commit cf3d9a58f2b52162dde608077543f54fab81da48
parent bb2eac4b2a5ab2552374a38909d03de79a3ad02a
Author: olikru <olikru@tkruger.se>
Date: Wed, 8 May 2024 11:54:42 +0200
working with contexts
Diffstat:
18 files changed, 1504 insertions(+), 105 deletions(-)
diff --git a/Makefile b/Makefile
@@ -21,6 +21,8 @@ TESTBIN=testbin
HEADERS=smallfactor.h
OBJ=\
+precomputed.o\
+context.o\
smallfactor.o\
hnp.o\
cyclefind.o\
@@ -36,7 +38,8 @@ tools/pierre\
tools/varmkorv\
tools/small
PRECOMPUTERS=\
-precomputers/primorial16bit
+precomputers/primorial16bit\
+precomputers/header
TEST=test
SHARED=angrepp.so
LIBSHARED=libangrepp.so
@@ -85,6 +88,9 @@ tools/dbtool: $(OBJ) $(@:S/$/.c/)
precomputers/primorial16bit: $(OBJ) $(@:S/$/.c/)
$(CC) -I. $(CFLAGS) -o precomputers/primorial16bit $(PRECOMPUTERS_DIR)/primorial16bit.c $(BUILD_OBJS) $(LDFLAGS)
+precomputers/header: $(@:S/$/.c/)
+ $(CC) -I. $(CFLAGS) -o precomputers/header $(PRECOMPUTERS_DIR)/header.c $(LDFLAGS)
+
install:
mkdir -p $(INSTALL_PATH)/lib/angrepp
cp $(BUILD)/$(SHARED) $(INSTALL_PATH)/lib/angrepp/$(LIBSHARED)
diff --git a/context.c b/context.c
@@ -4,14 +4,12 @@ void
ctx_init(ctx_t *ctx)
{
ctx->zs_alloc = INITIAL_NUMBER_OF_ZS;
- ctx->nzs = 0;
- _fmpz_vec_init(ctx->zs, ctx->zs_alloc);
+ ctx->zs = _fmpz_vec_init(ctx->zs_alloc);
ctx->qs_alloc = INITIAL_NUMBER_OF_QS;
- ctx->nqs = 0;
- _fmpq_vec_init(ctx->qs, ctx->qs_alloc);
+ ctx->qs = _fmpq_vec_init(ctx->qs_alloc);
- ctx->primorial = NULL;
+ ctx->has_primorial = 0;
ctx->smallprimes = NULL;
ctx->nsmallprimes = 0;
}
@@ -22,23 +20,36 @@ ctx_clear(ctx_t *ctx)
_fmpz_vec_clear(ctx->zs, ctx->zs_alloc);
_fmpq_vec_clear(ctx->qs, ctx->qs_alloc);
- if (ctx->primorial != NULL) {
+ if (ctx->has_primorial) {
fmpz_clear(ctx->primorial);
- ctx->primorial = NULL;
+ ctx->has_primorial = 0;
}
if (ctx->smallprimes != NULL) {
_fmpz_vec_clear(ctx->smallprimes, ctx->nsmallprimes);
ctx->smallprimes = NULL;
+ ctx->nsmallprimes = 0;
}
}
void
ctx_set_precomputed_primorial(ctx_t *ctx)
{
+ fmpz_init(ctx->primorial);
+ fmpz_set_ui_array(ctx->primorial, pc_primorial_ui_array,
+ PC_PRIMORIAL_UI_ARRAY_LEN);
+ ctx->has_primorial = 1;
}
void
ctx_set_precomputed_smallprimes(ctx_t *ctx)
{
+ size_t i;
+
+ ctx->nsmallprimes = PC_SMALLPRIMES_LEN;
+ ctx->smallprimes = _fmpz_vec_init(ctx->nsmallprimes);
+
+ for (i = 0; i < PC_SMALLPRIMES_LEN; i++) {
+ fmpz_init_set_ui(&(ctx->smallprimes[i]), pc_smallprimes[i]);
+ }
}
diff --git a/context.h b/context.h
@@ -2,24 +2,30 @@
#define CONTEXT_H
#include <flint.h>
-#include <fmpz.h>
-#include <fmpz_vec.h>
#include <fmpq.h>
#include <fmpq_vec.h>
+#include <fmpz.h>
+#include <fmpz_vec.h>
+
+#include "precomputed.h"
+
+extern const ulong pc_primorial_ui_array[PC_PRIMORIAL_UI_ARRAY_LEN];
+extern const ulong pc_smallprimes[PC_SMALLPRIMES_LEN];
#define INITIAL_NUMBER_OF_ZS 4
-#define INITIAL_NIMBER_OF_QS 4
+#define INITIAL_NUMBER_OF_QS 4
typedef struct _context_t {
fmpz *zs;
- slong nzs;
+ // slong nzs;
slong zs_alloc;
fmpq *qs;
- slong nqs;
+ // slong nqs;
slong qs_alloc;
- fmpz_t *primorial;
+ int has_primorial;
+ fmpz_t primorial;
fmpz *smallprimes;
slong nsmallprimes;
diff --git a/fmpzio.c b/fmpzio.c
@@ -126,7 +126,7 @@ read_hex_lines(fmpz **v)
}
// ignore last if it is the empty string
- if(tokens[ntokens][0] == '\0') {
+ if (tokens[ntokens][0] == '\0') {
ntokens--;
}
diff --git a/fmpzio.h b/fmpzio.h
@@ -29,6 +29,6 @@ int read_next_hex_fmpz(fmpz_t res);
* @param v pointer to vector to initialize
* @returns the length of the new vector
*/
-slong read_hex_lines(fmpz** v);
+slong read_hex_lines(fmpz **v);
#endif
diff --git a/hnp.c b/hnp.c
@@ -1,6 +1,5 @@
#include "hnp.h"
-
int
hidden_number_problem(fmpz *res, const slong nres, const fmpz *t,
const fmpz *a, const slong m, const fmpz_t n,
diff --git a/pierre.h b/pierre.h
@@ -1,7 +1,6 @@
#ifndef _PIERRE_H_
#define _PIERRE_H_
-
#include <fmpz.h>
#include <fmpz_vec.h>
#include <stdint.h>
@@ -11,7 +10,7 @@
#define FERMAT_CTX_NZS 1
typedef struct __fermat_ctx {
- fmpz* zs;
+ fmpz *zs;
} fermat_ctx;
void fermat_ctx_init(fermat_ctx *ctx);
diff --git a/precomputed.c b/precomputed.c
@@ -0,0 +1,1233 @@
+// ------------- precomputed.c ------------------------
+/**
+ * This file has been automatically computed using the
+ * precompute/header utility. The purpose is to store
+ * some constant values, such as
+ *
+ * - limbs of a primorial (product of small primes)
+ * - list of small primes
+ */
+
+#include "precomputed.h"
+const ulong pc_primorial_ui_array[PC_PRIMORIAL_UI_ARRAY_LEN] = {
+ 0x7cba1517256cc1d2, 0x2c0c3b0cb9e40db8, 0xf48d15cf65f008f3,
+ 0x11c7a08d9aec66ec, 0x9ba5f9e14adcb846, 0x09e285823e7893bf,
+ 0x00f639ef1d034a04, 0xc5a24bc7ac91f11e, 0x922bfd94cdd67796,
+ 0x0aafa0154ce2ea8d, 0x242000da70dfaec8, 0x693293a11d1fec6b,
+ 0x998bc14b59daa253, 0xf9f4dc348d70db03, 0xdd4c2bd94e81b7ba,
+ 0x83369888b726806a, 0xf09f8c0e5f1337ea, 0x690b71fe5d362e89,
+ 0x36d1d9ddabb35a70, 0xe68956234e899b11, 0xc74fd63ec6e66d2d,
+ 0x8f36b8b1e5088dd7, 0x10848442f5155d12, 0x8e10d9f9688c74ed,
+ 0x9f8369b185349d5a, 0x104643c1736a2883, 0x48075eff51477404,
+ 0xc3ebd87ffd278bb9, 0x683377a2e69dd36e, 0x100e6d528fd7d37f,
+ 0x52f412ea20600a51, 0x29558b049272cacd, 0xad6fe690393515f1,
+ 0xfa2cdb6866f51245, 0xc2f29245951b253a, 0xf5dfed3785a71b14,
+ 0x33656b9c17ac5c31, 0xd4bdc4c1f5faf1c5, 0x9ad978e5121e26b1,
+ 0xbf01fbadd989e601, 0xb814c8e7f37690fd, 0x6af3c4ff74d491b9,
+ 0x4a683eefdb679bbc, 0xf3b36bb0f6f44ff8, 0xf8052a61fa4db261,
+ 0x00790e11eee6215b, 0x8549e1c6f90c5358, 0xd4bcad019007cf73,
+ 0xdbcbe3b736bcd969, 0x2bd77a7445bd51c6, 0xfaa5ea793a7ce071,
+ 0x614dda46ca626c88, 0x257dd3d2c6873fb6, 0xa63cff91046ed3a7,
+ 0xd211e64f3648c91e, 0x025c292f26d6f706, 0xd12b956bd0e3b486,
+ 0x96284066c4913c9e, 0x4feeef311e62b368, 0x1f74437b0147672b,
+ 0xf1718e0235d0c08d, 0xf01c03c19d03647c, 0xf6cb209f86ee322a,
+ 0xab2dc8e75fd7d3cf, 0x162a5061eede9ad2, 0x6b32ab7b7d2fb3d5,
+ 0xab2631571661028a, 0x92cb5d29e9e67379, 0x732fd39861d0eb17,
+ 0x64d642359323bafa, 0xaee0d89514c3c7d9, 0xae726610f46a6cca,
+ 0x4949ca350873a0dd, 0x295121537ad12ce6, 0x42dbb69ac7e07a5c,
+ 0x8f4305b82925e684, 0xf12ad24af68ba798, 0xacf97920d0c7ec01,
+ 0x79f665dfd9001f68, 0xd31414a85ef055fd, 0x232ab7dbc83296d7,
+ 0xbf7454b79a11d6fe, 0x20934577a470e006, 0x9449c59c5e6d1336,
+ 0xe057e99a9d6e508c, 0x0309dfe40fbb7cfa, 0x8118c5f04fc90b15,
+ 0xe8a699949e10e6f1, 0x96fabd9db448e983, 0xca471a8bdbd4b4b3,
+ 0x684d6f9ad4433cc7, 0xb0004d8f09ace0b7, 0xd3b56de569418d23,
+ 0x2de71c98157cbdf2, 0x69568b67774927c7, 0x183c391f83f781d8,
+ 0xa88ae4c65b32f71b, 0x609e19069211c9c0, 0x907a7e595d4fe151,
+ 0xedea46f2ac6986ae, 0x7f4881d28c319e25, 0x35c1a8cc37c9b79c,
+ 0xb84753f5149b03b7, 0x900fbe932bf2ba71, 0x1d32d83902837c6e,
+ 0x4ad1bdc5d445e1ba, 0x27388fa608ebf564, 0x7a5e5dcdeb7220ca,
+ 0xae5e8d71346f278b, 0x6e56a6eda40e1943, 0xa3da5fdae47b8dbf,
+ 0x2b8d9b4f60a91cea, 0xaa967715b26e39b7, 0xa51a63972543aa32,
+ 0x75d6b68d4c2e1c56, 0x642efe1f5a121be1, 0x9310ef27e86a1bc3,
+ 0xf5ec8a1faa424bd0, 0x897bf9411739edc4, 0x6c4b7de6ddbf5cbb,
+ 0xb6a9482c4a996145, 0x86cb695a9b92c5a0, 0x183248d027a672db,
+ 0xa4d48f6ac7260567, 0x6f5a6f8b2280e5f7, 0xe40d5d48ef9e100e,
+ 0xf8c4b4fee8dd6cf4, 0xc919571e596c6a7d, 0x7a9b056312ccc3d6,
+ 0x458fe930a6073b0f, 0x43b98a704060b628, 0xc734e2ffacc5fbb7,
+ 0xa05490ab5cb0dade, 0x7029a113095c3a17, 0x4d7cbca108cfd75d,
