build/libraries/libsodium/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c
#include <stddef.h>
#include <stdint.h>
#include <string.h>
#include "crypto_verify_32.h"
#include "private/curve25519_ref10.h"
static inline uint64_t
load_3(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
return result;
}
static inline uint64_t
load_4(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
result |= ((uint64_t) in[3]) << 24;
return result;
}
/*
h = 0
*/
void
fe_0(fe h)
{
memset(&h[0], 0, 10 * sizeof h[0]);
}
/*
h = 1
*/
void
fe_1(fe h)
{
h[0] = 1;
h[1] = 0;
memset(&h[2], 0, 8 * sizeof h[0]);
}
/*
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)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t h0 = f0 + g0;
int32_t h1 = f1 + g1;
int32_t h2 = f2 + g2;
int32_t h3 = f3 + g3;
int32_t h4 = f4 + g4;
int32_t h5 = f5 + g5;
int32_t h6 = f6 + g6;
int32_t h7 = f7 + g7;
int32_t h8 = f8 + g8;
int32_t h9 = f9 + g9;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.
*
Preconditions: b in {0,1}.
*/
static void
fe_cmov(fe f, const fe g, unsigned int b)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t x0 = f0 ^ g0;
int32_t x1 = f1 ^ g1;
int32_t x2 = f2 ^ g2;
int32_t x3 = f3 ^ g3;
int32_t x4 = f4 ^ g4;
int32_t x5 = f5 ^ g5;
int32_t x6 = f6 ^ g6;
int32_t x7 = f7 ^ g7;
int32_t x8 = f8 ^ g8;
int32_t x9 = f9 ^ g9;
b = (unsigned int) (-(int) b);
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
f[0] = f0 ^ x0;
f[1] = f1 ^ x1;
f[2] = f2 ^ x2;
f[3] = f3 ^ x3;
f[4] = f4 ^ x4;
f[5] = f5 ^ x5;
f[6] = f6 ^ x6;
f[7] = f7 ^ x7;
f[8] = f8 ^ x8;
f[9] = f9 ^ x9;
}
/*
h = f
*/
void
fe_copy(fe h, const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
h[0] = f0;
h[1] = f1;
h[2] = f2;
h[3] = f3;
h[4] = f4;
h[5] = f5;
h[6] = f6;
h[7] = f7;
h[8] = f8;
h[9] = f9;
}
/*
Ignores top bit of h.
*/
void
fe_frombytes(fe h, const unsigned char *s)
{
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = (load_3(s + 29) & 8388607) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 * ((uint64_t) 1L << 25);
carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
h2 += carry1;
h1 -= carry1 * ((uint64_t) 1L << 25);
carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
h4 += carry3;
h3 -= carry3 * ((uint64_t) 1L << 25);
carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
h6 += carry5;
h5 -= carry5 * ((uint64_t) 1L << 25);
carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
h8 += carry7;
h7 -= carry7 * ((uint64_t) 1L << 25);
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
h3 += carry2;
h2 -= carry2 * ((uint64_t) 1L << 26);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
h7 += carry6;
h6 -= carry6 * ((uint64_t) 1L << 26);
carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
h9 += carry8;
h8 -= carry8 * ((uint64_t) 1L << 26);
h[0] = (int32_t) h0;
h[1] = (int32_t) h1;
h[2] = (int32_t) h2;
h[3] = (int32_t) h3;
h[4] = (int32_t) h4;
h[5] = (int32_t) h5;
h[6] = (int32_t) h6;
h[7] = (int32_t) h7;
h[8] = (int32_t) h8;
h[9] = (int32_t) 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.
*/
void
fe_tobytes(unsigned char *s, const fe h)
{
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
int32_t h3 = h[3];
int32_t h4 = h[4];
int32_t h5 = h[5];
int32_t h6 = h[6];
int32_t h7 = h[7];
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
int32_t carry0;
int32_t carry1;
int32_t carry2;
int32_t carry3;
int32_t carry4;
int32_t carry5;
int32_t carry6;
int32_t carry7;
int32_t carry8;
int32_t carry9;
q = (19 * h9 + ((uint32_t) 1L << 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 * ((uint32_t) 1L << 26);
carry1 = h1 >> 25;
h2 += carry1;
h1 -= carry1 * ((uint32_t) 1L << 25);
carry2 = h2 >> 26;
h3 += carry2;
h2 -= carry2 * ((uint32_t) 1L << 26);
carry3 = h3 >> 25;
h4 += carry3;
h3 -= carry3 * ((uint32_t) 1L << 25);
carry4 = h4 >> 26;
h5 += carry4;
h4 -= carry4 * ((uint32_t) 1L << 26);
carry5 = h5 >> 25;
h6 += carry5;
h5 -= carry5 * ((uint32_t) 1L << 25);
carry6 = h6 >> 26;
h7 += carry6;
h6 -= carry6 * ((uint32_t) 1L << 26);
carry7 = h7 >> 25;
h8 += carry7;
h7 -= carry7 * ((uint32_t) 1L << 25);
carry8 = h8 >> 26;
h9 += carry8;
h8 -= carry8 * ((uint32_t) 1L << 26);
carry9 = h9 >> 25;
h9 -= carry9 * ((uint32_t) 1L << 25);
/* h10 = carry9 */
/*
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.
