10 += s20 * 654183`
`	s11 -= s20 * 997805`
`	s12 += s20 * 136657`
`	s13 -= s20 * 683901`
`	s20 = 0`

`	s7 += s19 * 666643`
`	s8 += s19 * 470296`
`	s9 += s19 * 654183`
`	s10 -= s19 * 997805`
`	s11 += s19 * 136657`
`	s12 -= s19 * 683901`
`	s19 = 0`

`	s6 += s18 * 666643`
`	s7 += s18 * 470296`
`	s8 += s18 * 654183`
`	s9 -= s18 * 997805`
`	s10 += s18 * 136657`
`	s11 -= s18 * 683901`
`	s18 = 0`

`	carry[6] = (s6 + (1 << 20)) >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[8] = (s8 + (1 << 20)) >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[10] = (s10 + (1 << 20)) >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`
`	carry[12] = (s12 + (1 << 20)) >> 21`
`	s13 += carry[12]`
`	s12 -= carry[12] << 21`
`	carry[14] = (s14 + (1 << 20)) >> 21`
`	s15 += carry[14]`
`	s14 -= carry[14] << 21`
`	carry[16] = (s16 + (1 << 20)) >> 21`
`	s17 += carry[16]`
`	s16 -= carry[16] << 21`

`	carry[7] = (s7 + (1 << 20)) >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[9] = (s9 + (1 << 20)) >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[11] = (s11 + (1 << 20)) >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`
`	carry[13] = (s13 + (1 << 20)) >> 21`
`	s14 += carry[13]`
`	s13 -= carry[13] << 21`
`	carry[15] = (s15 + (1 << 20)) >> 21`
`	s16 += carry[15]`
`	s15 -= carry[15] << 21`

`	s5 += s17 * 666643`
`	s6 += s17 * 470296`
`	s7 += s17 * 654183`
`	s8 -= s17 * 997805`
`	s9 += s17 * 136657`
`	s10 -= s17 * 683901`
`	s17 = 0`

`	s4 += s16 * 666643`
`	s5 += s16 * 470296`
`	s6 += s16 * 654183`
`	s7 -= s16 * 997805`
`	s8 += s16 * 136657`
`	s9 -= s16 * 683901`
`	s16 = 0`

`	s3 += s15 * 666643`
`	s4 += s15 * 470296`
`	s5 += s15 * 654183`
`	s6 -= s15 * 997805`
`	s7 += s15 * 136657`
`	s8 -= s15 * 683901`
`	s15 = 0`

`	s2 += s14 * 666643`
`	s3 += s14 * 470296`
`	s4 += s14 * 654183`
`	s5 -= s14 * 997805`
`	s6 += s14 * 136657`
`	s7 -= s14 * 683901`
`	s14 = 0`

`	s1 += s13 * 666643`
`	s2 += s13 * 470296`
`	s3 += s13 * 654183`
`	s4 -= s13 * 997805`
`	s5 += s13 * 136657`
`	s6 -= s13 * 683901`
`	s13 = 0`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = (s0 + (1 << 20)) >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[2] = (s2 + (1 << 20)) >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[4] = (s4 + (1 << 20)) >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[6] = (s6 + (1 << 20)) >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[8] = (s8 + (1 << 20)) >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[10] = (s10 + (1 << 20)) >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`

`	carry[1] = (s1 + (1 << 20)) >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[3] = (s3 + (1 << 20)) >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[5] = (s5 + (1 << 20)) >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[7] = (s7 + (1 << 20)) >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[9] = (s9 + (1 << 20)) >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[11] = (s11 + (1 << 20)) >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = s0 >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[1] = s1 >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[2] = s2 >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[3] = s3 >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[4] = s4 >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[5] = s5 >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[6] = s6 >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[7] = s7 >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[8] = s8 >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[9] = s9 >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[10] = s10 >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`
`	carry[11] = s11 >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = s0 >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[1] = s1 >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[2] = s2 >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[3] = s3 >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[4] = s4 >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[5] = s5 >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[6] = s6 >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[7] = s7 >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[8] = s8 >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[9] = s9 >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[10] = s10 >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`

