#include "config.h"
+#include "ct.h"
#include "fgoldi.h"
/*----- Basic setup -------------------------------------------------------*
for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i];
}
+/* --- @fgoldi_neg@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z = -x@.
+ */
+
+void fgoldi_neg(fgoldi *z, const fgoldi *x)
+{
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = -x->P[i];
+}
+
/*----- Constant-time utilities -------------------------------------------*/
+/* --- @fgoldi_pick2@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
+ * @z = x@. If @m@ has some other value, then scramble @z@ in
+ * an unhelpful way.
+ */
+
+void fgoldi_pick2(fgoldi *z, const fgoldi *x, const fgoldi *y, uint32 m)
+{
+ mask32 mm = FIX_MASK32(m);
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = PICK2(x->P[i], y->P[i], mm);
+}
+
+/* --- @fgoldi_pickn@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result
+ * @const fgoldi *v@ = a table of entries
+ * @size_t n@ = the number of entries in @v@
+ * @size_t i@ = an index
+ *
+ * Returns: ---
+ *
+ * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
+ * do something unhelpful; otherwise, if @i >= n@ then set @z@
+ * to zero.
+ */
+
+void fgoldi_pickn(fgoldi *z, const fgoldi *v, size_t n, size_t i)
+{
+ uint32 b = (uint32)1 << (31 - i);
+ mask32 m;
+ unsigned j;
+
+ for (j = 0; j < NPIECE; j++) z->P[j] = 0;
+ while (n--) {
+ m = SIGN(b);
+ for (j = 0; j < NPIECE; j++) CONDPICK(z->P[j], v->P[j], m);
+ v++; b <<= 1;
+ }
+}
+
/* --- @fgoldi_condswap@ --- *
*
* Arguments: @fgoldi *x, *y@ = two operands
for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm);
}
+/* --- @fgoldi_condneg@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
+ * @z = -x@. If @m@ has some other value then scramble @z@ in
+ * an unhelpful way.
+ */
+
+void fgoldi_condneg(fgoldi *z, const fgoldi *x, uint32 m)
+{
+#ifdef NEG_TWOC
+ mask32 m_xor = FIX_MASK32(m);
+ piece m_add = m&1;
+# define CONDNEG(x) (((x) ^ m_xor) + m_add)
+#else
+ int s = PICK2(-1, +1, m);
+# define CONDNEG(x) (s*(x))
+#endif
+
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = CONDNEG(x->P[i]);
+
+#undef CONDNEG
+}
+
/*----- Multiplication ----------------------------------------------------*/
#if FGOLDI_IMPL == 28
#undef SQRN
}
+/* --- @fgoldi_quosqrt@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
+ *
+ * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
+ * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
+ * \ne 0$% then the operation fails. If you wanted a specific
+ * square root then you'll have to pick it yourself.
+ */
+
+int fgoldi_quosqrt(fgoldi *z, const fgoldi *x, const fgoldi *y)
+{
+ fgoldi t, u, v;
+ octet xb[56], b0[56];
+ int32 rc = -1;
+ mask32 m;
+ unsigned i;
+
+#define SQRN(z, x, n) do { \
+ fgoldi_sqr((z), (x)); \
+ for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \
+} while (0)
+
+ /* This is, fortunately, significantly easier than the equivalent problem
+ * in GF(2^255 - 19), since p == 3 (mod 4).
+ *
+ * If x/y is square, then so is v = y^2 x/y = x y, and therefore u has
+ * order r = (p - 1)/2. Let w = v^{(p-3)/4}. Then w^2 = v^{(p-3)/2} =
+ * u^{r-1} = 1/v = 1/x y. Clearly, then, (x w)^2 = x^2/x y = x/y, so x w
+ * is one of the square roots we seek.
+ *
+ * The addition chain, then, is a prefix of the previous one.
+ */
+ fgoldi_mul(&v, x, y);
+
+ fgoldi_sqr(&u, &v); /* 1 | 2 */
+ fgoldi_mul(&t, &u, &v); /* 2 | 3 */
+ SQRN(&u, &t, 2); /* 4 | 12 */
+ fgoldi_mul(&t, &u, &t); /* 5 | 15 */
+ SQRN(&u, &t, 4); /* 9 | 240 */
+ fgoldi_mul(&u, &u, &t); /* 10 | 255 = 2^8 - 1 */
+ SQRN(&u, &u, 4); /* 14 | 2^12 - 16 */
+ fgoldi_mul(&t, &u, &t); /* 15 | 2^12 - 1 */
+ SQRN(&u, &t, 12); /* 27 | 2^24 - 2^12 */
+ fgoldi_mul(&u, &u, &t); /* 28 | 2^24 - 1 */
+ SQRN(&u, &u, 12); /* 40 | 2^36 - 2^12 */
+ fgoldi_mul(&t, &u, &t); /* 41 | 2^36 - 1 */
+ fgoldi_sqr(&t, &t); /* 42 | 2^37 - 2 */
+ fgoldi_mul(&t, &t, &v); /* 43 | 2^37 - 1 */
+ SQRN(&u, &t, 37); /* 80 | 2^74 - 2^37 */
+ fgoldi_mul(&u, &u, &t); /* 81 | 2^74 - 1 */
+ SQRN(&u, &u, 37); /* 118 | 2^111 - 2^37 */
+ fgoldi_mul(&t, &u, &t); /* 119 | 2^111 - 1 */
+ SQRN(&u, &t, 111); /* 230 | 2^222 - 2^111 */
+ fgoldi_mul(&t, &u, &t); /* 231 | 2^222 - 1 */
+ fgoldi_sqr(&u, &t); /* 232 | 2^223 - 2 */
+ fgoldi_mul(&u, &u, &v); /* 233 | 2^223 - 1 */
+ SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */
+ fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */
+
+#undef SQRN
+
+ /* Now we must decide whether the answer was right. We should have z^2 =
+ * x/y, so y z^2 = x.