*/
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
s[3] = (h0 >> 24) | (h1 * ((uint32_t) 1 << 2));
s[4] = h1 >> 6;
s[5] = h1 >> 14;
s[6] = (h1 >> 22) | (h2 * ((uint32_t) 1 << 3));
s[7] = h2 >> 5;
s[8] = h2 >> 13;
s[9] = (h2 >> 21) | (h3 * ((uint32_t) 1 << 5));
s[10] = h3 >> 3;
s[11] = h3 >> 11;
s[12] = (h3 >> 19) | (h4 * ((uint32_t) 1 << 6));
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
s[19] = (h5 >> 24) | (h6 * ((uint32_t) 1 << 1));
s[20] = h6 >> 7;
s[21] = h6 >> 15;
s[22] = (h6 >> 23) | (h7 * ((uint32_t) 1 << 3));
s[23] = h7 >> 5;
s[24] = h7 >> 13;
s[25] = (h7 >> 21) | (h8 * ((uint32_t) 1 << 4));
s[26] = h8 >> 4;
s[27] = h8 >> 12;
s[28] = (h8 >> 20) | (h9 * ((uint32_t) 1 << 6));
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
}
/*
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.
*/
static int
fe_isnegative(const fe f)
{
unsigned char s[32];
fe_tobytes(s, f);
return s[0] & 1;
}
/*
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.
*/
static unsigned char zero[32];
int
fe_isnonzero(const fe f)
{
unsigned char s[32];
fe_tobytes(s, f);
return crypto_verify_32(s, zero);
}
/*
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.
*/
void
fe_mul(fe h, const fe f, const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int32_t g3_19 = 19 * g3;
int32_t g4_19 = 19 * g4;
int32_t g5_19 = 19 * g5;
int32_t g6_19 = 19 * g6;
int32_t g7_19 = 19 * g7;
int32_t g8_19 = 19 * g8;
int32_t g9_19 = 19 * g9;
int32_t f1_2 = 2 * f1;
int32_t f3_2 = 2 * f3;
int32_t f5_2 = 2 * f5;
int32_t f7_2 = 2 * f7;
int32_t f9_2 = 2 * f9;
int64_t f0g0 = f0 * (int64_t) g0;
int64_t f0g1 = f0 * (int64_t) g1;
int64_t f0g2 = f0 * (int64_t) g2;
int64_t f0g3 = f0 * (int64_t) g3;
int64_t f0g4 = f0 * (int64_t) g4;
int64_t f0g5 = f0 * (int64_t) g5;
int64_t f0g6 = f0 * (int64_t) g6;
int64_t f0g7 = f0 * (int64_t) g7;
int64_t f0g8 = f0 * (int64_t) g8;
int64_t f0g9 = f0 * (int64_t) g9;
int64_t f1g0 = f1 * (int64_t) g0;
int64_t f1g1_2 = f1_2 * (int64_t) g1;
int64_t f1g2 = f1 * (int64_t) g2;
int64_t f1g3_2 = f1_2 * (int64_t) g3;
int64_t f1g4 = f1 * (int64_t) g4;
int64_t f1g5_2 = f1_2 * (int64_t) g5;
int64_t f1g6 = f1 * (int64_t) g6;
int64_t f1g7_2 = f1_2 * (int64_t) g7;
int64_t f1g8 = f1 * (int64_t) g8;
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
int64_t f2g0 = f2 * (int64_t) g0;
int64_t f2g1 = f2 * (int64_t) g1;
int64_t f2g2 = f2 * (int64_t) g2;
int64_t f2g3 = f2 * (int64_t) g3;
int64_t f2g4 = f2 * (int64_t) g4;
int64_t f2g5 = f2 * (int64_t) g5;
int64_t f2g6 = f2 * (int64_t) g6;
int64_t f2g7 = f2 * (int64_t) g7;
int64_t f2g8_19 = f2 * (int64_t) g8_19;
int64_t f2g9_19 = f2 * (int64_t) g9_19;
int64_t f3g0 = f3 * (int64_t) g0;
int64_t f3g1_2 = f3_2 * (int64_t) g1;
int64_t f3g2 = f3 * (int64_t) g2;
int64_t f3g3_2 = f3_2 * (int64_t) g3;
int64_t f3g4 = f3 * (int64_t) g4;
int64_t f3g5_2 = f3_2 * (int64_t) g5;
int64_t f3g6 = f3 * (int64_t) g6;
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
int64_t f3g8_19 = f3 * (int64_t) g8_19;
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
int64_t f4g0 = f4 * (int64_t) g0;
int64_t f4g1 = f4 * (int64_t) g1;
int64_t f4g2 = f4 * (int64_t) g2;
int64_t f4g3 = f4 * (int64_t) g3;
int64_t f4g4 = f4 * (int64_t) g4;
int64_t f4g5 = f4 * (int64_t) g5;
int64_t f4g6_19 = f4 * (int64_t) g6_19;
int64_t f4g7_19 = f4 * (int64_t) g7_19;
int64_t f4g8_19 = f4 * (int64_t) g8_19;
int64_t f4g9_19 = f4 * (int64_t) g9_19;
int64_t f5g0 = f5 * (int64_t) g0;
int64_t f5g1_2 = f5_2 * (int64_t) g1;
int64_t f5g2 = f5 * (int64_t) g2;
int64_t f5g3_2 = f5_2 * (int64_t) g3;
int64_t f5g4 = f5 * (int64_t) g4;
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
int64_t f5g6_19 = f5 * (int64_t) g6_19;
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
int64_t f5g8_19 = f5 * (int64_t) g8_19;
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
