[Boost-commit] svn:boost r49475 - in sandbox/mp_math: boost/mp_math/mp_int libs/mp_math/test

Subject: [Boost-commit] svn:boost r49475 - in sandbox/mp_math: boost/mp_math/mp_int libs/mp_math/test
From: baraclese_at_[hidden]
Date: 2008-10-28 13:25:49

Author: baraclese
Date: 2008-10-28 13:25:48 EDT (Tue, 28 Oct 2008)
New Revision: 49475
URL: http://svn.boost.org/trac/boost/changeset/49475

Log:
* boost/mp_math/mp_int/pow.hpp: added pow(const mp_int<>&, const mp_int<>&)
* libs/mp_math/test/pow.cpp: added test cases for new functionality
* boost/mp_math/mp_int/div.hpp: converted /* ... */ to // ... comments

Text files modified: 
   sandbox/mp_math/boost/mp_math/mp_int/div.hpp |   106 +++++-----                              
   sandbox/mp_math/boost/mp_math/mp_int/pow.hpp |    18 +                                       
   sandbox/mp_math/libs/mp_math/test/pow.cpp    |   380 ++++++++++++++++++++++++++++++++++++++++
   3 files changed, 448 insertions(+), 56 deletions(-)

Modified: sandbox/mp_math/boost/mp_math/mp_int/div.hpp
==============================================================================
--- sandbox/mp_math/boost/mp_math/mp_int/div.hpp	(original)
+++ sandbox/mp_math/boost/mp_math/mp_int/div.hpp	2008-10-28 13:25:48 EDT (Tue, 28 Oct 2008)
@@ -49,18 +49,18 @@
   return static_cast<digit_type>(w);
 }
 
-/* b = a/2 */
+// *this /= 2
 template<class A, class T>
 void mp_int<A,T>::divide_by_2()
 {
   digit_type carry = 0;
   for (reverse_iterator d = rbegin(); d != rend(); ++d)
   {
-    /* get the carry for the next iteration */
+    // get the carry for the next iteration
     const digit_type rr = *d & 1;
-    /* shift the current digit, add in carry and store */
+    // shift the current digit, add in carry and store
     *d = (*d >> 1) | (carry << (valid_bits - 1));
-    /* forward carry to next iteration */
+    // forward carry to next iteration
     carry = rr;
   }
   clamp();
@@ -68,13 +68,14 @@
     sign_ = 1;
 }
 
-/* divide by three (based on routine from MPI and the GMP manual) */
+// divide by three (based on routine from MPI and the GMP manual)
 template<class A, class T>
 typename mp_int<A,T>::digit_type
 mp_int<A,T>::divide_by_3()
 {
-  /* b = 2**valid_bits / 3 */
-  const word_type b = (word_type(1) << static_cast<word_type>(valid_bits)) / word_type(3);
+  // b = 2**valid_bits / 3
+  const word_type b = (word_type(1) << static_cast<word_type>(valid_bits))
+                    / word_type(3);
 
   word_type w = 0;
   for (reverse_iterator d = rbegin(); d != rend(); ++d)
@@ -84,15 +85,13 @@
     word_type t;
     if (w >= 3)
     {
-      /* multiply w by [1/3] */
+      // multiply w by [1/3]
       t = (w * b) >> static_cast<word_type>(valid_bits);
 
-      /* now subtract 3 * [w/3] from w, to get the remainder */
+      // now subtract 3 * [w/3] from w, to get the remainder
       w -= t+t+t;
 
-      /* fixup the remainder as required since
-       * the optimization is not exact.
-       */
+      // fixup the remainder as required since the optimization is not exact.
       while (w >= 3)
       {
         t += 1;
@@ -110,7 +109,7 @@
   return static_cast<digit_type>(w);
 }
 
-/* shift right by a certain bit count */
+// shift right by a certain bit count
 template<class A, class T>
 void mp_int<A,T>::shift_right(size_type b, mp_int* remainder)
 {
@@ -121,7 +120,7 @@
     return;
   }
 
-  /* get the remainder */
+  // get the remainder
   mp_int t;
   if (remainder)
   {
@@ -129,29 +128,29 @@
     remainder->modulo_2_to_the_power_of(b);
   }
 
-  /* shift by as many digits in the bit count */
+  // shift by as many digits in the bit count
   if (b >= static_cast<size_type>(valid_bits))
     shift_digits_right(b / valid_bits);
 