+ *
+ * The easiest way to compare is to encode. This isn't as wasteful as it
+ * sounds: the hard part is normalizing the representations, which we have
+ * to do anyway.
+ */
+ fgoldi_mul(z, x, &t);
+ fgoldi_sqr(&t, z);
+ fgoldi_mul(&t, &t, y);
+ fgoldi_store(xb, x);
+ fgoldi_store(b0, &t);
+ m = -ct_memeq(xb, b0, 56);
+ rc = PICK2(0, rc, m);
+ return (rc);
+}
+
/*----- Test rig ----------------------------------------------------------*/
#ifdef TEST_RIG
TEST_UNOP(sqr)
TEST_UNOP(inv)
+TEST_UNOP(neg)
#define TEST_BINOP(op) \
static int vrf_##op(dstr dv[]) \
return (ok);
}
+static int vrf_condneg(dstr dv[])
+{
+ fgoldi *x = (fgoldi *)dv[0].buf;
+ uint32 m = *(uint32 *)dv[1].buf;
+ fgoldi z;
+ int ok = 1;
+
+ fgoldi_condneg(&z, x, m);
+ if (!eq(&z, &dv[2])) {
+ ok = 0;
+ fprintf(stderr, "failed!\n");
+ fdump(stderr, "x", x->P);
+ fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m);
+ fdump(stderr, "calc z", z.P);
+ fgoldi_load(&z, (const octet *)dv[1].buf);
+ fdump(stderr, "want z", z.P);
+ }
+
+ return (ok);
+}
+
+static int vrf_pick2(dstr dv[])
+{
+ fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf;
+ uint32 m = *(uint32 *)dv[2].buf;
+ fgoldi z;
+ int ok = 1;
+
+ fgoldi_pick2(&z, x, y, m);
+ if (!eq(&z, &dv[3])) {
+ ok = 0;
+ fprintf(stderr, "failed!\n");
+ fdump(stderr, "x", x->P);
+ fdump(stderr, "y", y->P);
+ fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m);
+ fdump(stderr, "calc z", z.P);
+ fgoldi_load(&z, (const octet *)dv[3].buf);
+ fdump(stderr, "want z", z.P);
+ }
+
+ return (ok);
+}
+
+static int vrf_pickn(dstr dv[])
+{
+ dstr d = DSTR_INIT;
+ fgoldi v[32], z;
+ size_t i = *(uint32 *)dv[1].buf, j, n;
+ const char *p;
+ char *q;
+ int ok = 1;
+
+ for (q = dv[0].buf, n = 0; (p = str_qword(&q, 0)) != 0; n++)
+ { cvt_fgoldi(p, &d); v[n] = *(fgoldi *)d.buf; }
+
+ fgoldi_pickn(&z, v, n, i);
+ if (!eq(&z, &dv[2])) {
+ ok = 0;
+ fprintf(stderr, "failed!\n");
+ for (j = 0; j < n; j++) {
+ fprintf(stderr, "v[%2u]", (unsigned)j);
+ fdump(stderr, "", v[j].P);
+ }
+ fprintf(stderr, "i = %u\n", (unsigned)i);
+ fdump(stderr, "calc z", z.P);
+ fgoldi_load(&z, (const octet *)dv[2].buf);
+ fdump(stderr, "want z", z.P);
+ }
+
+ dstr_destroy(&d);
+ return (ok);
+}
+
static int vrf_condswap(dstr dv[])
{
fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf;
return (ok);
}
+static int vrf_quosqrt(dstr dv[])
+{
+ fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf;
+ fgoldi z, zz;
+ int rc;
+ int ok = 1;
+
+ if (dv[2].len) { fixdstr(&dv[2]); fixdstr(&dv[3]); }
+ rc = fgoldi_quosqrt(&z, x, y);
+ if (!dv[2].len ? !rc : (rc || (!eq(&z, &dv[2]) && !eq(&z, &dv[3])))) {
+ ok = 0;
+ fprintf(stderr, "failed!\n");
+ fdump(stderr, "x", x->P);
+ fdump(stderr, "y", y->P);
+ if (rc) fprintf(stderr, "calc: FAIL\n");
+ else fdump(stderr, "calc", z.P);
+ if (!dv[2].len)
+ fprintf(stderr, "exp: FAIL\n");
+ else {
+ fgoldi_load(&zz, (const octet *)dv[2].buf);
+ fdump(stderr, "z", zz.P);
+ fgoldi_load(&zz, (const octet *)dv[3].buf);
+ fdump(stderr, "z'", zz.P);
+ }
+ }
+
+ return (ok);
+}
+
static int vrf_sub_mulc_add_sub_mul(dstr dv[])
{
fgoldi *u = (fgoldi *)dv[0].buf, *v = (fgoldi *)dv[1].buf,