int64_t f6g0 = f6 * (int64_t) g0;
int64_t f6g1 = f6 * (int64_t) g1;
int64_t f6g2 = f6 * (int64_t) g2;
int64_t f6g3 = f6 * (int64_t) g3;
int64_t f6g4_19 = f6 * (int64_t) g4_19;
int64_t f6g5_19 = f6 * (int64_t) g5_19;
int64_t f6g6_19 = f6 * (int64_t) g6_19;
int64_t f6g7_19 = f6 * (int64_t) g7_19;
int64_t f6g8_19 = f6 * (int64_t) g8_19;
int64_t f6g9_19 = f6 * (int64_t) g9_19;
int64_t f7g0 = f7 * (int64_t) g0;
int64_t f7g1_2 = f7_2 * (int64_t) g1;
int64_t f7g2 = f7 * (int64_t) g2;
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
int64_t f7g4_19 = f7 * (int64_t) g4_19;
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
int64_t f7g6_19 = f7 * (int64_t) g6_19;
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
int64_t f7g8_19 = f7 * (int64_t) g8_19;
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
int64_t f8g0 = f8 * (int64_t) g0;
int64_t f8g1 = f8 * (int64_t) g1;
int64_t f8g2_19 = f8 * (int64_t) g2_19;
int64_t f8g3_19 = f8 * (int64_t) g3_19;
int64_t f8g4_19 = f8 * (int64_t) g4_19;
int64_t f8g5_19 = f8 * (int64_t) g5_19;
int64_t f8g6_19 = f8 * (int64_t) g6_19;
int64_t f8g7_19 = f8 * (int64_t) g7_19;
int64_t f8g8_19 = f8 * (int64_t) g8_19;
int64_t f8g9_19 = f8 * (int64_t) g9_19;
int64_t f9g0 = f9 * (int64_t) g0;
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
int64_t f9g2_19 = f9 * (int64_t) g2_19;
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
int64_t f9g4_19 = f9 * (int64_t) g4_19;
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
int64_t f9g6_19 = f9 * (int64_t) g6_19;
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
int64_t f9g8_19 = f9 * (int64_t) g8_19;
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 +
f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 +
f7g4_19 + f8g3_19 + f9g2_19;
int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 +
f7g5_38 + f8g4_19 + f9g3_38;
int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 +
f7g6_19 + f8g5_19 + f9g4_19;
int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 +
f7g7_38 + f8g6_19 + f9g5_38;
int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 +
f8g7_19 + f9g6_19;
int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 +
f7g9_38 + f8g8_19 + f9g7_38;
int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 +
f8g9_19 + f9g8_19;
int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 +
f8g0 + f9g9_38;
int64_t h9 =
f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t 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 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
h2 += carry1;
h1 -= carry1 * ((uint64_t) 1L << 25);
carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
h6 += carry5;
h5 -= carry5 * ((uint64_t) 1L << 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 + (int64_t)(1L << 25)) >> 26;
h3 += carry2;
h2 -= carry2 * ((uint64_t) 1L << 26);
carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
h7 += carry6;
h6 -= carry6 * ((uint64_t) 1L << 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 + (int64_t)(1L << 24)) >> 25;
h4 += carry3;
h3 -= carry3 * ((uint64_t) 1L << 25);
carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
h8 += carry7;
h7 -= carry7 * ((uint64_t) 1L << 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 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
h9 += carry8;
h8 -= carry8 * ((uint64_t) 1L << 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 + (int64_t)(1L << 24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 * ((uint64_t) 1L << 25);
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h[0] = (int32_t) h0;
h[1] = (int32_t) h1;
h[2] = (int32_t) h2;
h[3] = (int32_t) h3;
h[4] = (int32_t) h4;
h[5] = (int32_t) h5;
h[6] = (int32_t) h6;
h[7] = (int32_t) h7;
h[8] = (int32_t) h8;
h[9] = (int32_t) 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.
