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Subject: [Boost-commit] svn:boost r74781 - in sandbox/big_number: boost/multiprecision/detail/functions libs/multiprecision/test
From: john_at_[hidden]
Date: 2011-10-07 14:14:37

Author: johnmaddock
Date: 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
New Revision: 74781
URL: http://svn.boost.org/trac/boost/changeset/74781

Log:
Added pow, exp, log, sinh, cosh and tanh support.
Added:
   sandbox/big_number/libs/multiprecision/test/test_cosh.cpp (contents, props changed)
   sandbox/big_number/libs/multiprecision/test/test_pow.cpp (contents, props changed)
   sandbox/big_number/libs/multiprecision/test/test_sinh.cpp (contents, props changed)
   sandbox/big_number/libs/multiprecision/test/test_tanh.cpp (contents, props changed)
Text files modified:
   sandbox/big_number/boost/multiprecision/detail/functions/pow.hpp | 292 ++++++++++++++++++++++++++++++++++++++-
   sandbox/big_number/libs/multiprecision/test/Jamfile.v2 | 80 ++++++++++
   sandbox/big_number/libs/multiprecision/test/test_exp.cpp | 12 +
   sandbox/big_number/libs/multiprecision/test/test_log.cpp | 7
   4 files changed, 383 insertions(+), 8 deletions(-)

Modified: sandbox/big_number/boost/multiprecision/detail/functions/pow.hpp
==============================================================================
--- sandbox/big_number/boost/multiprecision/detail/functions/pow.hpp (original)
+++ sandbox/big_number/boost/multiprecision/detail/functions/pow.hpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -12,11 +12,6 @@
// This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp
//

-template<typename T>
-inline void eval_pow(T& result, const T& t, const T& p)
-{
-}
-
namespace detail{

template<typename T, typename U>
@@ -103,6 +98,7 @@

    typedef typename mpl::front<typename T::unsigned_types>::type ui_type;

+ BOOST_ASSERT(&H0F0 != &x);
    long tol = std::numeric_limits<mp_number<T> >::digits;
    T t;

@@ -133,6 +129,58 @@
       throw std::runtime_error("H0F0 failed to converge");
}

+template <class T>
+void hyp1F0(T& H1F0, const T& a, const T& x)
+{
+ // Compute the series representation of Hypergeometric1F0 taken from
+ // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F0/06/01/01/
+ // and also see the corresponding section for the power function (i.e. x^a).
+ // There are no checks on input range or parameter boundaries.
+
+ typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
+ typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
+ typedef typename T::exponent_type exp_type;
+ typedef typename boost::multiprecision::detail::canonical<exp_type, T>::type canonical_exp_type;
+ typedef typename mpl::front<typename T::real_types>::type fp_type;
+
+ BOOST_ASSERT(&H1F0 != &x);
+ BOOST_ASSERT(&H1F0 != &a);
+
+ T x_pow_n_div_n_fact(x);
+ T pochham_a (a);
+ T ap (a);
+
+ multiply(H1F0, pochham_a, x_pow_n_div_n_fact);
+ add(H1F0, si_type(1));
+
+ si_type n;
+ T term, part;
+
+ // Series expansion of hyperg_1f0(a; ; x).
+ for(n = 2; n < 1000; n++)
+ {
+ multiply(x_pow_n_div_n_fact, x);
+ divide(x_pow_n_div_n_fact, n);
+ increment(ap);
+
+ multiply(pochham_a, ap);
+
+ multiply(term, pochham_a, x_pow_n_div_n_fact);
+
+ if(n > 20)
+ {
+ exp_type e1, e2;
+ eval_frexp(part, H1F0, &e1);
+ eval_frexp(part, term, &e2);
+ if(e1 - e2 >= std::numeric_limits<mp_number<T> >::digits)
+ break;
+ }
+
+ add(H1F0, term);
+ }
+ if(n >= 1000)
+ throw std::runtime_error("H1F0 failed to converge");
+}

template <class T>
void eval_exp(T& result, const T& x)
@@ -147,6 +195,8 @@
    typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
    typedef typename T::exponent_type exp_type;
    typedef typename boost::multiprecision::detail::canonical<exp_type, T>::type canonical_exp_type;
+ typedef typename boost::multiprecision::detail::canonical<float, T>::type float_type;
+
    // Handle special arguments.
    int type = eval_fpclassify(x);
    bool isneg = get_sign(x) < 0;
@@ -188,6 +238,34 @@
          result = std::numeric_limits<mp_number<T> >::has_infinity ? std::numeric_limits<mp_number<T> >::infinity().backend() : (std::numeric_limits<mp_number<T> >::max)().backend();
       return;
    }
+ if(xx.compare(si_type(1)) <= 0)
+ {
+ //
+ // Use series for exp(x) - 1:
+ //
+ T lim = std::numeric_limits<mp_number<T> >::epsilon().backend();
+ unsigned k = 2;
+ exp_series = xx;
+ result = si_type(1);
+ if(isneg)
+ subtract(result, exp_series);
+ else
+ add(result, exp_series);
+ multiply(exp_series, xx);
+ divide(exp_series, ui_type(k));
+ add(result, exp_series);
+ while(exp_series.compare(lim) > 0)
+ {
+ ++k;
+ multiply(exp_series, xx);
+ divide(exp_series, ui_type(k));
+ if(isneg && (k&1))
+ subtract(result, exp_series);
+ else
+ add(result, exp_series);
+ }
+ return;
+ }