`	s[0] = byte(s0 >> 0)`
`	s[1] = byte(s0 >> 8)`
`	s[2] = byte((s0 >> 16) | (s1 << 5))`
`	s[3] = byte(s1 >> 3)`
`	s[4] = byte(s1 >> 11)`
`	s[5] = byte((s1 >> 19) | (s2 << 2))`
`	s[6] = byte(s2 >> 6)`
`	s[7] = byte((s2 >> 14) | (s3 << 7))`
`	s[8] = byte(s3 >> 1)`
`	s[9] = byte(s3 >> 9)`
`	s[10] = byte((s3 >> 17) | (s4 << 4))`
`	s[11] = byte(s4 >> 4)`
`	s[12] = byte(s4 >> 12)`
`	s[13] = byte((s4 >> 20) | (s5 << 1))`
`	s[14] = byte(s5 >> 7)`
`	s[15] = byte((s5 >> 15) | (s6 << 6))`
`	s[16] = byte(s6 >> 2)`
`	s[17] = byte(s6 >> 10)`
`	s[18] = byte((s6 >> 18) | (s7 << 3))`
`	s[19] = byte(s7 >> 5)`
`	s[20] = byte(s7 >> 13)`
`	s[21] = byte(s8 >> 0)`
`	s[22] = byte(s8 >> 8)`
`	s[23] = byte((s8 >> 16) | (s9 << 5))`
`	s[24] = byte(s9 >> 3)`
`	s[25] = byte(s9 >> 11)`
`	s[26] = byte((s9 >> 19) | (s10 << 2))`
`	s[27] = byte(s10 >> 6)`
`	s[28] = byte((s10 >> 14) | (s11 << 7))`
`	s[29] = byte(s11 >> 1)`
`	s[30] = byte(s11 >> 9)`
`	s[31] = byte(s11 >> 17)`
`}`

`// Input:`
`//   s[0]+256*s[1]+...+256^63*s[63] = s`
`//`
`// Output:`
`//   s[0]+256*s[1]+...+256^31*s[31] = s mod l`
`//   where l = 2^252 + 27742317777372353535851937790883648493.`
`func scReduce(out *[32]byte, s *[64]byte) {`
`	s0 := 2097151 & load3(s[:])`
`	s1 := 2097151 & (load4(s[2:]) >> 5)`
`	s2 := 2097151 & (load3(s[5:]) >> 2)`
`	s3 := 2097151 & (load4(s[7:]) >> 7)`
`	s4 := 2097151 & (load4(s[10:]) >> 4)`
`	s5 := 2097151 & (load3(s[13:]) >> 1)`
`	s6 := 2097151 & (load4(s[15:]) >> 6)`
`	s7 := 2097151 & (load3(s[18:]) >> 3)`
`	s8 := 2097151 & load3(s[21:])`
`	s9 := 2097151 & (load4(s[23:]) >> 5)`
`	s10 := 2097151 & (load3(s[26:]) >> 2)`
`	s11 := 2097151 & (load4(s[28:]) >> 7)`
`	s12 := 2097151 & (load4(s[31:]) >> 4)`
`	s13 := 2097151 & (load3(s[34:]) >> 1)`
`	s14 := 2097151 & (load4(s[36:]) >> 6)`
`	s15 := 2097151 & (load3(s[39:]) >> 3)`
`	s16 := 2097151 & load3(s[42:])`
`	s17 := 2097151 & (load4(s[44:]) >> 5)`
`	s18 := 2097151 & (load3(s[47:]) >> 2)`
`	s19 := 2097151 & (load4(s[49:]) >> 7)`
`	s20 := 2097151 & (load4(s[52:]) >> 4)`
`	s21 := 2097151 & (load3(s[55:]) >> 1)`
`	s22 := 2097151 & (load4(s[57:]) >> 6)`
`	s23 := (load4(s[60:]) >> 3)`

`	s11 += s23 * 666643`
`	s12 += s23 * 470296`
`	s13 += s23 * 654183`
`	s14 -= s23 * 997805`
`	s15 += s23 * 136657`
`	s16 -= s23 * 683901`
`	s23 = 0`

`	s10 += s22 * 666643`
`	s11 += s22 * 470296`
`	s12 += s22 * 654183`
`	s13 -= s22 * 997805`
`	s14 += s22 * 136657`
`	s15 -= s22 * 683901`
`	s22 = 0`

`	s9 += s21 * 666643`
`	s10 += s21 * 470296`
`	s11 += s21 * 654183`
`	s12 -= s21 * 997805`
`	s13 += s21 * 136657`
`	s14 -= s21 * 683901`
`	s21 = 0`

`	s8 += s20 * 666643`
`	s9 += s20 * 470296`
`	s10 += s20 * 654183`
`	s11 -= s20 * 997805`
`	s12 += s20 * 136657`
`	s13 -= s20 * 683901`
`	s20 = 0`

`	s7 += s19 * 666643`
`	s8 += s19 * 470296`
`	s9 += s19 * 654183`
`	s10 -= s19 * 997805`
`	s11 += s19 * 136657`
`	s12 -= s19 * 683901`
`	s19 = 0`

`	s6 += s18 * 666643`
`	s7 += s18 * 470296`
`	s8 += s18 * 654183`
`	s9 -= s18 * 997805`
`	s10 += s18 * 136657`
`	s11 -= s18 * 683901`
`	s18 = 0`

