/*
h = -f
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
internal static void fe_neg(out FieldElement h, ref FieldElement f)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int h0 = -f0;
int h1 = -f1;
int h2 = -f2;
int h3 = -f3;
int h4 = -f4;
int h5 = -f5;
int h6 = -f6;
int h7 = -f7;
int h8 = -f8;
int h9 = -f9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
h = -f
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
internal static void fe_neg(out FieldElement h, ref FieldElement f)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 h0 = -f0;
Int32 h1 = -f1;
Int32 h2 = -f2;
Int32 h3 = -f3;
Int32 h4 = -f4;
Int32 h5 = -f5;
Int32 h6 = -f6;
Int32 h7 = -f7;
Int32 h8 = -f8;
Int32 h9 = -f9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
Preconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
Proof:
Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
Then 0<y<1.
Write r=h-pq.
Have 0<=r<=p-1=2^255-20.
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
Write x=r+19(2^-255)r+y.
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/
internal static void fe_tobytes(byte[] s, int offset, ref FieldElement h)
{
FieldElement hr;
fe_reduce(out hr, ref h);
Int32 h0 = hr.x0;
Int32 h1 = hr.x1;
Int32 h2 = hr.x2;
Int32 h3 = hr.x3;
Int32 h4 = hr.x4;
Int32 h5 = hr.x5;
Int32 h6 = hr.x6;
Int32 h7 = hr.x7;
Int32 h8 = hr.x8;
Int32 h9 = hr.x9;
/*
Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
Have h0+...+2^230 h9 between 0 and 2^255-1;
evidently 2^255 h10-2^255 q = 0.
Goal: Output h0+...+2^230 h9.
*/
unchecked
{
s[offset + 0] = (byte) (h0 >> 0);
s[offset + 1] = (byte) (h0 >> 8);
s[offset + 2] = (byte) (h0 >> 16);
s[offset + 3] = (byte) ((h0 >> 24) | (h1 << 2));
s[offset + 4] = (byte) (h1 >> 6);
s[offset + 5] = (byte) (h1 >> 14);
s[offset + 6] = (byte) ((h1 >> 22) | (h2 << 3));
s[offset + 7] = (byte) (h2 >> 5);
s[offset + 8] = (byte) (h2 >> 13);
s[offset + 9] = (byte) ((h2 >> 21) | (h3 << 5));
s[offset + 10] = (byte) (h3 >> 3);
s[offset + 11] = (byte) (h3 >> 11);
s[offset + 12] = (byte) ((h3 >> 19) | (h4 << 6));
s[offset + 13] = (byte) (h4 >> 2);
s[offset + 14] = (byte) (h4 >> 10);
s[offset + 15] = (byte) (h4 >> 18);
s[offset + 16] = (byte) (h5 >> 0);
s[offset + 17] = (byte) (h5 >> 8);
s[offset + 18] = (byte) (h5 >> 16);
s[offset + 19] = (byte) ((h5 >> 24) | (h6 << 1));
s[offset + 20] = (byte) (h6 >> 7);
s[offset + 21] = (byte) (h6 >> 15);
s[offset + 22] = (byte) ((h6 >> 23) | (h7 << 3));
s[offset + 23] = (byte) (h7 >> 5);
s[offset + 24] = (byte) (h7 >> 13);
s[offset + 25] = (byte) ((h7 >> 21) | (h8 << 4));
s[offset + 26] = (byte) (h8 >> 4);
s[offset + 27] = (byte) (h8 >> 12);
s[offset + 28] = (byte) ((h8 >> 20) | (h9 << 6));
s[offset + 29] = (byte) (h9 >> 2);
s[offset + 30] = (byte) (h9 >> 10);
s[offset + 31] = (byte) (h9 >> 18);
}
}
/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
//void fe_cmov(fe f,const fe g,unsigned int b)
internal static void fe_cmov(ref FieldElement f, ref FieldElement g, int b)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int x0 = f0 ^ g0;
int x1 = f1 ^ g1;
int x2 = f2 ^ g2;
int x3 = f3 ^ g3;
int x4 = f4 ^ g4;
int x5 = f5 ^ g5;
int x6 = f6 ^ g6;
int x7 = f7 ^ g7;
int x8 = f8 ^ g8;
int x9 = f9 ^ g9;
b = -b;
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
}
/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
//void fe_cmov(fe f,const fe g,unsigned int b)
internal static void fe_cmov(ref FieldElement f, ref FieldElement g, int b)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 x0 = f0 ^ g0;
Int32 x1 = f1 ^ g1;
Int32 x2 = f2 ^ g2;
Int32 x3 = f3 ^ g3;
Int32 x4 = f4 ^ g4;
Int32 x5 = f5 ^ g5;
Int32 x6 = f6 ^ g6;
Int32 x7 = f7 ^ g7;
Int32 x8 = f8 ^ g8;
Int32 x9 = f9 ^ g9;
b = -b;
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
}
internal static void fe_divpowm1(out FieldElement r, ref FieldElement u, ref FieldElement v)
{
fe_sq(out FieldElement v3, ref v);
fe_mul(out v3, ref v3, ref v); /* v3 = v^3 */
fe_sq(out FieldElement uv7, ref v3);
fe_mul(out uv7, ref uv7, ref v);
fe_mul(out uv7, ref uv7, ref u); /* uv7 = uv^7 */
/*fe_pow22523(uv7, uv7);*/
fe_pow22523(out uv7, ref uv7);
/* t0 = (uv^7)^((q-5)/8) */
fe_mul(out FieldElement t0, ref uv7, ref v3);
fe_mul(out r, ref t0, ref u); /* u^(m+1)v^(-(m+1)) */
}
/*
h = f * 121666
Can overlap h with f.
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
public static void fe_mul121666(out FieldElement h, ref FieldElement f)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
var h0 = f0 * 121666L;
var h1 = f1 * 121666L;
var h2 = f2 * 121666L;
var h3 = f3 * 121666L;
var h4 = f4 * 121666L;
var h5 = f5 * 121666L;
var h6 = f6 * 121666L;
var h7 = f7 * 121666L;
var h8 = f8 * 121666L;
var h9 = f9 * 121666L;
var carry9 = (h9 + (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
var carry1 = (h1 + (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
var carry3 = (h3 + (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
var carry5 = (h5 + (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
var carry7 = (h7 + (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
var carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
var carry2 = (h2 + (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
var carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
var carry6 = (h6 + (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
var carry8 = (h8 + (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
/*
* h = f * 121666
* Can overlap h with f.
*
* Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
public static void fe_mul121666(out FieldElement h, ref FieldElement f)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
var h0 = f0 * 121666L;
var h1 = f1 * 121666L;
var h2 = f2 * 121666L;
var h3 = f3 * 121666L;
var h4 = f4 * 121666L;
var h5 = f5 * 121666L;
var h6 = f6 * 121666L;
var h7 = f7 * 121666L;
var h8 = f8 * 121666L;
var h9 = f9 * 121666L;
var carry9 = (h9 + (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
var carry1 = (h1 + (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
var carry3 = (h3 + (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
var carry5 = (h5 + (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
var carry7 = (h7 + (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
var carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
var carry2 = (h2 + (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
var carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
var carry6 = (h6 + (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
var carry8 = (h8 + (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
// does NOT ignore top bit
internal static void fe_frombytes2(out FieldElement h, byte[] data, int offset)
{
Int64 h0 = load_4(data, offset);
Int64 h1 = load_3(data, offset + 4) << 6;
Int64 h2 = load_3(data, offset + 7) << 5;
Int64 h3 = load_3(data, offset + 10) << 3;
Int64 h4 = load_3(data, offset + 13) << 2;
Int64 h5 = load_4(data, offset + 16);
Int64 h6 = load_3(data, offset + 20) << 7;
Int64 h7 = load_3(data, offset + 23) << 5;
Int64 h8 = load_3(data, offset + 26) << 4;
Int64 h9 = load_3(data, offset + 29) << 2;
Int64 carry0;
Int64 carry1;
Int64 carry2;
Int64 carry3;
Int64 carry4;
Int64 carry5;
Int64 carry6;
Int64 carry7;
Int64 carry8;
Int64 carry9;
carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
/*
h = f - g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
internal static void fe_sub(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int h0 = f0 - g0;
int h1 = f1 - g1;
int h2 = f2 - g2;
int h3 = f3 - g3;
int h4 = f4 - g4;
int h5 = f5 - g5;
int h6 = f6 - g6;
int h7 = f7 - g7;
int h8 = f8 - g8;
int h9 = f9 - g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
* h = f - g
* Can overlap h with f or g.
*
* Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
internal static void fe_sub(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int h0 = f0 - g0;
int h1 = f1 - g1;
int h2 = f2 - g2;
int h3 = f3 - g3;
int h4 = f4 - g4;
int h5 = f5 - g5;
int h6 = f6 - g6;
int h7 = f7 - g7;
int h8 = f8 - g8;
int h9 = f9 - g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
return 1 if f == 0
return 0 if f != 0
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
// Todo: Discuss this with upstream
// Above comment is from the original code. But I believe the original code returned
// 0 if f == 0
// -1 if f != 0
// This code actually returns 0 if f==0 and 1 if f != 0
internal static int fe_isnonzero(ref FieldElement f)
{
FieldElement fr;
fe_reduce(out fr, ref f);
int differentBits = 0;
differentBits |= fr.x0;
differentBits |= fr.x1;
differentBits |= fr.x2;
differentBits |= fr.x3;
differentBits |= fr.x4;
differentBits |= fr.x5;
differentBits |= fr.x6;
differentBits |= fr.x7;
differentBits |= fr.x8;
differentBits |= fr.x9;
return (int)((unchecked((uint)differentBits - 1) >> 31) ^ 1);
}
/*
* h = f - g
* Can overlap h with f or g.
*
* Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
internal static void fe_sub(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 h0 = f0 - g0;
Int32 h1 = f1 - g1;
Int32 h2 = f2 - g2;
Int32 h3 = f3 - g3;
Int32 h4 = f4 - g4;
Int32 h5 = f5 - g5;
Int32 h6 = f6 - g6;
Int32 h7 = f7 - g7;
Int32 h8 = f8 - g8;
Int32 h9 = f9 - g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
* h = f + g
* Can overlap h with f or g.
*
* Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//void fe_add(fe h,const fe f,const fe g)
internal static void fe_add(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int h0 = f0 + g0;
int h1 = f1 + g1;
int h2 = f2 + g2;
int h3 = f3 + g3;
int h4 = f4 + g4;
int h5 = f5 + g5;
int h6 = f6 + g6;
int h7 = f7 + g7;
int h8 = f8 + g8;
int h9 = f9 + g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
* h = f + g
* Can overlap h with f or g.