static test_chunk tests[] = {
{ "add", vrf_add, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
{ "sub", vrf_sub, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
+ { "neg", vrf_neg, { &type_fgoldi, &type_fgoldi_ref } },
+ { "condneg", vrf_condneg,
+ { &type_fgoldi, &type_uint32, &type_fgoldi_ref } },
{ "mul", vrf_mul, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
{ "mulconst", vrf_mulc, { &type_fgoldi, &type_long, &type_fgoldi_ref } },
+ { "pick2", vrf_pick2,
+ { &type_fgoldi, &type_fgoldi, &type_uint32, &type_fgoldi_ref } },
+ { "pickn", vrf_pickn,
+ { &type_string, &type_uint32, &type_fgoldi_ref } },
{ "condswap", vrf_condswap,
{ &type_fgoldi, &type_fgoldi, &type_uint32,
&type_fgoldi_ref, &type_fgoldi_ref } },
{ "sqr", vrf_sqr, { &type_fgoldi, &type_fgoldi_ref } },
{ "inv", vrf_inv, { &type_fgoldi, &type_fgoldi_ref } },
+ { "quosqrt", vrf_quosqrt,
+ { &type_fgoldi, &type_fgoldi, &type_hex, &type_hex } },
{ "sub-mulc-add-sub-mul", vrf_sub_mulc_add_sub_mul,
{ &type_fgoldi, &type_fgoldi, &type_long, &type_fgoldi,
&type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
81a3d26fcb1461ce12ca47a5a640ca496ca3a6c2234ad151bae95b9c8d0580c4a281bcd78fd72a7ed142013b98eed06d3cda9556ad8946af;
}
+neg {
+ d9896c114cda5ec75cc8c83b3c40dc902488ba8120386566d5d0e2565cd95239af0b13e7c5cbb10a4945287a2c08377e77e757b17fcb92ab
+ 267693eeb325a138a33737c4c3bf236fdb77457edfc79a992a2f1da9a226adc650f4ec183a344ef5b6bad785d3f7c8818818a84e80346d54;
+ 949b01988f46422a30731b9f068a8f0c306d1c473e21f2e6d863d8113bfa2a14f509b62075523b79b8235700da7232229f28432bc68fda06
+ 6b64fe6770b9bdd5cf8ce460f97570f3cf92e3b8c1de0d19279c27eec305d5eb0af649df8aadc48647dca8ff258dcddd60d7bcd4397025f9;
+ 8bc90df2665b8fa08bd56786c48bac6d979bfbeb4075e8e6977384e76a67d29e361f44cf37d0731a8e7f4372ebcc7e1dcb6c6c3d11ff8dfb
+ 7436f20d99a4705f742a98793b74539268640414bf8a1719688c7b1894982d61c9e0bb30c82f8ce57180bc8d143381e2349393c2ee007204;
+ 9024073bf10dbc8920b3bc44885bf0824cb802059db0516eba89bb1999318809772e5ab763f1f247642e91af8abb26b89c7afb2bc8396201
+ 6fdbf8c40ef24376df4c43bb77a40f7db347fdfa624fae91457644e665ce77f688d1a5489c0e0db89bd16e507544d947638504d437c69dfe;
+ b8c5af6a467e916b164b32c92d3d39992bab6a1d0224cc524e33fb18375e6e2d1b11ddaf6bbfb65232fd4746e7a8bc3414c281e45149de1c
+ 473a5095b9816e94e9b4cd36d2c2c666d45495e2fddb33adb1cc04e7c7a191d2e4ee2250944049adcd02b8b9185743cbeb3d7e1baeb621e3;
+ c6410909ea127f2e65866bba1a06597092f91acf99183d2e93cde9c0d4a0cd93fc257c4e26f5353bfda8475bede2e97b4b2d2015c2d4d4ba
+ 39bef6f615ed80d19a799445e5f9a68f6d06e53066e7c2d16c32163f2a5f326c03da83b1d90acac40257b8a4121d1684b4d2dfea3d2b2b45;
+ 7701cc2280295f4672194b1ed8ab9a15c0326921d3bcf7021df3bf04c95300d5142e0871eaa8af63aa392df32a7a58062f297b49409fdff5
+ 88fe33dd7fd6a0b98de6b4e1275465ea3fcd96de2c4308fde20c40fb35acff2aebd1f78e1557509c55c6d20cd585a7f9d0d684b6bf60200a;
+ 036a68a27955c5a1b6f5a3e5e9fff0e2b10f6793c56f33e30b77ad044d518dc4bfe970c066af5ece389010de893fe68ab112eaae8655168c
+ fc95975d86aa3a5e490a5c1a16000f1d4ef0986c3a90cc1cf48852fbb1ae723b40168f3f9950a131c76fef2176c019754eed155179aae973;
+ efc6d5d9e176498e572908e2df6dc9e3e42115b86fc83986ce46437bb051ad44f738e5be55e749a9deed3e82756780ecc84b4360a084552c