`	var carry [17]int64`

`	carry[6] = (s6 + (1 << 20)) >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[8] = (s8 + (1 << 20)) >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[10] = (s10 + (1 << 20)) >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`
`	carry[12] = (s12 + (1 << 20)) >> 21`
`	s13 += carry[12]`
`	s12 -= carry[12] << 21`
`	carry[14] = (s14 + (1 << 20)) >> 21`
`	s15 += carry[14]`
`	s14 -= carry[14] << 21`
`	carry[16] = (s16 + (1 << 20)) >> 21`
`	s17 += carry[16]`
`	s16 -= carry[16] << 21`

`	carry[7] = (s7 + (1 << 20)) >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[9] = (s9 + (1 << 20)) >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[11] = (s11 + (1 << 20)) >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`
`	carry[13] = (s13 + (1 << 20)) >> 21`
`	s14 += carry[13]`
`	s13 -= carry[13] << 21`
`	carry[15] = (s15 + (1 << 20)) >> 21`
`	s16 += carry[15]`
`	s15 -= carry[15] << 21`

`	s5 += s17 * 666643`
`	s6 += s17 * 470296`
`	s7 += s17 * 654183`
`	s8 -= s17 * 997805`
`	s9 += s17 * 136657`
`	s10 -= s17 * 683901`
`	s17 = 0`

`	s4 += s16 * 666643`
`	s5 += s16 * 470296`
`	s6 += s16 * 654183`
`	s7 -= s16 * 997805`
`	s8 += s16 * 136657`
`	s9 -= s16 * 683901`
`	s16 = 0`

`	s3 += s15 * 666643`
`	s4 += s15 * 470296`
`	s5 += s15 * 654183`
`	s6 -= s15 * 997805`
`	s7 += s15 * 136657`
`	s8 -= s15 * 683901`
`	s15 = 0`

`	s2 += s14 * 666643`
`	s3 += s14 * 470296`
`	s4 += s14 * 654183`
`	s5 -= s14 * 997805`
`	s6 += s14 * 136657`
`	s7 -= s14 * 683901`
`	s14 = 0`

`	s1 += s13 * 666643`
`	s2 += s13 * 470296`
`	s3 += s13 * 654183`
`	s4 -= s13 * 997805`
`	s5 += s13 * 136657`
`	s6 -= s13 * 683901`
`	s13 = 0`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = (s0 + (1 << 20)) >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[2] = (s2 + (1 << 20)) >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[4] = (s4 + (1 << 20)) >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[6] = (s6 + (1 << 20)) >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[8] = (s8 + (1 << 20)) >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[10] = (s10 + (1 << 20)) >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`

`	carry[1] = (s1 + (1 << 20)) >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[3] = (s3 + (1 << 20)) >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[5] = (s5 + (1 << 20)) >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[7] = (s7 + (1 << 20)) >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[9] = (s9 + (1 << 20)) >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[11] = (s11 + (1 << 20)) >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = s0 >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[1] = s1 >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[2] = s2 >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[3] = s3 >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[4] = s4 >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[5] = s5 >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[6] = s6 >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[7] = s7 >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[8] = s8 >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[9] = s9 >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[10] = s10 >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`
`	carry[11] = s11 >> 21`
`	s12 += carry[11]`
`	s11 -= carry[11] << 21`

`	s0 += s12 * 666643`
`	s1 += s12 * 470296`
`	s2 += s12 * 654183`
`	s3 -= s12 * 997805`
`	s4 += s12 * 136657`
`	s5 -= s12 * 683901`
`	s12 = 0`

`	carry[0] = s0 >> 21`
`	s1 += carry[0]`
`	s0 -= carry[0] << 21`
`	carry[1] = s1 >> 21`
`	s2 += carry[1]`
`	s1 -= carry[1] << 21`
`	carry[2] = s2 >> 21`
`	s3 += carry[2]`
`	s2 -= carry[2] << 21`
`	carry[3] = s3 >> 21`
`	s4 += carry[3]`
`	s3 -= carry[3] << 21`
`	carry[4] = s4 >> 21`
`	s5 += carry[4]`
`	s4 -= carry[4] << 21`
`	carry[5] = s5 >> 21`
`	s6 += carry[5]`
`	s5 -= carry[5] << 21`
`	carry[6] = s6 >> 21`
`	s7 += carry[6]`
`	s6 -= carry[6] << 21`
`	carry[7] = s7 >> 21`
`	s8 += carry[7]`
`	s7 -= carry[7] << 21`
`	carry[8] = s8 >> 21`
`	s9 += carry[8]`
`	s8 -= carry[8] << 21`
`	carry[9] = s9 >> 21`
`	s10 += carry[9]`
`	s9 -= carry[9] << 21`
`	carry[10] = s10 >> 21`
`	s11 += carry[10]`
`	s10 -= carry[10] << 21`