+ 0x1c99362ebe0aaaaf, 0x9f0defba2d8e94c8, 0xbd2034e3090ca070,
+ 0xc81d67f6cc2fcbac, 0x67486592d8eb646a, 0x4d6b26f8d01f1bde,
+ 0x5e51df5acebeb66c, 0xa555614adc6d47d8, 0xf4352c9ebe1a7f05,
+ 0x81bb07c50453cbc1, 0x6f32300f12ef53e9, 0xc9d89a483bf04543,
+ 0xcc8937fd016f1dc6, 0x0b579fd0612051ad, 0x129c9b4185b26b12,
+ 0xdbe7e17801c8d2f2, 0xc5a344846bebc1de, 0xd89c4a71dd3b9412,
+ 0xb8b564269aa42964, 0x7f63d3694e7050c6, 0x5f3152b0e8cf519c,
+ 0xc400fbb57fcad39f, 0x13900be669dcb36b, 0x327695ee1c87d8ef,
+ 0xf553a2316f75c763, 0xed0f0fbf4dec2d69, 0x4f87ff4e7a734cb3,
+ 0xd4c52cdc7d4e0f5d, 0x2e6050671ac11bdb, 0xdef57c791865dcb0,
+ 0x18e4101e432e5d19, 0x3079760afd19ad1c, 0xb06dd6390d42f221,
+ 0x5ca0f3b91224093a, 0xbb0bdec7d9ba0804, 0xeae0635c8dec3aec,
+ 0x842818c1788915aa, 0x9efb3a29ccfd8f1e, 0x6a7dd1d43bce1617,
+ 0x2eada6ad61e77616, 0x61cb02e3153f0d65, 0x163ef753d6c3e9f3,
+ 0x0f24cc14e73573f2, 0x2bd33bd10a0ae580, 0xf87d04f3544d6b47,
+ 0x6d558ffae0ff7a98, 0x7d796bc5b860c33a, 0x0399c643a54d5e11,
+ 0x7430ae4913bdd068, 0xa408114ecad5cbc8, 0xe9533e11dc6688ce,
+ 0x4742930a773d0556, 0x2f3a9bead719d03c, 0xcefa83b7cb9cfc5d,
+ 0xf3b8d1eb025cb4ca, 0xd386697c8d1398b1, 0x30b580aff74296d5,
+ 0x9cc1369d6a8e262c, 0xed0613f3baa6efca, 0x19e73c0082d88c63,
+ 0x8af93f7987e77351, 0xe4083dcb31e16fd9, 0xea09016666c11499,
+ 0x22c7d1e48b7d4ad7, 0xb914c954f0b52602, 0x4a5ba4aad4667093,
+ 0x9cd7789a456aad43, 0x974a47104439be8a, 0xadd350952cf6a3c8,
+ 0x638ace9ba7769569, 0xa53d940c3e94a8f9, 0x9d26f95b53c57006,
+ 0xaf531c7db6da7e7c, 0x938e8b901f6bbf88, 0x751600aeaf097146,
+ 0xbd5a98b8ebaa4b7c, 0x21d57ae41fc0f604, 0x6eff1b01c6294c57,
+ 0xf3f2b329aaa3719d, 0xaee662027e4ad95e, 0xcb5e7f5291eb6185,
+ 0xdc33e0ca0deeff01, 0xc4eec6b4ca0c4a2f, 0x12a33900c8fbcfff,
+ 0xc1456ba0950b716c, 0xa8b6e1b1f9125ae8, 0x2d04ad34ab86c33b,
+ 0xe5de0b6240d0eadb, 0x3affe24fc1b42fe3, 0x721c7a12ee81ca45,
+ 0x0400479b158d7403, 0xc9f3ac939129c377, 0x27c194a30fdf5056,
+ 0xe63a1091924cb177, 0xf5c7e2c3fd41c76a, 0x74e03c717de6f513,
+ 0x2f70d4ce1d3d88ba, 0x4805fd28235890ae, 0x77f7e99862d7d456,
+ 0x8bfe5268872732cf, 0x4787cd826f18125f, 0x8fd6c7b472e5d6b7,
+ 0x03298e24743275c5, 0xdef4b89b7d1b10e3, 0x55ac38e8d6feaa55,
+ 0x6d3cb42adf941ef5, 0xc2fbe2d624016c29, 0x28a8b5318ee29c51,
+ 0x2fede7b009505162, 0xd3d8205fd4526310, 0x42d3bba3ed321d65,
+ 0x388ffd6252adf539, 0xb4a036fb35624112, 0x6a378a0d9ab2796e,
+ 0xc4d697eff34e9fb3, 0x57984d6db477d3be, 0xefdc28ce90b0576f,
+ 0x096be3e26ba8a06d, 0x21be63f7d3e07d18, 0x845d2369e4f01a6a,
+ 0x7f1aaefeeb29e126, 0xc60ef12cfd28b82e, 0x1b768cff47ed9647,
+ 0x687f609009061ce2, 0xde85e2f3ed21478d, 0x9a3ea3b1687cd818,
+ 0xd7d37a053e1d5141, 0xe78c6f78ce290f88, 0x5b8cea1a833baa3c,
+ 0x6dc9d971b6460ce8, 0x4dc2b542cc28253e, 0x40ddce6f1d1f3593,
+ 0x1f897eaf5e80e3ee, 0xd2575c9140503ef2, 0x6239b6b8d8c85900,
+ 0xeca714489d44eeda, 0xd89a85f8a06aea34, 0xa55ee4612c16364f,
+ 0x09b6ec21de46ac5d, 0xa730684a58bd3c48, 0x0a6c7acb8382b835,
+ 0x9a6db74d437fd529, 0x6a0987d913d406d5, 0x58e4c5dfd65c68d3,
+ 0xbd049ac964ebc6c4, 0xb4e0e175a54a853b, 0x62b47e8c74e58039,
+ 0x597deeee39957e83, 0x5c795c890b677b71, 0x992eedd21cc5943a,
+ 0xd6c2d3e06388ce14, 0xd70bf283b7e3027e, 0x7f46241a3023c08b,
+ 0xc4db2b7d5abbacba, 0xaa960a32eb01b5b1, 0x9e9eb48ced9c4323,
+ 0x010a78152feb8f1c, 0xe207934cad84db0e, 0x9b3d6c4daf2a063e,
+ 0x0a40810db7e86ee4, 0x819531600c41726e, 0x289dc736f801c4b8,
+ 0x71d67b47ff6c50f1, 0xfea0f758670280d3, 0xd7c7bfed5c237170,
+ 0xb3630fc5e5678b5e, 0x96c14b532c9c387f, 0x8dd8ba33fe976523,
+ 0x842680ebfde46d97, 0x8389e96ea85d7b67, 0x182a3e1989f6d5b7,
+ 0x14250c964f80d497, 0x8660499fec8e09cf, 0xe329ef8a94b636cd,
+ 0xef247bab1a6082bf, 0x607eb06aafd35c8a, 0x15b0b5a63fa01c2d,
+ 0xed9c88c3c18d3825, 0xeeb6a279f148e762, 0xc926d61703c722f3,
+ 0xa7da9b6d5d084938, 0xf432b87543790083, 0xbe99f5d3105d8473,
+ 0xa8480fd2add5b7d0, 0x1465ca91485d2d14, 0x905040316753b266,
+ 0x3265f17ade8a07c1, 0x5628a086bcf01aea, 0x44c8ccb0680706c9,
+ 0xd12f4799e343f734, 0x5e4d40ce89ae9a0d, 0xfb074bbcc98e8237,
+ 0x2c01539292497f59, 0x35e6957fe9b1951e, 0x6b8381c01ce55f74,
+ 0xdc3d58be0652a42a, 0xe963d65777954e26, 0x7f10e1e1c9356133,
+ 0xb50cecb5a4f03d02, 0x46cf7d09ad14f6c8, 0x7f47f947aa83be3a,
+ 0xa2aa77fb0a491aa8, 0x1c4e42dcc562aeac, 0xf0d44a9e6d09e379,
+ 0x0a593210f673f78d, 0x4d95e301b287f62f, 0xacbfadf3d30f3838,
+ 0x03e24408a4525cfa, 0x6f296717812f6352, 0x7bd2f9f0556a0634,
+ 0xfa2e53e7194af324, 0x4cdbcba1be99f047, 0x70186c63c7e43b9a,
+ 0x3c773abeabf35a5d, 0x00c708bd00cd0f63, 0x9b452ebfc4199801,
+ 0xaf564e705c899a49, 0x53e14d7cac2cb9e8, 0x89200b4ed2eae168,
+ 0x4e9eb62f1a1eff39, 0x82e4ac84fe627256, 0x49ebeb9afbf762cc,
+ 0x69988cb5e0e55b94, 0x518cdc73f70115e6, 0x03bc4d7e842de1c1,
+ 0xada460562e1a314f, 0x0d663635e58d2789, 0xeb1607a0bc6fd682,
+ 0x299ba17e6da685ae, 0xe76497d13afda0a2, 0x524be664c10411d4,
+ 0xeebc70579a83e429, 0xd090701b55e76c87, 0x6405420d3228d2d7,
+ 0xf65cb641b6efec74, 0x3e8162912d3aaf8e, 0xdb2f9ad89569462b,
+ 0x5d80a7f09d2e75df, 0x194360ba7a87a659, 0x26fad6ad474cdceb,
+ 0x8c345709834e3def, 0x89f4ad492ad50851, 0xf22af8b3fdf9f7c6,
+ 0x98ce676313193113, 0x8f51cb5544d75be6, 0x9b5664cdb4e0e510,
+ 0x5b2a6ce423a7253f, 0x927c1d014fb4ad0b, 0xc4887eaadbfa42bd,
+ 0x8ecb99e5badd6648, 0xa52200cb28c82169, 0x1e976468380bf090,
+ 0x9730e4bd8fa5807d, 0xf05257776d52ff94, 0x3eaca698f111022e,
+ 0xc294fb31aff3e0a2, 0x32e505aca4a04b7d, 0xaef3e96a94030401,
+ 0x5667bc0584f134be, 0x20aa9b4cb6c8c9b7, 0x85a3237fdc48819a,
+ 0xe5be407f84b779cc, 0xcb4643afdf1e880d, 0x7ff3063bcceb868b,
+ 0x3b66899edb16b7ed, 0x621839eafc9773ae, 0x0ea9056f4bbd6cfe,
+ 0x02a05121b5ebb4f8, 0xd5ca70cf7edbf468, 0xd6d36d0a922f8400,
+ 0x8e2430df70a4eed5, 0x74896b623f48b632, 0xbd5a1f3cd87f0bb4,
+ 0xb71ea3948f4af7e5, 0x42545f71d69c92d2, 0x1f58fe25e65eff4e,
+ 0x2104e488a3a9e85e, 0x1640781a348d4e51, 0x5449c39e08366611,
+ 0xa0e69e6be76ee51e, 0xec7b68a2d1dcdba5, 0x19eda81b4e9bfc21,
+ 0xdff8c17f6af7c2ee, 0x208ca251241e4277, 0x5d87b03457e66716,
+ 0xbb78ef69cbd294c4, 0xc103767696c10cf8, 0x5efd9d7166306e1f,
+ 0x9c5e6c71ae910f72, 0x821ba4e9c45c655f, 0xea45aa3584e2c740,
+ 0x4bebbd82e1fa500a, 0xe7d48885e56a13b1, 0x68a3bb56c3cc45f5,
+ 0x1e8831f7f30522f6, 0xf67742cbc313828b, 0xdab339d87b185b9a,
+ 0x2193744955857d0b, 0x37349090be0a3a86, 0x933b477a083e26ce,
+ 0x4838d0374ec52d81, 0x43e463bdd2dcf8e0, 0x8e4fb3276eaf487a,
+ 0x0fdfaacd310a6b4a, 0x157a7536f56e0762, 0xf8c0bf8497d4ab20,
+ 0x0b68158a39d20a04, 0x26b25fa25fe5c03e, 0x4194f41dce95652f,
+ 0x4bc0d8c36094a55e, 0x20d47bbfe1c71020, 0x8ff1bb2ca504fcda,
+ 0x39cd964a6bdd430d, 0xe2223131755e4aa1, 0xab02089b535fb9a2,
+ 0x43560635857fd8e9, 0xbc9bb4ce5cfd3c95, 0x1af582c27cf6ac35,
+ 0xdd9e362a2f33fe07, 0x4bd65b10abf012d9, 0x540b022ae16fb55c,
+ 0x086dd5c0d8332914, 0x7f68aaa95cb7fa88, 0x650b4adac58f8457,
+ 0x56d43a0af0d9f646, 0xac515962098494dd, 0xd76c7ba514d5f76f,
+ 0xb64f9c91b6ef40a8, 0xd259a4ab6aa41db3, 0x4e51733eb0593231,
+ 0x751e0c27026d9e43, 0xc1f9329b6c72797b, 0x355c7811013fbcbe,
+ 0x951d728f773b1c84, 0x1b697d24e85d3161, 0xf7af4b34ecfc1bdd,
+ 0x207c5b2c539de8c9, 0xb82a5306dddf637e, 0xfc43c667974700a2,
+ 0xdc87c5761d4919d7, 0x2ed0e5fa84a42981, 0x2f731083db9f378e,
+ 0x5fa1d861e12585ee, 0x9fed2f8db42f4d34, 0xae0a717f30987811,
+ 0x6e62698169243159, 0x438bf4d8602e474b, 0x60ab462a7a9e6008,
+ 0x96b71b16bd07480f, 0xc556c8be30ac86d3, 0xa2882d60da8c3c38,