*
* Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//void fe_add(fe h,const fe f,const fe g)
internal static void fe_add(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 h0 = f0 + g0;
Int32 h1 = f1 + g1;
Int32 h2 = f2 + g2;
Int32 h3 = f3 + g3;
Int32 h4 = f4 + g4;
Int32 h5 = f5 + g5;
Int32 h6 = f6 + g6;
Int32 h7 = f7 + g7;
Int32 h8 = f8 + g8;
Int32 h9 = f9 + g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
h = f + g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//void fe_add(fe h,const fe f,const fe g)
internal static void fe_add(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int h0 = f0 + g0;
int h1 = f1 + g1;
int h2 = f2 + g2;
int h3 = f3 + g3;
int h4 = f4 + g4;
int h5 = f5 + g5;
int h6 = f6 + g6;
int h7 = f7 + g7;
int h8 = f8 + g8;
int h9 = f9 + g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
* return 1 if f == 0
* return 0 if f != 0
*
* Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
// Todo: Discuss this with upstream
// Above comment is from the original code. But I believe the original code returned
// 0 if f == 0
// -1 if f != 0
// This code actually returns 0 if f==0 and 1 if f != 0
internal static int fe_isnonzero(ref FieldElement f)
{
FieldElement fr;
fe_reduce(out fr, ref f);
int differentBits = 0;
differentBits |= fr.x0;
differentBits |= fr.x1;
differentBits |= fr.x2;
differentBits |= fr.x3;
differentBits |= fr.x4;
differentBits |= fr.x5;
differentBits |= fr.x6;
differentBits |= fr.x7;
differentBits |= fr.x8;
differentBits |= fr.x9;
return((int)((unchecked ((uint)differentBits - 1) \ > \ \ > \ 31) ^ 1));
}
/*
h = f + g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//void fe_add(fe h,const fe f,const fe g)
internal static void fe_add(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 h0 = f0 + g0;
Int32 h1 = f1 + g1;
Int32 h2 = f2 + g2;
Int32 h3 = f3 + g3;
Int32 h4 = f4 + g4;
Int32 h5 = f5 + g5;
Int32 h6 = f6 + g6;
Int32 h7 = f7 + g7;
Int32 h8 = f8 + g8;
Int32 h9 = f9 + g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
/*
h = f - g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
internal static void fe_sub(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 h0 = f0 - g0;
Int32 h1 = f1 - g1;
Int32 h2 = f2 - g2;
Int32 h3 = f3 - g3;
Int32 h4 = f4 - g4;
Int32 h5 = f5 - g5;
Int32 h6 = f6 - g6;
Int32 h7 = f7 - g7;
Int32 h8 = f8 - g8;
Int32 h9 = f9 - g9;
h.x0 = h0;
h.x1 = h1;
h.x2 = h2;
h.x3 = h3;
h.x4 = h4;
h.x5 = h5;
h.x6 = h6;
h.x7 = h7;
h.x8 = h8;
h.x9 = h9;
}
internal static void fe_copy(out FieldElement h, ref FieldElement f)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
h.x0 = f0;
h.x1 = f1;
h.x2 = f2;
h.x3 = f3;
h.x4 = f4;
h.x5 = f5;
h.x6 = f6;
h.x7 = f7;
h.x8 = f8;
h.x9 = f9;
}
// does NOT ignore top bit
internal static void fe_frombytes2(out FieldElement h, byte[] data, int offset)
{
var h0 = load_4(data, offset);
var h1 = load_3(data, offset + 4) << 6;
var h2 = load_3(data, offset + 7) << 5;
var h3 = load_3(data, offset + 10) << 3;
var h4 = load_3(data, offset + 13) << 2;
var h5 = load_4(data, offset + 16);
var h6 = load_3(data, offset + 20) << 7;
var h7 = load_3(data, offset + 23) << 5;
var h8 = load_3(data, offset + 26) << 4;
var h9 = load_3(data, offset + 29) << 2;
var carry9 = (h9 + (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
var carry1 = (h1 + (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
var carry3 = (h3 + (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
var carry5 = (h5 + (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
var carry7 = (h7 + (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
var carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
var carry2 = (h2 + (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
var carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
var carry6 = (h6 + (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
var carry8 = (h8 + (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
internal static void fe_0(out FieldElement h)
{
h = default(FieldElement);
}
/*
return 1 if f is in {1,3,5,...,q-2}
return 0 if f is in {0,2,4,...,q-1}
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//int fe_isnegative(const fe f)
public static int fe_isnegative(ref FieldElement f)
{
FieldElement fr;
fe_reduce(out fr, ref f);
return fr.x0 & 1;
}
internal static void fe_pow22523(out FieldElement result, ref FieldElement z)
{
FieldElement t0;
FieldElement t1;
FieldElement t2;
int i;
/* qhasm: fe z1 */
/* qhasm: fe z2 */
/* qhasm: fe z8 */
/* qhasm: fe z9 */
/* qhasm: fe z11 */
/* qhasm: fe z22 */
/* qhasm: fe z_5_0 */
/* qhasm: fe z_10_5 */
/* qhasm: fe z_10_0 */
/* qhasm: fe z_20_10 */
/* qhasm: fe z_20_0 */
/* qhasm: fe z_40_20 */
/* qhasm: fe z_40_0 */
/* qhasm: fe z_50_10 */
/* qhasm: fe z_50_0 */
/* qhasm: fe z_100_50 */
/* qhasm: fe z_100_0 */
/* qhasm: fe z_200_100 */
/* qhasm: fe z_200_0 */
/* qhasm: fe z_250_50 */
/* qhasm: fe z_250_0 */
/* qhasm: fe z_252_2 */
/* qhasm: fe z_252_3 */
/* qhasm: enter pow22523 */
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(\>\z2=fe#1,\\z2=fe#1,\>\z2=fe#1); */
/* asm 2: fe_sq(\>\z2=t0,\\z2=t0,\>\z2=t0); */
fe_sq(out t0, ref z); //for (i = 1; i \\z8=fe#2,\\z8=fe#2,\>\z8=fe#2); */
/* asm 2: fe_sq(\>\z8=t1,\\z8=t1,\>\z8=t1); */
fe_sq(out t1, ref t0); for (i = 1; i \\z9=fe#2,\\z9=t1,\\z11=fe#1,\\z11=t0,\\z22=fe#1,\\z22=fe#1,\>\z22=fe#1); */
/* asm 2: fe_sq(\>\z22=t0,\\z22=t0,\>\z22=t0); */
fe_sq(out t0, ref t0); //for (i = 1; i \\z_5_0=fe#1,\\z_5_0=t0,\\z_10_5=fe#2,\\z_10_5=fe#2,\>\z_10_5=fe#2); */
/* asm 2: fe_sq(\>\z_10_5=t1,\\z_10_5=t1,\>\z_10_5=t1); */
fe_sq(out t1, ref t0); for (i = 1; i \\z_10_0=fe#1,\\z_10_0=t0,\\z_20_10=fe#2,\\z_20_10=fe#2,\>\z_20_10=fe#2); */
/*
* return 1 if f is in {1,3,5,...,q-2}
* return 0 if f is in {0,2,4,...,q-1}
*
* Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
//int fe_isnegative(const fe f)
public static int fe_isnegative(ref FieldElement f)
{
byte[] b = new byte[32];
fe_tobytes(b, 0, ref f);
return(b[0] & 1);
}
public GroupElementPreComp(FieldElement yplusx, FieldElement yminusx, FieldElement xy2d)
{
this.yplusx = yplusx;
this.yminusx = yminusx;
this.xy2d = xy2d;
}
public GroupElementPreComp(FieldElement yplusx, FieldElement yminusx, FieldElement xy2d)
{
this.yplusx = yplusx;
this.yminusx = yminusx;
this.xy2d = xy2d;
}
internal static void scalarmult(
out FieldElement q,
byte[] n, int noffset,
ref FieldElement p)
{
byte[] e = new byte[32];//ToDo: remove allocation
FieldElement x1, x2, x3;
FieldElement z2, z3;
FieldElement tmp0, tmp1;
for (int i = 0; i < 32; ++i)
e[i] = n[noffset + i];
ScalarOperations.sc_clamp(e, 0);
x1 = p;
FieldOperations.fe_1(out x2);
FieldOperations.fe_0(out z2);
x3 = x1;
FieldOperations.fe_1(out z3);
uint swap = 0;
for (int pos = 254; pos >= 0; --pos)
{
uint b = (uint)(e[pos / 8] >> (pos & 7));
b &= 1;
swap ^= b;
FieldOperations.fe_cswap(ref x2, ref x3, swap);
FieldOperations.fe_cswap(ref z2, ref z3, swap);
swap = b;
/* qhasm: enter ladder */
/* qhasm: D = X3-Z3 */
/* asm 1: fe_sub(>D=fe#5,<X3=fe#3,<Z3=fe#4); */
/* asm 2: fe_sub(>D=tmp0,<X3=x3,<Z3=z3); */
FieldOperations.fe_sub(out tmp0, ref x3, ref z3);
/* qhasm: B = X2-Z2 */
/* asm 1: fe_sub(>B=fe#6,<X2=fe#1,<Z2=fe#2); */
/* asm 2: fe_sub(>B=tmp1,<X2=x2,<Z2=z2); */
FieldOperations.fe_sub(out tmp1, ref x2, ref z2);
/* qhasm: A = X2+Z2 */
/* asm 1: fe_add(>A=fe#1,<X2=fe#1,<Z2=fe#2); */
/* asm 2: fe_add(>A=x2,<X2=x2,<Z2=z2); */
FieldOperations.fe_add(out x2, ref x2, ref z2);
/* qhasm: C = X3+Z3 */
/* asm 1: fe_add(>C=fe#2,<X3=fe#3,<Z3=fe#4); */
/* asm 2: fe_add(>C=z2,<X3=x3,<Z3=z3); */
FieldOperations.fe_add(out z2, ref x3, ref z3);
/* qhasm: DA = D*A */
/* asm 1: fe_mul(>DA=fe#4,<D=fe#5,<A=fe#1); */
/* asm 2: fe_mul(>DA=z3,<D=tmp0,<A=x2); */
FieldOperations.fe_mul(out z3, ref tmp0, ref x2);
/* qhasm: CB = C*B */
/* asm 1: fe_mul(>CB=fe#2,<C=fe#2,<B=fe#6); */
