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-rw-r--r--3rd_party/ed25519/fe.c1491
1 files changed, 1491 insertions, 0 deletions
diff --git a/3rd_party/ed25519/fe.c b/3rd_party/ed25519/fe.c
new file mode 100644
index 0000000..2105eb7
--- /dev/null
+++ b/3rd_party/ed25519/fe.c
@@ -0,0 +1,1491 @@
+#include "fixedint.h"
+#include "fe.h"
+
+
+/*
+ helper functions
+*/
+static 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 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) {
+ h[0] = 0;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+ h[4] = 0;
+ h[5] = 0;
+ h[6] = 0;
+ h[7] = 0;
+ h[8] = 0;
+ h[9] = 0;
+}
+
+
+
+/*
+ h = 1
+*/
+
+void fe_1(fe h) {
+ h[0] = 1;
+ h[1] = 0;
+ h[2] = 0;
+ h[3] = 0;
+ h[4] = 0;
+ h[5] = 0;
+ h[6] = 0;
+ h[7] = 0;
+ h[8] = 0;
+ h[9] = 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}.
+*/
+
+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); /* silence warning */
+ 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;
+}
+
+/*
+ Replace (f,g) with (g,f) if b == 1;
+ replace (f,g) with (f,g) if b == 0.
+
+ Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,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); /* silence warning */
+ 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;
+ g[0] = g0 ^ x0;
+ g[1] = g1 ^ x1;
+ g[2] = g2 ^ x2;
+ g[3] = g3 ^ x3;
+ g[4] = g4 ^ x4;
+ g[5] = g5 ^ x5;
+ g[6] = g6 ^ x6;
+ g[7] = g7 ^ x7;
+ g[8] = g8 ^ x8;
+ g[9] = g9 ^ 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) (1 << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 << 25;
+ carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 << 25;
+ carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 << 25;
+ carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 << 25;
+ carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 << 25;
+ carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 26;
+ carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 << 26;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 << 26;
+ carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 << 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);
+
+ for (i = 1; i < 1; ++i) {
+ fe_sq(t0, t0);
+ }
+
+ fe_sq(t1, t0);
+
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t1, t1);
+ }
+
+ fe_mul(t1, z, t1);
+ fe_mul(t0, t0, t1);
+ fe_sq(t2, t0);
+
+ for (i = 1; i < 1; ++i) {
+ fe_sq(t2, t2);
+ }
+
+ 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);
+}
+
+
+
+/*
+ return 1 if f is in {1,3,5,...,q-2}
+ return 0 if f is in {0,2,4,...,q-1}
+
+ Preconditions:
+ |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f) {
+ 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.
+*/
+
+int fe_isnonzero(const fe f) {
+ unsigned char s[32];
+ unsigned char r;
+
+ fe_tobytes(s, f);
+
+ r = s[0];
+ #define F(i) r |= s[i]
+ F(1);
+ F(2);
+ F(3);
+ F(4);
+ F(5);
+ F(6);
+ F(7);
+ F(8);
+ F(9);
+ F(10);
+ F(11);
+ F(12);
+ F(13);
+ F(14);
+ F(15);
+ F(16);
+ F(17);
+ F(18);
+ F(19);
+ F(20);
+ F(21);
+ F(22);
+ F(23);
+ F(24);
+ F(25);
+ F(26);
+ F(27);
+ F(28);
+ F(29);
+ F(30);
+ F(31);
+ #undef F
+
+ return r != 0;
+}
+
+
+
+/*
+ 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;
+
+ carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 26;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+
+ carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 << 25;
+ carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 << 25;
+
+ carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 << 26;
+ carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 << 26;
+
+ carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 << 25;
+ carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 << 25;
+
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 << 26;
+
+ carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 << 25;
+
+ carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 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 = f * 121666
+Can overlap h with f.
+
+Preconditions:
+ |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+ |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h, 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];
+ int64_t h0 = f0 * (int64_t) 121666;
+ int64_t h1 = f1 * (int64_t) 121666;
+ int64_t h2 = f2 * (int64_t) 121666;
+ int64_t h3 = f3 * (int64_t) 121666;
+ int64_t h4 = f4 * (int64_t) 121666;
+ int64_t h5 = f5 * (int64_t) 121666;
+ int64_t h6 = f6 * (int64_t) 121666;
+ int64_t h7 = f7 * (int64_t) 121666;
+ int64_t h8 = f8 * (int64_t) 121666;
+ int64_t h9 = f9 * (int64_t) 121666;
+ 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) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+ carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+ carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+ carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+ carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+ carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 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 = -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.