+ 0x2bc99e7d61879d8e, 0x840262f9f42dd740, 0x0d6ede2379f97250,
+ 0xc6861488ea927ac2, 0x22b843f02711c5f5, 0x1a25f953488bdc56,
+ 0xcceeba8736b2b768, 0x1412b6a897f8252c, 0xf9632127f567e1af,
+ 0x900477de94222517, 0x7f70ed85e27140e5, 0x54b3eb951874b7ad,
+ 0xa6fe47f1d540c0e6, 0x520c6cb49b3123a6, 0x48aed8dc94051e4c,
+ 0x14489b4de0aa446d, 0x082268e2f274b1d5, 0x0559cf5db3ab5c24,
+ 0xf067c0e7396f19ae, 0xe1740d6e5badfeca, 0x4d913b25f40a8f35,
+ 0x59bd11f3754acfe4, 0x9598b488499c0651, 0x3e409d5c7d944e1e,
+ 0xa76b2e719a43e51f, 0xcaf407f02ee57374, 0x73a9269d1c79f662,
+ 0xf0f45948a0edbe85, 0xd508b48ed7bc3292, 0x1701a1a1bef244bd,
+ 0x77c8f91485e7bed3, 0xf7c54f714f0c3898, 0x5e0f816e84ddda33,
+ 0x7bfd0d4a0fcea6bb, 0x1eaf767577242fbc, 0x0ae0e1ac66e9ee2e,
+ 0xf48c546daf2d6b06, 0xc569da6f3ce41be8, 0x89bac83da0d6547c,
+ 0xfc01e4d00da7157a, 0xa064af194eae3e37, 0x0c5e0f456db3de45,
+ 0xb06fe3b47ffa750d, 0xa3a310151e436f2a, 0xf6594ef7d83b7b34,
+ 0xe5ba5d4d9e221b06, 0x7bb9fd85d6697f98, 0x07f62f4dcef0fe45,
+ 0xaeb576249787e8ed, 0xb47e05cc851e31d5, 0x8f17e4c1b7550c20,
+ 0x4947562e342d7749, 0xa9a4db0b3b1b099a, 0xe8ab2f1f2aa63b8b,
+ 0x079a7f8366b1566b, 0xdfdea7a6efbad193, 0x575e09eb77ae4a0a,
+ 0xf791d6ef37d7a875, 0x2003a1f2686834c3, 0x396f5cc3788b78cb,
+ 0x1ec6cf7432c2505b, 0xee78b559d1eeb461, 0x43855167bbbb4bbf,
+ 0x11317e127d802559, 0x1099feac2204aa9c, 0xf425cc29107a3a2f,
+ 0xf0c512899f6ec2ec, 0xc3234dcac8443e80, 0x43ae989d6758ac0c,
+ 0xa4390997ed24bbae, 0x0aca3ba790f4d08d, 0x64df9c87777f38a8,
+ 0x37eb3cf0d15d9c84, 0x81c70d1f92d03396, 0x4c63155761c90d4e,
+ 0xfc94f4e52eaee65d, 0x9312b14445ed1dc6, 0x15c8446cc3503074,
+ 0xcf6793908487ed8f, 0x9288dd516d132e8b, 0xa42059b9ed0786b9,
+ 0x61ad35c0afcd1421, 0x1713845528425834, 0x214675670ee34af1,
+ 0x456a6ac499098771, 0xd97b37154b1c7a7f, 0x61bcba72019f0b84,
+ 0xeec4d1afcd2a7e78, 0x04ddc3d98ede9c6d, 0x3426b7af3ec4dc0a,
+ 0x3cd8c5d4c621363e, 0x2a0a734504d4f026, 0x0dc81e82fad464cf,
+ 0xaab34d681f63b34a, 0x70371fee3ddc84c9, 0x27ddb2f06c11614b,
+ 0xdc90d2a516e8008a, 0xb85f8d9219cefdc7, 0x40d4a41d2b70e039,
+ 0x2e69ea72c8c13f28, 0x717e37b9bea45409, 0x1f68fb6ae1957190,
+ 0x0381de992c3d8ce0, 0xd484ee4bbbb657a0, 0x031307d743127ca6,
+ 0x9a48e81cb3072ddc, 0x5efdf670dcaa8902, 0x80caec42c0714563,
+ 0x80fdb92c69db8f9a, 0x54be0108873dac1f, 0x6a87cc0ad07ad082,
+ 0x6a502d04b3817538, 0x728e72d8fcfa674b, 0x9fd440f8457ba1ee,
+ 0x1cc136bbbf6c8e62, 0x310b5a1720d737ea, 0x66db2d467aed04c9,
+ 0xa5a45ee1d8feb57c, 0x8c9091ac1b2114ac, 0xfc7b3c8a4f94b421,
+ 0xa5dad41afe757bcc, 0xc7f853b9206eeec6, 0x3787ecdcd4531363,
+ 0xcd19c16d8ea5ab88, 0x163fcdb9a5769aa0, 0x4099f7152be87640,
+ 0x946fefb4ee0ee85a, 0x03274763151adeeb, 0xd594a2116f747ccb,
+ 0x88cb2e8274539139, 0x84573de2440e9462, 0x97e92f7cf9d1a003,
+ 0x193352072047c6ad, 0x55aacb118e071ca3, 0x89d08e065521e659,
+ 0x49171be047fd000e, 0xbd236fb47d28e5d2, 0x6299a10a7dc43cc6,
+ 0x9880286cf720e507, 0xb0d290b3b855d3e4, 0x8a0295f4d2e8ead2,
+ 0x5c7eb0625886edca, 0xf7b5af4044a91d2c, 0xc663519737d32d71,
+ 0x3aaf011d3fdf93d7, 0xc63df0b86d876ebe, 0xa039385d38e370fe,
+ 0xc834905d23a31ab5, 0x64064fd41bf706d9, 0xca5e76a0b5b87129,
+ 0xd264b1380c4189a0, 0x5e73eef170db7e46, 0xfe904181d5ec61d0,
+ 0xb9129944b9d99f6a, 0xb72697544c7df709, 0x1ad113872406db3e,
+ 0xcefb26fe57fa9132, 0xc4c8e41cc32fe17a, 0x533f3852bbd841de,
+ 0x19591e9d1a669837, 0x72beb7e5ac8bd69c, 0x27f66c20316e45ee,
+ 0x2453cddb3b613cf2, 0x9b142745274e9c67, 0x9bc5a7e27165d6f3,
+ 0x39c746a739bf4a76, 0xcb514276aeb0e393, 0x041d84257c90af17,
+ 0x060d1cf649c121e3, 0x581bcb1bcf3cb136, 0x96ecaafe26190486,
+ 0x6ed28525ab641a49, 0x1c85412d1d506d6e, 0x94de1849a1475291,
+ 0xc198a7a2844ffa4f, 0x2bce8be68975d74e, 0x468e2f92cc82e9d6,
+ 0x141bd295454b298a, 0x0dccea18984554f4, 0xb5f8f55f282062d5,
+ 0xd6ef068ad91ae16e, 0x1fd49e404bb24e62, 0xad44fe121705f492,
+ 0xa01577a38be07dbc, 0xb71ae06ce7689485, 0x10e1f9a77b27145a,
+ 0x8f475ab468f81161, 0x75c7d520d3940760, 0xa0f18f89d0494e4c,
+ 0x063a65c9a20ed1da, 0x8a0714e0bcfb1a03, 0x3e061d78aaaf3bf7,
+ 0x5e0af763f63459d9, 0xc9b2bf5280debc1b, 0xf57e02fa3d72516f,
+ 0x3ef29eba3bf96578, 0x4123248ae2e44422, 0xc1cd79afa812bde6,
+ 0x46c49a72c3c598f9, 0xf87ab50559be3643, 0x9e9d51ccc4ccb3c6,
+ 0x211b637cee212779, 0x069ea2b02f1b8c43, 0xb9ab8246712d2bb9,
+ 0x4064c637bcb18595, 0x990e4d217d498ccb, 0x3b4b9a1447b938e6,
+ 0x6fe416feddd44050, 0x91d150b6ccf3c57d, 0x2f0adb18484dbb5d,
+ 0x3f5468c9c0cfc8c6, 0x2d4fdbf1e407a1f1, 0xf68fd0309ccf1aef,
+ 0x8c42e5540092e5b9, 0x1a19c38fe22a78c6, 0xe132fe435fbada50,
+ 0x8a01649c83e2762a, 0x90b59a8b2e16700d, 0xa237e68bed05d94b,
+ 0x08036cc6b0f4aaf6, 0xd8f71d36a48ba43e, 0xdcdda179c093deac,
+ 0x5f3b30445a475603, 0x3792fa35e7dd6d2b, 0xbb1acc4c9c48672a,
+ 0x211b0ed19cbf2dee, 0x2c4d846b85cce11d, 0x310642772ce18f62,
+ 0xa3e5f31d0445232e, 0xc7d223f6977ea127, 0x20c6df5a7cd70737,
+ 0xfca2c5c64dc3ef91, 0xaa04ebb7b1efce49, 0xc4927cc8af1f80ef,
+ 0x932334e85754169a, 0xd5255c024e2d8da3, 0x29379c2691dd1109,
+ 0xbf8437edc73aa16d, 0x305f6b9c6a45b371, 0xb13aa7bf900d11f0,
+ 0xc493d9495c380199, 0x47c8fe0ffaec3002, 0xf3843c7b36655568,
+ 0x45dc1568ac6348dc, 0x568be2960c4641d2, 0x39808bba18f1ab61,
+ 0x10d581a96db0b3cb, 0xf08a82aec3addd01, 0x9cb2c601c2cd8615,
+ 0xa06387a12ea6fb85, 0xbd51767a9373745f, 0xbd6ff996759d4a35,
+ 0x01f73ec2065ce539, 0xdc9d3cbba4d1208c, 0x89001d726d56fb73,
+ 0x8258b8b8f346700c, 0xc8e4e968f0778fd9, 0xa94a37908f3ba810,
+ 0xa68626416bf9c5b0, 0x9e20a4173f9918c3, 0x11ef7ca8e5fe6a10,
+ 0xba154365fff6fc10, 0x5452d1d70de95d1e, 0xa304b8a652014e3a,
+ 0x7521ed6ce12a20fc, 0x596dde932b31d79b, 0xf99d1ee9a705b606,
+ 0x571c0e9d9c71c4b7, 0x9df8e6ed138a253c, 0xde5e5f8508acba61,
+ 0x557ce08be9d4afac, 0xdd851fb0b709899c, 0xe33bd1be23139ded,
+ 0x40f58601de184fe4, 0x77dc8cfd252d3c7b, 0x95772a35b6788a9a,
+ 0x7dfa8ab7de1dbb71, 0xecd093f03949ae20, 0x66ada2e6618bd758,
+ 0xe3eecb1d825ee7ef, 0x53a9f119c847e229, 0xfa7b49dd2dd1eee9,
+ 0xfcd8db04ca4fa9ac, 0xde57b7f258215ae7, 0x5cd0cf07a1231b98,
+ 0x72c0ca2c7b231ecb, 0x4ba5a5eab57dbd90, 0xed540f375655e89e,
+ 0xd3a308f1bb470161, 0x9cb4b6f0c47ff021, 0x37390a78bc890eb3,
+ 0x678de7601be77a5d, 0xd1f09fcd18493bf6, 0xe86cbb6d6e28ffcf,
+ 0x185f48c4e6e63c3b, 0x5c6b03998dd5c207, 0x4b6ef0ffba3aa010,
+ 0x5082c326f4d87a4c, 0x85373c2376808ee4, 0xaec9f871f068c894,
+ 0x8f202db46e78fc23, 0x9c194a73bcc809d2, 0xd33efae820d5ada6,
+ 0xf153a5bf1e1dc6fd, 0x0d62a73cf8b0b461, 0x3d83328ac4db18ba,
+ 0x05c1605c6c34ad4f, 0x96701b2743370011, 0x8978bc251ea1debf,
+ 0xd3916b010888d721, 0x1e1e61637d4227c9, 0x2c7d1312a6f9a493,
+ 0xf7030a4f6ea38203, 0x2dcdc8271e28045c, 0x561a841028cf4d4e,
+ 0x89d2b755e474c72a, 0x11f6baea1932c73d, 0xe9926666c3df3548,
+ 0xf2cd4f27779c3d27, 0xc17689bf22c5bbce, 0x048f31673a3f636b,
+ 0x9b6c150d0b800bb4, 0x8497f253a23ff157, 0xcce25aa2c191c9e9,
+ 0x509a076c53482648, 0x1280f5c49a4d6256, 0xdbf7277b00bbadc8,
+ 0xd4f82fed65a2098d, 0x67f25152dde712c3, 0x0050710bcd549ef7,
+ 0x608bf39a37b0fc31, 0xe3ceb07f9f011222, 0x2c7c238a631a65bd,
+ 0x57892b3fcd2c7bb2, 0x6dcc63e80aae7e95, 0x2479feae46630eb7,
+ 0xb99c33c2c4450927, 0x0271f907108c192f, 0x84c53dc30fd8121e,
+ 0xad0964dd39afd9f9, 0xf4461bcd1632ef3e, 0xa3aab6f8d807ff6c,
+ 0xdd358e00a3d134d1, 0x979601e1cce155d9, 0x850d6e4633a47017,
+ 0xd31f325f350a9367, 0x87c51d01308f0251, 0x55594293c4b847e5,
+ 0xb9a83e6101406b9c, 0x17e66141ff047f74, 0xd35948c0ae9f453b,