/* asm 2: fe_mul(>CB=z2,<C=z2,<B=tmp1); */
FieldOperations.fe_mul(out z2, ref z2, ref tmp1);
/* qhasm: BB = B^2 */
/* asm 1: fe_sq(>BB=fe#5,<B=fe#6); */
/* asm 2: fe_sq(>BB=tmp0,<B=tmp1); */
FieldOperations.fe_sq(out tmp0, ref tmp1);
/* qhasm: AA = A^2 */
/* asm 1: fe_sq(>AA=fe#6,<A=fe#1); */
/* asm 2: fe_sq(>AA=tmp1,<A=x2); */
FieldOperations.fe_sq(out tmp1, ref x2);
/* qhasm: t0 = DA+CB */
/* asm 1: fe_add(>t0=fe#3,<DA=fe#4,<CB=fe#2); */
/* asm 2: fe_add(>t0=x3,<DA=z3,<CB=z2); */
FieldOperations.fe_add(out x3, ref z3, ref z2);
/* qhasm: assign x3 to t0 */
/* qhasm: t1 = DA-CB */
/* asm 1: fe_sub(>t1=fe#2,<DA=fe#4,<CB=fe#2); */
/* asm 2: fe_sub(>t1=z2,<DA=z3,<CB=z2); */
FieldOperations.fe_sub(out z2, ref z3, ref z2);
/* qhasm: X4 = AA*BB */
/* asm 1: fe_mul(>X4=fe#1,<AA=fe#6,<BB=fe#5); */
/* asm 2: fe_mul(>X4=x2,<AA=tmp1,<BB=tmp0); */
FieldOperations.fe_mul(out x2, ref tmp1, ref tmp0);
/* qhasm: E = AA-BB */
/* asm 1: fe_sub(>E=fe#6,<AA=fe#6,<BB=fe#5); */
/* asm 2: fe_sub(>E=tmp1,<AA=tmp1,<BB=tmp0); */
FieldOperations.fe_sub(out tmp1, ref tmp1, ref tmp0);
/* qhasm: t2 = t1^2 */
/* asm 1: fe_sq(>t2=fe#2,<t1=fe#2); */
/* asm 2: fe_sq(>t2=z2,<t1=z2); */
FieldOperations.fe_sq(out z2, ref z2);
/* qhasm: t3 = a24*E */
/* asm 1: fe_mul121666(>t3=fe#4,<E=fe#6); */
/* asm 2: fe_mul121666(>t3=z3,<E=tmp1); */
FieldOperations.fe_mul121666(out z3, ref tmp1);
/* qhasm: X5 = t0^2 */
/* asm 1: fe_sq(>X5=fe#3,<t0=fe#3); */
/* asm 2: fe_sq(>X5=x3,<t0=x3); */
FieldOperations.fe_sq(out x3, ref x3);
/* qhasm: t4 = BB+t3 */
/* asm 1: fe_add(>t4=fe#5,<BB=fe#5,<t3=fe#4); */
/* asm 2: fe_add(>t4=tmp0,<BB=tmp0,<t3=z3); */
FieldOperations.fe_add(out tmp0, ref tmp0, ref z3);
/* qhasm: Z5 = X1*t2 */
/* asm 1: fe_mul(>Z5=fe#4,x1,<t2=fe#2); */
/* asm 2: fe_mul(>Z5=z3,x1,<t2=z2); */
FieldOperations.fe_mul(out z3, ref x1, ref z2);
/* qhasm: Z4 = E*t4 */
/* asm 1: fe_mul(>Z4=fe#2,<E=fe#6,<t4=fe#5); */
/* asm 2: fe_mul(>Z4=z2,<E=tmp1,<t4=tmp0); */
FieldOperations.fe_mul(out z2, ref tmp1, ref tmp0);
/* qhasm: return */
}
FieldOperations.fe_cswap(ref x2, ref x3, swap);
FieldOperations.fe_cswap(ref z2, ref z3, swap);
FieldOperations.fe_invert(out z2, ref z2);
FieldOperations.fe_mul(out x2, ref x2, ref z2);
q = x2;
CryptoBytes.Wipe(e);
}
public static void fe_1(out FieldElement h)
{
h = default(FieldElement);
h.x0 = 1;
}
/*
Replace (f,g) with (g,f) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
public static void fe_cswap(ref FieldElement f, ref FieldElement g, uint b)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int x0 = f0 ^ g0;
int x1 = f1 ^ g1;
int x2 = f2 ^ g2;
int x3 = f3 ^ g3;
int x4 = f4 ^ g4;
int x5 = f5 ^ g5;
int x6 = f6 ^ g6;
int x7 = f7 ^ g7;
int x8 = f8 ^ g8;
int x9 = f9 ^ g9;
int negb = unchecked((int)-b);
x0 &= negb;
x1 &= negb;
x2 &= negb;
x3 &= negb;
x4 &= negb;
x5 &= negb;
x6 &= negb;
x7 &= negb;
x8 &= negb;
x9 &= negb;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
g.x0 = g0 ^ x0;
g.x1 = g1 ^ x1;
g.x2 = g2 ^ x2;
g.x3 = g3 ^ x3;
g.x4 = g4 ^ x4;
g.x5 = g5 ^ x5;
g.x6 = g6 ^ x6;
g.x7 = g7 ^ x7;
g.x8 = g8 ^ x8;
g.x9 = g9 ^ x9;
}
/*
h = 2 * f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
internal static void fe_sq2(out FieldElement h, ref FieldElement f)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int f0_2 = 2 * f0;
int f1_2 = 2 * f1;
int f2_2 = 2 * f2;
int f3_2 = 2 * f3;
int f4_2 = 2 * f4;
int f5_2 = 2 * f5;
int f6_2 = 2 * f6;
int f7_2 = 2 * f7;
int f5_38 = 38 * f5; /* 1.959375*2^30 */
int f6_19 = 19 * f6; /* 1.959375*2^30 */
int f7_38 = 38 * f7; /* 1.959375*2^30 */
int f8_19 = 19 * f8; /* 1.959375*2^30 */
int f9_38 = 38 * f9; /* 1.959375*2^30 */
var f0f0 = f0 * (long)f0;
var f0f1_2 = f0_2 * (long)f1;
var f0f2_2 = f0_2 * (long)f2;
var f0f3_2 = f0_2 * (long)f3;
var f0f4_2 = f0_2 * (long)f4;
var f0f5_2 = f0_2 * (long)f5;
var f0f6_2 = f0_2 * (long)f6;
var f0f7_2 = f0_2 * (long)f7;
var f0f8_2 = f0_2 * (long)f8;
var f0f9_2 = f0_2 * (long)f9;
var f1f1_2 = f1_2 * (long)f1;
var f1f2_2 = f1_2 * (long)f2;
var f1f3_4 = f1_2 * (long)f3_2;
var f1f4_2 = f1_2 * (long)f4;
var f1f5_4 = f1_2 * (long)f5_2;
var f1f6_2 = f1_2 * (long)f6;
var f1f7_4 = f1_2 * (long)f7_2;
var f1f8_2 = f1_2 * (long)f8;
var f1f9_76 = f1_2 * (long)f9_38;
var f2f2 = f2 * (long)f2;
var f2f3_2 = f2_2 * (long)f3;
var f2f4_2 = f2_2 * (long)f4;
var f2f5_2 = f2_2 * (long)f5;
var f2f6_2 = f2_2 * (long)f6;
var f2f7_2 = f2_2 * (long)f7;
var f2f8_38 = f2_2 * (long)f8_19;
var f2f9_38 = f2 * (long)f9_38;
var f3f3_2 = f3_2 * (long)f3;
var f3f4_2 = f3_2 * (long)f4;
var f3f5_4 = f3_2 * (long)f5_2;
var f3f6_2 = f3_2 * (long)f6;
var f3f7_76 = f3_2 * (long)f7_38;
var f3f8_38 = f3_2 * (long)f8_19;
var f3f9_76 = f3_2 * (long)f9_38;
var f4f4 = f4 * (long)f4;
var f4f5_2 = f4_2 * (long)f5;
var f4f6_38 = f4_2 * (long)f6_19;
var f4f7_38 = f4 * (long)f7_38;
var f4f8_38 = f4_2 * (long)f8_19;
var f4f9_38 = f4 * (long)f9_38;
var f5f5_38 = f5 * (long)f5_38;
var f5f6_38 = f5_2 * (long)f6_19;
var f5f7_76 = f5_2 * (long)f7_38;
var f5f8_38 = f5_2 * (long)f8_19;
var f5f9_76 = f5_2 * (long)f9_38;
var f6f6_19 = f6 * (long)f6_19;
var f6f7_38 = f6 * (long)f7_38;
var f6f8_38 = f6_2 * (long)f8_19;
var f6f9_38 = f6 * (long)f9_38;
var f7f7_38 = f7 * (long)f7_38;
var f7f8_38 = f7_2 * (long)f8_19;
var f7f9_76 = f7_2 * (long)f9_38;
var f8f8_19 = f8 * (long)f8_19;
var f8f9_38 = f8 * (long)f9_38;
var f9f9_38 = f9 * (long)f9_38;
var h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
var h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
var h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
var h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
var h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
var h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
var h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
var h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
var h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
var h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
h0 += h0;
h1 += h1;
h2 += h2;
h3 += h3;
h4 += h4;
h5 += h5;
h6 += h6;
h7 += h7;
h8 += h8;
h9 += h9;
var carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
var carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
var carry1 = (h1 + (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
var carry5 = (h5 + (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
var carry2 = (h2 + (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
var carry6 = (h6 + (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
var carry3 = (h3 + (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
var carry7 = (h7 + (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
var carry8 = (h8 + (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
var carry9 = (h9 + (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
/*
h = f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
internal static void fe_sq(out FieldElement h, ref FieldElement f)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 f0_2 = 2 * f0;
Int32 f1_2 = 2 * f1;
Int32 f2_2 = 2 * f2;
Int32 f3_2 = 2 * f3;
Int32 f4_2 = 2 * f4;
Int32 f5_2 = 2 * f5;
Int32 f6_2 = 2 * f6;
Int32 f7_2 = 2 * f7;
Int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
Int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
Int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
Int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
Int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
Int64 f0f0 = f0 * (Int64)f0;
Int64 f0f1_2 = f0_2 * (Int64)f1;
Int64 f0f2_2 = f0_2 * (Int64)f2;
Int64 f0f3_2 = f0_2 * (Int64)f3;
Int64 f0f4_2 = f0_2 * (Int64)f4;
Int64 f0f5_2 = f0_2 * (Int64)f5;
Int64 f0f6_2 = f0_2 * (Int64)f6;
Int64 f0f7_2 = f0_2 * (Int64)f7;
Int64 f0f8_2 = f0_2 * (Int64)f8;
Int64 f0f9_2 = f0_2 * (Int64)f9;
Int64 f1f1_2 = f1_2 * (Int64)f1;
Int64 f1f2_2 = f1_2 * (Int64)f2;
Int64 f1f3_4 = f1_2 * (Int64)f3_2;
Int64 f1f4_2 = f1_2 * (Int64)f4;