    // Check for pure-integer arguments which can be either signed or unsigned.
    boost::intmax_t ll;
@@ -285,15 +363,16 @@
    T pow = t;
    T lim;
    T t2;
- multiply(lim, result, std::numeric_limits<mp_number<T> >::epsilon().backend());
- if(get_sign(lim) < 0)
- lim.negate();

    if(alternate)
       add(result, t);
    else
       subtract(result, t);

+ multiply(lim, result, std::numeric_limits<mp_number<T> >::epsilon().backend());
+ if(get_sign(lim) < 0)
+ lim.negate();
+
    ui_type k = 1;
    do
    {
@@ -307,3 +386,200 @@
    }while(lim.compare(t2) < 0);
}

+template<typename T>
+inline void eval_pow(T& result, const T& x, const T& a)
+{
+ typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
+ typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
+ typedef typename T::exponent_type exp_type;
+ typedef typename boost::multiprecision::detail::canonical<exp_type, T>::type canonical_exp_type;
+ typedef typename mpl::front<typename T::real_types>::type fp_type;
+
+ if((&result == &x) || (&result == &a))
+ {
+ T t;
+ eval_pow(t, x, a);
+ result = t;
+ }
+
+ if(a.compare(si_type(1)) == 0)
+ {
+ result = x;
+ return;
+ }
+
+ int type = eval_fpclassify(x);
+
+ switch(type)
+ {
+ case FP_INFINITE:
+ result = x;
+ return;
+ case FP_ZERO:
+ result = si_type(1);
+ return;
+ case FP_NAN:
+ result = x;
+ return;
+ default: ;
+ }
+
+ if(get_sign(a) == 0)
+ {
+ result = si_type(1);
+ return;
+ }
+
+ boost::intmax_t an;
+ convert_to(&an, a);
+ const bool bo_a_isint = a.compare(an) == 0;
+
+ if((get_sign(x) < 0) && !bo_a_isint)
+ {
+ result = std::numeric_limits<mp_number<T> >::quiet_NaN().backend();
+ }
+
+ T t;
+ T da(a);
+ subtract(da, an);
+
+ if(a.compare(si_type(-1)) < 0)
+ {
+ t = a;
+ t.negate();
+ eval_pow(da, x, t);
+ divide(result, si_type(1), da);
+ return;
+ }
+
+ subtract(da, a, an);
+
+ if(bo_a_isint)
+ {
+ detail::pow_imp(result, x, an, mpl::true_());
+ return;
+ }
+
+ if((get_sign(x) > 0) && (x.compare(fp_type(0.1)) > 0) && (x.compare(fp_type(0.9)) < 0))
+ {
+ if(a.compare(fp_type(1e-5f)) <= 0)
+ {
+ // Series expansion for small a.
+ eval_log(t, x);
+ multiply(t, a);
+ hyp0F0(result, t);
+ return;
+ }
+ else
+ {
+ // Series expansion for moderately sized x. Note that for large power of a,
+ // the power of the integer part of a is calculated using the pown function.
+ if(an)
+ {
+ da.negate();
+ t = si_type(1);
+ subtract(t, x);
+ hyp1F0(result, da, t);
+ detail::pow_imp(t, x, an, mpl::true_());
+ multiply(result, t);
+ }
+ else
+ {
+ da = a;
+ da.negate();
+ t = si_type(1);
+ subtract(t, x);
+ hyp1F0(result, da, t);
+ }
+ }
+ }
+ else
+ {
+ // Series expansion for pow(x, a). Note that for large power of a, the power
+ // of the integer part of a is calculated using the pown function.
+ if(an)
+ {
+ eval_log(t, x);
+ multiply(t, da);
+ eval_exp(result, t);
+ detail::pow_imp(t, x, an, mpl::true_());
+ multiply(result, t);
+ }
+ else
+ {
+ eval_log(t, x);
+ multiply(t, a);
+ eval_exp(result, t);
+ }
+ }
+}
+
+namespace detail{
+
+ template <class T>
+ void sinhcosh(const T& x, T* p_sinh, T* p_cosh)
+ {
+ typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
+ typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
+ typedef typename T::exponent_type exp_type;
+ typedef typename boost::multiprecision::detail::canonical<exp_type, T>::type canonical_exp_type;
+ typedef typename mpl::front<typename T::real_types>::type fp_type;
+
+ switch(eval_fpclassify(x))
+ {
+ case FP_NAN:
+ case FP_INFINITE:
+ if(p_sinh)
+ *p_sinh = x;
+ if(p_cosh)
+ *p_cosh = x;
+ return;
+ case FP_ZERO:
+ if(p_sinh)
+ *p_sinh = x;
+ if(p_cosh)
+ *p_cosh = ui_type(1);
+ return;
+ default: ;
+ }
+
+
+ T e_px;
+ eval_exp(e_px, x);
+ T e_mx;
+ divide(e_mx, ui_type(1), e_px);
+
+ if(p_sinh)
+ {
+ subtract(*p_sinh, e_px, e_mx);
+ divide(*p_sinh, ui_type(2));
+ }
+ if(p_cosh)
+ {
+ add(*p_cosh, e_px, e_mx);
+ divide(*p_cosh, ui_type(2));
+ }
+ }
+
+} // namespace detail
+
+template <class T>
+inline void eval_sinh(T& result, const T& x)
+{
+ detail::sinhcosh(x, &result, static_cast<T*>(0));
+}
+
+template <class T>
+inline void eval_cosh(T& result, const T& x)
+{
+ detail::sinhcosh(x, static_cast<T*>(0), &result);
+}
+
+template <class T>
+inline void eval_tanh(T& result, const T& x)
+{
+ T c;
+ detail::sinhcosh(x, &result, &c);
+ divide(result, c);
+}
+