`	out[0] = byte(s0 >> 0)`
`	out[1] = byte(s0 >> 8)`
`	out[2] = byte((s0 >> 16) | (s1 << 5))`
`	out[3] = byte(s1 >> 3)`
`	out[4] = byte(s1 >> 11)`
`	out[5] = byte((s1 >> 19) | (s2 << 2))`
`	out[6] = byte(s2 >> 6)`
`	out[7] = byte((s2 >> 14) | (s3 << 7))`
`	out[8] = byte(s3 >> 1)`
`	out[9] = byte(s3 >> 9)`
`	out[10] = byte((s3 >> 17) | (s4 << 4))`
`	out[11] = byte(s4 >> 4)`
`	out[12] = byte(s4 >> 12)`
`	out[13] = byte((s4 >> 20) | (s5 << 1))`
`	out[14] = byte(s5 >> 7)`
`	out[15] = byte((s5 >> 15) | (s6 << 6))`
`	out[16] = byte(s6 >> 2)`
`	out[17] = byte(s6 >> 10)`
`	out[18] = byte((s6 >> 18) | (s7 << 3))`
`	out[19] = byte(s7 >> 5)`
`	out[20] = byte(s7 >> 13)`
`	out[21] = byte(s8 >> 0)`
`	out[22] = byte(s8 >> 8)`
`	out[23] = byte((s8 >> 16) | (s9 << 5))`
`	out[24] = byte(s9 >> 3)`
`	out[25] = byte(s9 >> 11)`
`	out[26] = byte((s9 >> 19) | (s10 << 2))`
`	out[27] = byte(s10 >> 6)`
`	out[28] = byte((s10 >> 14) | (s11 << 7))`
`	out[29] = byte(s11 >> 1)`
`	out[30] = byte(s11 >> 9)`
`	out[31] = byte(s11 >> 17)`
`}`

`// nonAdjacentForm computes a width-w non-adjacent form for this scalar.`
`//`
`// w must be between 2 and 8, or nonAdjacentForm will panic.`
`func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {`
`	// This implementation is adapted from the one`
`	// in curve25519-dalek and is documented there:`
`	// https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/scalar.rs#L800-L871`
`	if s.s[31] > 127 {`
`		panic("scalar has high bit set illegally")`
`	}`
`	if w < 2 {`
`		panic("w must be at least 2 by the definition of NAF")`
`	} else if w > 8 {`
`		panic("NAF digits must fit in int8")`
`	}`

`	var naf [256]int8`
`	var digits [5]uint64`

`	for i := 0; i < 4; i++ {`
`		digits[i] = binary.LittleEndian.Uint64(s.s[i*8:])`
`	}`

`	width := uint64(1 << w)`
`	windowMask := uint64(width - 1)`

`	pos := uint(0)`
`	carry := uint64(0)`
`	for pos < 256 {`
`		indexU64 := pos / 64`
`		indexBit := pos % 64`
`		var bitBuf uint64`
`		if indexBit < 64-w {`
`			// This window's bits are contained in a single u64`
`			bitBuf = digits[indexU64] >> indexBit`
`		} else {`
`			// Combine the current 64 bits with bits from the next 64`
`			bitBuf = (digits[indexU64] >> indexBit) | (digits[1+indexU64] << (64 - indexBit))`
`		}`

`		// Add carry into the current window`
`		window := carry + (bitBuf & windowMask)`

`		if window&1 == 0 {`
`			// If the window value is even, preserve the carry and continue.`
`			// Why is the carry preserved?`
`			// If carry == 0 and window & 1 == 0,`
`			//    then the next carry should be 0`
`			// If carry == 1 and window & 1 == 0,`
`			//    then bit_buf & 1 == 1 so the next carry should be 1`
`			pos += 1`
`			continue`
`		}`

`		if window < width/2 {`
`			carry = 0`
`			naf[pos] = int8(window)`
`		} else {`
`			carry = 1`
`			naf[pos] = int8(window) - int8(width)`
`		}`

`		pos += w`
`	}`
`	return naf`
`}`

`func (s *Scalar) signedRadix16() [64]int8 {`
`	if s.s[31] > 127 {`
`		panic("scalar has high bit set illegally")`
`	}`

`	var digits [64]int8`

`	// Compute unsigned radix-16 digits:`
`	for i := 0; i < 32; i++ {`
`		digits[2*i] = int8(s.s[i] & 15)`
`		digits[2*i+1] = int8((s.s[i] >> 4) & 15)`
`	}`

`	// Recenter coefficients:`
`	for i := 0; i < 63; i++ {`
`		carry := (digits[i] + 8) >> 4`
`		digits[i] -= carry << 4`
`		digits[i+1] += carry`
`	}`

`	return digits`
`}`
```