Int64 f1f5_4 = f1_2 * (Int64)f5_2;
Int64 f1f6_2 = f1_2 * (Int64)f6;
Int64 f1f7_4 = f1_2 * (Int64)f7_2;
Int64 f1f8_2 = f1_2 * (Int64)f8;
Int64 f1f9_76 = f1_2 * (Int64)f9_38;
Int64 f2f2 = f2 * (Int64)f2;
Int64 f2f3_2 = f2_2 * (Int64)f3;
Int64 f2f4_2 = f2_2 * (Int64)f4;
Int64 f2f5_2 = f2_2 * (Int64)f5;
Int64 f2f6_2 = f2_2 * (Int64)f6;
Int64 f2f7_2 = f2_2 * (Int64)f7;
Int64 f2f8_38 = f2_2 * (Int64)f8_19;
Int64 f2f9_38 = f2 * (Int64)f9_38;
Int64 f3f3_2 = f3_2 * (Int64)f3;
Int64 f3f4_2 = f3_2 * (Int64)f4;
Int64 f3f5_4 = f3_2 * (Int64)f5_2;
Int64 f3f6_2 = f3_2 * (Int64)f6;
Int64 f3f7_76 = f3_2 * (Int64)f7_38;
Int64 f3f8_38 = f3_2 * (Int64)f8_19;
Int64 f3f9_76 = f3_2 * (Int64)f9_38;
Int64 f4f4 = f4 * (Int64)f4;
Int64 f4f5_2 = f4_2 * (Int64)f5;
Int64 f4f6_38 = f4_2 * (Int64)f6_19;
Int64 f4f7_38 = f4 * (Int64)f7_38;
Int64 f4f8_38 = f4_2 * (Int64)f8_19;
Int64 f4f9_38 = f4 * (Int64)f9_38;
Int64 f5f5_38 = f5 * (Int64)f5_38;
Int64 f5f6_38 = f5_2 * (Int64)f6_19;
Int64 f5f7_76 = f5_2 * (Int64)f7_38;
Int64 f5f8_38 = f5_2 * (Int64)f8_19;
Int64 f5f9_76 = f5_2 * (Int64)f9_38;
Int64 f6f6_19 = f6 * (Int64)f6_19;
Int64 f6f7_38 = f6 * (Int64)f7_38;
Int64 f6f8_38 = f6_2 * (Int64)f8_19;
Int64 f6f9_38 = f6 * (Int64)f9_38;
Int64 f7f7_38 = f7 * (Int64)f7_38;
Int64 f7f8_38 = f7_2 * (Int64)f8_19;
Int64 f7f9_76 = f7_2 * (Int64)f9_38;
Int64 f8f8_19 = f8 * (Int64)f8_19;
Int64 f8f9_38 = f8 * (Int64)f9_38;
Int64 f9f9_38 = f9 * (Int64)f9_38;
Int64 h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
Int64 h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
Int64 h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
Int64 h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
Int64 h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
Int64 h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
Int64 h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
Int64 h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
Int64 h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
Int64 h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
Int64 carry0;
Int64 carry1;
Int64 carry2;
Int64 carry3;
Int64 carry4;
Int64 carry5;
Int64 carry6;
Int64 carry7;
Int64 carry8;
Int64 carry9;
carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
h.x0 = (Int32)h0;
h.x1 = (Int32)h1;
h.x2 = (Int32)h2;
h.x3 = (Int32)h3;
h.x4 = (Int32)h4;
h.x5 = (Int32)h5;
h.x6 = (Int32)h6;
h.x7 = (Int32)h7;
h.x8 = (Int32)h8;
h.x9 = (Int32)h9;
}
public static void fe_0(out FieldElement h)
{
h = default(FieldElement);
}
/*
h = f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
internal static void fe_sq(out FieldElement h, ref FieldElement f)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 f0_2 = 2 * f0;
Int32 f1_2 = 2 * f1;
Int32 f2_2 = 2 * f2;
Int32 f3_2 = 2 * f3;
Int32 f4_2 = 2 * f4;
Int32 f5_2 = 2 * f5;
Int32 f6_2 = 2 * f6;
Int32 f7_2 = 2 * f7;
Int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
Int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
Int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
Int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
Int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
Int64 f0f0 = f0 * (Int64)f0;
Int64 f0f1_2 = f0_2 * (Int64)f1;
Int64 f0f2_2 = f0_2 * (Int64)f2;
Int64 f0f3_2 = f0_2 * (Int64)f3;
Int64 f0f4_2 = f0_2 * (Int64)f4;
Int64 f0f5_2 = f0_2 * (Int64)f5;
Int64 f0f6_2 = f0_2 * (Int64)f6;
Int64 f0f7_2 = f0_2 * (Int64)f7;
Int64 f0f8_2 = f0_2 * (Int64)f8;
Int64 f0f9_2 = f0_2 * (Int64)f9;
Int64 f1f1_2 = f1_2 * (Int64)f1;
Int64 f1f2_2 = f1_2 * (Int64)f2;
Int64 f1f3_4 = f1_2 * (Int64)f3_2;
Int64 f1f4_2 = f1_2 * (Int64)f4;
Int64 f1f5_4 = f1_2 * (Int64)f5_2;
Int64 f1f6_2 = f1_2 * (Int64)f6;
Int64 f1f7_4 = f1_2 * (Int64)f7_2;
Int64 f1f8_2 = f1_2 * (Int64)f8;
Int64 f1f9_76 = f1_2 * (Int64)f9_38;
Int64 f2f2 = f2 * (Int64)f2;
Int64 f2f3_2 = f2_2 * (Int64)f3;
Int64 f2f4_2 = f2_2 * (Int64)f4;
Int64 f2f5_2 = f2_2 * (Int64)f5;
Int64 f2f6_2 = f2_2 * (Int64)f6;
Int64 f2f7_2 = f2_2 * (Int64)f7;
Int64 f2f8_38 = f2_2 * (Int64)f8_19;
Int64 f2f9_38 = f2 * (Int64)f9_38;
Int64 f3f3_2 = f3_2 * (Int64)f3;
Int64 f3f4_2 = f3_2 * (Int64)f4;
Int64 f3f5_4 = f3_2 * (Int64)f5_2;
Int64 f3f6_2 = f3_2 * (Int64)f6;
Int64 f3f7_76 = f3_2 * (Int64)f7_38;
Int64 f3f8_38 = f3_2 * (Int64)f8_19;
Int64 f3f9_76 = f3_2 * (Int64)f9_38;
Int64 f4f4 = f4 * (Int64)f4;
Int64 f4f5_2 = f4_2 * (Int64)f5;
Int64 f4f6_38 = f4_2 * (Int64)f6_19;
Int64 f4f7_38 = f4 * (Int64)f7_38;
Int64 f4f8_38 = f4_2 * (Int64)f8_19;
Int64 f4f9_38 = f4 * (Int64)f9_38;
Int64 f5f5_38 = f5 * (Int64)f5_38;
Int64 f5f6_38 = f5_2 * (Int64)f6_19;
Int64 f5f7_76 = f5_2 * (Int64)f7_38;
Int64 f5f8_38 = f5_2 * (Int64)f8_19;
Int64 f5f9_76 = f5_2 * (Int64)f9_38;
Int64 f6f6_19 = f6 * (Int64)f6_19;
Int64 f6f7_38 = f6 * (Int64)f7_38;
Int64 f6f8_38 = f6_2 * (Int64)f8_19;
Int64 f6f9_38 = f6 * (Int64)f9_38;
Int64 f7f7_38 = f7 * (Int64)f7_38;
Int64 f7f8_38 = f7_2 * (Int64)f8_19;
Int64 f7f9_76 = f7_2 * (Int64)f9_38;
Int64 f8f8_19 = f8 * (Int64)f8_19;
Int64 f8f9_38 = f8 * (Int64)f9_38;
Int64 f9f9_38 = f9 * (Int64)f9_38;
Int64 h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
Int64 h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
Int64 h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
Int64 h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
Int64 h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
Int64 h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
Int64 h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
Int64 h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
Int64 h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
Int64 h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
Int64 carry0;
Int64 carry1;
Int64 carry2;
Int64 carry3;
Int64 carry4;
Int64 carry5;
Int64 carry6;
Int64 carry7;
Int64 carry8;
Int64 carry9;
carry0 = (h0 + (Int64)(1 \\\>\ 26; h1 += carry0; h0 -= carry0 \\\>\ 26; h5 += carry4; h4 -= carry4 \\\>\ 25; h2 += carry1; h1 -= carry1 \\\>\ 25; h6 += carry5; h5 -= carry5 \\\>\ 26; h3 += carry2; h2 -= carry2 \\\>\ 26; h7 += carry6; h6 -= carry6 \\\>\ 25; h4 += carry3; h3 -= carry3 \\\>\ 25; h8 += carry7; h7 -= carry7 \\\>\ 26; h5 += carry4; h4 -= carry4 \\\>\ 26; h9 += carry8; h8 -= carry8 \\\>\ 25; h0 += carry9 * 19; h9 -= carry9 \\\>\ 26; h1 += carry0; h0 -= carry0 \
/*
* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
* Preconditions: b in {0,1}.
*/
public static void fe_cswap(ref FieldElement f, ref FieldElement g, uint b)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int x0 = f0 ^ g0;
int x1 = f1 ^ g1;
int x2 = f2 ^ g2;
int x3 = f3 ^ g3;
int x4 = f4 ^ g4;
int x5 = f5 ^ g5;
int x6 = f6 ^ g6;
int x7 = f7 ^ g7;
int x8 = f8 ^ g8;
int x9 = f9 ^ g9;
int negb = unchecked ((int)-b);
x0 &= negb;
x1 &= negb;
x2 &= negb;
x3 &= negb;
x4 &= negb;
x5 &= negb;
x6 &= negb;
x7 &= negb;
x8 &= negb;
x9 &= negb;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
g.x0 = g0 ^ x0;
g.x1 = g1 ^ x1;
g.x2 = g2 ^ x2;
g.x3 = g3 ^ x3;
g.x4 = g4 ^ x4;
g.x5 = g5 ^ x5;
g.x6 = g6 ^ x6;
g.x7 = g7 ^ x7;
g.x8 = g8 ^ x8;
g.x9 = g9 ^ x9;
}
internal static void scalarmult(
out FieldElement q,
byte[] n, int noffset,
ref FieldElement p)
{
byte[] e = new byte[32]; //ToDo: remove allocation
UInt32 i;
FieldElement x1;
FieldElement x2;
FieldElement z2;
FieldElement x3;
FieldElement z3;
FieldElement tmp0;
FieldElement tmp1;
int pos;
UInt32 swap;
UInt32 b;
for (i = 0; i < 32; ++i)
{
e[i] = n[noffset + i];
}
ScalarOperations.sc_clamp(e, 0);
x1 = p;
FieldOperations.fe_1(out x2);
FieldOperations.fe_0(out z2);
x3 = x1;
FieldOperations.fe_1(out z3);
swap = 0;
for (pos = 254; pos >= 0; --pos)
{
b = (uint)(e[pos / 8] >> (pos & 7));
b &= 1;
swap ^= b;
FieldOperations.fe_cswap(ref x2, ref x3, swap);
FieldOperations.fe_cswap(ref z2, ref z3, swap);
swap = b;
/* qhasm: fe X2 */
/* qhasm: fe Z2 */
/* qhasm: fe X3 */
/* qhasm: fe Z3 */
/* qhasm: fe X4 */