+ 0x2528dbdaf132a7df, 0x27d8e5fc621b183e, 0xba802045ec409148,
+ 0x45de0bf7452cfbae, 0x16a1164457ea6af8, 0xb943ed124fd42cc7,
+ 0x63f6decb80f357df, 0xdba6ae7be26abb2c, 0x69fef2d4e190a29b,
+ 0x48a58abcee25330a, 0x7aeafaa0e952ca69, 0x288c0953bd6f40c5,
+ 0xc55e774f1a7f5565, 0xeb78af4c2425cadb, 0x4f0f7edd748e2eeb,
+ 0x51c56ed96259f0c3, 0xefaaf595d17dca00, 0xa9ccd2cbea8e660b,
+ 0x705b96021825f1e4, 0x8df4179c4069979c, 0xf05ee79c5494b750,
+ 0x47ed1ef040dce1d8, 0x7234e581c48c1b8c, 0x86a46dd332de054b,
+ 0x0c3fa54a499be340, 0xf01846e692a92a94, 0x3890a756e7481f90,
+ 0xf84693ad55864d30, 0x1d181ce6cbe1e2bf, 0x1e0b0d75bbb9a697,
+ 0x6edd660e23ad15eb, 0x08207178750e3ce6, 0x0504b3e3efbe3f61,
+ 0x53f524e9e18dcfa1, 0x832c220e21ea4b6f, 0x61155a643392a1e6,
+ 0x9c140e1a6afa77bf, 0x962b780f38d7eeaf, 0x97189f423f11df0e,
+ 0x8865ffee133fa099, 0x2d2a4bb917e9f7eb, 0xe3ec5fb4ddc88667,
+ 0xba830b8b61b9d9a0, 0x3b0745c0795d5570, 0xb3ce9902df771f26,
+ 0xd54716f27802000b, 0xfafc9a68a18e6282, 0x5431bb4280f0956a,
+ 0x2b98e9a09da8b9fe, 0xd9bf593904945f6c, 0xa7cc31346ee14457,
+ 0x48d88d54182890d8, 0x42ac64566d56e28c, 0xb26c606cc263d904,
+ 0x9900c2eb1ab4a00c, 0x2eef4ff370f28fd9, 0xf1a11c98fa1c4f0d,
+ 0x24fbf085136e3c74, 0xd4e8406fdff12838, 0xcfcc6e90b3c64cc4,
+ 0x3656a89946c1f041, 0x9fe1cc2021fd1b90, 0xa682cab79d4c0174,
+ 0x2887f820b9b1b0ef, 0xc1afa7d6c583fcc0, 0x4bab35941dc4c1f5,
+ 0x460e01ca0a18eda9, 0xf0bbbc678597d64e, 0x6ffb280aac42cd97,
+ 0x0a751d072cace593, 0xe5411822f51315e2, 0x9f84d4a4c25273e9,
+ 0x8a301fed19a1819c, 0x165b1bb53e99e449, 0x180dc106989adc71,
+ 0xf65de714ba802744, 0x7ace664d55b51d0f, 0xe75341cfd6cf9d7d,
+ 0x43fe520d88ddbdce, 0x9c39c2a70d47ebb6, 0x8169a1641588590e,
+ 0x816db8f284d67ebb, 0xe3243b979b9cfeb7, 0x84615c74d5e2f85f,
+ 0xc984acb22742132f, 0xc57c591b5697e6b2, 0x054532b05a26fc2a,
+ 0x5e12aaa17aebacc8, 0xd048ccd9637620d5, 0xcfa90ab87bd92b25,
+ 0x231e08408ba92bae, 0xe25534ba5af1a82e, 0x2bdf31543deeee24,
+ 0x685bd406b1682d80, 0x8875298146449283, 0xdf43b257ea9120b1,
+ 0xb137c8a2eb232352, 0x7b6f4ca2ec265786, 0xe355feb4353b604e,
+ 0x3c99fcce317b0d29, 0xe1fd97ef30b078de, 0xc7705c0339aba7f4,
+ 0x0f568197d4f61d6c, 0xe97dda63630eb11c, 0xb5ccff9982c02799,
+ 0xc31f95383c67fbe3, 0xf232b937eb301459, 0xbf0731c2adaf823d,
+ 0x1b2ca1555fc819de, 0xa10fcc86d9035747, 0xa295c45fd8d793e3,
+ 0xfa0c59f64b52c163, 0x8fbcc9525ddd9e10, 0xdb37df0a47868045,
+ 0x8a4cd11ce78862ee, 0x7259ed6040c82c1e, 0x97a61be38b872fda,
+ 0xb45eb4f326d5212f, 0xdc64dbff6710220a, 0x575c96247871cda3,
+ 0x14f42831fff082bf, 0x739e05fec3a2d90e, 0x96062f7e26889de7,
+ 0xea288713c1d2ffd6, 0xa5bca08edc9aa2d7, 0x113a5ebdeed43424,
+ 0xefbbcae986983c35, 0x863784c696cf7c15, 0x88098b2aaab605ec,
+ 0xe8e84dc21c558984, 0x278aac64668e37bf, 0x491f44b88327148a,
+ 0x93916957b79cba71, 0x9d56cea316612c6a, 0x39ef966c434c3e28,
+ 0xa8748fa53eab9249, 0xa45050c0090bade2, 0x48b9b2e5250941f7,
+ 0xe90d980a43dc5d32, 0x46ecf53efe533616, 0x56285fe798892a93,
+ 0xbcf69c46d57d6dfc, 0x3c3b8890a8264226, 0xecaa0b2050f9a1b2,
+ 0x6e0e97090f01c87b, 0x5111fcd2a22b35aa, 0xbd17dee69a5dcfd9,
+ 0xbf42b9c259572295, 0xef0fd3e33aa4f5e4, 0x33789d69e04b5d8b,
+ 0x3c0f6bb3458aae26, 0x44ddfcaa3052809d, 0x85204c5c03ff6beb,
+ 0x23042acfa77984a4, 0x3195b647f256701c, 0x211460562637ed26,
+ 0xaffc8059e7d3545e, 0x1281affd39b78053, 0xea66a77508d165c4,
+ 0xb39ffdf98d0ca1ae, 0x2d43b575928c784c, 0xd1c8d7d1efc1888d,
+ 0xe61994bb75fb0eeb, 0x65dea778bdc14d9b, 0x887b174bdc1927ea,
+ 0xfc41335a6072e9ab, 0x7fa9deaa176beda8, 0x990a465566816d63,
+ 0x07bba7136c396c34, 0x16d501727a5da7b4, 0xe849f948a79e88e2,
+ 0xa43b779f342e5b0a, 0x262d246a2a4662aa, 0xa63007413cdc5361,
+ 0xd423b33256128a57, 0x58d317f3e7264260, 0xb330320c4d003566,
+ 0x8477154ae71e1464, 0x8143f7311a8ae37c, 0x1748fd8387c2c607,
+ 0x74b5bbde0057d952, 0xd533b5c9bd4b40d7, 0x9bca9dda9347dc9a,
+ 0x7901fbdbad4dbe54, 0xb198a07aa5559363, 0x39da9900be1a2182,
+ 0x2a88760e7ffd5324, 0x8b6e4c0e9b7e7e7a, 0x26ceeb0348b928ca,
+ 0xfbde635e4db0cf4c, 0x0b1de958196f25b7, 0xd962736abdd0ef30,
+ 0xb22cdfca0428e941, 0x34d894d08faecb9b, 0x56e399ce516f4eb9,
+ 0x9aebf4930d946385, 0x3c0b44755a80a865, 0xeefd92ee2d48ca6a,
+ 0xc25f52f7ca4588aa, 0xe8e33ece554d6087, 0x47e4a3288f64aa9a,
+ 0xe91ae16698e2e075, 0x8ec613ae2a3cf647, 0x4dc0ead5eb4cbdc6,
+ 0x1670c3fd6a1627a6, 0x7c7050b350f1f8e4, 0x912212ee6511ce52,
+ 0xbbe3a3724a0cb9aa, 0x84a1893ba98f715d, 0x20fd1db4124a2a27,
+ 0xebe32ecfff812a60, 0x443d404a93cdf142, 0xc4107af5a1620094,
+ 0x7a21a22b1b901f45, 0x96bf30c84b8bb6a2, 0xedf4be97c58b1505,
+ 0x39b990b924299310, 0x036eebffaa19ebf0, 0xaad6c517e269ecb3,
+ 0x9a4de0ea339c4840, 0x0692829b58f18008, 0x0bbf1e6157456873,
+ 0x76f20780047afd00, 0x96b41c40dcf0a3a8, 0xde2d19361a58d42e,
+ 0x513f7f99b1e1ff00, 0x4ce4c755b1f9755c, 0xc63a522f5c0305e8,
+ 0xb49bf703c417bce3, 0xab9db760b10bf739, 0xa0d99de6d98f913a,
+ 0x2e809a68288dbf1f, 0x53543408dd783ff7, 0xd2bb81aef87c69d4,
+ 0x273641e640b77a1e, 0x64239b349a92741d, 0x0892520ff335ef26,
+ 0x2e5dc1b20f902b24, 0x2fa8f748eca86a2b, 0x087d1d2b8efb07bd,
+ 0xfda21cfbddb16ed1, 0x6346d5869c3a8065, 0x1082857197c40daa,
+ 0x8fd29f61f4093bc5, 0x2a8f641902204fa9, 0x53a933313bbcfa7b,
+ 0x586e7c6d47ca4e8f, 0x10b1800e69daa1a6, 0x909f458c1c6a2cf0,
+ 0xa7cb88efcc6f7513, 0xc17f9b577ec89ced, 0x7411782ea6f087c6,
+ 0x37792f06ec8293e7, 0x858216c959d67f00, 0x087314768be5b8d5,
+ 0xa3aa7e373ca49cc5, 0x34c0038f7ab4c6cf, 0xef897a5965e82b68,
+ 0xdcb69db51670ff6a, 0x2059c383dab220e3, 0xaca38fb55641b5f2,
+ 0x52f6b1227ec85297, 0x81822348b95f0e8c, 0x445c777123c03a16,
+ 0x3c84a17a3c9faf1b, 0xec9ea5d12bd0fd76, 0x7a561d43f72a0b74,
+ 0x739257bb90b9223d, 0x710869d51586fb32, 0x637065dfaf508bee,
+ 0x5631b5231eac7133, 0x70414701984490c9, 0xf0e3c7a1e82cee5e,
+ 0x5d443bed969bd049, 0x69c2f1f11766b699, 0xaa278103c93d27fe,
+ 0xc4086e9cb0f624c4, 0x4d2a3fa6816c4911, 0x5ef1dacac38a6c3e,
+ 0xbb7fd86fa7909e02, 0xdc50791a8152e0df, 0xae63838b1a0bf624,
+ 0x79b654a485f29cb4, 0xc7ea11460bbc72c9, 0x08c8cde9f7cf6161,
+ 0x17939ac3799186bf, 0x7b2f54b7a636cbf4, 0xeddbf3fc5142788c,
+ 0x1d9d7d22b2884220, 0xbce0bd6b7f96bdfb, 0xa701078e6fe487b2,
+ 0x3694bcd1869b5c67, 0xeff6f2b9ab174d80, 0x373df453522cfa09,
+ 0x474a58f2d3fb4c9c, 0x49304c953e63dff6, 0x23020e1cf9165100,
+ 0x218e45070f66aec3, 0xd01ac77ea88c2bc9, 0x48ab189f8eb1c6f7,
+ 0xeb76f80960f50622, 0x13c5cfad64b6605d, 0xf84370bfa39553f0,
+ 0x39abb661f9de42ab, 0xbd1445dc5bd699f5, 0x4a712a4ec0f6ad16,
+ 0xb030578e126271d9, 0x016c7786ad811f2f, 0x3f008771cbc51da3,
+ 0xee54029d620a268b, 0xf113fb4db1e61178, 0x4d9b17b8d749d33c,
+ 0x3fae1a7d6a75eae0, 0x0a82e733284829bb, 0x428cd66f1111ea6b,
+ 0xcde75290940e163c, 0x2ac36f4275e6b1f3, 0x55218c3b23a5c0af,
+ 0x702561c51c7ae39d, 0x9742a7d7734ec8ad, 0x44e315fd1d3cc11c,
+ 0xe9df1b82b51afde9, 0x8bfcd51ef53786b0, 0x50f72953b97fcd8a,
+ 0x9e5e0e328a9fb379, 0xe00503e1bf695662, 0x570877efb55fe16c,
+ 0x8b5d9fa4492d308d, 0xe8ce667f65be3292, 0xcfe03b6dc1b5e23e,
+ 0xabe78bbaa44dd140, 0x9b8f6fc066d006f6, 0xc5cfb9e25f5dc3bd,
+ 0xcd7192239e683a57, 0x45f09fe3e185ef0e, 0x71c2f9dd7e142ee0,
+ 0x3c9753fcdc338282, 0x297fea93a0b45f17, 0x5973f41e5cd33e59,
+ 0x47e5debd710929b1, 0xbb2ec8f92110b963, 0x9e5b513fac57aa5d,
+ 0x880ce151c8885aeb, 0xe06dcc2a38e01e7b, 0x59a67fb6dfc45f9d,
+ 0xc9689eee5af6ca69, 0xb4a4434deac0e0f6, 0x80635c419b64414e,
+ 0xec11e7690cbc9654, 0x40d19437677669e8, 0xe6b9a15967cca92a,
