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/*
Ignores top bit of h.
*/
void
fe25519_frombytes(fe25519 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.
*/
static void
fe25519_reduce(fe25519 h, const fe25519 f)
{
int32_t h0 = f[0];
int32_t h1 = f[1];
int32_t h2 = f[2];
int32_t h3 = f[3];
int32_t h4 = f[4];
int32_t h5 = f[5];
int32_t h6 = f[6];
int32_t h7 = f[7];
int32_t h8 = f[8];
int32_t h9 = f[9];
int32_t q;
int32_t carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, 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);
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;
}
/*
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.
*/
void
fe25519_tobytes(unsigned char *s, const fe25519 h)
{
fe25519 t;
fe25519_reduce(t, h);
s[0] = t[0] >> 0;
s[1] = t[0] >> 8;
s[2] = t[0] >> 16;
s[3] = (t[0] >> 24) | (t[1] * ((uint32_t) 1 << 2));
s[4] = t[1] >> 6;
s[5] = t[1] >> 14;
s[6] = (t[1] >> 22) | (t[2] * ((uint32_t) 1 << 3));
s[7] = t[2] >> 5;
s[8] = t[2] >> 13;
s[9] = (t[2] >> 21) | (t[3] * ((uint32_t) 1 << 5));
s[10] = t[3] >> 3;
s[11] = t[3] >> 11;
s[12] = (t[3] >> 19) | (t[4] * ((uint32_t) 1 << 6));
s[13] = t[4] >> 2;
s[14] = t[4] >> 10;
s[15] = t[4] >> 18;
s[16] = t[5] >> 0;
s[17] = t[5] >> 8;
s[18] = t[5] >> 16;
s[19] = (t[5] >> 24) | (t[6] * ((uint32_t) 1 << 1));
s[20] = t[6] >> 7;
s[21] = t[6] >> 15;
s[22] = (t[6] >> 23) | (t[7] * ((uint32_t) 1 << 3));
s[23] = t[7] >> 5;
s[24] = t[7] >> 13;
s[25] = (t[7] >> 21) | (t[8] * ((uint32_t) 1 << 4));
s[26] = t[8] >> 4;
s[27] = t[8] >> 12;
s[28] = (t[8] >> 20) | (t[9] * ((uint32_t) 1 << 6));
s[29] = t[9] >> 2;
s[30] = t[9] >> 10;
s[31] = t[9] >> 18;
}
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