/* qhasm: fe Z4 */
/* qhasm: fe X5 */
/* qhasm: fe Z5 */
/* qhasm: fe A */
/* qhasm: fe B */
/* qhasm: fe C */
/* qhasm: fe D */
/* qhasm: fe E */
/* qhasm: fe AA */
/* qhasm: fe BB */
/* qhasm: fe DA */
/* qhasm: fe CB */
/* qhasm: fe t0 */
/* qhasm: fe t1 */
/* qhasm: fe t2 */
/* qhasm: fe t3 */
/* qhasm: fe t4 */
/* qhasm: enter ladder */
/* qhasm: D = X3-Z3 */
/* asm 1: fe_sub(>D=fe#5,<X3=fe#3,<Z3=fe#4); */
/* asm 2: fe_sub(>D=tmp0,<X3=x3,<Z3=z3); */
FieldOperations.fe_sub(out tmp0, ref x3, ref z3);
/* qhasm: B = X2-Z2 */
/* asm 1: fe_sub(>B=fe#6,<X2=fe#1,<Z2=fe#2); */
/* asm 2: fe_sub(>B=tmp1,<X2=x2,<Z2=z2); */
FieldOperations.fe_sub(out tmp1, ref x2, ref z2);
/* qhasm: A = X2+Z2 */
/* asm 1: fe_add(>A=fe#1,<X2=fe#1,<Z2=fe#2); */
/* asm 2: fe_add(>A=x2,<X2=x2,<Z2=z2); */
FieldOperations.fe_add(out x2, ref x2, ref z2);
/* qhasm: C = X3+Z3 */
/* asm 1: fe_add(>C=fe#2,<X3=fe#3,<Z3=fe#4); */
/* asm 2: fe_add(>C=z2,<X3=x3,<Z3=z3); */
FieldOperations.fe_add(out z2, ref x3, ref z3);
/* qhasm: DA = D*A */
/* asm 1: fe_mul(>DA=fe#4,<D=fe#5,<A=fe#1); */
/* asm 2: fe_mul(>DA=z3,<D=tmp0,<A=x2); */
FieldOperations.fe_mul(out z3, ref tmp0, ref x2);
/* qhasm: CB = C*B */
/* asm 1: fe_mul(>CB=fe#2,<C=fe#2,<B=fe#6); */
/* asm 2: fe_mul(>CB=z2,<C=z2,<B=tmp1); */
FieldOperations.fe_mul(out z2, ref z2, ref tmp1);
/* qhasm: BB = B^2 */
/* asm 1: fe_sq(>BB=fe#5,<B=fe#6); */
/* asm 2: fe_sq(>BB=tmp0,<B=tmp1); */
FieldOperations.fe_sq(out tmp0, ref tmp1);
/* qhasm: AA = A^2 */
/* asm 1: fe_sq(>AA=fe#6,<A=fe#1); */
/* asm 2: fe_sq(>AA=tmp1,<A=x2); */
FieldOperations.fe_sq(out tmp1, ref x2);
/* qhasm: t0 = DA+CB */
/* asm 1: fe_add(>t0=fe#3,<DA=fe#4,<CB=fe#2); */
/* asm 2: fe_add(>t0=x3,<DA=z3,<CB=z2); */
FieldOperations.fe_add(out x3, ref z3, ref z2);
/* qhasm: assign x3 to t0 */
/* qhasm: t1 = DA-CB */
/* asm 1: fe_sub(>t1=fe#2,<DA=fe#4,<CB=fe#2); */
/* asm 2: fe_sub(>t1=z2,<DA=z3,<CB=z2); */
FieldOperations.fe_sub(out z2, ref z3, ref z2);
/* qhasm: X4 = AA*BB */
/* asm 1: fe_mul(>X4=fe#1,<AA=fe#6,<BB=fe#5); */
/* asm 2: fe_mul(>X4=x2,<AA=tmp1,<BB=tmp0); */
FieldOperations.fe_mul(out x2, ref tmp1, ref tmp0);
/* qhasm: E = AA-BB */
/* asm 1: fe_sub(>E=fe#6,<AA=fe#6,<BB=fe#5); */
/* asm 2: fe_sub(>E=tmp1,<AA=tmp1,<BB=tmp0); */
FieldOperations.fe_sub(out tmp1, ref tmp1, ref tmp0);
/* qhasm: t2 = t1^2 */
/* asm 1: fe_sq(>t2=fe#2,<t1=fe#2); */
/* asm 2: fe_sq(>t2=z2,<t1=z2); */
FieldOperations.fe_sq(out z2, ref z2);
/* qhasm: t3 = a24*E */
/* asm 1: fe_mul121666(>t3=fe#4,<E=fe#6); */
/* asm 2: fe_mul121666(>t3=z3,<E=tmp1); */
FieldOperations.fe_mul121666(out z3, ref tmp1);
/* qhasm: X5 = t0^2 */
/* asm 1: fe_sq(>X5=fe#3,<t0=fe#3); */
/* asm 2: fe_sq(>X5=x3,<t0=x3); */
FieldOperations.fe_sq(out x3, ref x3);
/* qhasm: t4 = BB+t3 */
/* asm 1: fe_add(>t4=fe#5,<BB=fe#5,<t3=fe#4); */
/* asm 2: fe_add(>t4=tmp0,<BB=tmp0,<t3=z3); */
FieldOperations.fe_add(out tmp0, ref tmp0, ref z3);
/* qhasm: Z5 = X1*t2 */
/* asm 1: fe_mul(>Z5=fe#4,x1,<t2=fe#2); */
/* asm 2: fe_mul(>Z5=z3,x1,<t2=z2); */
FieldOperations.fe_mul(out z3, ref x1, ref z2);
/* qhasm: Z4 = E*t4 */
/* asm 1: fe_mul(>Z4=fe#2,<E=fe#6,<t4=fe#5); */
/* asm 2: fe_mul(>Z4=z2,<E=tmp1,<t4=tmp0); */
FieldOperations.fe_mul(out z2, ref tmp1, ref tmp0);
/* qhasm: return */
}
FieldOperations.fe_cswap(ref x2, ref x3, swap);
FieldOperations.fe_cswap(ref z2, ref z3, swap);
FieldOperations.fe_invert(out z2, ref z2);
FieldOperations.fe_mul(out x2, ref x2, ref z2);
q = x2;
CryptoBytes.Wipe(e);
}
internal static void fe_reduce(out FieldElement hr, ref FieldElement h)
{
Int32 h0 = h.x0;
Int32 h1 = h.x1;
Int32 h2 = h.x2;
Int32 h3 = h.x3;
Int32 h4 = h.x4;
Int32 h5 = h.x5;
Int32 h6 = h.x6;
Int32 h7 = h.x7;
Int32 h8 = h.x8;
Int32 h9 = h.x9;
Int32 q;
Int32 carry0;
Int32 carry1;
Int32 carry2;
Int32 carry3;
Int32 carry4;
Int32 carry5;
Int32 carry6;
Int32 carry7;
Int32 carry8;
Int32 carry9;
q = (19 * h9 + (((Int32)1) << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = h9 >> 25; h9 -= carry9 << 25;
/* h10 = carry9 */
hr.x0 = h0;
hr.x1 = h1;
hr.x2 = h2;
hr.x3 = h3;
hr.x4 = h4;
hr.x5 = h5;
hr.x6 = h6;
hr.x7 = h7;
hr.x8 = h8;
hr.x9 = h9;
}
internal static void fe_invert(out FieldElement result, ref FieldElement z)
{
FieldElement t0;
FieldElement t1;
FieldElement t2;
FieldElement t3;
int i;
/* qhasm: fe z1 */
/* qhasm: fe z2 */
/* qhasm: fe z8 */
/* qhasm: fe z9 */
/* qhasm: fe z11 */
/* qhasm: fe z22 */
/* qhasm: fe z_5_0 */
/* qhasm: fe z_10_5 */
/* qhasm: fe z_10_0 */
/* qhasm: fe z_20_10 */
/* qhasm: fe z_20_0 */
/* qhasm: fe z_40_20 */
/* qhasm: fe z_40_0 */
/* qhasm: fe z_50_10 */
/* qhasm: fe z_50_0 */
/* qhasm: fe z_100_50 */
/* qhasm: fe z_100_0 */
/* qhasm: fe z_200_100 */
/* qhasm: fe z_200_0 */
/* qhasm: fe z_250_50 */
/* qhasm: fe z_250_0 */
/* qhasm: fe z_255_5 */
/* qhasm: fe z_255_21 */
/* qhasm: enter pow225521 */
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(out t0, ref z); //for (i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 2; ++i)
{
fe_sq(out t1, ref t1);
}
/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(out t1, ref z, ref t1);
/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(out t0, ref t0, ref t1);
/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
fe_sq(out t2, ref t0); //for (i = 1; i < 1; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
fe_mul(out t1, ref t1, ref t2);
/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 5; ++i)
{
fe_sq(out t2, ref t2);
}
/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 10; ++i)
{
fe_sq(out t2, ref t2);
}
/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
fe_mul(out t2, ref t2, ref t1);
/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
fe_sq(out t3, ref t2); for (i = 1; i < 20; ++i)
{
fe_sq(out t3, ref t3);
}
/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
fe_mul(out t2, ref t3, ref t2);
/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
fe_sq(out t2, ref t2); for (i = 1; i < 10; ++i)
{
fe_sq(out t2, ref t2);
}
/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 50; ++i)
{
fe_sq(out t2, ref t2);
}
/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
fe_mul(out t2, ref t2, ref t1);
/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
fe_sq(out t3, ref t2); for (i = 1; i < 100; ++i)
{
fe_sq(out t3, ref t3);
}
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
fe_mul(out t2, ref t3, ref t2);
/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
fe_sq(out t2, ref t2); for (i = 1; i < 50; ++i)
{
fe_sq(out t2, ref t2);
}
/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_255_5 = z_250_0^2^5 */
/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
fe_sq(out t1, ref t1); for (i = 1; i < 5; ++i)
{
fe_sq(out t1, ref t1);
}
/* qhasm: z_255_21 = z_255_5*z11 */
/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
fe_mul(out result, ref t1, ref t0);
/* qhasm: return */
return;
}
internal static void fe_1(out FieldElement h)
{
h = default(FieldElement);
h.x0 = 1;
}
internal static void EdwardsToMontgomeryX(out FieldElement montgomeryX, ref FieldElement edwardsY, ref FieldElement edwardsZ)
{
FieldElement tempX, tempZ;
FieldOperations.fe_add(out tempX, ref edwardsZ, ref edwardsY);
FieldOperations.fe_sub(out tempZ, ref edwardsZ, ref edwardsY);
FieldOperations.fe_invert(out tempZ, ref tempZ);
FieldOperations.fe_mul(out montgomeryX, ref tempX, ref tempZ);
}
public static void fe_1(out FieldElement h)
{
h = default(FieldElement);
h.x0 = 1;
}
/*
h = f * g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
Notes on implementation strategy:
Using schoolbook multiplication.
Karatsuba would save a little in some cost models.
Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.
There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.
There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.
With tighter constraints on inputs can squeeze carries into int32.
