diff options
Diffstat (limited to 'src/libstrongswan/plugins/curve25519/ref10/ref10.c')
| -rw-r--r-- | src/libstrongswan/plugins/curve25519/ref10/ref10.c | 2731 |
1 files changed, 2731 insertions, 0 deletions
diff --git a/src/libstrongswan/plugins/curve25519/ref10/ref10.c b/src/libstrongswan/plugins/curve25519/ref10/ref10.c new file mode 100644 index 000000000..1e6ff778e --- /dev/null +++ b/src/libstrongswan/plugins/curve25519/ref10/ref10.c @@ -0,0 +1,2731 @@ +/* + * Copyright (C) 2016 Andreas Steffen + * HSR Hochschule fuer Technik Rapperswil + * + * Based on the public domain libsodium adaptation by Frank Denis + * of the SUPERCOP ref10 implementation by Daniel J. Bernstein, + * Niels Duif, Peter Schwabe, Tanja Lange and Bo-Yin Yang. + */ + +#include <stddef.h> +#include <stdint.h> +#include <string.h> + +#include "ref10.h" + +#include <utils/utils.h> + +static uint64_t load_3(const uint8_t *in) +{ + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + + return result; +} + +static uint64_t load_4(const uint8_t *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 + */ +static void fe_0(fe h) +{ + memset(&h[0], 0, 10 * sizeof h[0]); +} + +/** + * h = 1 + */ +static 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. + */ +static 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 + */ +static 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. + */ +static void fe_frombytes(fe h, const uint8_t *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, carry1, carry2, carry3, carry4; + int64_t carry5, carry6, carry7, carry8, 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 fe_tobytes(uint8_t *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 carry0, carry1, carry2, carry3, carry4; + int32_t carry5, carry6, carry7, carry8, carry9; + int32_t q; + + 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) +{ + uint8_t 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 uint8_t zero[32]; + +static int fe_isnonzero(const fe f) +{ + uint8_t s[32]; + + fe_tobytes(s, f); + + return !memeq_const(s, zero, 32); +} + +/** + * 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. + */ + +static 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, carry1, carry2, carry3, carry4; + int64_t carry5, carry6, carry7, carry8, 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); + /* |h0| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + /* |h4| <= 2^25 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = (h1 + (int64_t) (1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + + carry5 = (h5 + (int64_t) (1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = (h2 + (int64_t) (1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + + carry6 = (h6 + (int64_t) (1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h7| <= 1.71*2^59 */ + + carry3 = (h3 + (int64_t) (1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + + carry7 = (h7 + (int64_t) (1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h8| <= 1.41*2^60 */ + + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + + carry8 = (h8 + (int64_t) (1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |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. + */ +static 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, carry1, carry2, carry3, carry4; + int64_t carry5, carry6, carry7, carry8, 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, carry1, carry2, carry3, carry4; + int64_t carry5, carry6, carry7, carry8, 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; +} + +static void fe_invert(fe out, const fe z) +{ + fe t0, t1, t2, 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, t1, 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. + */ +static 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 + */ +static 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(int8_t *r, const uint8_t *a) +{ + int i, b, k; + + 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]) + { + if (r[i] + (r[i + b] << b) <= 15) + { + r[i] += r[i + b] << b; r[i + b] = 0; + } + else if (r[i] - (r[i + b] << b) >= -15) + { + r[i] -= r[i + b] << b; + + 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 uint8_t *s) +{ + fe u, v, v3, vxx, 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 + */ +static 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 +}; + +static 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(uint8_t *s, const ge_p3 *h) +{ + fe recip, x, 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 uint8_t equal(int8_t b, int8_t c) +{ + uint8_t ub = b; + uint8_t uc = c; + uint8_t 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 uint8_t negative(int8_t 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, uint8_t 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, int8_t b) +{ + ge_precomp minust; + uint8_t bnegative = negative(b); + uint8_t babs = b - (((-bnegative) & b) * ((int8_t) 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(uint8_t *s, const ge_p2 *h) +{ + fe recip, x, 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 uint8_t *a, const ge_p3 *A, + const uint8_t *b) +{ + int8_t aslide[256]; + int8_t bslide[256]; + ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge_p1p1 t; + ge_p3 u, 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); + } +} + +void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) +{ + int8_t e[64]; + int8_t carry = 0; + 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 */ + + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry * ((int8_t) 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); + } +} + +/** + * 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(uint8_t *s, const uint8_t *a, const uint8_t *b, const uint8_t *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, s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11; + int64_t s12, s13, s14, s15, s16, s17, s18, s19, s20, s21, s22, s23; + + int64_t carry0, carry1, carry2, carry3, carry4, carry5, carry6; + int64_t carry7, carry8, carry9, carry10, carry11, carry12, carry13; + int64_t carry14, carry15, carry16, carry17, carry18, carry19, carry20; + int64_t carry21, 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(uint8_t *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, carry1, carry2, carry3, carry4, carry5, carry6; + int64_t carry7, carry8, carry9, carry10, carry11, carry12, carry13; + int64_t carry14, carry15, 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; +} |