+*/
+
+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;
+}
+
+
+void fe_pow22523(fe out, const fe z) {
+ fe t0;
+ fe t1;
+ fe t2;
+ int i;
+ fe_sq(t0, z);
+
+ for (i = 1; i < 1; ++i) {
+ fe_sq(t0, t0);
+ }
+
+ fe_sq(t1, t0);
+
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t1, t1);
+ }
+
+ fe_mul(t1, z, t1);
+ fe_mul(t0, t0, t1);
+ fe_sq(t0, t0);
+
+ for (i = 1; i < 1; ++i) {
+ 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);
+
+ for (i = 1; i < 2; ++i) {
+ fe_sq(t0, t0);
+ }
+
+ fe_mul(out, t0, z);
+ return;
+}
+
+
+/*
+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) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 26;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 << 25;
+ carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 << 25;
+ carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 << 26;
+ carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 << 26;
+ carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 << 25;
+ carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 << 25;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 << 26;
+ carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 << 25;
+ carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 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.
+*/
+
+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) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 26;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 << 25;
+ carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 << 25;
+ carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 << 26;
+ carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 << 26;
+ carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 << 25;
+ carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 << 25;
+ carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 << 26;
+ carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 << 25;
+ carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 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 = 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;
+}
+
+
+
+/*
+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 + (((int32_t) 1) << 24)) >> 25;
+ q = (h0 + q) >> 26;
+ q = (h1 + q) >> 25;
+ q = (h2 + q) >> 26;
+ q = (h3 + q) >> 25;
+ q = (h4 + q) >> 26;
+ q = (h5 + q) >> 25;
+ q = (h6 + q) >> 26;
+ q = (h7 + q) >> 25;
+ q = (h8 + q) >> 26;
+ q = (h9 + q) >> 25;
+ /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+ h0 += 19 * q;
+ /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+ carry0 = h0 >> 26;
+ h1 += carry0;
+ h0 -= carry0 << 26;
+ carry1 = h1 >> 25;
+ h2 += carry1;
+ h1 -= carry1 << 25;
+ carry2 = h2 >> 26;
+ h3 += carry2;
+ h2 -= carry2 << 26;
+ carry3 = h3 >> 25;
+ h4 += carry3;
+ h3 -= carry3 << 25;
+ carry4 = h4 >> 26;
+ h5 += carry4;
+ h4 -= carry4 << 26;
+ carry5 = h5 >> 25;
+ h6 += carry5;
+ h5 -= carry5 << 25;
+ carry6 = h6 >> 26;
+ h7 += carry6;
+ h6 -= carry6 << 26;
+ carry7 = h7 >> 25;
+ h8 += carry7;
+ h7 -= carry7 << 25;
+ carry8 = h8 >> 26;
+ h9 += carry8;
+ h8 -= carry8 << 26;
+ carry9 = h9 >> 25;
+ h9 -= carry9 << 25;
+
+ /* h10 = carry9 */
+ /*
+ 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] = (unsigned char) (h0 >> 0);
+ s[1] = (unsigned char) (h0 >> 8);
+ s[2] = (unsigned char) (h0 >> 16);
+ s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
+ s[4] = (unsigned char) (h1 >> 6);
+ s[5] = (unsigned char) (h1 >> 14);
+ s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
+ s[7] = (unsigned char) (h2 >> 5);
+ s[8] = (unsigned char) (h2 >> 13);
+ s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
+ s[10] = (unsigned char) (h3 >> 3);
+ s[11] = (unsigned char) (h3 >> 11);
+ s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
+ s[13] = (unsigned char) (h4 >> 2);
+ s[14] = (unsigned char) (h4 >> 10);
+ s[15] = (unsigned char) (h4 >> 18);
+ s[16] = (unsigned char) (h5 >> 0);
+ s[17] = (unsigned char) (h5 >> 8);
+ s[18] = (unsigned char) (h5 >> 16);
+ s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
+ s[20] = (unsigned char) (h6 >> 7);
+ s[21] = (unsigned char) (h6 >> 15);
+ s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
+ s[23] = (unsigned char) (h7 >> 5);
+ s[24] = (unsigned char) (h7 >> 13);
+ s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
+ s[26] = (unsigned char) (h8 >> 4);
+ s[27] = (unsigned char) (h8 >> 12);
+ s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
+ s[29] = (unsigned char) (h9 >> 2);
+ s[30] = (unsigned char) (h9 >> 10);
+ s[31] = (unsigned char) (h9 >> 18);
+}
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