-  /* shift any bit count < valid_bits */
+  // shift any bit count < valid_bits
   const digit_type D = b % valid_bits;
   if (D)
   {
     const digit_type mask = (digit_type(1) << D) - 1;
 
-    /* shift for lsb */
+    // shift for lsb
     const digit_type shift = valid_bits - D;
 
     digit_type carry = 0;
     for (reverse_iterator d = rbegin(); d != rend(); ++d)
     {
-      /* get the lower bits of this word in a temp */
+      // get the lower bits of this word in a temp
       const digit_type rr = *d & mask;
 
-      /* shift the current word and mix in the carry bits from the previous word */
+      // shift the current word and mix in the carry bits from the previous word
       *d = (*d >> D) | (carry << shift);
 
-      /* set the carry to the carry bits of the current word found above */
+      // set the carry to the carry bits of the current word found above
       carry = rr;
     }
   }
@@ -160,19 +159,17 @@
     sign_ = 1;
 }
 
-/* integer signed division. 
- * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
- * HAC pp.598 Algorithm 14.20
- *
- * Note that the description in HAC is horribly 
- * incomplete.  For example, it doesn't consider 
- * the case where digits are removed from 'x' in 
- * the inner loop.  It also doesn't consider the 
- * case that y has fewer than three digits, etc..
- *
- * The overall algorithm is as described as 
- * 14.20 from HAC but fixed to treat these cases.
-*/
+// integer signed division. 
+// c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+// HAC pp.598 Algorithm 14.20
+//
+// Note that the description in HAC is horribly incomplete.  For example, it
+// doesn't consider the case where digits are removed from 'x' in the inner
+// loop.  It also doesn't consider the case that y has fewer than three digits,
+// etc..
+// The overall algorithm is as described as 14.20 from HAC but fixed to treat
+// these cases.
+
 // divide *this by rhs, optionally store remainder
 template<class A, class T>
 void mp_int<A,T>::divide(const mp_int& rhs, mp_int* remainder)
@@ -180,7 +177,7 @@
   if (rhs.is_zero())
     throw std::domain_error("mp_int::divide: division by zero");
 
-  /* if *this < rhs then q=0, r = *this */
+  // if *this < rhs then q=0, r = *this
   if (compare_magnitude(rhs) == -1)
   {
     if (remainder)
@@ -197,11 +194,11 @@
   mp_int x(*this);
   mp_int y(rhs);
 
-  /* fix the sign */
+  // fix the sign
   const int neg = (sign_ == rhs.sign_) ? 1 : -1;
   x.sign_ = y.sign_ = 1;
 
-  /* normalize both x and y, ensure that y >= beta/2, [beta == 2**valid_bits] */
+  // normalize both x and y, ensure that y >= beta/2, [beta == 2**valid_bits]
   size_type norm = y.precision() % valid_bits;
   if (norm < valid_bits-1)
   {
@@ -212,13 +209,13 @@
   else
     norm = 0;
 
-  /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+  // note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4
   const size_type n = x.used_ - 1;
   const size_type t = y.used_ - 1;
 
   // find leading digit of the quotient
-  /* while (x >= y*beta**(n-t)) do { q[n-t] += 1; x -= y*beta**(n-t) } */
-  y.shift_digits_left(n - t); /* y = y*beta**(n-t) */
+  // while (x >= y*beta**(n-t)) do { q[n-t] += 1; x -= y*beta**(n-t) }
+  y.shift_digits_left(n - t); // y = y*beta**(n-t)
 
   while (x.compare(y) != -1)
   {
@@ -226,18 +223,18 @@
     x -= y;
   }
 
-  /* reset y by shifting it back down */
+  // reset y by shifting it back down
   y.shift_digits_right(n - t);
 
   // find the remainder of the digits
-  /* step 3. for i from n down to (t + 1) */
+  // step 3. for i from n down to (t + 1)
   for (size_type i = n; i >= (t + 1); i--)
   {
     if (i > x.used_)
       continue;
 