Modified: sandbox/big_number/libs/multiprecision/test/Jamfile.v2
==============================================================================
--- sandbox/big_number/libs/multiprecision/test/Jamfile.v2 (original)
+++ sandbox/big_number/libs/multiprecision/test/Jamfile.v2 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -202,3 +202,83 @@
               <define>TEST_MPF50
          [ check-target-builds ../config//has_gmp : : <build>no ]
         : test_log_mpf50 ;
+
+run test_pow.cpp gmp
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPF50
+ [ check-target-builds ../config//has_gmp : : <build>no ]
+ : test_pow_mpf50 ;
+
+run test_sinh.cpp gmp
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPF50
+ [ check-target-builds ../config//has_gmp : : <build>no ]
+ : test_sinh_mpf50 ;
+
+run test_cosh.cpp gmp
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPF50
+ [ check-target-builds ../config//has_gmp : : <build>no ]
+ : test_cosh_mpf50 ;
+
+run test_tanh.cpp gmp
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPF50
+ [ check-target-builds ../config//has_gmp : : <build>no ]
+ : test_tanh_mpf50 ;
+
+run test_exp.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_exp_mpfr50 ;
+
+run test_log.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_log_mpfr50 ;
+
+run test_pow.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_pow_mpfr50 ;
+
+run test_sinh.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_sinh_mpfr50 ;
+
+run test_cosh.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_cosh_mpfr50 ;
+
+run test_tanh.cpp mpfr
+ : # command line
+ : # input files
+ : # requirements
+ <define>TEST_MPFR_50
+ [ check-target-builds ../config//has_mpfr : : <build>no ]
+ : test_tanh_mpfr50 ;