+ 0xb1cfc4ab2c97d646, 0xb5f9b84aab024be7, 0xacb8ca17c1d43afc,
+ 0x4f2615eca86370c4, 0xea2e6e8cefa08fec, 0x6fe0d48cf4f9bb7a,
+ 0x819d50f8a0a2f4e7, 0x778229b6aeb7675c, 0xb48e63ade13c3efb,
+ 0x393d6b0148f3a1dd, 0xb34a17fe98c4ca22, 0x0fddc6975404c1c7,
+ 0xfd9a5dd77719d06b, 0x62ce27a613a02939, 0xa411fd8b9f38aad3,
+ 0x959fee309602208a, 0x94f58bea92da8157, 0x78d488d1a96562d0,
+ 0x50267632539b5670, 0x82346ba4dcd0c139, 0x6f7fa57f7370b7eb,
+ 0x99e61e66cbcbdd9f, 0x112062773b64a44c, 0x2f232e802187e965,
+ 0x0d97675119f49349, 0x19cd687daaef751c, 0x925f0de9a378f2dc,
+ 0x3e29fffc329e48b9, 0x28ec73d273a6af7b, 0xdb215426d47b2fac,
+ 0x69363d6442966fec, 0x22a1023f31d1c003, 0xa39683481befeab3,
+ 0x6a9ce2fb5b0413e6, 0x52278f8738a3c77f, 0x7efe929bc02210ab,
+ 0x84b521bef0794965, 0x8a54b10d10585800, 0xb699fd9798dc7600,
+ 0x1c7dec4b1206c6cf, 0x56dcf11409750d1d, 0xd3b9dd14e700778a,
+ 0xef8e3e8d316a7193, 0x1c4dc781286ed0ae, 0x2f4d92403b0686c6,
+ 0xf602c221eb263c0e, 0x56eb5b40a9e95d5a, 0x90e7430d882b27d0,
+ 0xd3db5a21218e760e, 0x83243843564a0c75, 0xdcbe098566caf812,
+ 0xa126594777635e3a, 0xf792d21d9b121e07, 0x7003ddd2078b9ef5,
+ 0x482f789dd535ab41, 0xc653f09859c1525a, 0x5432df7a54a8ca43,
+ 0xce2f01032e907477, 0x315865c590ec7532, 0x1e32514a3499e117,
+ 0x2d031ce4cf41bff8, 0xb97b106d4be29042, 0x7faea6fcd2dfb531,
+ 0x4efd476c84ca83e7, 0x8339ab2e18c3217a, 0xdcd871206159b55a,
+ 0x873035ded72ab02a, 0xab127fdb56d60070, 0x9a9de182e66987e9,
+ 0x1782019572601a4c, 0xa60be9baff96575a, 0x0714fb22f0318e9b,
+ 0x0e6e1d127f25d4b9, 0x380b6deef8724c83, 0x41ee41063bc27a10,
+ 0x1f25c3e5c255b1ab, 0x3200ee28c726cf42, 0x4d50112554b8cff9,
+ 0xf2bd5a0f724875cb, 0x263d633b1c2db127, 0xf309cd49c365c56a,
+ 0x5140770c2119da55, 0xd9d1da022eae02f2, 0x82b110e7b32686bf,
+ 0xc9bcd73d74886192, 0x20606cd1ce35faa4, 0xe7582de111d5aa8e,
+ 0x0ab975d7ad281f41, 0x6e2c02862c849c8e, 0xbb90b0fc5a001e1a,
+ 0x6d464c679dc429aa, 0x05c67785cdd843fc, 0xaea2420102900ce3,
+ 0xffcb87d18454fd37, 0x077a7fa5c2d6e0e7, 0x3784db7113ae81b7,
+ 0xb7921aad40c234b7, 0x278b80042d5ddc6f, 0x476b294282485fe7,
+ 0x7b2ddd24be97ed2c, 0x24cbb8b2365104a7, 0xef4c4976f47fb62c,
+ 0x55b0382e963d769d, 0x435660d7467979e4, 0x7a32667b11077322,
+ 0x0ad6dcb99ea12168, 0x33720004c4f49110, 0x06e309d36a426b5d,
+ 0x22d9a3027c7ea365, 0xefc487aedfa75e83, 0xa1945f93213d4026,
+ 0x08de616b53ea0a26, 0x59267b076245b03c, 0xd9f770cc079aa736,
+ 0xa8a5e7832132480f, 0x9561f31cc02747d6, 0x39a3854b34a4bf60,
+ 0x618dff22e84133e8, 0x6a68b99ae0a7bd97, 0xf550fda7488ec844,
+ 0x418548ca5b581579, 0x95306c4ebeb82ab2, 0xe76a8c127dbcc7f0,
+ 0x41093c9ed57c2850, 0x2d475a04fd6bb099, 0x8eff00d6a0a9b72c,
+ 0x0cdec36f32c63e47, 0x01b41c0c2bca6d0a, 0x09fbd8929ea4ecf1,
+ 0x15c596aafae28c11, 0xaae69bb178a0f551, 0x6f9c9284367b14fc,
+ 0xc010787f178dc7bd, 0x4f69a7e5b6e5ffdd, 0x0bfc188e9d01e957,
+ 0x5fe55cdd42088924, 0x5eb120f78a7a1dc7, 0x2830f8fbef3467e3,
+ 0x9fe168f5165872a3, 0xdca316cf5c1b8d38, 0xf5398dee1fbbf5b0,
+ 0xe3a20ae7e8137910, 0x010fc7c8aca95d23, 0x18f2b9763036551f,
+ 0x6cdda78c9c2e949a, 0x76470871f08d5485, 0x2ba5aed22736bd9e,
+ 0x4f699a5ddcc79c6d, 0x824ada73883ea2fe, 0x8afd594ef36ccb7b,
+ 0x47750f86b32d635b, 0x78e85472be4794d5, 0x3f339edeb79a720e,
+ 0x630962b1e15f5273, 0x6187bb74da965b77, 0xb3e59304443bb7ff,
+ 0x664a0113041d3c2d, 0xcea784476652dc97, 0x829567ee10aa2857,
+ 0x2dccf72f6f28190d, 0x0ec39401542615cb, 0x64aeae585d06173a,
+ 0x1a6c4d559736aea3, 0x1d5e7495676f21ac, 0xfc19bc52f9bf3e30,
+ 0xb3a59264e4ef95b5, 0xbdcd7302ea7faa2d, 0xd98551f73ab8ed58,
+ 0xfb324a56cf96d04f, 0xee9c1e176334d51b, 0x2ad9d156c6658123,
+ 0x8f8e3daa4999296a, 0xaaaf7c1c2620fb89, 0xaafd7aa956dc86be,
+ 0xd2abdb895dc43501, 0x6c73ccd01dcf50d1, 0x97f6d7544fc8285a,
+ 0xf3914305defbc0b6, 0xd2769433c3859cdb, 0x23e15aae6b12118b,
+ 0x35e8e9625c7d9f15, 0x4e12f6d108a8e214, 0xd7ef960ef2d9608c,
+ 0xd78b96b7f3333c2f, 0xd47d7397721a5abd, 0x20dd675b2b3e528f,
+ 0xfdd0f65e775b6f29, 0x0d0905377a313614, 0xcc08967d418755fa,
+ 0x8d08ae5210e2bd66, 0xed23b7c7e620f9a5, 0xb19558ea7b407ca3,
+ 0xd7546cd371e125ea, 0x65fb344ffe3fce1e, 0xbd0aff4f90398942,
+ 0x18eec4579a6513ef, 0xee46032eca3bd8f8, 0xcecf75a42b64ac92,
+ 0x840738d2a5036b77, 0x87f110b2d7b2f30c, 0x7eb3d6e2feaa4c27,
+ 0x9d14293a8d507e0b, 0x312c4224e649ac80, 0x78b7e688bab4e08c,
+ 0xf0445368e1e20fcc, 0x90aedf5712335e26, 0x406e29fc62c554e6,
+ 0x41ba4d0676acdf88, 0x4dc162db635e4e2d, 0x61a4ec66e3d33d36,
+ 0x657aa838bb43771d, 0xab67a59848b66f93, 0x95a346e32a8f068f,
+ 0x2e4e5f10d06eb234, 0x54a5f91f528e69cd, 0x07fe5001f2f5920d,
+ 0x712bd9fb5a456fe3, 0xcc31fc24e78483bc, 0xa99fcd595e4fc4c9,
+ 0x6de433cb874b6d21, 0xd70ca7ed81922e93, 0x80e092a5862869c6,
+ 0x19845fafb068554c, 0xbf38855e21ed8042, 0x6c041c4d1036761c,
+ 0x43a49f847ebed2e2, 0x88de1cc8339069d7, 0x6d0a09838d8ad25b,
+ 0x4ac147b6ac8001e6, 0x9512e9d6dd97b9a0, 0x7810aef0930819e7,
+ 0xcc5018aad164720b, 0x972051c2cd0b15f1, 0xff694c53a87b8e1c,
+ 0xc179cac2bae6d94c, 0x9f61f6dd19cc1c75, 0x92811bd14d2ce143,
+ 0xf9e60e3dcaa1922c, 0x391071ee5a3fe90c, 0x68c0bd7b76087923,
+ 0x463c3c1d0409ae7c, 0x0042bdf29dc74e95, 0x00d88d2841e320fb,
+ 0x36be524556fddd38, 0xe78637781afc8c89, 0xe6a2faaa4e91a364,
+ 0x756595847eacce0c, 0xefbf1db10abe8412, 0xe7c5ef9963bf0029,
+ 0xeeae9e62ea636bcf, 0x5f91f4b8c0b9e747, 0xf61ef37e01ce18c5,
+ 0x9c91d841f20223ec, 0xc74f303e055c6692, 0x36938ce9d194a2ae,
+ 0xe68304239d68512e, 0x31c5630c99e37e72, 0x94a8f7f28eadd7a6,
+ 0x274f91b691dd4110, 0x862bbc615c8e9119, 0x18b3f4de82b84c0c,
+ 0x362174aa177b3934, 0x5ee0b572d79f33b0, 0x5015663c7c0a1898,
+ 0x6e98ae22acfb7d26, 0xf1c798857164d2d9, 0x38475f99bdd51384,
+ 0x69d5b2521197dec0, 0x16e8e95521adc2e7, 0x979b510a203d9fbd,
+ 0x86fc15ac3e9c53d4, 0x064c689f6b4a3cbf, 0x88c7307d728eaa30,
+ 0xd71e339ac972cee6, 0xc504b10f2cee045e, 0x6381c36dee9569c3,
+ 0x1dabd24fb2d6801e, 0x8e9522b2061dcb45, 0xa47a75969c3b945c,
+ 0xda80510a0f881646, 0xa2bad4ea35a04327, 0x00000000000005ff,
+};
+
+const ulong pc_smallprimes[PC_SMALLPRIMES_LEN] = {
+ 2, 3, 5, 7, 11, 13, 17, 19, 23,
+ 29, 31, 37, 41, 43, 47, 53, 59, 61,
+ 67, 71, 73, 79, 83, 89, 97, 101, 103,
+ 107, 109, 113, 127, 131, 137, 139, 149, 151,
+ 157, 163, 167, 173, 179, 181, 191, 193, 197,
+ 199, 211, 223, 227, 229, 233, 239, 241, 251,
+ 257, 263, 269, 271, 277, 281, 283, 293, 307,
+ 311, 313, 317, 331, 337, 347, 349, 353, 359,
+ 367, 373, 379, 383, 389, 397, 401, 409, 419,
+ 421, 431, 433, 439, 443, 449, 457, 461, 463,
+ 467, 479, 487, 491, 499, 503, 509, 521, 523,
+ 541, 547, 557, 563, 569, 571, 577, 587, 593,
+ 599, 601, 607, 613, 617, 619, 631, 641, 643,
+ 647, 653, 659, 661, 673, 677, 683, 691, 701,
+ 709, 719, 727, 733, 739, 743, 751, 757, 761,
+ 769, 773, 787, 797, 809, 811, 821, 823, 827,
+ 829, 839, 853, 857, 859, 863, 877, 881, 883,
+ 887, 907, 911, 919, 929, 937, 941, 947, 953,
+ 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
+ 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
+ 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129,
+ 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
+ 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
+ 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
+ 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427,
+ 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481,
+ 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543,