+ 10392a261e89b671a8d6f71d2092361c1bdeea479037c67931b9bc844eae52bb08c71a41aa18b6562112c17d8a987f1337b4bc9f5f7baad3;
+ e7ffd0c07e713cacd8818c62af15b301d32e6ed32869d05177d1259b8e5b5ac23f78a521ce5fd41e9cf5531414aeb698e8672c8dcf296d48
+ 18002f3f818ec353277e739d50ea4cfe2cd1912cd7962fae882eda6470a4a53dc0875ade31a02be1630aacebeb5149671798d37230d692b7;
+ fa61a67bb3c9dc4200c3c3b411bdf278b0fd88d4a555e8e3e216d6c2bcc859ce91b3bf6a4dc89e84bcfef5e1f300f70ea4ce7260cd731718
+ 059e59844c3623bdff3c3c4bee420d874f02772b5aaa171c1de9293d4237a6316e4c4095b237617b43010a1e0cff08f15b318d9f328ce8e7;
+ 024f59ff23bf83c2ccaeaead5e72dc5c97babbcf3f8af77b51ac7f66889bc1365f7b679c9cb9525883ebf4e0bfb754667330b253df8e7f12
+ fdb0a600dc407c3d33515152a18d23a368454430c0750884ae53809976643ec9a08498636346ada77c140b1f4048ab998ccf4dac207180ed;
+ dbfb52b68131b340dcce6558ae4aa0c6c86ffe3773346d926015f0408a297ea7ce06499d52da453787b415ca03eb55ac5aeb55d0f34b0e64
+ 2404ad497ece4cbf23319aa751b55f39379001c88ccb926d9fea0fbf74d6815831f9b662ad25bac8784bea35fc14aa53a514aa2f0cb4f19b;
+ f8d76b01b9535f2124a793c9d089e37d8ba8e1de70555b26dc7fa1818bce8ab0b5d8351697d2b87efe312f22a1cb6607cb03b5a75167161c
+ 072894fe46aca0dedb586c362f761c8274571e218faaa4d923805e7e7331754f4a27cae9682d478101ced0dd5e3499f834fc4a58ae98e9e3;
+ 118e8ba034869d617a4abd5d8be3cf89b0fb27f4f59aeefcb4b9d7f4c82d45a9f9f28a95d6461def92ba4f9c1c03f35020d8e9365afa845d
+ ee71745fcb79629e85b542a2741c30764f04d80b0a6511034b46280b36d2ba56060d756a29b9e2106d45b063e3fc0cafdf2716c9a5057ba2;
+ 1d6d927d1d83ce210b5b507d5904d057c94a904a3e47725bcad8b97855027ae074dde4a4f6b7c858b4e80122dc633b380dbc18d6c835cd88
+ e2926d82e27c31def4a4af82a6fb2fa836b56fb5c1b88da435274687a9fd851f8b221b5b094837a74b17fedd239cc4c7f243e72937ca3277;
+ c2fe9dc69d09f11da27fab3a411330eb14184fedd50e848641caa58dd679218915e4b27860a64363ab6320dd01e9f92479dfe15b7961cb48
+ 3d01623962f60ee25d8054c5beeccf14ebe7b0122af17b79be355a722886de76ea1b4d879f59bc9c549cdf22fe1606db86201ea4869e34b7;
+ 38d96118fba44851468a78979e93f4266c8c8a74acfce812bae9e27534fe386a49987008dc468bd349eb8b8b51bb6bdc5a39f783e8f502e0
+ c7269ee7045bb7aeb9758768616c0bd99373758b530317ed45161d8aca01c795b6678ff723b9742cb6147474ae449423a5c6087c170afd1f;
+ 50d37cca9bd507dfd5a9d7f0020a2c62adaceb7e8e684cd649ddfdbaba964e3b625b7687a9cb732e1f62afccf4a5cc7e6b5372029d5b6401
+ af2c8335642af8202a56280ffdf5d39d525314817197b329b62202454469b1c49da4897856348cd1e09d50330b5a338194ac8dfd62a49bfe;
+ 607ebda1658ac485ca10ddbd5ae8644520680b5cc88841ef2504b61be1d41129c7ab98994dde7c5fe2510c3f474ee1671b95fd0ff060a4aa
+ 9f81425e9a753b7a35ef2242a5179bbadf97f4a33777be10dafb49e41d2beed638546766b22183a01daef3c0b8b11e98e46a02f00f9f5b55;
+}
+
+condneg {
+ 7dfa038f1acab8951c3a21c91e13a79697f9a2f3093a3bac6c2c3f522fc54da8b437f8e062bddcaf7eeeef0b2676360bcb2673105d02a0c8
+ 0xffffffff
+ 8205fc70e535476ae3c5de36e1ec586968065d0cf6c5c45393d3c0adcf3ab2574bc8071f9d422350811110f4d989c9f434d98cefa2fd5f37;
+ 197b6ee90f9f42e3107619b8aa2c078ce46d6dff7b2e79c92ebe9907abcfa758d266b9f90859f73982d201dd636e80e093a2c519649f3779
+ 0x00000000
+ 197b6ee90f9f42e3107619b8aa2c078ce46d6dff7b2e79c92ebe9907abcfa758d266b9f90859f73982d201dd636e80e093a2c519649f3779;