Added: sandbox/big_number/libs/multiprecision/test/test_cosh.cpp
==============================================================================
--- (empty file)
+++ sandbox/big_number/libs/multiprecision/test/test_cosh.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -0,0 +1,137 @@
+///////////////////////////////////////////////////////////////
+// Copyright Christopher Kormanyos 2002 - 2011.
+// Copyright 2011 John Maddock. Distributed under the Boost
+// Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#include <boost/detail/lightweight_test.hpp>
+#include <boost/array.hpp>
+
+#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ)
+# define TEST_MPF50
+//# define TEST_MPF
+# define TEST_BACKEND
+# define TEST_E_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF50)
+#include <boost/multiprecision/gmp.hpp>
+#endif
+#if defined(TEST_MPFR_50)
+#include <boost/multiprecision/mpfr.hpp>
+#endif
+#ifdef TEST_BACKEND
+#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
+#endif
+#ifdef TEST_E_FLOAT
+#include <boost/multiprecision/e_float.hpp>
+#endif
+
+template <class T>
+void test()
+{
+ static const boost::array<T, 51u> data =
+ {{
+ T("1.0560191127459844751259038114395241283965590525302917878166464679729562764239266483419824023679041866569431842053263976225991679105269492268050148624443706785607467750929028856273183654547152707568642275917435773104050171284580773949313906303074811586096214771879801872225500237540725592288167903987152007171391207680034517664218965133028298959753155835975555361514087618679892905973726581183754237665"),
+ T("6.0577917650974496023981039346694689204850927958941226507775366589415588030232830758139222010716099059155799853188868489737439396141346120898610181630988217093945337280471788812956307352429914669334599644412036010014302812555700905490062030666482387008384856645533100266205122930455496234252478878949675888122615795451076521244771554025667181070733415815608287241160724578541982548132473721865287585003"),
+ T("383.32956577005424506758441449272199796616394738942294350035763341369127219359132618750028176886177362785452836065735889720098699937365992620246167965376788963171659530350198190156275836547285437366012371175910490835823389352716981464503672749829183569550509561579181434088407652213421105693358960196044447948190823567291153397039759820680087749250557665869797605969680417240900163183563482342795870741"),
+ T("180470.88335034971169904627554690213669106779370247753503772451628313223853228134148123711258586005038324156900626143047383382773083164188515409766952843294484598668304799186411411329575367546332731190431166613267871177008493921416649792646568096789971466064344922873643120446759328638447781504932928745974584136039698220604099816877847080168890581112550484205291341188894903342677757367415636409890558"),
+ T("6.2781497954189513287619297175142770025826052476955600323495790530946900406209789437212923381830889846578651793922971071825731424267985994598149826652782605981764572599129753631344305259620294513472869937699509893247230674850025066547664563263958672029867981296029855675095947587305949634130736118694040608573981560192569935477462121110619100122692626135788198431038121227062383110684489973794745342204e8"),
+ T("1.613783114750852113223226710244634574082654363427931747177970610142560035434819323665197978270795707611590961019502906079030261920109649748962125930850198625621792763842224096823299250338750953491004408731082880660125641628213970297576817341593254767125933119462446651783267917469179893016103516988279473907996009458208097272806046395206212403180775656514566222835047724943633607736647735739948551096e13"),
+ T("3.0651210048650948869531196671342477415226643123350617715268971834881834615138925908518703584506447138436613632341330640449725016173384960626760387649747643297918807083363913015806893683786389067836005832038060734248371426886808175554210317756018846109627572546314172492701544345965940408777570519312837860014177872754358662463423939942202520475422342889660750666147940146262635303938752019875745307992e18"),
+ T("4.3016893602106215864771434464025735547192956887050537014696231526954713331351791376069506688795159316625154458115179050297716224800318064110052445970764898870599885508391064218065806885129697936678362276766771902589638957537168339190488273555753876162633237990462617955892238424402124353124736879474651977422350856642986446591941163073842974714357745162365700428610167249762162775568692443158879770006e24"),
+ T("4.4608685929681360001024935791890661655506049487122331222491789277138083092507844933483858468341107613657448783043064935174812965310544903547535217357996429824403225005261842368679242972243707736489629610256554995236901040773902962370130989883960298987808008001651650799892267761089302132749037069497452309074389846493140222931714618697738906019885122076310868220596765753447232222740129365498326869428e31"),
+ T("3.4181315955816806472569357441100390029536003312981931954091744304974491527743601285017456624487264929971022746516079644284683284072159616291298593217459064246713801084801182706805865477209408120733740982340972570739267039630582468876075574706187115643861449939429503730606743466086010115127464706315791765264572070452800816054590653675962889901898843712936126341807733200610910325052666512334161414655e39"),
+ T("1.935294628272790810141453021278524976364077691905248015888165919062516673344977091262644262832934899971824373171672037249361491844419302323587942915162859665992916625636813244576210109931852761921719987632855596663907494303248513195744818730879742963301327852160193919379798462926667740594397712731448572837824802330973561570848397758210619453310032286208701226098998940360395267237151018055781640126e48"),
+ T("8.0964449511890098565841496436016431651692307764702784234901741408135381374668439020986470675941110923614446905696411023621632714191313583360826598468217983223558130595633054971338824192327248896500337050246640453410159732184419096917171044075711156867804851018388576371530520943696439917673720450911725466781235347212700849702742625663288687644090935756560022610000629006347244369388824818661974220426e57"),
+ T("2.5028257092625174549175008952222569141816383637904981644379473858250736896174216539673733521627607209322019413420937570273676341726636307131078699799472622998437404149614292337267153201903296102921815263736653035269935857816159086496594269187082442244280898258397047045746728729079796167987895368614037770286371191530575814695859433478185016171380286325273493350193132538052551497175771289873181595171e68"),
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+ T("9.0936326753636727240574546678839170665019169110943878894933093211555976995701468041449327370073681898690638466136204694745206283652338526673125958055131610409923286526192661778126811265116493171283319361595267283588121098349703951929669281966675596890266483864217591555707552765565756842701056144290075867893520379419521775913047964393758374891516340929062076304350159966063972713118995033247759001609e679"),
+ T("5.8798281636930489964162009429009257867906792508058801627042121953599912951265315933723440185825519080102988056836911095299854840387008575164090793635997912930561430335216151607097220208013034399895832350235280120270626904356196935166701773768680311063264380891331021514518757839220818506905997847228783439015252768055166165941582030353226255576433910936297965207260585437762430381969160714956727596198e714"),
+ T("2.8091881292911108404345975896815558958477835260737794579417284512413473388968057587088555041266297486841923628702282019643659456724373332519583025947015025975126598748630623031951723754960589046233996595466021913942587558326660593063197905288573353559106884645285531497626940379800500474282446929237914568534665868703742731713632349090897884403966643055728471509474896855575286123275564417626861566706e750"),
+ T("9.917129372597671132067673866739246238179742417231064062960232866725337575281938597212073697168000155027158148165861617400080837699968785505107579831803685516054837447325150388867488754170677228096524224392410232206238263933144338637103531441623303187445874039234973380151391274490746625993568552049954630793219419614845431626975962881182662815760423226111647056071831411664335144052772436215105801395e786"),
+ T("2.5869027163543111121878679987081647715187872826677398475096738640583659800068967379551376322170347537454918190603891312949716382621902484616361664158953484778255247083652726854621059785392022847887382779010079407502679229021085320675903109573769331277413372272363218896397965662581357886739691376204316908974081821980432178065394228926767529685562155837452626029223937027004015040825450642409597700449e824"),
+ T("4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862"),
+ T("7.1012569014339068241101751233953234216522840280342406520909288232012799547871960723719836516359548198842749536961644100550279020276709043358260853581760590386456213180291689322352732545965831405519844109680619067101311180959399339922706596098526969148981173519865139508665631317310424178378833370605922449094745510812618563813537347841030916512147874232760564378443782164868016244561788356251308121716e901"),
+ T("7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941"),
+ T("5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982"),
+ T("3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024"),
+ T("1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067"),
+ T("4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110"),
+ }};
+
+ T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
+
+ unsigned max_err = 0;
+ for(unsigned k = 0; k < data.size(); k++)
+ {
+ const T x = eg + k;
+ T val = boost::multiprecision::cosh(x * x);
+ T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits<T>::epsilon());
+ unsigned err = e.template convert_to<unsigned>();
+ if(err > max_err)
+ max_err = err;
+ }
+ std::cout << "Max error was: " << max_err << std::endl;
+ BOOST_TEST(max_err < 1200);
+}
+
+
+int main()
+{
+#ifdef TEST_BACKEND
+ test<boost::multiprecision::mp_number<boost::multiprecision::concepts::mp_number_backend_real_architype> >();
+#endif
+#ifdef TEST_MPF50
+ test<boost::multiprecision::mpf_real_50>();
+ test<boost::multiprecision::mpf_real_100>();
+#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
+#ifdef TEST_E_FLOAT
+ test<boost::multiprecision::e_float>();
+#endif
+ return boost::report_errors();
+}
+
+
+