+ 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
+ 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
+ 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
+ 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801,
+ 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
+ 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951,
+ 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
+ 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087,
+ 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143,
+ 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239,
+ 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
+ 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
+ 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
+ 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521,
+ 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593,
+ 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671,
+ 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713,
+ 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789,
+ 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
+ 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927,
+ 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
+ 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
+ 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181,
+ 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253,
+ 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
+ 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389,
+ 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
+ 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
+ 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
+ 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673,
+ 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739,
+ 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823,
+ 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
+ 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967,
+ 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
+ 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
+ 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
+ 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261,
+ 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349,
+ 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441,
+ 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513,
+ 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591,
+ 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
+ 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733,
+ 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813,
+ 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919,
+ 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973,
+ 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039,
+ 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113,
+ 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209,
+ 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297,
+ 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393,
+ 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
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+ 54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073,
+ 55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201,
+ 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291,
+ 55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381,
+ 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 55511,
+ 55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621,
+ 55631, 55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691,
+ 55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793, 55799,
+ 55807, 55813, 55817, 55819, 55823, 55829, 55837, 55843, 55849,
+ 55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933,
+ 55949, 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053,
+ 56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149,
+ 56167, 56171, 56179, 56197, 56207, 56209, 56237, 56239, 56249,
+ 56263, 56267, 56269, 56299, 56311, 56333, 56359, 56369, 56377,
+ 56383, 56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467,
+ 56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519, 56527,
+ 56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629,
+ 56633, 56659, 56663, 56671, 56681, 56687, 56701, 56711, 56713,
+ 56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807, 56809,
+ 56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897,
+ 56909, 56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963,
+ 56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073,
+ 57077, 57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149,
+ 57163, 57173, 57179, 57191, 57193, 57203, 57221, 57223, 57241,
+ 57251, 57259, 57269, 57271, 57283, 57287, 57301, 57329, 57331,
+ 57347, 57349, 57367, 57373, 57383, 57389, 57397, 57413, 57427,
+ 57457, 57467, 57487, 57493, 57503, 57527, 57529, 57557, 57559,
+ 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667,
+ 57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737,
+ 57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809, 57829,
+ 57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923,
+ 57943, 57947, 57973, 57977, 57991, 58013, 58027, 58031, 58043,
+ 58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129,
+ 58147, 58151, 58153, 58169, 58171, 58189, 58193, 58199, 58207,
+ 58211, 58217, 58229, 58231, 58237, 58243, 58271, 58309, 58313,
+ 58321, 58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403,
+ 58411, 58417, 58427, 58439, 58441, 58451, 58453, 58477, 58481,
+ 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, 58603,
+ 58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711,
+ 58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831,
+ 58889, 58897, 58901, 58907, 58909, 58913, 58921, 58937, 58943,
+ 58963, 58967, 58979, 58991, 58997, 59009, 59011, 59021, 59023,
+ 59029, 59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107,
+ 59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197,
+ 59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273,
+ 59281, 59333, 59341, 59351, 59357, 59359, 59369, 59377, 59387,
+ 59393, 59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453,
+ 59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557, 59561,
+ 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, 59659,
+ 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743,
+ 59747, 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863,
+ 59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999,
+ 60013, 60017, 60029, 60037, 60041, 60077, 60083, 60089, 60091,
+ 60101, 60103, 60107, 60127, 60133, 60139, 60149, 60161, 60167,
+ 60169, 60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289,
+ 60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397,
+ 60413, 60427, 60443, 60449, 60457, 60493, 60497, 60509, 60521,
+ 60527, 60539, 60589, 60601, 60607, 60611, 60617, 60623, 60631,
+ 60637, 60647, 60649, 60659, 60661, 60679, 60689, 60703, 60719,
+ 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779, 60793,
+ 60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913,
+ 60917, 60919, 60923, 60937, 60943, 60953, 60961, 61001, 61007,
+ 61027, 61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129,
+ 61141, 61151, 61153, 61169, 61211, 61223, 61231, 61253, 61261,