*/
internal static void fe_mul(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int g1_19 = 19 * g1; /* 1.959375*2^29 */
int g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int g3_19 = 19 * g3;
int g4_19 = 19 * g4;
int g5_19 = 19 * g5;
int g6_19 = 19 * g6;
int g7_19 = 19 * g7;
int g8_19 = 19 * g8;
int g9_19 = 19 * g9;
int f1_2 = 2 * f1;
int f3_2 = 2 * f3;
int f5_2 = 2 * f5;
int f7_2 = 2 * f7;
int f9_2 = 2 * f9;
long f0g0 = f0 * (long)g0;
long f0g1 = f0 * (long)g1;
long f0g2 = f0 * (long)g2;
long f0g3 = f0 * (long)g3;
long f0g4 = f0 * (long)g4;
long f0g5 = f0 * (long)g5;
long f0g6 = f0 * (long)g6;
long f0g7 = f0 * (long)g7;
long f0g8 = f0 * (long)g8;
long f0g9 = f0 * (long)g9;
long f1g0 = f1 * (long)g0;
long f1g1_2 = f1_2 * (long)g1;
long f1g2 = f1 * (long)g2;
long f1g3_2 = f1_2 * (long)g3;
long f1g4 = f1 * (long)g4;
long f1g5_2 = f1_2 * (long)g5;
long f1g6 = f1 * (long)g6;
long f1g7_2 = f1_2 * (long)g7;
long f1g8 = f1 * (long)g8;
long f1g9_38 = f1_2 * (long)g9_19;
long f2g0 = f2 * (long)g0;
long f2g1 = f2 * (long)g1;
long f2g2 = f2 * (long)g2;
long f2g3 = f2 * (long)g3;
long f2g4 = f2 * (long)g4;
long f2g5 = f2 * (long)g5;
long f2g6 = f2 * (long)g6;
long f2g7 = f2 * (long)g7;
long f2g8_19 = f2 * (long)g8_19;
long f2g9_19 = f2 * (long)g9_19;
long f3g0 = f3 * (long)g0;
long f3g1_2 = f3_2 * (long)g1;
long f3g2 = f3 * (long)g2;
long f3g3_2 = f3_2 * (long)g3;
long f3g4 = f3 * (long)g4;
long f3g5_2 = f3_2 * (long)g5;
long f3g6 = f3 * (long)g6;
long f3g7_38 = f3_2 * (long)g7_19;
long f3g8_19 = f3 * (long)g8_19;
long f3g9_38 = f3_2 * (long)g9_19;
long f4g0 = f4 * (long)g0;
long f4g1 = f4 * (long)g1;
long f4g2 = f4 * (long)g2;
long f4g3 = f4 * (long)g3;
long f4g4 = f4 * (long)g4;
long f4g5 = f4 * (long)g5;
long f4g6_19 = f4 * (long)g6_19;
long f4g7_19 = f4 * (long)g7_19;
long f4g8_19 = f4 * (long)g8_19;
long f4g9_19 = f4 * (long)g9_19;
long f5g0 = f5 * (long)g0;
long f5g1_2 = f5_2 * (long)g1;
long f5g2 = f5 * (long)g2;
long f5g3_2 = f5_2 * (long)g3;
long f5g4 = f5 * (long)g4;
long f5g5_38 = f5_2 * (long)g5_19;
long f5g6_19 = f5 * (long)g6_19;
long f5g7_38 = f5_2 * (long)g7_19;
long f5g8_19 = f5 * (long)g8_19;
long f5g9_38 = f5_2 * (long)g9_19;
long f6g0 = f6 * (long)g0;
long f6g1 = f6 * (long)g1;
long f6g2 = f6 * (long)g2;
long f6g3 = f6 * (long)g3;
long f6g4_19 = f6 * (long)g4_19;
long f6g5_19 = f6 * (long)g5_19;
long f6g6_19 = f6 * (long)g6_19;
long f6g7_19 = f6 * (long)g7_19;
long f6g8_19 = f6 * (long)g8_19;
long f6g9_19 = f6 * (long)g9_19;
long f7g0 = f7 * (long)g0;
long f7g1_2 = f7_2 * (long)g1;
long f7g2 = f7 * (long)g2;
long f7g3_38 = f7_2 * (long)g3_19;
long f7g4_19 = f7 * (long)g4_19;
long f7g5_38 = f7_2 * (long)g5_19;
long f7g6_19 = f7 * (long)g6_19;
long f7g7_38 = f7_2 * (long)g7_19;
long f7g8_19 = f7 * (long)g8_19;
long f7g9_38 = f7_2 * (long)g9_19;
long f8g0 = f8 * (long)g0;
long f8g1 = f8 * (long)g1;
long f8g2_19 = f8 * (long)g2_19;
long f8g3_19 = f8 * (long)g3_19;
long f8g4_19 = f8 * (long)g4_19;
long f8g5_19 = f8 * (long)g5_19;
long f8g6_19 = f8 * (long)g6_19;
long f8g7_19 = f8 * (long)g7_19;
long f8g8_19 = f8 * (long)g8_19;
long f8g9_19 = f8 * (long)g9_19;
long f9g0 = f9 * (long)g0;
long f9g1_38 = f9_2 * (long)g1_19;
long f9g2_19 = f9 * (long)g2_19;
long f9g3_38 = f9_2 * (long)g3_19;
long f9g4_19 = f9 * (long)g4_19;
long f9g5_38 = f9_2 * (long)g5_19;
long f9g6_19 = f9 * (long)g6_19;
long f9g7_38 = f9_2 * (long)g7_19;
long f9g8_19 = f9 * (long)g8_19;
long f9g9_38 = f9_2 * (long)g9_19;
long h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
long h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
long h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
long h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
long h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
long h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
long h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
long h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
long h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
long h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
long carry0;
long carry1;
long carry2;
long carry3;
long carry4;
long carry5;
long carry6;
long carry7;
long carry8;
long carry9;
/*
|h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = (h2 + (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = (h3 + (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = (h4 + (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = (h9 + (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
/*
* h = f * f
* Can overlap h with f.
*
* Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
* See fe_mul.c for discussion of implementation strategy.
*/
internal static void fe_sq(out FieldElement h, ref FieldElement f)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 f0_2 = 2 * f0;
Int32 f1_2 = 2 * f1;
Int32 f2_2 = 2 * f2;
Int32 f3_2 = 2 * f3;
Int32 f4_2 = 2 * f4;
Int32 f5_2 = 2 * f5;
Int32 f6_2 = 2 * f6;
Int32 f7_2 = 2 * f7;
Int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
Int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
Int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
Int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
Int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
Int64 f0f0 = f0 * (Int64)f0;
Int64 f0f1_2 = f0_2 * (Int64)f1;
Int64 f0f2_2 = f0_2 * (Int64)f2;
Int64 f0f3_2 = f0_2 * (Int64)f3;
Int64 f0f4_2 = f0_2 * (Int64)f4;
Int64 f0f5_2 = f0_2 * (Int64)f5;
Int64 f0f6_2 = f0_2 * (Int64)f6;
Int64 f0f7_2 = f0_2 * (Int64)f7;
Int64 f0f8_2 = f0_2 * (Int64)f8;
Int64 f0f9_2 = f0_2 * (Int64)f9;
Int64 f1f1_2 = f1_2 * (Int64)f1;
Int64 f1f2_2 = f1_2 * (Int64)f2;
Int64 f1f3_4 = f1_2 * (Int64)f3_2;
Int64 f1f4_2 = f1_2 * (Int64)f4;
Int64 f1f5_4 = f1_2 * (Int64)f5_2;
Int64 f1f6_2 = f1_2 * (Int64)f6;
Int64 f1f7_4 = f1_2 * (Int64)f7_2;
Int64 f1f8_2 = f1_2 * (Int64)f8;
Int64 f1f9_76 = f1_2 * (Int64)f9_38;
Int64 f2f2 = f2 * (Int64)f2;
Int64 f2f3_2 = f2_2 * (Int64)f3;
Int64 f2f4_2 = f2_2 * (Int64)f4;
Int64 f2f5_2 = f2_2 * (Int64)f5;
Int64 f2f6_2 = f2_2 * (Int64)f6;
Int64 f2f7_2 = f2_2 * (Int64)f7;
Int64 f2f8_38 = f2_2 * (Int64)f8_19;
Int64 f2f9_38 = f2 * (Int64)f9_38;
Int64 f3f3_2 = f3_2 * (Int64)f3;
Int64 f3f4_2 = f3_2 * (Int64)f4;
Int64 f3f5_4 = f3_2 * (Int64)f5_2;
Int64 f3f6_2 = f3_2 * (Int64)f6;
Int64 f3f7_76 = f3_2 * (Int64)f7_38;
Int64 f3f8_38 = f3_2 * (Int64)f8_19;
Int64 f3f9_76 = f3_2 * (Int64)f9_38;
Int64 f4f4 = f4 * (Int64)f4;
Int64 f4f5_2 = f4_2 * (Int64)f5;
Int64 f4f6_38 = f4_2 * (Int64)f6_19;
Int64 f4f7_38 = f4 * (Int64)f7_38;
Int64 f4f8_38 = f4_2 * (Int64)f8_19;
Int64 f4f9_38 = f4 * (Int64)f9_38;
Int64 f5f5_38 = f5 * (Int64)f5_38;
Int64 f5f6_38 = f5_2 * (Int64)f6_19;
Int64 f5f7_76 = f5_2 * (Int64)f7_38;
Int64 f5f8_38 = f5_2 * (Int64)f8_19;
Int64 f5f9_76 = f5_2 * (Int64)f9_38;
Int64 f6f6_19 = f6 * (Int64)f6_19;
Int64 f6f7_38 = f6 * (Int64)f7_38;
Int64 f6f8_38 = f6_2 * (Int64)f8_19;
Int64 f6f9_38 = f6 * (Int64)f9_38;
Int64 f7f7_38 = f7 * (Int64)f7_38;
Int64 f7f8_38 = f7_2 * (Int64)f8_19;
Int64 f7f9_76 = f7_2 * (Int64)f9_38;
Int64 f8f8_19 = f8 * (Int64)f8_19;
Int64 f8f9_38 = f8 * (Int64)f9_38;
Int64 f9f9_38 = f9 * (Int64)f9_38;
Int64 h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
Int64 h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
Int64 h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
Int64 h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
Int64 h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
Int64 h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
Int64 h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
Int64 h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
Int64 h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
Int64 h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
Int64 carry0;
Int64 carry1;
Int64 carry2;
Int64 carry3;
Int64 carry4;
Int64 carry5;
Int64 carry6;
Int64 carry7;
Int64 carry8;
Int64 carry9;
carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
h.x0 = (Int32)h0;
h.x1 = (Int32)h1;
h.x2 = (Int32)h2;
h.x3 = (Int32)h3;
h.x4 = (Int32)h4;
h.x5 = (Int32)h5;
h.x6 = (Int32)h6;
h.x7 = (Int32)h7;
h.x8 = (Int32)h8;
h.x9 = (Int32)h9;
}
internal static void fe_reduce(out FieldElement hr, ref FieldElement h)
{
Int32 h0 = h.x0;
Int32 h1 = h.x1;
Int32 h2 = h.x2;
Int32 h3 = h.x3;
Int32 h4 = h.x4;
Int32 h5 = h.x5;
Int32 h6 = h.x6;
Int32 h7 = h.x7;
Int32 h8 = h.x8;
Int32 h9 = h.x9;
Int32 q;
Int32 carry0;
Int32 carry1;
Int32 carry2;
Int32 carry3;
Int32 carry4;
Int32 carry5;
Int32 carry6;
Int32 carry7;
Int32 carry8;
Int32 carry9;
q = (19 * h9 + (((Int32)1) << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = h9 >> 25; h9 -= carry9 << 25;
/* h10 = carry9 */
hr.x0 = h0;
hr.x1 = h1;
hr.x2 = h2;
hr.x3 = h3;
hr.x4 = h4;
hr.x5 = h5;
hr.x6 = h6;
hr.x7 = h7;
hr.x8 = h8;
hr.x9 = h9;
}
internal static void fe_pow22523(out FieldElement result, ref FieldElement z)
{
FieldElement t0;
FieldElement t1;
FieldElement t2;
int i;
/* qhasm: fe z1 */
/* qhasm: fe z2 */
/* qhasm: fe z8 */
/* qhasm: fe z9 */
/* qhasm: fe z11 */
/* qhasm: fe z22 */
/* qhasm: fe z_5_0 */
/* qhasm: fe z_10_5 */
/* qhasm: fe z_10_0 */
/* qhasm: fe z_20_10 */
/* qhasm: fe z_20_0 */
/* qhasm: fe z_40_20 */
/* qhasm: fe z_40_0 */
/* qhasm: fe z_50_10 */
/* qhasm: fe z_50_0 */
/* qhasm: fe z_100_50 */
/* qhasm: fe z_100_0 */
/* qhasm: fe z_200_100 */
/* qhasm: fe z_200_0 */
/* qhasm: fe z_250_50 */
/* qhasm: fe z_250_0 */
/* qhasm: fe z_252_2 */
/* qhasm: fe z_252_3 */
/* qhasm: enter pow22523 */
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(out t0, ref z); //for (i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 2; ++i) fe_sq(out t1, ref t1);
/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(out t1, ref z, ref t1);
/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(out t0, ref t0, ref t1);
/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */
/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */
fe_sq(out t0, ref t0); //for (i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */
/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */
fe_mul(out t0, ref t1, ref t0);
/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */
/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 5; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */
/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */
fe_mul(out t0, ref t1, ref t0);
/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */
/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 10; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */
fe_mul(out t1, ref t1, ref t0);
/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */
/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 20; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */
/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */
/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */
fe_sq(out t1, ref t1); for (i = 1; i < 10; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */
fe_mul(out t0, ref t1, ref t0);
/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */
/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 50; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */
fe_mul(out t1, ref t1, ref t0);
/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */
/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 100; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */
/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */
/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */
fe_sq(out t1, ref t1); for (i = 1; i < 50; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */
fe_mul(out t0, ref t1, ref t0);
/* qhasm: z_252_2 = z_250_0^2^2 */
/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */
/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */
fe_sq(out t0, ref t0); for (i = 1; i < 2; ++i) fe_sq(out t0, ref t0);
/* qhasm: z_252_3 = z_252_2*z1 */
/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */
/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */
fe_mul(out result, ref t0, ref z);
/* qhasm: return */
}
/*
h = f * g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
Notes on implementation strategy:
Using schoolbook multiplication.