Modified: sandbox/big_number/libs/multiprecision/test/test_exp.cpp
==============================================================================
--- sandbox/big_number/libs/multiprecision/test/test_exp.cpp (original)
+++ sandbox/big_number/libs/multiprecision/test/test_exp.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -29,6 +29,9 @@
#if defined(TEST_MPF50)
#include <boost/multiprecision/gmp.hpp>
#endif
+#if defined(TEST_MPFR_50)
+#include <boost/multiprecision/mpfr.hpp>
+#endif
#ifdef TEST_BACKEND
#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
#endif
@@ -104,6 +107,11 @@
       unsigned err = e.template convert_to<unsigned>();
       if(err > max_err)
          max_err = err;
+ val = boost::multiprecision::exp(-boost::multiprecision::sqrt((pi * (100 * k)) * (100 * k)));
+ e = ceil(fabs((val - (1/data[k])) / (1/data[k])) / std::numeric_limits<T>::epsilon());
+ err = e.template convert_to<unsigned>();
+ if(err > max_err)
+ max_err = err;
    }
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 1200);
@@ -119,6 +127,10 @@
    test<boost::multiprecision::mpf_real_50>();
    test<boost::multiprecision::mpf_real_100>();
#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
#ifdef TEST_E_FLOAT
    test<boost::multiprecision::e_float>();
#endif

Modified: sandbox/big_number/libs/multiprecision/test/test_log.cpp
==============================================================================
--- sandbox/big_number/libs/multiprecision/test/test_log.cpp (original)
+++ sandbox/big_number/libs/multiprecision/test/test_log.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -29,6 +29,9 @@
#if defined(TEST_MPF50)
#include <boost/multiprecision/gmp.hpp>
#endif
+#ifdef TEST_MPFR_50
+#include <boost/multiprecision/mpfr.hpp>
+#endif
#ifdef TEST_BACKEND
#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
#endif
@@ -172,6 +175,10 @@
    test<boost::multiprecision::mpf_real_50>();
    test<boost::multiprecision::mpf_real_100>();
#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
#ifdef TEST_E_FLOAT
    test<boost::multiprecision::e_float>();
#endif

Added: sandbox/big_number/libs/multiprecision/test/test_pow.cpp
==============================================================================
--- (empty file)
+++ sandbox/big_number/libs/multiprecision/test/test_pow.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -0,0 +1,583 @@
+///////////////////////////////////////////////////////////////
+// Copyright Christopher Kormanyos 2002 - 2011.
+// Copyright 2011 John Maddock. Distributed under the Boost
+// Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#include <boost/detail/lightweight_test.hpp>
+#include <boost/array.hpp>
+
+#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ)
+# define TEST_MPF50
+//# define TEST_MPF
+# define TEST_BACKEND
+# define TEST_E_FLOAT
+# define TEST_MPFR_50
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF50)
+#include <boost/multiprecision/gmp.hpp>
+#endif
+#if defined(TEST_MPFR_50)
+#include <boost/multiprecision/mpfr.hpp>
+#endif
+#ifdef TEST_BACKEND
+#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
+#endif
+#ifdef TEST_E_FLOAT
+#include <boost/multiprecision/e_float.hpp>
+#endif
+
+template <class T>
+void test()
+{
+ static const boost::array<boost::array<T, 3>, 500> data =
+ {{
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+ { static_cast<T>("2.15534801432384071073755649194936268031597137451171875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2"), static_cast<T>("4.05812814671632215990371150837745517492294311523437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2"), static_cast<T>("8.55799445393602464144976083125961944702079982479924287374752573999342183140040918969698718557087349720031284500593972794455976395816766982409031253828819168807248785638632014800512514311905184872890032777260194266023572565329278809193542262172193713145497824126566400120337339261082686915643720103934e-1") },
+ }};
+
+ unsigned max_err = 0;
+ for(unsigned k = 0; k < data.size(); k++)
+ {
+ T val = boost::multiprecision::pow(data[k][0], data[k][1]);
+ T e = ceil(fabs((val - data[k][2]) / data[k][2]) / std::numeric_limits<T>::epsilon());
+ unsigned err = e.template convert_to<unsigned>();
+ if(err > max_err)
+ max_err = err;
+ }
+ std::cout << "Max error was: " << max_err << std::endl;
+}
+
+
+int main()
+{
+#ifdef TEST_BACKEND
+ test<boost::multiprecision::mp_number<boost::multiprecision::concepts::mp_number_backend_real_architype> >();
+#endif
+#ifdef TEST_MPF50
+ test<boost::multiprecision::mpf_real_50>();
+ test<boost::multiprecision::mpf_real_100>();
+#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
+#ifdef TEST_E_FLOAT
+ test<boost::multiprecision::e_float>();
+#endif
+ return boost::report_errors();
+}
+
+
+