+ a5e54cbd5a218159a5ba7835b00e639a014e516a551dfc1174074f968856a446e997f453f0f0416f11fbcdd3792d4c6a65ccd3ec38d33dbe
+ 0x00000000
+ a5e54cbd5a218159a5ba7835b00e639a014e516a551dfc1174074f968856a446e997f453f0f0416f11fbcdd3792d4c6a65ccd3ec38d33dbe;
+ 25d7150e99dd1648661388751c86948a3c76b3f104e4c767af863d658e1f4e4b0d1a4d4f7f66dcbd46c0d302e6e2a2964c1694faaae7513a
+ 0x00000000
+ 25d7150e99dd1648661388751c86948a3c76b3f104e4c767af863d658e1f4e4b0d1a4d4f7f66dcbd46c0d302e6e2a2964c1694faaae7513a;
+ fd58dde069ed4e9422011f16b79c407333e2b9683e92009f2288c20c72f2b44d5715cbc13d7e60ffd4fecba31430235829aa6cddb5e418a4
+ 0x00000000
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+ 36cc9dbcfbea98cd1956c8bcfb38c237456ee1987fc474bb504538210f155da6e1102d2511278f3890654ed6134df4461242173aebe070a4
+ 0x00000000
+ 36cc9dbcfbea98cd1956c8bcfb38c237456ee1987fc474bb504538210f155da6e1102d2511278f3890654ed6134df4461242173aebe070a4;
+ 19ffe362cba138117e21df0dd008bcb285127e5f7790fc108be5bec8f14878c355b47770a1138ddd8029390e88aa0d3087ef5d6452f656ad
+ 0xffffffff
+ e6001c9d345ec7ee81de20f22ff7434d7aed81a0886f03ef741a41370db7873caa4b888f5eec72227fd6c6f17755f2cf7810a29bad09a952;
+ 8814ecf8c0cc3323b5260f1617788ad2059fca72c0671d0aa26ee9500e5a11d57c9365886a6c9d93aceb8e613a25926c79f8a9b3a29177a0
+ 0x00000000
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+ 6d9c88f9558b04bae55eb44d0bc8f0dbadf888a80e8b52f84dae150b070e2e0ab92a5229c7e453bfecfb51dbe164f3b3777f1dceef0808ee
+ 0x00000000
+ 6d9c88f9558b04bae55eb44d0bc8f0dbadf888a80e8b52f84dae150b070e2e0ab92a5229c7e453bfecfb51dbe164f3b3777f1dceef0808ee;
+ f3cee5e619e94efc433d88126c3148ae98d546011a69c347682010aafa688cd7271bcbfd9d5f7bb9ae88da3897ff5b8e685d129d68caa2d4
+ 0xffffffff
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+ 0c547e2eee557a3e7c845fa8bdb92869c3f5590ef9b1e1a7e5751fafef9126845249706748ba670c3b59003122d1a046e547436e0ba7d7a1
+ 0xffffffff
+ f3ab81d111aa85c1837ba0574246d7963c0aa6f1064e1e581a8ae0500f6ed97badb68f98b74598f3c4a6ffcedd2e5fb91ab8bc91f458285e;
+ f9e339c89305a8a8a1a2abddc0126e0fff89eeffecbe9b852f55f78db40861ca33ac676df746a81686d158dee8b9ae5a347f46764558a293
+ 0xffffffff
+ 061cc6376cfa57575e5d54223fed91f0007611001341647ad0aa08724af79e35cc53989208b957e9792ea721174651a5cb80b989baa75d6c;
+ d26b1098dfb25f4c7433509b2907b4525951f6106523b248e77c680d12d2f4a6e4a384b7487f061e02eec80ac8cbf04139519cce03fa11cb
+ 0x00000000
+ d26b1098dfb25f4c7433509b2907b4525951f6106523b248e77c680d12d2f4a6e4a384b7487f061e02eec80ac8cbf04139519cce03fa11cb;
+ 41e3ffb83686f06084d1e22f3a625f2563f02cca14b2eaa024359b671e491f52372f945590e67031bca91fa033cf8a1d51bd39dc45339336
+ 0x00000000
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+ 4a1354afe9dac02b4b8e5ec74c2fe12ef7df09a568bcb7504aac77a3faa480228ea9d3d87d7652448deb7f34fb1ff85c9b5bb6b3e8bd521b
+ 0xffffffff
+ b5ecab5016253fd4b471a138b3d01ed10820f65a974348afb553885c045b7fdd71562c278289adbb721480cb04e007a364a4494c1742ade4;
+ 19b757ffe399587fbba2f444c529497f9006f43987ff52eb9003da41da827f519d82bfdcb9a30cf2d7bc742c69d1ef6c28d0fbc77d85f4d9
+ 0xffffffff