Karatsuba would save a little in some cost models.
Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.
There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.
There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.
With tighter constraints on inputs can squeeze carries into int32.
*/
internal static void fe_mul(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
Int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
Int32 g3_19 = 19 * g3;
Int32 g4_19 = 19 * g4;
Int32 g5_19 = 19 * g5;
Int32 g6_19 = 19 * g6;
Int32 g7_19 = 19 * g7;
Int32 g8_19 = 19 * g8;
Int32 g9_19 = 19 * g9;
Int32 f1_2 = 2 * f1;
Int32 f3_2 = 2 * f3;
Int32 f5_2 = 2 * f5;
Int32 f7_2 = 2 * f7;
Int32 f9_2 = 2 * f9;
Int64 f0g0 = f0 * (Int64)g0;
Int64 f0g1 = f0 * (Int64)g1;
Int64 f0g2 = f0 * (Int64)g2;
Int64 f0g3 = f0 * (Int64)g3;
Int64 f0g4 = f0 * (Int64)g4;
Int64 f0g5 = f0 * (Int64)g5;
Int64 f0g6 = f0 * (Int64)g6;
Int64 f0g7 = f0 * (Int64)g7;
Int64 f0g8 = f0 * (Int64)g8;
Int64 f0g9 = f0 * (Int64)g9;
Int64 f1g0 = f1 * (Int64)g0;
Int64 f1g1_2 = f1_2 * (Int64)g1;
Int64 f1g2 = f1 * (Int64)g2;
Int64 f1g3_2 = f1_2 * (Int64)g3;
Int64 f1g4 = f1 * (Int64)g4;
Int64 f1g5_2 = f1_2 * (Int64)g5;
Int64 f1g6 = f1 * (Int64)g6;
Int64 f1g7_2 = f1_2 * (Int64)g7;
Int64 f1g8 = f1 * (Int64)g8;
Int64 f1g9_38 = f1_2 * (Int64)g9_19;
Int64 f2g0 = f2 * (Int64)g0;
Int64 f2g1 = f2 * (Int64)g1;
Int64 f2g2 = f2 * (Int64)g2;
Int64 f2g3 = f2 * (Int64)g3;
Int64 f2g4 = f2 * (Int64)g4;
Int64 f2g5 = f2 * (Int64)g5;
Int64 f2g6 = f2 * (Int64)g6;
Int64 f2g7 = f2 * (Int64)g7;
Int64 f2g8_19 = f2 * (Int64)g8_19;
Int64 f2g9_19 = f2 * (Int64)g9_19;
Int64 f3g0 = f3 * (Int64)g0;
Int64 f3g1_2 = f3_2 * (Int64)g1;
Int64 f3g2 = f3 * (Int64)g2;
Int64 f3g3_2 = f3_2 * (Int64)g3;
Int64 f3g4 = f3 * (Int64)g4;
Int64 f3g5_2 = f3_2 * (Int64)g5;
Int64 f3g6 = f3 * (Int64)g6;
Int64 f3g7_38 = f3_2 * (Int64)g7_19;
Int64 f3g8_19 = f3 * (Int64)g8_19;
Int64 f3g9_38 = f3_2 * (Int64)g9_19;
Int64 f4g0 = f4 * (Int64)g0;
Int64 f4g1 = f4 * (Int64)g1;
Int64 f4g2 = f4 * (Int64)g2;
Int64 f4g3 = f4 * (Int64)g3;
Int64 f4g4 = f4 * (Int64)g4;
Int64 f4g5 = f4 * (Int64)g5;
Int64 f4g6_19 = f4 * (Int64)g6_19;
Int64 f4g7_19 = f4 * (Int64)g7_19;
Int64 f4g8_19 = f4 * (Int64)g8_19;
Int64 f4g9_19 = f4 * (Int64)g9_19;
Int64 f5g0 = f5 * (Int64)g0;
Int64 f5g1_2 = f5_2 * (Int64)g1;
Int64 f5g2 = f5 * (Int64)g2;
Int64 f5g3_2 = f5_2 * (Int64)g3;
Int64 f5g4 = f5 * (Int64)g4;
Int64 f5g5_38 = f5_2 * (Int64)g5_19;
Int64 f5g6_19 = f5 * (Int64)g6_19;
Int64 f5g7_38 = f5_2 * (Int64)g7_19;
Int64 f5g8_19 = f5 * (Int64)g8_19;
Int64 f5g9_38 = f5_2 * (Int64)g9_19;
Int64 f6g0 = f6 * (Int64)g0;
Int64 f6g1 = f6 * (Int64)g1;
Int64 f6g2 = f6 * (Int64)g2;
Int64 f6g3 = f6 * (Int64)g3;
Int64 f6g4_19 = f6 * (Int64)g4_19;
Int64 f6g5_19 = f6 * (Int64)g5_19;
Int64 f6g6_19 = f6 * (Int64)g6_19;
Int64 f6g7_19 = f6 * (Int64)g7_19;
Int64 f6g8_19 = f6 * (Int64)g8_19;
Int64 f6g9_19 = f6 * (Int64)g9_19;
Int64 f7g0 = f7 * (Int64)g0;
Int64 f7g1_2 = f7_2 * (Int64)g1;
Int64 f7g2 = f7 * (Int64)g2;
Int64 f7g3_38 = f7_2 * (Int64)g3_19;
Int64 f7g4_19 = f7 * (Int64)g4_19;
Int64 f7g5_38 = f7_2 * (Int64)g5_19;
Int64 f7g6_19 = f7 * (Int64)g6_19;
Int64 f7g7_38 = f7_2 * (Int64)g7_19;
Int64 f7g8_19 = f7 * (Int64)g8_19;
Int64 f7g9_38 = f7_2 * (Int64)g9_19;
Int64 f8g0 = f8 * (Int64)g0;
Int64 f8g1 = f8 * (Int64)g1;
Int64 f8g2_19 = f8 * (Int64)g2_19;
Int64 f8g3_19 = f8 * (Int64)g3_19;
Int64 f8g4_19 = f8 * (Int64)g4_19;
Int64 f8g5_19 = f8 * (Int64)g5_19;
Int64 f8g6_19 = f8 * (Int64)g6_19;
Int64 f8g7_19 = f8 * (Int64)g7_19;
Int64 f8g8_19 = f8 * (Int64)g8_19;
Int64 f8g9_19 = f8 * (Int64)g9_19;
Int64 f9g0 = f9 * (Int64)g0;
Int64 f9g1_38 = f9_2 * (Int64)g1_19;
Int64 f9g2_19 = f9 * (Int64)g2_19;
Int64 f9g3_38 = f9_2 * (Int64)g3_19;
Int64 f9g4_19 = f9 * (Int64)g4_19;
Int64 f9g5_38 = f9_2 * (Int64)g5_19;
Int64 f9g6_19 = f9 * (Int64)g6_19;
Int64 f9g7_38 = f9_2 * (Int64)g7_19;
Int64 f9g8_19 = f9 * (Int64)g8_19;
Int64 f9g9_38 = f9_2 * (Int64)g9_19;
Int64 h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
Int64 h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
Int64 h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
Int64 h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
Int64 h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
Int64 h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
Int64 h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
Int64 h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
Int64 h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
Int64 h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
Int64 carry0;
Int64 carry1;
Int64 carry2;
Int64 carry3;
Int64 carry4;
Int64 carry5;
Int64 carry6;
Int64 carry7;
Int64 carry8;
Int64 carry9;
/*
Replace (f,g) with (g,f) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
public static void fe_cswap(ref FieldElement f, ref FieldElement g, uint b)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 x0 = f0 ^ g0;
Int32 x1 = f1 ^ g1;
Int32 x2 = f2 ^ g2;
Int32 x3 = f3 ^ g3;
Int32 x4 = f4 ^ g4;
Int32 x5 = f5 ^ g5;
Int32 x6 = f6 ^ g6;
Int32 x7 = f7 ^ g7;
Int32 x8 = f8 ^ g8;
Int32 x9 = f9 ^ g9;
int negb = unchecked((int)-b);
x0 &= negb;
x1 &= negb;
x2 &= negb;
x3 &= negb;
x4 &= negb;
x5 &= negb;
x6 &= negb;
x7 &= negb;
x8 &= negb;
x9 &= negb;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
g.x0 = g0 ^ x0;
g.x1 = g1 ^ x1;
g.x2 = g2 ^ x2;
g.x3 = g3 ^ x3;
g.x4 = g4 ^ x4;
g.x5 = g5 ^ x5;
g.x6 = g6 ^ x6;
g.x7 = g7 ^ x7;
g.x8 = g8 ^ x8;
g.x9 = g9 ^ x9;
}
public static void fe_0(out FieldElement h)
{
h = default(FieldElement);
}
/*
* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
* Preconditions: b in {0,1}.