*/
static void
fe_neg(fe h, const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t h0 = -f0;
int32_t h1 = -f1;
int32_t h2 = -f2;
int32_t h3 = -f3;
int32_t h4 = -f4;
int32_t h5 = -f5;
int32_t h6 = -f6;
int32_t h7 = -f7;
int32_t h8 = -f8;
int32_t h9 = -f9;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = 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.
*/
void
fe_sq(fe h, const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
h2 += carry1;
h1 -= carry1 * ((uint64_t) 1L << 25);
carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
h6 += carry5;
h5 -= carry5 * ((uint64_t) 1L << 25);
carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
h3 += carry2;
h2 -= carry2 * ((uint64_t) 1L << 26);
carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
h7 += carry6;
h6 -= carry6 * ((uint64_t) 1L << 26);
carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
h4 += carry3;
h3 -= carry3 * ((uint64_t) 1L << 25);
carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
h8 += carry7;
h7 -= carry7 * ((uint64_t) 1L << 25);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
h9 += carry8;
h8 -= carry8 * ((uint64_t) 1L << 26);
carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 * ((uint64_t) 1L << 25);
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
h[0] = (int32_t) h0;
h[1] = (int32_t) h1;
h[2] = (int32_t) h2;
h[3] = (int32_t) h3;
h[4] = (int32_t) h4;
h[5] = (int32_t) h5;
h[6] = (int32_t) h6;
h[7] = (int32_t) h7;
h[8] = (int32_t) h8;
h[9] = (int32_t) h9;
}
/*
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.
*/
static void
fe_sq2(fe h, const fe f)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
h0 += h0;
h1 += h1;
h2 += h2;
h3 += h3;
h4 += h4;
h5 += h5;
h6 += h6;
h7 += h7;
h8 += h8;
h9 += h9;
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
h2 += carry1;
h1 -= carry1 * ((uint64_t) 1L << 25);
carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
h6 += carry5;
h5 -= carry5 * ((uint64_t) 1L << 25);
carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
h3 += carry2;
h2 -= carry2 * ((uint64_t) 1L << 26);
carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
h7 += carry6;
h6 -= carry6 * ((uint64_t) 1L << 26);
carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
h4 += carry3;
h3 -= carry3 * ((uint64_t) 1L << 25);
carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
h8 += carry7;
h7 -= carry7 * ((uint64_t) 1L << 25);
carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
h5 += carry4;
h4 -= carry4 * ((uint64_t) 1L << 26);
carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
h9 += carry8;
h8 -= carry8 * ((uint64_t) 1L << 26);
carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 * ((uint64_t) 1L << 25);
carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
h1 += carry0;
h0 -= carry0 * ((uint64_t) 1L << 26);
h[0] = (int32_t) h0;
h[1] = (int32_t) h1;
h[2] = (int32_t) h2;
h[3] = (int32_t) h3;
h[4] = (int32_t) h4;
h[5] = (int32_t) h5;
h[6] = (int32_t) h6;
h[7] = (int32_t) h7;
h[8] = (int32_t) h8;
h[9] = (int32_t) h9;
}
void
fe_invert(fe out, const fe z)
{
fe t0;
fe t1;
fe t2;
fe t3;
int i;
fe_sq(t0, z);
fe_sq(t1, t0);
fe_sq(t1, t1);
fe_mul(t1, z, t1);
fe_mul(t0, t0, t1);
fe_sq(t2, t0);
fe_mul(t1, t1, t2);
fe_sq(t2, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 20; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 100; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t1, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t1, t1);
}
fe_mul(out, t1, t0);
}
static void
fe_pow22523(fe out, const fe z)
{
fe t0;
fe t1;
fe t2;
int i;
fe_sq(t0, z);
fe_sq(t1, t0);
fe_sq(t1, t1);
fe_mul(t1, z, t1);
fe_mul(t0, t0, t1);
fe_sq(t0, t0);
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 1; i < 5; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 1; i < 10; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, t1, t0);