+ e648a8001c66a780445d0bbb3ad6b6806ff90bc67800ad146ffc25be247d80ae627d4023465cf30d28438bd3962e1093d72f0438827a0b26;
+ 06e66f7f99e3e1154fdbdd7110fa1ce13c3395154106c677422196864d23d3d688e29c1113a4e695d5a633a5fc766a173c4abc5a5fccd617
+ 0xffffffff
+ f9199080661c1eeab024228eef05e31ec3cc6aeabef93988bdde6979b1dc2c29771d63eeec5b196a2a59cc5a038995e8c3b543a5a03329e8;
+ f192679b0f3cc35ea26650ce64dacbee9ac76f3aa1fc7038ccbe279b0e0ac8a5b539a7e84fb879ff377ea8247697e5e916e6f31d1bb3ddb5
+ 0x00000000
+ f192679b0f3cc35ea26650ce64dacbee9ac76f3aa1fc7038ccbe279b0e0ac8a5b539a7e84fb879ff377ea8247697e5e916e6f31d1bb3ddb5;
+ 4a9b13b1ddb93d1000b6175e695048c7583f3ed00aa24f0f24bef8fbefbbcb70bf092710d904e000796cc1dada03bf0cf23dc71aee9fbe08
+ 0xffffffff
+ b564ec4e2246c2efff49e8a196afb738a7c0c12ff55db0f0db4107040f44348f40f6d8ef26fb1fff86933e2525fc40f30dc238e5116041f7;
+ afcf052c2711fa86d84902e8e36ba390e8cc05024edc48f36542a1d606f725a1f2734a65d52aa6cd3df5ed76492f748ecc67ba6e7a0dd6e3
+ 0x00000000
+ afcf052c2711fa86d84902e8e36ba390e8cc05024edc48f36542a1d606f725a1f2734a65d52aa6cd3df5ed76492f748ecc67ba6e7a0dd6e3;
+}
+
+pick2 {
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+ 0xffffffff
+ 7a55c27ebd6c3ffcad279ed64e2601ae7da07db4eb8b5d10e50b3f91bebc856069a0dcc55d3863a3bf1901e4efcb33408184713bacbf4bb9;
+ 6182ed9478343417a7a144ebb6744ba9b71c592a076cd39e253377e3cdb158f565a8f2b5aa018da89f1f1278fc7a5e3caf998aa850f863fb
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+ 0x00000000
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+ 2f332b50c57c29b114fbbf0fb902230eb33ed85987b53e4b6ff24a7e57243728db92642e6500cc17ddf69348e09f1f00eb29ecdd601c808e
+ 0bbacc95ae142ce1ea25b2d52e22d89b10877972f6b2c2ef0ef815e0c6cfa203b6a175d37b9bbdd92c132c13a24d77249eecd664589f704e
+ 0xffffffff
+ 2f332b50c57c29b114fbbf0fb902230eb33ed85987b53e4b6ff24a7e57243728db92642e6500cc17ddf69348e09f1f00eb29ecdd601c808e;
+ 1d63593f536dc9027c3ac672cdb1b323f647ac11e0e3d5797884c330a897718a5b120c58dd1fa50272f065cc650be36d747df128d7a3afd1
+ 29282ede408ea3755c43949b96b8494c3083b65a0fcc0e9737e35c573db0109b1aaca9024154e56db389e874be900b6ce66618e976c34ada
+ 0xffffffff
+ 1d63593f536dc9027c3ac672cdb1b323f647ac11e0e3d5797884c330a897718a5b120c58dd1fa50272f065cc650be36d747df128d7a3afd1;
+ ca76f29f750d228a9fa5e9795152ddbdf59a245d34efce86d1781e16d1ef4b996fcab77b83704d59ef2b2945e52c506f97bfada6aa97edfb
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+ 0x00000000
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+ a9c03a383e3b424e7f04db6d8c3c2a37efec54d0158d7ab03848cc6ed70f083138c48003995724b49978587e8ede7f6cb1de8fef59654fb2
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+ 0x00000000
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+ f790450391bc9d9616d768d1c2d065e1c70a780e0ede7bbcbce3c6f395a1f40a526d8f7e5a41b412cf3856a7a8cae34217db68874676cfe0
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+ 0xffffffff
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+ 95d0462a02c45400d97615d14968e90a32a0d3b8a19046f96777cc6def800c7e938d0b65669515d1de2c9d0d5de740589861493f87257f0e
+ 967eb0d765904def8c6fc9d0bb710d838897429cccf444cd243892bcfac20eb704b82cc33e89599d7cbd02d9f44a24afb05b8f6da76de800
+ 0x00000000