+ 61283, 61291, 61297, 61331, 61333, 61339, 61343, 61357, 61363,
+ 61379, 61381, 61403, 61409, 61417, 61441, 61463, 61469, 61471,
+ 61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553,
+ 61559, 61561, 61583, 61603, 61609, 61613, 61627, 61631, 61637,
+ 61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 61717,
+ 61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843,
+ 61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967,
+ 61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047,
+ 62053, 62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137,
+ 62141, 62143, 62171, 62189, 62191, 62201, 62207, 62213, 62219,
+ 62233, 62273, 62297, 62299, 62303, 62311, 62323, 62327, 62347,
+ 62351, 62383, 62401, 62417, 62423, 62459, 62467, 62473, 62477,
+ 62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581,
+ 62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 62659,
+ 62683, 62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773,
+ 62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873, 62897,
+ 62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983,
+ 62987, 62989, 63029, 63031, 63059, 63067, 63073, 63079, 63097,
+ 63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211,
+ 63241, 63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331,
+ 63337, 63347, 63353, 63361, 63367, 63377, 63389, 63391, 63397,
+ 63409, 63419, 63421, 63439, 63443, 63463, 63467, 63473, 63487,
+ 63493, 63499, 63521, 63527, 63533, 63541, 63559, 63577, 63587,
+ 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649,
+ 63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719,
+ 63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799, 63803,
+ 63809, 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907,
+ 63913, 63929, 63949, 63977, 63997, 64007, 64013, 64019, 64033,
+ 64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, 64153,
+ 64157, 64171, 64187, 64189, 64217, 64223, 64231, 64237, 64271,
+ 64279, 64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381,
+ 64399, 64403, 64433, 64439, 64451, 64453, 64483, 64489, 64499,
+ 64513, 64553, 64567, 64577, 64579, 64591, 64601, 64609, 64613,
+ 64621, 64627, 64633, 64661, 64663, 64667, 64679, 64693, 64709,
+ 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849,
+ 64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927,
+ 64937, 64951, 64969, 64997, 65003, 65011, 65027, 65029, 65033,
+ 65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123,
+ 65129, 65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203,
+ 65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, 65323,
+ 65327, 65353, 65357, 65371, 65381, 65393, 65407, 65413, 65419,
+ 65423, 65437, 65447, 65449, 65479, 65497, 65519, 65521,
+};
diff --git a/precomputed.h b/precomputed.h
@@ -0,0 +1,21 @@
+// --------------- precomputed.h ---------------------
+#ifndef PRECOMPUTED_H
+#define PRECOMPUTED_H
+
+/**
+ * This file has been automatically computed using the
+ * precompute/header utility. The purpose is to store
+ * some constant values, such as
+ *
+ * - limbs of a primorial (product of small primes)
+ * - list of small primes
+ */
+
+#include <flint.h>
+
+#define PC_PRIMORIAL_UI_ARRAY_LEN 1470
+#define PC_SMALLPRIMES_LEN 6542
+
+extern const ulong pc_primorial_ui_array[PC_PRIMORIAL_UI_ARRAY_LEN];
+extern const ulong pc_smallprimes[PC_SMALLPRIMES_LEN];
+#endif
diff --git a/precomputers/header.c b/precomputers/header.c
@@ -0,0 +1,139 @@
+/**
+ * Precomputer for metaprogramming generated precomputed.h header
+ * file that is useful.
+ */
+#include <flint.h>
+#include <fmpz.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <assert.h>
+
+#define SMALLPRIME_LIMIT (1<<16)
+
+static slong
+calc_len(fmpz_t n)
+{
+ assert(fmpz_cmp_ui(n, 0) > 0);
+ return (slong) fmpz_size(n);
+}
+
+static void
+pparray(FILE* f, const ulong *a, const slong len)
+{
+ slong i;
+ for(i = 0; i < len; i++) {
+ if(i == 0) {
+ fprintf(f, " ");
+ } else if(i % 8 == 0) {
+ fprintf(f, "\n ");
+ }
+ fprintf(f, "0x%016lx, ", a[i]);
+ }
+}
+
+// ugly, but okay for precomputer
+static size_t
+count_smallprimes(size_t limit)
+{
+ fmpz_t p;
+ fmpz_init_set_ui(p, 2);
+ size_t i = 0;
+
+ while (fmpz_cmp_ui(p, limit) < 0) {
+ fmpz_nextprime(p, p, 0);
+ i++;
+ }
+ fmpz_clear(p);
+
+ return i;
+}
+
+static void
+print_disclaimer(FILE* f)
+{
+ fprintf(f, "/**\n"
+ " * This file has been automatically computed using the\n"
+ " * precompute/header utility. The purpose is to store\n"
+ " * some constant values, such as\n"
+ " *\n"
+ " * - limbs of a primorial (product of small primes)\n"
+ " * - list of small primes\n"
+ " */\n\n");
+}
+
+int
+main(void)
+{
+ // -= header file =-
+
+ fmpz_t primorial;
+ fmpz_init(primorial);
+
+ fmpz_primorial(primorial, 1 << 16);
+
+ slong len = calc_len(primorial);
+ ulong *out = malloc(len * sizeof(*out));
+
+ fmpz_get_ui_array(out, len, primorial);
+
+ FILE* header = fopen("/tmp/precomputed.h", "w");
+ fprintf(header, "// --------------- precomputed.h ---------------------\n");
+ fprintf(header, "#ifndef PRECOMPUTED_H\n"
+ "#define PRECOMPUTED_H\n\n");
+ print_disclaimer(header);
+ fprintf(header, "#include <flint.h>\n\n");
+
+ fprintf(header, "#define PC_PRIMORIAL_UI_ARRAY_LEN %ld\n", len);
+ fprintf(header, "#define PC_SMALLPRIMES_LEN %ld\n\n",
+ count_smallprimes(SMALLPRIME_LIMIT));
+ fprintf(header, "extern const ulong "
+ "pc_primorial_ui_array[PC_PRIMORIAL_UI_ARRAY_LEN];\n"
+ "extern const ulong "
+ "pc_smallprimes[PC_SMALLPRIMES_LEN];\n"
+ "#endif\n\n");
+ fclose(header);
+
+ // -= source file =-
+
+ FILE* source = fopen("/tmp/precomputed.c", "w");
+ fprintf(source, "// ------------- precomputed.c ------------------------\n");
+
+ print_disclaimer(source);
+ fprintf(source, "#include \"precomputed.h\"\n");
+ fprintf(source, "const ulong "
+ "pc_primorial_ui_array[PC_PRIMORIAL_UI_ARRAY_LEN] = {\n");
+ pparray(source, out, len);
+ fprintf(source, "};\n\n");
+
+ fmpz_clear(primorial);
+ free(out);
+
+ // -= small primes =-
+
+ fmpz_t p;
+ fmpz_init_set_ui(p, 2);
+ size_t i = 0;
+
+ fprintf(source, "const ulong pc_smallprimes[PC_SMALLPRIMES_LEN] = {\n");
+ while (fmpz_cmp_ui(p, (1 << 16)) < 0) {
+ if (i == 0) {
+ fprintf(source, " ");
+ } else if (i % 8 == 0) {
+ fprintf(source, "\n ");
+ }
+
+ fmpz_fprint(source, p);
+ fprintf(source, ", ");
+
+ fmpz_nextprime(p, p, 0);
+
+ i++;
+ }
+ fprintf(source, "};\n\n");
+
+ fclose(source);
+ fmpz_clear(p);
+
+ return 0;
+}
diff --git a/prodtree.c b/prodtree.c
@@ -1,8 +1,8 @@
-#include <stdlib.h>
#include <err.h>
#include <fmpz.h>
#include <fmpz_vec.h>
#include <stdio.h>
+#include <stdlib.h>
#include "prodtree.h"
@@ -50,7 +50,7 @@ prodtree_compute(fmpz **res, const fmpz *v, slong nv)
}
void
-prodtree_pprint(const fmpz* v, const slong nv)
+prodtree_pprint(const fmpz *v, const slong nv)
{
slong i, j = 0, row_len = (nv + 1) >> 1;
@@ -59,7 +59,7 @@ prodtree_pprint(const fmpz* v, const slong nv)
printf(" ");
j++;
-
+
if (j == row_len) {
printf("\n");
row_len >>= 1;
diff --git a/prodtree.h b/prodtree.h
@@ -18,7 +18,7 @@
* @param nv size of the vector n
* @returns size of the product tree
*/
-slong prodtree_compute(fmpz** res, const fmpz* v, slong nv);
+slong prodtree_compute(fmpz **res, const fmpz *v, slong nv);
/**
* Pretty print a product tree.