fe_sq(t2, t1);
for (i = 1; i < 20; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t1, t1);
for (i = 1; i < 10; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t1, t0);
for (i = 1; i < 50; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, t1, t0);
fe_sq(t2, t1);
for (i = 1; i < 100; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t1, t1);
for (i = 1; i < 50; ++i) {
fe_sq(t1, t1);
}
fe_mul(t0, t1, t0);
fe_sq(t0, t0);
fe_sq(t0, t0);
fe_mul(out, t0, z);
}
/*
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_sub(fe h, const fe f, const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t h0 = f0 - g0;
int32_t h1 = f1 - g1;
int32_t h2 = f2 - g2;
int32_t h3 = f3 - g3;
int32_t h4 = f4 - g4;
int32_t h5 = f5 - g5;
int32_t h6 = f6 - g6;
int32_t h7 = f7 - g7;
int32_t h8 = f8 - g8;
int32_t h9 = f9 - g9;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/*
r = p + q
*/
void
ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
{
fe t0;
fe_add(r->X, p->Y, p->X);
fe_sub(r->Y, p->Y, p->X);
fe_mul(r->Z, r->X, q->YplusX);
fe_mul(r->Y, r->Y, q->YminusX);
fe_mul(r->T, q->T2d, p->T);
fe_mul(r->X, p->Z, q->Z);
fe_add(t0, r->X, r->X);
fe_sub(r->X, r->Z, r->Y);
fe_add(r->Y, r->Z, r->Y);
fe_add(r->Z, t0, r->T);
fe_sub(r->T, t0, r->T);
}
static void
slide(signed char *r, const unsigned char *a)
{
int i;
int b;
int k;
int ribs;
int cmp;
for (i = 0; i < 256; ++i) {
r[i] = 1 & (a[i >> 3] >> (i & 7));
}
for (i = 0; i < 256; ++i) {
if (r[i]) {
for (b = 1; b <= 6 && i + b < 256; ++b) {
if (r[i + b]) {
ribs = r[i + b] << b;
cmp = r[i] + ribs;
if (cmp <= 15) {
r[i] = cmp;
r[i + b] = 0;
} else {
cmp = r[i] - ribs;
if (cmp >= -15) {
r[i] = cmp;
for (k = i + b; k < 256; ++k) {
if (!r[k]) {
r[k] = 1;
break;
}
r[k] = 0;
}
} else {
break;
}
}
}
}
}
}
}
static const ge_precomp Bi[8] = {
#include "base2.h"
};
/* 37095705934669439343138083508754565189542113879843219016388785533085940283555
*/
static const fe d = { -10913610, 13857413, -15372611, 6949391, 114729,
-8787816, -6275908, -3247719, -18696448, -12055116 };
/* sqrt(-1) */
static const fe sqrtm1 = { -32595792, -7943725, 9377950, 3500415, 12389472,
-272473, -25146209, -2005654, 326686, 11406482 };
int
ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s)
{
fe u;
fe v;
fe v3;
fe vxx;
fe check;
fe_frombytes(h->Y, s);
fe_1(h->Z);
fe_sq(u, h->Y);
fe_mul(v, u, d);
fe_sub(u, u, h->Z); /* u = y^2-1 */
fe_add(v, v, h->Z); /* v = dy^2+1 */
fe_sq(v3, v);
fe_mul(v3, v3, v); /* v3 = v^3 */
fe_sq(h->X, v3);
fe_mul(h->X, h->X, v);
fe_mul(h->X, h->X, u); /* x = uv^7 */
fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
fe_mul(h->X, h->X, v3);
fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
fe_sq(vxx, h->X);
fe_mul(vxx, vxx, v);
fe_sub(check, vxx, u); /* vx^2-u */
if (fe_isnonzero(check)) {
fe_add(check, vxx, u); /* vx^2+u */
if (fe_isnonzero(check)) {
return -1;
}
fe_mul(h->X, h->X, sqrtm1);
}
if (fe_isnegative(h->X) == (s[31] >> 7)) {
fe_neg(h->X, h->X);
}
fe_mul(h->T, h->X, h->Y);
return 0;
}
/*
r = p + q
*/
static void
ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
{
fe t0;
fe_add(r->X, p->Y, p->X);
fe_sub(r->Y, p->Y, p->X);
fe_mul(r->Z, r->X, q->yplusx);
fe_mul(r->Y, r->Y, q->yminusx);
fe_mul(r->T, q->xy2d, p->T);
fe_add(t0, p->Z, p->Z);
fe_sub(r->X, r->Z, r->Y);
fe_add(r->Y, r->Z, r->Y);
fe_add(r->Z, t0, r->T);
fe_sub(r->T, t0, r->T);
}
/*
r = p - q
*/
static void
ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
{
fe t0;
fe_add(r->X, p->Y, p->X);
fe_sub(r->Y, p->Y, p->X);
fe_mul(r->Z, r->X, q->yminusx);
fe_mul(r->Y, r->Y, q->yplusx);
fe_mul(r->T, q->xy2d, p->T);
fe_add(t0, p->Z, p->Z);
fe_sub(r->X, r->Z, r->Y);
fe_add(r->Y, r->Z, r->Y);
fe_sub(r->Z, t0, r->T);
fe_add(r->T, t0, r->T);
}
/*
r = p
*/
void
ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
{
fe_mul(r->X, p->X, p->T);
fe_mul(r->Y, p->Y, p->Z);
fe_mul(r->Z, p->Z, p->T);
}
/*
r = p
*/
static void
ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
{
fe_mul(r->X, p->X, p->T);
fe_mul(r->Y, p->Y, p->Z);
fe_mul(r->Z, p->Z, p->T);
fe_mul(r->T, p->X, p->Y);
}
static void
ge_p2_0(ge_p2 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
}
/*
r = 2 * p
*/
static void
ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
{
fe t0;
fe_sq(r->X, p->X);
fe_sq(r->Z, p->Y);
fe_sq2(r->T, p->Z);
fe_add(r->Y, p->X, p->Y);
fe_sq(t0, r->Y);
fe_add(r->Y, r->Z, r->X);
fe_sub(r->Z, r->Z, r->X);
fe_sub(r->X, t0, r->Y);
fe_sub(r->T, r->T, r->Z);
}
static void
ge_p3_0(ge_p3 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
fe_0(h->T);
}
/*
r = p
*/
/* 2 * d =
* 16295367250680780974490674513165176452449235426866156013048779062215315747161
*/
static const fe d2 = { -21827239, -5839606, -30745221, 13898782, 229458,
15978800, -12551817, -6495438, 29715968, 9444199 };
void
ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
{
fe_add(r->YplusX, p->Y, p->X);
fe_sub(r->YminusX, p->Y, p->X);
fe_copy(r->Z, p->Z);
fe_mul(r->T2d, p->T, d2);
}
/*
r = p
*/
static void
ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
{
fe_copy(r->X, p->X);
fe_copy(r->Y, p->Y);
fe_copy(r->Z, p->Z);
}
void
ge_p3_tobytes(unsigned char *s, const ge_p3 *h)
{
fe recip;
fe x;
fe y;
fe_invert(recip, h->Z);
fe_mul(x, h->X, recip);
fe_mul(y, h->Y, recip);
fe_tobytes(s, y);
s[31] ^= fe_isnegative(x) << 7;
}
/*
r = 2 * p
*/
static void
ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
{
ge_p2 q;
ge_p3_to_p2(&q, p);
ge_p2_dbl(r, &q);
}
static void
ge_precomp_0(ge_precomp *h)
{
fe_1(h->yplusx);
fe_1(h->yminusx);
fe_0(h->xy2d);
}
static unsigned char
equal(signed char b, signed char c)
{
unsigned char ub = b;
unsigned char uc = c;
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
uint32_t y = x; /* 0: yes; 1..255: no */
y -= 1; /* 4294967295: yes; 0..254: no */
y >>= 31; /* 1: yes; 0: no */
return y;
}
static unsigned char
negative(signed char b)
{
uint64_t x =
b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
x >>= 63; /* 1: yes; 0: no */
return x;
}
static void
cmov(ge_precomp *t, const ge_precomp *u, unsigned char b)
{
fe_cmov(t->yplusx, u->yplusx, b);
fe_cmov(t->yminusx, u->yminusx, b);
fe_cmov(t->xy2d, u->xy2d, b);
}
/* base[i][j] = (j+1)*256^i*B */
static const ge_precomp base[32][8] = {
#include "base.h"
};
static void
ge_select(ge_precomp *t, int pos, signed char b)
{
ge_precomp minust;
unsigned char bnegative = negative(b);
unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1));
ge_precomp_0(t);
cmov(t, &base[pos][0], equal(babs, 1));
cmov(t, &base[pos][1], equal(babs, 2));
cmov(t, &base[pos][2], equal(babs, 3));
cmov(t, &base[pos][3], equal(babs, 4));
cmov(t, &base[pos][4], equal(babs, 5));
cmov(t, &base[pos][5], equal(babs, 6));
cmov(t, &base[pos][6], equal(babs, 7));
cmov(t, &base[pos][7], equal(babs, 8));
fe_copy(minust.yplusx, t->yminusx);
fe_copy(minust.yminusx, t->yplusx);
fe_neg(minust.xy2d, t->xy2d);
cmov(t, &minust, bnegative);
}
/*
r = p - q
*/
static void
ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
{
fe t0;
fe_add(r->X, p->Y, p->X);
fe_sub(r->Y, p->Y, p->X);
fe_mul(r->Z, r->X, q->YminusX);
fe_mul(r->Y, r->Y, q->YplusX);
fe_mul(r->T, q->T2d, p->T);
fe_mul(r->X, p->Z, q->Z);
fe_add(t0, r->X, r->X);
fe_sub(r->X, r->Z, r->Y);
fe_add(r->Y, r->Z, r->Y);
fe_sub(r->Z, t0, r->T);
fe_add(r->T, t0, r->T);
}
void
ge_tobytes(unsigned char *s, const ge_p2 *h)
{
fe recip;
fe x;
fe y;
fe_invert(recip, h->Z);
fe_mul(x, h->X, recip);
fe_mul(y, h->Y, recip);
fe_tobytes(s, y);
s[31] ^= fe_isnegative(x) << 7;
}
/*
h = a * B
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.