-    /* step 3.1 if xi == yt then set q{i-t-1} to beta-1, 
-     * otherwise set q{i-t-1} to (xi*beta + x{i-1})/yt */
+    // step 3.1 if xi == yt then set q{i-t-1} to beta-1, 
+    // otherwise set q{i-t-1} to (xi*beta + x{i-1})/yt
     if (x[i] == y[t])
       q[i - t - 1] = std::numeric_limits<digit_type>::max();
     else
@@ -250,11 +247,10 @@
     }
 
     // now fixup quotient estimation
-    /* while (q{i-t-1} * (yt * beta + y{t-1})) > 
-             xi * beta**2 + xi-1 * beta + xi-2 
-     
-       do q{i-t-1} -= 1; 
-    */
+    // while (q{i-t-1} * (yt * beta + y{t-1})) >
+    //       xi * beta**2 + xi-1 * beta + xi-2
+    //
+    // do q{i-t-1} -= 1;
 
     mp_int t1, t2;
     t1.grow_capacity(3);
@@ -265,27 +261,27 @@
     {
       --q[i - t - 1];
 
-      /* find left hand */
+      // find left hand
       t1.zero();
       t1[0] = (t == 0) ? 0 : y[t - 1];
       t1[1] = y[t];
       t1.used_ = 2;
       t1.multiply_by_digit(q[i - t - 1]);
 
-      /* find right hand */
+      // find right hand
       t2[0] = (i < 2) ? 0 : x[i - 2];
       t2[1] = (i == 0) ? 0 : x[i - 1];
       t2[2] = x[i];
       t2.used_ = 3;
     } while (t1.compare_magnitude(t2) == 1);
 
-    /* step 3.3 x = x - q{i-t-1} * y * beta**{i-t-1} */
+    // step 3.3 x = x - q{i-t-1} * y * beta**{i-t-1}
     t1 = y;
     t1.multiply_by_digit(q[i - t -1]);
     t1.shift_digits_left(i - t - 1);
     x -= t1;
 
-    /* if x < 0 then { x = x + y*beta**{i-t-1}; q{i-t-1} -= 1; } */
+    // if x < 0 then { x = x + y*beta**{i-t-1}; q{i-t-1} -= 1; }
     if (x.sign_ == -1)
     {
       t1 = y;
@@ -296,11 +292,9 @@
     }
   }
 
-  /* now q is the quotient and x is the remainder 
-   * [which we have to normalize] 
-   */
+  // now q is the quotient and x is the remainder [which we have to normalize]
   
-  /* get sign before writing to c */
+  // get sign before writing to *this
   x.sign_ = x.is_zero() ? 1 : sign_;
 
   q.clamp();

Modified: sandbox/mp_math/boost/mp_math/mp_int/pow.hpp
==============================================================================
--- sandbox/mp_math/boost/mp_math/mp_int/pow.hpp	(original)
+++ sandbox/mp_math/boost/mp_math/mp_int/pow.hpp	2008-10-28 13:25:48 EDT (Tue, 28 Oct 2008)
@@ -46,3 +46,21 @@
   return result;
 }
 
+template<class A, class T>
+mp_int<A,T> pow(const mp_int<A,T>& x, const mp_int<A,T>& y)
+{
+  if (y.size() == 1)
+    return pow(x, y[0]);
+
+  mp_int<A,T> y0(y);
+  
+  y0.divide_by_2();
+  
+  mp_int<A,T> y1(y0);
+
+  if (y.is_odd())
+    ++y1;
+
+  return pow(x, y0) * pow(x, y1);
+}
+

Modified: sandbox/mp_math/libs/mp_math/test/pow.cpp
==============================================================================
--- sandbox/mp_math/libs/mp_math/test/pow.cpp	(original)
+++ sandbox/mp_math/libs/mp_math/test/pow.cpp	2008-10-28 13:25:48 EDT (Tue, 28 Oct 2008)
@@ -48,3 +48,383 @@
   BOOST_CHECK_EQUAL(z, "18446744073709551616");
 }
 