@@ -26,6 +26,6 @@ slong prodtree_compute(fmpz** res, const fmpz* v, slong nv);
* @param v the product tree to print (as a vector)
* @param nv the size (number of nodes) of the prouct tree
*/
-void prodtree_pprint(const fmpz* v, const slong nv);
+void prodtree_pprint(const fmpz *v, const slong nv);
#endif
diff --git a/smallfactor.c b/smallfactor.c
@@ -1,47 +1,16 @@
#include "smallfactor.h"
-void
-euclidean_ctx_init(euclidean_ctx *ctx)
-{
- fmpz_init2(ctx->primorial, NLIMBS_PRECOMPUTE_PRIMORIAL);
- fmpz_from_digits();
-}
-
-#define N_EIGHT_BIT_PRIMES 54
-const uint64_t EIGHT_BIT_PRIMES[N_EIGHT_BIT_PRIMES] = {
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
- 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79,
- 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137,
- 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
- 197, 199, 211, 223, 227, 229, 233, 239, 241, 251};
-
size_t
-smallfactor_euclidean(fmpz_t out, fmpz_t n)
+smallfactor_euclidean(ctx_t *ctx, fmpz_t out, const fmpz_t n)
{
- size_t i;
- fmpz_t r;
- FILE *primorial_file = fopen(SMALLFACTOR_PRIMORIAL_FILENAME, "rb");
-
- if (primorial_file == NULL) {
- fprintf(stderr,
- "Error! smallfactor_euclidean: "
- "could not open asset file %s\n",
- SMALLFACTOR_PRIMORIAL_FILENAME);
- exit(EXIT_FAILURE);
- }
+ assert(ctx->has_primorial);
+ assert(ctx->nsmallprimes > 0);
+ assert(ctx->smallprimes != NULL);
+ assert(ctx->zs_alloc > 1);
- fmpz_t primorial;
- fmpz_init(primorial);
-
- if (fmpz_inp_raw(primorial, primorial_file) == 0) {
- fprintf(stderr, "Error! smallfactor_euclidean: "
- "could not read primorial from asset file\n");
- exit(EXIT_FAILURE);
- }
-
- fclose(primorial_file);
+ size_t i;
- fmpz_gcd(out, n, primorial);
+ fmpz_gcd(out, n, ctx->primorial);
if (fmpz_cmp_ui(out, 1) > 0 && fmpz_cmp(out, n) < 0) {
// 1 < g < n
@@ -53,18 +22,17 @@ smallfactor_euclidean(fmpz_t out, fmpz_t n)
return SMALLFACTOR_NOT_FOUND;
} else {
// n is either prime or has an 8-bit prime factor, trial divide
- fmpz_init(r);
- for (i = 0; i < N_EIGHT_BIT_PRIMES; i++) {
- fmpz_set_ui(r, EIGHT_BIT_PRIMES[i]);
- fmpz_tdiv_qr(out, r, n, r);
+ i = 0;
+ while (fmpz_cmp_ui(&ctx->smallprimes[i], 256) < 0) {
+ fmpz_tdiv_qr(out, &(ctx->smallprimes[i]), n,
+ &(ctx->smallprimes[i]));
- if (fmpz_cmp_ui(r, 0) == 0)
- break;
- }
- fmpz_clear(r);
+ if (fmpz_cmp_ui(&(ctx->smallprimes[i]), 0) == 0) {
+ return SMALLFACTOR_FOUND;
+ }
- if (i < N_EIGHT_BIT_PRIMES)
- return SMALLFACTOR_FOUND;
+ i++;
+ }
}
}
diff --git a/smallfactor.h b/smallfactor.h
@@ -1,10 +1,13 @@
#ifndef SMALLFACTOR_H
#define SMALLFACTOR_H
+#include <assert.h>
#include <flint.h>
#include <fmpz.h>
#include <stdlib.h>
+#include "context.h"
+
#define SMALLFACTOR_FOUND 1
#define SMALLFACTOR_NOT_FOUND 0
@@ -27,6 +30,6 @@
* SMALLFACTOR_FOUND if out was set to a nontrivial factor of n
* SMALLFACTOR_NOT_FOUND otherwise
*/
-size_t smallfactor_euclidean(fmpz_t out, fmpz_t n);
+size_t smallfactor_euclidean(ctx_t *ctx, fmpz_t out, const fmpz_t n);
#endif
diff --git a/test_angrepp.c b/test_angrepp.c
@@ -1,15 +1,15 @@
#include <assert.h>
-#include <stdio.h>
-#include <stdlib.h>
#include <flint.h>
#include <fmpz.h>
#include <fmpz_vec.h>
+#include <stdio.h>
+#include <stdlib.h>
#include "cyclefind.h"
#include "pierre.h"
-#include "wiener.h"
-#include "smallfactor.h"
#include "prodtree.h"
+#include "smallfactor.h"
+#include "wiener.h"
static uint64_t
test_f(uint64_t x)
@@ -86,20 +86,27 @@ static void
test_smallfactor_euclidean(void)
{
fmpz_t N, res;
+ ctx_t ctx;
+
int ret;
fmpz_init(N);
fmpz_init(res);
+ ctx_init(&ctx);
+ ctx_set_precomputed_primorial(&ctx);
+ ctx_set_precomputed_smallprimes(&ctx);
+
// N = 61363 * 1278934673
fmpz_set_str(N, "78607161806599", 10);
- ret = smallfactor_euclidean(res, N);
+ ret = smallfactor_euclidean(&ctx, res, N);
assert(ret == SMALLFACTOR_FOUND);
assert(fmpz_divisible(N, res));
assert(fmpz_cmp_ui(res, 1) > 0);
assert(fmpz_cmp(res, N) < 0);
+ ctx_clear(&ctx);
fmpz_clear(N);
fmpz_clear(res);
}
@@ -113,17 +120,17 @@ test_prodtree(void)
fmpz_init_set_ui(sju, 7);
fmpz v[3] = {tre[0], fem[0], sju[0]};
- fmpz* res;
+ fmpz *res;
slong lres = prodtree_compute(&res, v, 3);
assert(lres == 7);
- assert(fmpz_cmp_ui(&res[0], 3) == 0);
- assert(fmpz_cmp_ui(&res[1], 5) == 0);
- assert(fmpz_cmp_ui(&res[2], 7) == 0);
- assert(fmpz_cmp_ui(&res[3], 1) == 0);
+ assert(fmpz_cmp_ui(&res[0], 3) == 0);
+ assert(fmpz_cmp_ui(&res[1], 5) == 0);
+ assert(fmpz_cmp_ui(&res[2], 7) == 0);
+ assert(fmpz_cmp_ui(&res[3], 1) == 0);
assert(fmpz_cmp_ui(&res[4], 15) == 0);
- assert(fmpz_cmp_ui(&res[5], 7) == 0);
+ assert(fmpz_cmp_ui(&res[5], 7) == 0);
assert(fmpz_cmp_ui(&res[6], 105) == 0);
_fmpz_vec_clear(res, lres);
diff --git a/tools/dbtool.c b/tools/dbtool.c
@@ -17,14 +17,13 @@
enum command { INSERT, CREATE, NONE };
// layout of tables to create as (table name, column definition) pairs
-const char* layout[][2] = {
- { "factor", "modulus TEXT, factor TEXT, callback INTEGER" },
- { "same", "id INTEGER PRIMARY KEY, row INTEGER" },
- { "products", "id INTEGER PRIMARY KEY, product TEXT" },
- { "tree", "node_id INTEGER, left_row INTEGER, right_row INTEGER" },
- { "forest", "root_row INTEGER" },
- { NULL, NULL }
-};
+const char *layout[][2] = {
+ {"factor", "modulus TEXT, factor TEXT, callback INTEGER"},
+ {"same", "id INTEGER PRIMARY KEY, row INTEGER"},
+ {"products", "id INTEGER PRIMARY KEY, product TEXT"},
+ {"tree", "node_id INTEGER, left_row INTEGER, right_row INTEGER"},
+ {"forest", "root_row INTEGER"},
+ {NULL, NULL}};
static void
usage(char *c)
@@ -46,37 +45,38 @@ create_tables(sqlite3 *db)
size_t i = 0;
while (layout[i][0] != NULL) {
- fprintf(stderr, "[+] Creating the \"%s\" table...\n", layout[i][0]);
-
- snprintf(buffer, 4096, "CREATE TABLE %s (%s);", layout[i][0], layout[i][1]);
-
+ fprintf(stderr, "[+] Creating the \"%s\" table...\n", layout[i][0]);
+
+ snprintf(buffer, 4096, "CREATE TABLE %s (%s);", layout[i][0],
+ layout[i][1]);
+
rc = sqlite3_prepare(db, buffer, -1, &ppStmt, NULL);
-
+
if (rc != SQLITE_OK) {
errx(EXIT_FAILURE, "prepare statement error: %s\n",
sqlite3_errmsg(db));
} else {
fprintf(stderr, " [-] Prepared statement successfully\n");
}
-
+
while ((rc = sqlite3_step(ppStmt)) == SQLITE_BUSY) {
fprintf(stderr, " [-] Busy, sleeping...\n");
sleep(1);
}
-
+
if (rc != SQLITE_DONE) {
errx(EXIT_FAILURE, "step error: %s\n", sqlite3_errmsg(db));
} else {
fprintf(stderr, " [-] Table creation returned okay\n");
}
-
+
rc = sqlite3_finalize(ppStmt);
-
+
if (rc != SQLITE_OK) {
errx(EXIT_FAILURE, "finalize prepared statement error: %s\n",
sqlite3_errmsg(db));
}
-
+
fprintf(stderr, "[+] Done creating the factor table\n");
i++;
diff --git a/tools/small.c b/tools/small.c
@@ -3,6 +3,7 @@
#include <stdio.h>
#include <stdlib.h>
+#include "context.h"
#include "fmpzio.h"
#include "smallfactor.h"
@@ -10,15 +11,21 @@ int
main(void)
{
fmpz_t read, factor;
+ ctx_t ctx;
fmpz_init(factor);
fmpz_init(read);
+ ctx_init(&ctx);
+ ctx_set_precomputed_primorial(&ctx);
+ ctx_set_precomputed_smallprimes(&ctx);
+
while (read_next_hex_fmpz(read) == 0) {
- smallfactor_euclidean(factor, read);
+ smallfactor_euclidean(&ctx, factor, read);
fmpz_print(factor);
printf("\n");
}
+ ctx_clear(&ctx);
fmpz_clear(factor);
fmpz_clear(read);
diff --git a/tools/varmkorv.c b/tools/varmkorv.c
@@ -10,7 +10,7 @@ int
main(void)
{
fmpz_t e, N, res;
- fmpz_init(e);
+ fmpz_init(e);
fmpz_init(N);
fmpz_init(res);
@@ -23,7 +23,7 @@ main(void)
break;
}
- if(wiener_factor_small_d(res, e, N)) {
+ if (wiener_factor_small_d(res, e, N)) {
fmpz_print(res);
printf("\n");
} else {