*
Preconditions:
a[31] <= 127
*/
/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/
void
ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A,
const unsigned char *b)
{
signed char aslide[256];
signed char bslide[256];
ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
slide(aslide, a);
slide(bslide, b);
ge_p3_to_cached(&Ai[0], A);
ge_p3_dbl(&t, A);
ge_p1p1_to_p3(&A2, &t);
ge_add(&t, &A2, &Ai[0]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[1], &u);
ge_add(&t, &A2, &Ai[1]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[2], &u);
ge_add(&t, &A2, &Ai[2]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[3], &u);
ge_add(&t, &A2, &Ai[3]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[4], &u);
ge_add(&t, &A2, &Ai[4]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[5], &u);
ge_add(&t, &A2, &Ai[5]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[6], &u);
ge_add(&t, &A2, &Ai[6]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[7], &u);
ge_p2_0(r);
for (i = 255; i >= 0; --i) {
if (aslide[i] || bslide[i])
break;
}
for (; i >= 0; --i) {
ge_p2_dbl(&t, r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Ai[aslide[i] / 2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
}
if (bslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_madd(&t, &u, &Bi[bslide[i] / 2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
}
ge_p1p1_to_p2(r, &t);
}
}
#ifndef MINIMAL
/* only used for verification of legacy (edwards25519sha512batch) signatures */
void
ge_scalarmult_vartime(ge_p3 *r, const unsigned char *a, const ge_p3 *A)
{
signed char aslide[256];
ge_cached Ai[8];
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
slide(aslide, a);
ge_p3_to_cached(&Ai[0], A);
ge_p3_dbl(&t, A);
ge_p1p1_to_p3(&A2, &t);
ge_add(&t, &A2, &Ai[0]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[1], &u);
ge_add(&t, &A2, &Ai[1]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[2], &u);
ge_add(&t, &A2, &Ai[2]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[3], &u);
ge_add(&t, &A2, &Ai[3]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[4], &u);
ge_add(&t, &A2, &Ai[4]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[5], &u);
ge_add(&t, &A2, &Ai[5]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[6], &u);
ge_add(&t, &A2, &Ai[6]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[7], &u);
ge_p3_0(r);
for (i = 255; i >= 0; --i) {
if (aslide[i])
break;
}
for (; i >= 0; --i) {
ge_p3_dbl(&t, r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Ai[aslide[i] / 2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
}
ge_p1p1_to_p3(r, &t);
}
}
#endif
void
ge_scalarmult_base(ge_p3 *h, const unsigned char *a)
{
signed char e[64];
signed char carry;
ge_p1p1 r;
ge_p2 s;
ge_precomp t;
int i;
for (i = 0; i < 32; ++i) {
e[2 * i + 0] = (a[i] >> 0) & 15;
e[2 * i + 1] = (a[i] >> 4) & 15;
}
/* each e[i] is between 0 and 15 */
/* e[63] is between 0 and 7 */
carry = 0;
for (i = 0; i < 63; ++i) {
e[i] += carry;
carry = e[i] + 8;
carry >>= 4;
e[i] -= carry * ((signed char) 1 << 4);
}
e[63] += carry;
/* each e[i] is between -8 and 8 */
ge_p3_0(h);
for (i = 1; i < 64; i += 2) {
ge_select(&t, i / 2, e[i]);
ge_madd(&r, h, &t);
ge_p1p1_to_p3(h, &r);
}
ge_p3_dbl(&r, h);
ge_p1p1_to_p2(&s, &r);
ge_p2_dbl(&r, &s);
ge_p1p1_to_p2(&s, &r);
ge_p2_dbl(&r, &s);
ge_p1p1_to_p2(&s, &r);
ge_p2_dbl(&r, &s);
ge_p1p1_to_p3(h, &r);
for (i = 0; i < 64; i += 2) {
ge_select(&t, i / 2, e[i]);
ge_madd(&r, h, &t);
ge_p1p1_to_p3(h, &r);
}
}
/* multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 */
void
ge_mul_l(ge_p3 *r, const ge_p3 *A)
{
static const signed char aslide[253] = {
13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
};
ge_cached Ai[8];
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
ge_p3_to_cached(&Ai[0], A);
ge_p3_dbl(&t, A);
ge_p1p1_to_p3(&A2, &t);
ge_add(&t, &A2, &Ai[0]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[1], &u);
ge_add(&t, &A2, &Ai[1]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[2], &u);
ge_add(&t, &A2, &Ai[2]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[3], &u);
ge_add(&t, &A2, &Ai[3]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[4], &u);
ge_add(&t, &A2, &Ai[4]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[5], &u);
ge_add(&t, &A2, &Ai[5]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[6], &u);
ge_add(&t, &A2, &Ai[6]);
ge_p1p1_to_p3(&u, &t);
ge_p3_to_cached(&Ai[7], &u);
ge_p3_0(r);
for (i = 252; i >= 0; --i) {
ge_p3_dbl(&t, r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u, &t);
ge_add(&t, &u, &Ai[aslide[i] / 2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u, &t);
ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
}
ge_p1p1_to_p3(r, &t);
}
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
*
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
void
sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b,
const unsigned char *c)
{
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t c0 = 2097151 & load_3(c);
int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
int64_t c8 = 2097151 & load_3(c + 21);
int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
int64_t c11 = (load_4(c + 28) >> 7);
int64_t s0;
int64_t s1;
int64_t s2;
int64_t s3;
int64_t s4;
int64_t s5;
int64_t s6;
int64_t s7;
int64_t s8;
int64_t s9;
int64_t s10;
int64_t s11;
int64_t s12;
int64_t s13;
int64_t s14;
int64_t s15;
int64_t s16;
int64_t s17;
int64_t s18;
int64_t s19;
int64_t s20;
int64_t s21;
int64_t s22;
int64_t s23;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