Added: sandbox/big_number/libs/multiprecision/test/test_sinh.cpp
==============================================================================
--- (empty file)
+++ sandbox/big_number/libs/multiprecision/test/test_sinh.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -0,0 +1,137 @@
+///////////////////////////////////////////////////////////////
+// Copyright Christopher Kormanyos 2002 - 2011.
+// Copyright 2011 John Maddock. Distributed under the Boost
+// Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#include <boost/detail/lightweight_test.hpp>
+#include <boost/array.hpp>
+
+#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ)
+# define TEST_MPF50
+//# define TEST_MPF
+# define TEST_BACKEND
+# define TEST_E_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF50)
+#include <boost/multiprecision/gmp.hpp>
+#endif
+#if defined(TEST_MPFR_50)
+#include <boost/multiprecision/mpfr.hpp>
+#endif
+#ifdef TEST_BACKEND
+#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
+#endif
+#ifdef TEST_E_FLOAT
+#include <boost/multiprecision/e_float.hpp>
+#endif
+
+template <class T>
+void test()
+{
+ static const boost::array<T, 51u> data =
+ {{
+ T("0.33937643772780730649735035088117439284797964277099188367427256402032493952288848579083622213428182842627923924487560393743204013166230906610274533504451302298480596207257724471359936027198954417317381228420986152562253196896619001418292769103034561794393400788635610424360775622370491149170501475453034747306600304507650361914904138327962144190354572359428689767990353722392457982930942617983634601752"),
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+ T("2.8985391304542768293172709775230767981477721528885408305355619530690119426207269563049756824939397157221877775531212262059946098575425050827283362457005503261796116156917077778477251551070762614233325253060283603452216492681531839154649232080928787066338399915850327381614672456102374248950210248266796072457623370079195574322846594267768883120374288952014885152055438195794090975578878933873824774214e306"),
+ T("9.57524433627083921372674145950563946532138741951042299439035158875449060589509856903496678820625880407684156184675763001790613289835869844325821965070261880894138207436003366195024403902162467929095155787852409710735775347490909311196315332711680552044467458169615366116872469435840608534489425322247278926672059747911266981024366989976214521515026692183039600169984107883592297128416659318858313127e329"),
+ T("2.3372734503362369375381009524197350830316472034721759761797536237738670471009423543542251572488229045699598160834162677357730620072441755506075897500940629883044875771104686291523502165266242030847074909362622098365719455332359938746138629161304717385265309980898079489959955157644566232440805137701071311495653330606071611331941246434767948905863368638163788562679785940566685500460815077065003612487e354"),
+ T("4.2155879126937199240969909448599186868484717887298729605150033299123534992857332918168135230843738695925698383815575417820480732378749635394939513838137876524333991937836847074991505476867647762082587225838063325020413513077128321581439429001485977751765798011101092072613053687422983352140468569171564773941232256057064161142341661775359191159220450305300322654184921617310753474842253496677498824723e379"),
+ T("5.6181811613375701248970224378256740494692066242437602652469740512738297599235414593999616891945156186827736326184687322137498447792007445397397290336810468925670064733464757082986791232916898141597610692740388799796632396708149027243436859752526805112778790645096555770227809873695589969805678601106157556386974221647669590827712353133603091803570183764883405340587430017053183637835511899658145649708e405"),
+ T("5.532511069282205350923830187073466127274584467195468607886763750877294392993663821432158885753563495238131394373865428654052604326264330104646257659760161386620716716703631608643312613245804625511813964275109451513736558514977338129201153666764317441936156609643185133981728847167450887861106642311329612564652645663234240748195490808151911497393974690166034839217817023634217121406163178148652748479e432"),
+ T("4.0256666306761331240653217136731531623017017695713942917027851762705346357330788586411431378972009980532310757689380174461664677676028378924382554201434975574729861177781849023768222381429947872325368088023224591306630434887529215459580760863075907686248521168590309636468448648513752893851767315693469638980874648457114335557202115472595647478331668869318302753802858726588719006447471192697846325955e460"),
+ T("2.1644237346681663424601781769159797919834245365230735589058796985974745594485988855971413936820871935714602237643458356241187573307428309041919648027960168541647193436225977495680484218384107820095589356463058222584008532497069179993678533431131233629312850771528970443634604290143149079209513868130585713006080733488491160321145735562062411305931183571279530201672366980412430529846635995189699318073e489"),
+ T("8.5987580981195983662047247216936066485731760315371506386077056691409579856014763032619539539935299716110411688793466397984311640631361934500807639285587334983206556915704635831992012926186843826981296831658998834850783404713050829093753126189556625095994621605300047199962332098857236359801681157419606676412198783092816364336047306243999363335004760439115355072350465422891365411868472688286678516314e518"),