+BOOST_AUTO_TEST_CASE_TEMPLATE(pow4, mp_int_type, mp_int_types)
+{
+  const mp_int_type x = pow(mp_int_type("301"), mp_int_type("259"));
+  const mp_int_type z(
+    "0x16becbb1b891cbbbab4825ed1335f0f4ef5250f620023061045e87ca80d80ea7daf0cda8"
+    "023aed1a969864de781297ae556f2bba6d951ae294805dc888f6de01dac2b7dd3ab47db207"
+    "b0f980f26a54f1c7dbb3ebc6cd5b952cccc67569487fd2aea057d4326cc56aad90ecd89b3c"
+    "74c1f30f6ac637a64b706087f2fe16c3bf2be3692106717387813a8a2c9da65b657a8a2a61"
+    "abdfdc6698a6f6543d8f5ae88b192293e2a76ed402d3c914ca0c40e21fb1508cb2c5a7dfe5"
+    "1a357fa58bf9e2f1d1fdd2c3e72b600a8e7390ac0ec65cda8b0636595a83dfeed163a0e161"
+    "b17acc476db2cc246bb3b14a1b33cdfd659d43437b2c4a203e07a8f297ad3a716b53d8ce28"
+    "e84f1b3ad36ba0d2f5");
+  BOOST_CHECK_EQUAL(x, z);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(pow5, mp_int_type, mp_int_types)
+{
+  const mp_int_type x = pow(mp_int_type("3"), mp_int_type("66666"));
+  const mp_int_type z(
+    "0x8a25f1339bf63db8e5881f75e7f89ad860d393776362040a47448cfbcb4a9402558acf60"
+    "7a590c1fa521b672329cc18a63eca1cadf87465bf8b44ef05fce12fb020ebf2c2b246d9a36"
+    "af527f947f3d238d3e2504dd5a0f3a071dc98784d1084cbfc4554fc21d72f72ae65766600a"
+    "007b364d2c182ba9b9b16011c2853a28fa2455bce4ac2af57f6c8337b85a8e01fd4086f128"
+    "bedf51902d90fb9e9a7e859e65219b46ee14d5a1660f37884801c65d2f580577f7644014a7"
+    "f26f648308b7e7852fcd1702740aeddf1c63d2e41e3a70f13347c1236f8dda54db58b1df1c"
+    "0849b96ec08286e3160db6c7c71b7488d8516af84eb08e8188a4bfbf045f3ed85ad3d63a16"
+    "79a4dab46fd15caf25543e21751c164b9e7bf0c3ca98ce518e95dc7dc9c949b114aac50935"
+    "f3744f4cea72d9f857c2aed3a1b9e682dd00d6c470365b2af4f95733c16cebdd56ca2d0f23"
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+    "43a2646a11e0600560f729e412859cd21e1325ed505f2d06b1f77f69306e689d1b0b91b7df"
+    "1b7d97d96609bbfec187bb7a93288b37cc96fb22ec72b0493f0a60f1e00858d056970e535c"
+    "e4803c135e97c999df22c34d2524913c7a70313bf3601b07e3fcf5a257b46a87f48d58e73f"
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+    "1641f7d7a335f4295abedafdbb71e1ac829402443b4953386c9302d141bb6cd9d218c66d26"
+    "6c460aca44a0c49f3fcd3347fb7bd0ff8858f2bd37efa64c73ca85b4830f0181079619aaeb"
+    "675bea0e15aa2afaa62d25a5a1b3d45573705986c1a8a67ca5be85b062e77685f69313d87b"
+    "a16bfa2cc2810fc3882313f640a1f1eb0ee759b8f52f89a2a9d5853bd24e7d09c150e4b294"
+    "d65ec1d246aceb217d5a0cba04673d3c70bb2630d914e513f4f6cf30ef82e6b8f43aa4e168"
+    "6c259c76f593a3dab623ca0440d90fd99e84ea49ff376f2e300f8628ea27a9dd57b4e44219"
+    "67d7d55945be9e75c06f2be4c96fbf1b2f379cfed2c7e28cc66b205fb87f3ecc6f81081253"
+    "65ba7443907fa9129be3abf3147b9be54f7c8dea7df51330078877a0974843eb6f0667969f"
+    "73b5a64b406459f6ba6b266ec8a0032be573ff5ae53637d9d343d41af68346d974681f4cb8"