int64_t carry17;
int64_t carry18;
int64_t carry19;
int64_t carry20;
int64_t carry21;
int64_t carry22;
s0 = c0 + a0 * b0;
s1 = c1 + a0 * b1 + a1 * b0;
s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 +
a6 * b0;
s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
a6 * b1 + a7 * b0;
s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
a6 * b2 + a7 * b1 + a8 * b0;
s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 +
a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 +
a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 +
a9 * b5 + a10 * b4 + a11 * b3;
s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 +
a10 * b5 + a11 * b4;
s16 =
a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
s20 = a9 * b11 + a10 * b10 + a11 * b9;
s21 = a10 * b11 + a11 * b10;
s22 = a11 * b11;
s23 = 0;
carry0 = (s0 + (int64_t)(1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t)(1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t)(1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t)(1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t)(1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t)(1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t)(1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t)(1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t)(1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry18 = (s18 + (int64_t)(1L << 20)) >> 21;
s19 += carry18;
s18 -= carry18 * ((uint64_t) 1L << 21);
carry20 = (s20 + (int64_t)(1L << 20)) >> 21;
s21 += carry20;
s20 -= carry20 * ((uint64_t) 1L << 21);
carry22 = (s22 + (int64_t)(1L << 20)) >> 21;
s23 += carry22;
s22 -= carry22 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t)(1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t)(1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t)(1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t)(1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t)(1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t)(1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t)(1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t)(1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
carry17 = (s17 + (int64_t)(1L << 20)) >> 21;
s18 += carry17;
s17 -= carry17 * ((uint64_t) 1L << 21);
carry19 = (s19 + (int64_t)(1L << 20)) >> 21;
s20 += carry19;
s19 -= carry19 * ((uint64_t) 1L << 21);
carry21 = (s21 + (int64_t)(1L << 20)) >> 21;
s22 += carry21;
s21 -= carry21 * ((uint64_t) 1L << 21);
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (int64_t)(1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t)(1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t)(1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t)(1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t)(1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t)(1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t)(1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t)(1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t)(1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t)(1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t)(1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (int64_t)(1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t)(1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t)(1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t)(1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t)(1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t)(1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t)(1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t)(1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t)(1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t)(1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t)(1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t)(1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/*
Input:
s[0]+256*s[1]+...+256^63*s[63] = s
*
Output:
s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
void
sc_reduce(unsigned char *s)
{
int64_t s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
int64_t s16 = 2097151 & load_3(s + 42);
int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
int64_t s23 = (load_4(s + 60) >> 3);
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (int64_t)(1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t)(1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t)(1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t)(1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t)(1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t)(1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t)(1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t)(1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t)(1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t)(1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t)(1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (int64_t)(1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t)(1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t)(1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t)(1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t)(1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t)(1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t)(1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t)(1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t)(1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t)(1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t)(1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t)(1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}