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+ 004b205b5877056695259d930cc8de77af754369b49e5040016f3d84a18e9022f8203a6fd7df4d576d4ce7f7a91a6342596dc0b8d5ef102f
+ 640b649372ebcffb4f87f2bf4430a9e70028b75e6d3e838686ac4737dd48a1cff113b8f83082cd37b2550605cf087a4d8e0d5df6247bce0b
+ 0xffffffff
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+ e47a20b61c777f8cea3d3560163b30f00912aa3e0371273fc6126a1bc6d4657d4e1546193169a174424479685ded08f84db407371854ff2a
+ 1d8c7ecebe575309ad46aa947afa16bdbb7013681273fae0d4f1c3c4cbefe7711d33080665cc904553ad5389ae8632657563404348a6cfed
+ 0xffffffff
+ e47a20b61c777f8cea3d3560163b30f00912aa3e0371273fc6126a1bc6d4657d4e1546193169a174424479685ded08f84db407371854ff2a;
+ 02aadd15ef52a17127be8544587ab64a497a2408e34821505a8d8b2a7f4ae43beb027aff78379668bc80bf54507107de4725773e0d39d8a1
+ 4af336b21ee8d83886c8159f3dd61a79affd12ac1b105989d2b6aec3e62616f2753b8f7c4b19717f9643b06025fe46a41ed6f665b2fec236
+ 0xffffffff
+ 02aadd15ef52a17127be8544587ab64a497a2408e34821505a8d8b2a7f4ae43beb027aff78379668bc80bf54507107de4725773e0d39d8a1;
+ 316fa09d97d9f6de3e932dc58d08431b6bc2e5efefbacd1f7b53df5a0400b4e82de675893704298557c7c5f0614333d636c4133c75d7165b
+ 2032908acfe8ea2ff0f9863734ffcf7203218d58660795978486a151b0c38019146dba917a393012de90eac47ba1264e53d1ea2291e9adfe
+ 0xffffffff
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+ 470221fe5cb385fac6cbdae93ecb144c6b6d79196feed7d3dca54376f97d222a5ae435f87a164f11b87b1526ae5aebfb0527e3adfa16f18d
+ 1481f5b202094c6328d07778e261e5509802792d603aa64b5f20a2c10d9e4dc8d0ca7e4868564823ec547746a6938dfc521afd719eeecbeb
+ 0x00000000
+ 1481f5b202094c6328d07778e261e5509802792d603aa64b5f20a2c10d9e4dc8d0ca7e4868564823ec547746a6938dfc521afd719eeecbeb;
+ febd75b83d9aecaba9b1ee2d5b299874ba62a338fab52e6c85a0fdd172591e5f09764ad473c6e5b0aebc74e553aea0d9cd201834cca122ce
+ fc1750a2d1438a1779e26207c0da139847d21533285857549555d2f445b76cef302c56e29e724c9a8af3ecaf2064d5626fec066f58eda2e5
+ 0xffffffff
+ febd75b83d9aecaba9b1ee2d5b299874ba62a338fab52e6c85a0fdd172591e5f09764ad473c6e5b0aebc74e553aea0d9cd201834cca122ce;
+ 39fd301ac8fe36dd77bfbdc5566fb2c6eab8c983bae9d248a679ced3153c17419bd951e0feb0508881cb8464adc3da30753cf005bf98a83e
+ 0b164941ab9f2670c523549f1f86c06446f5f84a037e58e44f9b689332f807ebbecc7460187e40f31b92944a13f9f9886b31cf8d325e6c57
+ 0xffffffff
+ 39fd301ac8fe36dd77bfbdc5566fb2c6eab8c983bae9d248a679ced3153c17419bd951e0feb0508881cb8464adc3da30753cf005bf98a83e;
+ df87ee832636112c76789f71cf8f9b1153b78cc1640dec69f93b7c6598604725464eee088cdb78731f9f119b13e64dbe776dd498ffb90b1e
+ 092ff08a968b0ca27f3b7029c044ec12c091bf6c5cba203b109577967200dc403a8763c87bc64f0eb85923aceabe98466680ddf0e1d35d20
+ 0x00000000
+ 092ff08a968b0ca27f3b7029c044ec12c091bf6c5cba203b109577967200dc403a8763c87bc64f0eb85923aceabe98466680ddf0e1d35d20;
+ b266f3cced76432399eccc2093f9041acce722ff0f2214a539ef61e96306af2fa1c103305fc9b23a9f4d8aa20cc44086dcd15d02140a93dd
+ 2e446cf54eb539fbe9981ec3c2665ca435824813ef49d856a8f1d2019bc10f51854432cea7f0d31370b6612734e3e480963f3f68bbb916bd
+ 0x00000000
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+ ba30728ef7df7f7e89fd6cb3f5693700e3c21844a3612bd60f319b95d95ed86d20c785f742e07c2d1c0bd0f4c6a14b875a9663ded379cbde