+    "922b3cd1ebbf695ed46dab551a245675f82a8f53e178684ea4da62fd817d0a9fbadfc12df5"
+    "9d18f6373fb111f0d3f9712b98ff16611f8eabc59997d0f975b67c47daaedf03521eea6beb"
+    "3dd569be0e9d14af9a6eda4650fe712789a6d59b8388997e9e0a8f1b215b5bb327ac5b4984"
+    "e1513baf6053ad05bd4eec0162ba25b5a3f37a2219230b9f940f7337a047dc2b6f71267fcc"
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+    "04c2c2a8f81551161a1b015e36db1fdcf9520c2c5fe02c8bde49e1e422dcc7d04ba746e3f3"
+    "442a2b9a2443579058eb91bf39575f7f03fdf8d8cfdbfa22095834356ca28eddd87e174ceb"
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+    "569fb6ce070ae60811af0e8d88ec983b9b00d492b3a28ac0c64aff11bb9054406b7eb464ab"
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+    "a3b708d3beea806720a179a7fd20de94c24e87fe3dd3856ce5381cb4d1ccd33d1b5323bd48"
+    "f364f8c995a3f8ab098118f66f5f111c4efa9739b69be6f8a09ea4a88c6d24d5d9ab3bb595"
+    "0ecb7fc5f3f9c3c1aac7c89c95ca75931c64651f081181f182d3235dd726329f9ec43c8c2a"
+    "fa9d8ec5058b22ef627105d6dcad48158ec6e8ad202a6c2f034d37c022342fcaec10fc9800"
+    "51c3c3d5d014e58a2be79061a78811860bf2137ee1a1510d4e72f7029252ec8e1f691ddcb0"
+    "8cfa7ab971d1f7b6e20d7c012177eb0f3f6e4a1cab589ee85e09f4c27579f3ff52c09a416b"
+    "5c585b7e6a1b7424779734820eb93e66be93044d09ee8ca34126b47358244b5bc25299b69c"
+    "5d39ed2826de5cfb285981e2ea043cbfbc603ebf6c6a885f68edcff2f0cf4addf628ad5992"
+    "84a798f3ad659f36fae28cb16fcd439ffa5a69c516dff3dad3760f663fb7ba084bc3dc66d4"
+    "6b31f3120c57bf46f7a20c6b225e867977245b3acf75e2136c39fe744999b76dbf44152043"
+    "b7af96a3a0ed4463f6b1b61d5f07a1e0c395c0051656959767e654eb163f53b80026dd5b49"
+    "b90cdbf2ab50306a23287665afc61d7e4bf0d6d5ff4c6416c07d1ca8d6390c1a69084d408e"
+    "1cb35a3afa0bca0c9fe58344d7e992c23b05c22c6cf57349b90f523e7227becdb320f39255"
+    "c3ffbf8e43b20fbd1e898cd181c6abcef5456807bf2914766bc70fb406228ae3c7c23a64ae"
+    "42b3293e17bb4dd622052f433a65fa781c221187aedcfefa816cb040ba11647c785f64ba3a"
+    "1e2eadd17bc6f8eb7e2ba480da06b6606e6f4ede7f9fdaf26fe89cc7cdb0ec08f1c53ea273"
+    "6a83a53824d1f9d05022aba64e65a59f19e6713d60e7c64f5270befed0570ac245490c77ea"
+    "af2baa4165a8cd1b268458b634df1f38c20e79b20d1fa6453e9ceb74c447c53705fab82e7f"
+    "a23251e425215c1fd55818ddcf4449f58ec238ffb1a3cb24b53caaa8430f8b01a1cfd515d9"
+    "91c6547c165b34d3608bc117207480396338645097f84499296425333bb68bf39349c59d04"
+    "dca85341a816fabed09c2d42c601c1966ad4e2baf3eea257f75524e96798b9af773169cf95"
+    "0186968f5aec8fd5906e55c9486a70f44f5435b112a47a33b782f01b5a0dd26ebb6ebb95fa"
+    "0a83d02b444416e2a340f5bade3c76a9217f993d508d48d013737da2c6ed9af245a0877ea1"
+    "b50719b77d26eb1085cd2a418f7c04b9fc413629923aea6b7ecc795958b0ecfec3b820d5b5"
+    "ea6bd1f7cb1b555c2820165f01aa85c49343f7b7005b28a28bcad9bc77999207559b60295a"