+ T("2.5241673163187127276134610716954724162270290228773641734420864618245211926017624829840685860130579257772126398622324109858115624706486522844752512951837805396709793171502497523431473021570806024043139443284538862368635312799539108264084028032731295487282188616820261689634926427135060887942797635147693849950058672753458576476491733064455826768562371858057444914175251596852571637211466017938478085247e549"),
+ T("5.475067911823387661325942057081957044927796274441278042805014835144678321092623034147031518807063234976073102574257079170283458172046752719724152941316842521196069804425876507927418423409523739261726681120662097159943049401039490818332686968135012747332468921142470970507219403290422458185430415836291605355383658657658638112408092789126678938878667507151950931633694006471359998448912249374833586727e580"),
+ T("8.7750549689950256776639468724574158629603320014390275681028674550826357080136422399476213432791376656222763800628593282303459051561266270006921840049305819767639184391149913915312831894296821356222752594264134130151457242713539248421883837353442181724530706933220158507240760325182068001553294949268596178418634164323874971937997072367419479635154591248667559627811893588163238012665671798461211917208e612"),
+ T("1.0392000158337773273751156576416024664653679689973856373456304843339302977923254238376497044027728158058903302390909588333829463843362779584402914847447592731182614369968957680281500946805571235013941407979569788567794900810257154433592958167545186687137810101848000107335074486050959387974516414654638879740966175786016492797845169374594168995878543584318334800124941205910589727264397237600733483158e646"),
+ T("9.0936326753636727240574546678839170665019169110943878894933093211555976995701468041449327370073681898690638466136204694745206283652338526673125958055131610409923286526192661778126811265116493171283319361595267283588121098349703951929669281966675596890266483864217591555707552765565756842701056144290075867893520379419521775913047964393758374891516340929062076304350159966063972713118995033247759001609e679"),
+ T("5.8798281636930489964162009429009257867906792508058801627042121953599912951265315933723440185825519080102988056836911095299854840387008575164090793635997912930561430335216151607097220208013034399895832350235280120270626904356196935166701773768680311063264380891331021514518757839220818506905997847228783439015252768055166165941582030353226255576433910936297965207260585437762430381969160714956727596198e714"),
+ T("2.8091881292911108404345975896815558958477835260737794579417284512413473388968057587088555041266297486841923628702282019643659456724373332519583025947015025975126598748630623031951723754960589046233996595466021913942587558326660593063197905288573353559106884645285531497626940379800500474282446929237914568534665868703742731713632349090897884403966643055728471509474896855575286123275564417626861566706e750"),
+ T("9.917129372597671132067673866739246238179742417231064062960232866725337575281938597212073697168000155027158148165861617400080837699968785505107579831803685516054837447325150388867488754170677228096524224392410232206238263933144338637103531441623303187445874039234973380151391274490746625993568552049954630793219419614845431626975962881182662815760423226111647056071831411664335144052772436215105801395e786"),
+ T("2.5869027163543111121878679987081647715187872826677398475096738640583659800068967379551376322170347537454918190603891312949716382621902484616361664158953484778255247083652726854621059785392022847887382779010079407502679229021085320675903109573769331277413372272363218896397965662581357886739691376204316908974081821980432178065394228926767529685562155837452626029223937027004015040825450642409597700449e824"),
+ T("4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862"),
+ T("7.1012569014339068241101751233953234216522840280342406520909288232012799547871960723719836516359548198842749536961644100550279020276709043358260853581760590386456213180291689322352732545965831405519844109680619067101311180959399339922706596098526969148981173519865139508665631317310424178378833370605922449094745510812618563813537347841030916512147874232760564378443782164868016244561788356251308121716e901"),
+ T("7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941"),
+ T("5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982"),
+ T("3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024"),
+ T("1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067"),
+ T("4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110"),
+ }};
+
+ T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
+
+ unsigned max_err = 0;
+ for(unsigned k = 0; k < data.size(); k++)
+ {
+ const T x = eg + k;
+ T val = boost::multiprecision::sinh(x * x);
+ T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits<T>::epsilon());
+ unsigned err = e.template convert_to<unsigned>();
+ if(err > max_err)
+ max_err = err;
+ }
+ std::cout << "Max error was: " << max_err << std::endl;
+ BOOST_TEST(max_err < 1200);
+}
+
+
+int main()
+{
+#ifdef TEST_BACKEND
+ test<boost::multiprecision::mp_number<boost::multiprecision::concepts::mp_number_backend_real_architype> >();
+#endif
+#ifdef TEST_MPF50
+ test<boost::multiprecision::mpf_real_50>();
+ test<boost::multiprecision::mpf_real_100>();
+#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
+#ifdef TEST_E_FLOAT
+ test<boost::multiprecision::e_float>();
+#endif
+ return boost::report_errors();
+}
+
+
+