*/
internal static void fe_cswap(ref FieldElement f, ref FieldElement g, uint b)
{
Int32 f0 = f.x0;
Int32 f1 = f.x1;
Int32 f2 = f.x2;
Int32 f3 = f.x3;
Int32 f4 = f.x4;
Int32 f5 = f.x5;
Int32 f6 = f.x6;
Int32 f7 = f.x7;
Int32 f8 = f.x8;
Int32 f9 = f.x9;
Int32 g0 = g.x0;
Int32 g1 = g.x1;
Int32 g2 = g.x2;
Int32 g3 = g.x3;
Int32 g4 = g.x4;
Int32 g5 = g.x5;
Int32 g6 = g.x6;
Int32 g7 = g.x7;
Int32 g8 = g.x8;
Int32 g9 = g.x9;
Int32 x0 = f0 ^ g0;
Int32 x1 = f1 ^ g1;
Int32 x2 = f2 ^ g2;
Int32 x3 = f3 ^ g3;
Int32 x4 = f4 ^ g4;
Int32 x5 = f5 ^ g5;
Int32 x6 = f6 ^ g6;
Int32 x7 = f7 ^ g7;
Int32 x8 = f8 ^ g8;
Int32 x9 = f9 ^ g9;
int negb = unchecked ((int)-b);
x0 &= negb;
x1 &= negb;
x2 &= negb;
x3 &= negb;
x4 &= negb;
x5 &= negb;
x6 &= negb;
x7 &= negb;
x8 &= negb;
x9 &= negb;
f.x0 = f0 ^ x0;
f.x1 = f1 ^ x1;
f.x2 = f2 ^ x2;
f.x3 = f3 ^ x3;
f.x4 = f4 ^ x4;
f.x5 = f5 ^ x5;
f.x6 = f6 ^ x6;
f.x7 = f7 ^ x7;
f.x8 = f8 ^ x8;
f.x9 = f9 ^ x9;
g.x0 = g0 ^ x0;
g.x1 = g1 ^ x1;
g.x2 = g2 ^ x2;
g.x3 = g3 ^ x3;
g.x4 = g4 ^ x4;
g.x5 = g5 ^ x5;
g.x6 = g6 ^ x6;
g.x7 = g7 ^ x7;
g.x8 = g8 ^ x8;
g.x9 = g9 ^ x9;
}
/*
* h = f * g
* Can overlap h with f or g.
*
* Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
* Notes on implementation strategy:
*
* Using schoolbook multiplication.
* Karatsuba would save a little in some cost models.
*
* Most multiplications by 2 and 19 are 32-bit precomputations;
* cheaper than 64-bit postcomputations.
*
* There is one remaining multiplication by 19 in the carry chain;
* one *19 precomputation can be merged into this,
* but the resulting data flow is considerably less clean.
*
* There are 12 carries below.
* 10 of them are 2-way parallelizable and vectorizable.
* Can get away with 11 carries, but then data flow is much deeper.
*
* With tighter constraints on inputs can squeeze carries into int32.
*/
internal static void fe_mul(out FieldElement h, ref FieldElement f, ref FieldElement g)
{
int f0 = f.x0;
int f1 = f.x1;
int f2 = f.x2;
int f3 = f.x3;
int f4 = f.x4;
int f5 = f.x5;
int f6 = f.x6;
int f7 = f.x7;
int f8 = f.x8;
int f9 = f.x9;
int g0 = g.x0;
int g1 = g.x1;
int g2 = g.x2;
int g3 = g.x3;
int g4 = g.x4;
int g5 = g.x5;
int g6 = g.x6;
int g7 = g.x7;
int g8 = g.x8;
int g9 = g.x9;
int g1_19 = 19 * g1; /* 1.959375*2^29 */
int g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int g3_19 = 19 * g3;
int g4_19 = 19 * g4;
int g5_19 = 19 * g5;
int g6_19 = 19 * g6;
int g7_19 = 19 * g7;
int g8_19 = 19 * g8;
int g9_19 = 19 * g9;
int f1_2 = 2 * f1;
int f3_2 = 2 * f3;
int f5_2 = 2 * f5;
int f7_2 = 2 * f7;
int f9_2 = 2 * f9;
long f0g0 = f0 * (long)g0;
long f0g1 = f0 * (long)g1;
long f0g2 = f0 * (long)g2;
long f0g3 = f0 * (long)g3;
long f0g4 = f0 * (long)g4;
long f0g5 = f0 * (long)g5;
long f0g6 = f0 * (long)g6;
long f0g7 = f0 * (long)g7;
long f0g8 = f0 * (long)g8;
long f0g9 = f0 * (long)g9;
long f1g0 = f1 * (long)g0;
long f1g1_2 = f1_2 * (long)g1;
long f1g2 = f1 * (long)g2;
long f1g3_2 = f1_2 * (long)g3;
long f1g4 = f1 * (long)g4;
long f1g5_2 = f1_2 * (long)g5;
long f1g6 = f1 * (long)g6;
long f1g7_2 = f1_2 * (long)g7;
long f1g8 = f1 * (long)g8;
long f1g9_38 = f1_2 * (long)g9_19;
long f2g0 = f2 * (long)g0;
long f2g1 = f2 * (long)g1;
long f2g2 = f2 * (long)g2;
long f2g3 = f2 * (long)g3;
long f2g4 = f2 * (long)g4;
long f2g5 = f2 * (long)g5;
long f2g6 = f2 * (long)g6;
long f2g7 = f2 * (long)g7;
long f2g8_19 = f2 * (long)g8_19;
long f2g9_19 = f2 * (long)g9_19;
long f3g0 = f3 * (long)g0;
long f3g1_2 = f3_2 * (long)g1;
long f3g2 = f3 * (long)g2;
long f3g3_2 = f3_2 * (long)g3;
long f3g4 = f3 * (long)g4;
long f3g5_2 = f3_2 * (long)g5;
long f3g6 = f3 * (long)g6;
long f3g7_38 = f3_2 * (long)g7_19;
long f3g8_19 = f3 * (long)g8_19;
long f3g9_38 = f3_2 * (long)g9_19;
long f4g0 = f4 * (long)g0;
long f4g1 = f4 * (long)g1;
long f4g2 = f4 * (long)g2;
long f4g3 = f4 * (long)g3;
long f4g4 = f4 * (long)g4;
long f4g5 = f4 * (long)g5;
long f4g6_19 = f4 * (long)g6_19;
long f4g7_19 = f4 * (long)g7_19;
long f4g8_19 = f4 * (long)g8_19;
long f4g9_19 = f4 * (long)g9_19;
long f5g0 = f5 * (long)g0;
long f5g1_2 = f5_2 * (long)g1;
long f5g2 = f5 * (long)g2;
long f5g3_2 = f5_2 * (long)g3;
long f5g4 = f5 * (long)g4;
long f5g5_38 = f5_2 * (long)g5_19;
long f5g6_19 = f5 * (long)g6_19;
long f5g7_38 = f5_2 * (long)g7_19;
long f5g8_19 = f5 * (long)g8_19;
long f5g9_38 = f5_2 * (long)g9_19;
long f6g0 = f6 * (long)g0;
long f6g1 = f6 * (long)g1;
long f6g2 = f6 * (long)g2;
long f6g3 = f6 * (long)g3;
long f6g4_19 = f6 * (long)g4_19;
long f6g5_19 = f6 * (long)g5_19;
long f6g6_19 = f6 * (long)g6_19;
long f6g7_19 = f6 * (long)g7_19;
long f6g8_19 = f6 * (long)g8_19;
long f6g9_19 = f6 * (long)g9_19;
long f7g0 = f7 * (long)g0;
long f7g1_2 = f7_2 * (long)g1;
long f7g2 = f7 * (long)g2;
long f7g3_38 = f7_2 * (long)g3_19;
long f7g4_19 = f7 * (long)g4_19;
long f7g5_38 = f7_2 * (long)g5_19;
long f7g6_19 = f7 * (long)g6_19;
long f7g7_38 = f7_2 * (long)g7_19;
long f7g8_19 = f7 * (long)g8_19;
long f7g9_38 = f7_2 * (long)g9_19;
long f8g0 = f8 * (long)g0;
long f8g1 = f8 * (long)g1;
long f8g2_19 = f8 * (long)g2_19;
long f8g3_19 = f8 * (long)g3_19;
long f8g4_19 = f8 * (long)g4_19;
long f8g5_19 = f8 * (long)g5_19;
long f8g6_19 = f8 * (long)g6_19;
long f8g7_19 = f8 * (long)g7_19;
long f8g8_19 = f8 * (long)g8_19;
long f8g9_19 = f8 * (long)g9_19;
long f9g0 = f9 * (long)g0;
long f9g1_38 = f9_2 * (long)g1_19;
long f9g2_19 = f9 * (long)g2_19;
long f9g3_38 = f9_2 * (long)g3_19;
long f9g4_19 = f9 * (long)g4_19;
long f9g5_38 = f9_2 * (long)g5_19;
long f9g6_19 = f9 * (long)g6_19;
long f9g7_38 = f9_2 * (long)g7_19;
long f9g8_19 = f9 * (long)g8_19;
long f9g9_38 = f9_2 * (long)g9_19;
long h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
long h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
long h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
long h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
long h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
long h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
long h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
long h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
long h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
long h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
long carry0;
long carry1;
long carry2;
long carry3;
long carry4;
long carry5;
long carry6;
long carry7;
long carry8;
long carry9;
/*
|h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
* i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (long)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (long)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (long)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (long)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = (h2 + (long)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (long)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = (h3 + (long)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (long)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = (h4 + (long)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (long)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = (h9 + (long)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (long)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h.x0 = (int)h0;
h.x1 = (int)h1;
h.x2 = (int)h2;
h.x3 = (int)h3;
h.x4 = (int)h4;
h.x5 = (int)h5;
h.x6 = (int)h6;
h.x7 = (int)h7;
h.x8 = (int)h8;
h.x9 = (int)h9;
}
internal static void fe_invert(out FieldElement result, ref FieldElement z)
{
FieldElement t0, t1, t2, t3;
int i;
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(out t0, ref z); //for (i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(out t1, ref t0); for (i = 1; i < 2; ++i) fe_sq(out t1, ref t1);
/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(out t1, ref z, ref t1);
/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(out t0, ref t0, ref t1);
/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
fe_sq(out t2, ref t0); //for (i = 1; i < 1; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
fe_mul(out t1, ref t1, ref t2);
/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 5; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 10; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
fe_mul(out t2, ref t2, ref t1);
/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
fe_sq(out t3, ref t2); for (i = 1; i < 20; ++i) fe_sq(out t3, ref t3);
/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
fe_mul(out t2, ref t3, ref t2);
/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
fe_sq(out t2, ref t2); for (i = 1; i < 10; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
fe_sq(out t2, ref t1); for (i = 1; i < 50; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
fe_mul(out t2, ref t2, ref t1);
/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
fe_sq(out t3, ref t2); for (i = 1; i < 100; ++i) fe_sq(out t3, ref t3);
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
fe_mul(out t2, ref t3, ref t2);
/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
fe_sq(out t2, ref t2); for (i = 1; i < 50; ++i) fe_sq(out t2, ref t2);
/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
fe_mul(out t1, ref t2, ref t1);
/* qhasm: z_255_5 = z_250_0^2^5 */
/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
fe_sq(out t1, ref t1); for (i = 1; i < 5; ++i) fe_sq(out t1, ref t1);
/* qhasm: z_255_21 = z_255_5*z11 */
/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
fe_mul(out result, ref t1, ref t0);
/* qhasm: return */
return;
}