+    "e2ed8b11702e14b98c0026712400ec219ff867dd78aa2637927c9921238165292ab08409be"
+    "a2bc683b00e771510fa0db6c956603313a985e2dd1f13d0aaa1f7331aac6b8a5d5b195e8a9"
+    "3f5d5a07e4ce064258e2049f6c4eb1efcd3a7d890d881dfb080e990927d93bea148b5e7645"
+    "7c1bdf2a73d364cc30b81345edf3dcb375c5cc5bcf34536ad0481f3669ed32cb1e9c0895a5"
+    "0d2542bdb135878a8fa4fec38d46f0e3c8f9b14738ff36865d29c94b31faf6119b479b8e2f"
+    "dc9e1c838b82605809c66b08576b97b7b5d90d4865c77201c678cdcf770a7db91f2070c17c"
+    "67d4327e4d7ced8e2a73285993b1a19fe3eab29154035e4cac04d0cfada92aa5963e785f8c"
+    "a20d77e9f7e65169db4d9196abfc76c70f520b41017313d7ff8c43d129134a0f265ff6f10f"
+    "ad88054ddf128680ac133315bdd91b00d92d026a0d692f80069bb45aede03f09622237bae8"
+    "ef09462a0bfc4bbdda430833702a8481d6eb028f111b7305d33f30c8558a7d270a3aa5610c"
+    "aa8bcb39867efce7a44b0595c556c0befe0899908b82af48c07106e30c667ecd75df0df03f"
+    "9a606f680afff7c1b12625177d3f829adc2e304a5b1bb6c8788b712ebb6759629857d243d9"
+    "57b8aa44369fe3eda0474827c60ba9a042879c9e5896b71b35aa19f8d6e5ef5e0f713ed302"
+    "b8f50bc1d9083b7fd28765c8206e774ff62a522949c56dbe738b99d9e9b2eee7fce9029a92"
+    "b7c21f31cb36fdb974d237c7641060105e77a6a6a0e61d3a60aa4f792622e897e89bf6809c"
+    "d9f72674ee4aab58e636200e0de7d08efabbcbba05e408b16d9b472f8b993e0d3b5b74c105"
+    "e171ed02150e3a9c4a95a8b5cee3d35788a45bf328e2018501b86e973300221be59787fb68"
+    "1064a6f2bbaa44aa4be578bb8fa3c24e0dfcd16f8da1bcf72b9ee98c86ab8fea3913f5f3fa"
+    "c6840cf705fc1e1b945047e7301efa976135fc0bdbdc2188d9911cbb2ca2cc99f0d62b1888"
+    "cfbdff94ebd6b1583ebc07ad468ff5ca600e28438cc89e5a7ba3fa97742e51c45eddee2c21"
+    "46c29f0fd3f8ef8e2e3be6ca727e1d35ccfc5539f372103ea30803779089fb811aaf517213"
+    "ea35fb33c0d4a2464f37f286be1804030d59bf53be9bbc11fbdfa9b2fee8deb60f6ac7d6b4"
+    "070f4d666235ee4dc314b85869f339333a1b3cff2eaec781ea6a07a2440bb035b75a00ee0a"
+    "7d42672f160604a2e372c3ced65d4a556412837c8038f6a93e4eecfbcb4408a42159e76625"
+    "3b2e0f443edfb3e6f098021eb7b030f6d0d4b20243222604ea84d81e03a0f7e63a447f9bd1"
+    "a3f26485bf69912e16dcfb0222c8c5d74e7166e1f899101c74abcf4fc0558b4ae26a2c0e08"
+    "e2dc20c91d2c9fbe835d44ff15a26c6b976fcece277e4ff9fe80c0a28d5bf40bc40af5f782"
+    "13476c0b6873fe734a066fda3eb350302d7206168dd61ee4de813c8ac65a3a48cb40ccc821"
+    "c8efa14ce9320e6f0de35b5e68735bab8d03ef1185799151bb5f8a3f4d956752aec525cc73"
+    "d187665a0027189cd895f01422e59abed3bba5b655828d4aff00d77c846ea690c18a5a3f2b"
+    "86fd9da63f095da01f3778107b640a2813197a3f7023d652b2865ea8e2f93398fafa2f9af9"
+    "0ee81a8d6eba0d6671951ae831f85bb510605caf3ef2550ed0ded1fb90061857dd26eded72"
+    "5fe4399711fb2d0178a386046db054259a44896fcb795961e283fcda0d13be9b390fdc71a3"
+    "e3aadbac44dc71b9086e4b204cae1b0fa06268bd73b746807fd4c0ece38fdf877c490cdc7f"