+ a53d479c598379813a085d982b84494bcbf81a5cb40e2757d05ea1770b47afba2abcaa1a4b699b019db0c85f4c37408c8c740f205051b7cc
+ 0xffffffff
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+ 1c824caec1b5b45655d31d449de4b66c635ac916336becfc67c1c74192d9a960ba04915db34546a4f3f6aee95a15a9035043d60b4e6eceed
+ 1b5f89674c8970aa0e7e37b0d5d78648a22e74943d0498c0a80ab8f7eec14523d6a9c375e340051f8915473ecafe5eb99451b7ab5a7b86bc
+ 0x00000000
+ 1b5f89674c8970aa0e7e37b0d5d78648a22e74943d0498c0a80ab8f7eec14523d6a9c375e340051f8915473ecafe5eb99451b7ab5a7b86bc;
+ 2bc7f4385c02d100b9e1f3951eaac1f4d4da0efc673f99964d7c79f07f198aca2f58ddbd18cae49db1c609cf346fb1ec6d82040be3a8d21f
+ cb7eb21d871b3128c2a82731fb5cb11661f5633be69dde24392ad7b8397d2914da06df867e297e37371f2e2219037ea9790d7dc43d93c1df
+ 0x00000000
+ cb7eb21d871b3128c2a82731fb5cb11661f5633be69dde24392ad7b8397d2914da06df867e297e37371f2e2219037ea9790d7dc43d93c1df;
+}
+
+pickn {
+ "c111d1169e6d48f8307bb8000db91bec0b7c0359a138b765ee875467e67eabf50fd8202ee6395858d9dca1c6930b43bbb4fc8286a0d03b2d
+ a2ae5318d8970c6b23555f7a78fb2e1f939359fb50c1af1c1f45b3206b7dfe2a1a0bbc59ae80f3a1bad53d563227a1194a98aec5395a745a"
+ 0
+ c111d1169e6d48f8307bb8000db91bec0b7c0359a138b765ee875467e67eabf50fd8202ee6395858d9dca1c6930b43bbb4fc8286a0d03b2d;
+ "56652f690dda35003fd5a1bbfe3764c54ffae6d22e01c2502d980a644c5a24a506c8ad3b75172f8011398341cb4ba2be1b1e223717f295db
+ 6607761fb135db6d10f305aed2e03cadc7b72576f592151aebe49d81ee3337d538cd8b7de47a8aa51fbc25b39ffee729c436e4e28ac9c172
+ 89b3d0755fc7ba0a7be79c06ef733cbf936c59e9109fc6cc5fd2203c1b6461a23a4f4bb6049c08dd2d25323f2d095e9618f3a1ea06978eaa
+ c5a71a5570bbb041abca85711385157e3c45696ab4a21d82081db9f17004f0137fbf0a410052ae90575a6a654695957912081b3bad77ea7c
+ 5bab97e0accc3eb2cec060dc453dc134155efa7f328f602083d7171e3e55ba55d3700c53d1be75cae24c043ba2d9a37bd735443fdd14073f
+ 471f03e2a16a1d58a2db4622106d68523858d1a630e563f5eb2196ed8072e2389e0d2cfadf7ab7f22f14789d5f707408b75e9462cd9b13a4
+ 6b155c607498cd03aff93a8091391b1f7ad1c902e801f2a5761e8822ebde0312cc6ddf799006fe27d8dc1c9411f5bf844c40b02634e520d1
+ 6a98599067cdf9366e8b779c58981571040e72dbe821cad95e9d313a2ce960e4b52b8ab7278bdc7402c248035999ffc0d4cf1d7df1eda96d
+ 7fa1311eb8205d30d4cf98aa1634abaf2aded1d6e00e1f06d48a47280da3a5f5f7c2eef4fd4998b9fa7a92c71ee0457321378c76304fabf1
+ 05c9f88763636d1a2df050796aad0e775d6a198c205511d92ebfaf54537730f70f04f36673dccba4bf028d124e83c346e701d063fa8b1f40
+ 69c05dc94a3f889551e427f57a9b9e2f9983c703cd7cfb71382718bfbe72b6c47d2daf3037d718e93a934a82de6ec459eaa74219fe59ea11
+ 2c510a74adef807a7a53025f5e7c68cfd155ace0ee620d1724146d9e3741586439dda0549b6a298164099a972cf3b368b9f3d0b5f611d89d
+ c6feb2190597901c146dcb4d234d8c93f38713fcd77e3d4ffdde2784a9a7306866b15d4d752c11235ad6c543b2f1159383838d340cada73d
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+ "" "";
+}
+
sub-mulc-add-sub-mul {
07ebfe324f64b54e938951a1e437bab4d35c2bbf5f210c5d78ca2b4eb7ef9c3dab61724be4fa7c2e43086b58db7e961f62a44b029f9901d5
d44920bba642b8162d1c3e956e060bbe6f15484298c2ec55575ee378556b0e8826f627bebda963b7d4d9f1c768a49cd408957105d3c6008a -41997
~mdw / catacomb / commitdiff