+    "b622c8ec94b374a3b739c013476ba680edf46739c981ab095c175acc045c445ae15b208637"
+    "b13b841eae64b9b571630dc82119547ceefbab3288fa224d73b572ab1ac600258dbb7711c3"
+    "2801723744a2f80902b46286d52665d368892de15e283f30a5e3fe1d36284ad42afeb58a7f"
+    "a9850d6afd277ce4709c716160521dfabc755803932fdac96c096606be2690af795f418ba1"
+    "a3fd1e5758f570d702be4855c76c8ffeb3cf31056b47ca5d7aa498fd83302e490c61b32c8d"
+    "3586f43ea5772ad98b724cc51e2337d4674f086f915556b69ecfb837e4586c84b147cfbea8"
+    "a6427fd5cef19750866fb59dbc669de92972052b651c8d4c2f7cad2db4e2690b23db7830c1"
+    "c20658fce756d74db87eb7b93020dfbc49b86fb1ca81291f337d4642a0b330665aa8f4087f"
+    "ee34d22b190639bd02cf126ad96a34f21957e92549e0d96f54d0b1aeb904c33ea8e6733f0f"
+    "42abc821451471293415c18d4e01c044a3b96f85850c73a26aa01a382e424350f85eb5007c"
+    "d23878fd90f21c0413eeca6337a0a1b7bebf8042fbb10c6b6f6469dcd61ac494bd3efb2d5f"
+    "fbfd5e5398920d5a13e84da91a1636ae862c95b2a4d99e8e62eb43a7ce89a543db8c942926"
+    "e48b08d33b89afb9582bf56e50c5cd9d64e9e733e9a47404217b51d8854872800edcfd5426"
+    "39385e1f66242e01f97fd3a97e201eb95d16305956e57a8f9adede23791b8ee2fa3b81db49"
+    "f56cd02fa900439c2bb8b9fa7c65ee662d415164f5930a7c65769156080b3cce889e103330"
+    "a9a7934962d5ef10e8577438524c484aeccf8f556975a2006cc4e7d7143165f2f771d77a64"
+    "06d2251b8dd659c8a42aebac5d8e5513bd0527f9b6f709714bd82cceda33a18a572d7b1f28"
+    "e998a96d4fb596f021f68215356439f40ad42282bf784b954bc4900860bc07f4452ccae599"
+    "5a27afc8535b5854c5305ff02af7b876879512071f6d7aa7eb5ed7d37c0e657c00962f3441"
+    "2b23a694e75a52a60fc7a861deec2f27ce4f323dce313b98dcd9c4d419985ad696c5f58361"
+    "392563e2b0a0f72ca286e9a5a044a32685a01e4ade75983f3e53f74f4e1022b82479269ef5"
+    "279ec1765955642c27aa83847e0b9c029b63da839835575820699af9a038b587a468e556d4"
+    "26601282fbe9be24e1b33d0e1bcab5c5398f3ac6b67889f4c99b40cfa906fc2cf002868c2f"
+    "3d6f3bc73b683bf210ee4a5f5281c416898ae4cd14ced66f51e1c48a08420d275c90c3d3c7"
+    "7ca4eb22fdc5df97ff81eb1adf987118b7fc6b501b8a2c7a9be1933ab3b6f651ae93141ff9"
+    "7de2fe9ad3fc3852df6c89b2959a0fbfca0b63a7cec988e7eddc256962d58c2916f17b4981"
+    "0fe5543a37b5d74b52fa3bbb5385b7a08ad38b99b80b4744d48aaab4075c7672a45736e3d3"
+    "8c58f827472ba8550dff056e919f439796ba9c905a5a1df24e93d40958e215c59edba0886f"
+    "5c9f8c8b05dba2f2c9d4e568555ea29018cef66b10ebbbf76cfbf6d72c1795402a70bed95a"
+    "c819b0f05431b2203355e77827c72fb5b0270b1817df07cd9c99a4df89f8cbec7a87ab59e6"
+    "3cfc554d19d1f38a29206d3e5e590de1e6e329c2585d215945e9397d6762d60e23992a450b"
+    "e389e03eccdc0901808be8ebc45051b32956a1189649f25c37a09287762f5f4a5c69c54867"
+    "d63159662c6d83cfdaa0a9ffd19b356ef4aaeae58d6c481b84ede83decbbc44717f6e0be29"
+  );
+  BOOST_CHECK_EQUAL(x, z);
+}
+