Added: sandbox/big_number/libs/multiprecision/test/test_tanh.cpp
==============================================================================
--- (empty file)
+++ sandbox/big_number/libs/multiprecision/test/test_tanh.cpp 2011-10-07 14:14:34 EDT (Fri, 07 Oct 2011)
@@ -0,0 +1,137 @@
+///////////////////////////////////////////////////////////////
+// Copyright Christopher Kormanyos 2002 - 2011.
+// Copyright 2011 John Maddock. Distributed under the Boost
+// Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#include <boost/detail/lightweight_test.hpp>
+#include <boost/array.hpp>
+
+#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ)
+# define TEST_MPF50
+//# define TEST_MPF
+# define TEST_BACKEND
+# define TEST_E_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF50)
+#include <boost/multiprecision/gmp.hpp>
+#endif
+#if defined(TEST_MPFR_50)
+#include <boost/multiprecision/mpfr.hpp>
+#endif
+#ifdef TEST_BACKEND
+#include <boost/multiprecision/concepts/mp_number_architypes.hpp>
+#endif
+#ifdef TEST_E_FLOAT
+#include <boost/multiprecision/e_float.hpp>
+#endif
+
+template <class T>
+void test()
+{
+ static const boost::array<T, 51u> data =
+ {{
+ T("0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017"),
+ T("0.98628073997374759901559180515206275902189609982907214282364143439537215491113710345866034807991101303183938339561499559327886956280789743287824488269072297413440935381715378233031399015496124706604318545539544610760151756970229801074280545428642122005982857974921606264103186878499260552388713716032507770319550435738767597150644370033277228635793175246197730488375240713357827246166262087899961098648"),
+ T("0.99999659728082161113542951278514830809677661658635225532792520501703544628367875293677270218317428676793098034276042396396797568103263882451732810190507733063467333056356770774002596898762991629653041854653269824642873291146068535300466473399592751219449187768646625229500705182676930009096545254478199838990703077597971823456671241141900968900216742636822174010867343154474773040184900973368250708724"),
+ T("0.9999999999846483268200051609594321550129159997920576480976206867496512752486590660437091205989616108531910897733432934135954788151766561209164605337537937873588006552145390152387235783207736999759875845070169747521389728857476525437483543080651125798739562649414879487621858466223255239845627205850217328574865852922872737234283038190096982410137471391847466112651349436875974689271288261759782261321"),
+ T("0.9999999999999999987314527242099750648171958211319474558707792311593804963057878814487720997303512134007272111464990650500302215773762906820778949397525329109311974741708703536680512747226155618703318739024344621256722269608969415280035337052044425138281821760268269187377517243951584969175035549994883451471918693502477485385682884154959809285569290940740978684264145737164182111806308430952867505356"),
+ T("0.9999999999999999999999999980800953069847308586840237590563929855339557065536765765234844240789584487443451033349994294426525006157530320529970966048109743850154174651033567146346966529198814047607015842020039899630884318521543225160212193994911746894335846264878066530266737005606770102869237101848445559941638381625615207320468184414917265299980278164193202897754476112968080358662232635784904263624"),
+ T("0.9999999999999999999999999999999999999467800140220866754762922747687784133233134010432889959570821554455247528344437918197518545105332713456859236726383195243056599177018396579766073961540714510399202497404647103138524118065391185503678895059096790300665805648569647351935897874460587855127436472608470703384261586158923066272124216158518232588330799027603391275039552776308636189531809031683723259525"),
+ T("0.9999999999999999999999999999999999999999999999999729795912960133359928587562229512337339217831178574875626619226954752643039860388090399659478676726654102118545764943682017611574275691203710439707807193180604656837503862242700430179591666329131728631752773789406064618682879167351725013888294859467540832310795515139677375807407622028485242969471516812171475098378942187864794497220152019202351747432"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999997487354938310440650220692519525261552411539996830587326435051159231522052011310872619940247463640019105467860778515384738650636054646551611609757125760437266415865214306396520500343113189907306851418957620080971645943305760132385139924583154317156560414548076370893360020924960120441059315311380109752919823616149973862196846266297710225"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999572050575304159358359221596743379014313563214857593401545331495211888415913558896516895286943572966865708195832339959764445194449615969154689769557903166971249521898883489362426386924297872088925852892350150865941427355319827260914834268754732102528105919811851193667193380541054520023003326858641189063542651960743457613"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998665016733514821204959171836698281165918083005790816030823236096080522860514417075411055633676502699904415882389102672678124683084429720879962355892225321369091298491658349178472270952759208443767848312111069127329160464884932271685986610697222434145553035947750809388321614695213754318979469071722942883"),
+ T("0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992372516628147584832950728021842198359205201519966391076994594773600474674435473005118571751514446148292787696117866094991476340344341061706866751156257825144909115117822189019766805825304055482958970512463798453229341693148012213183553546720540880444569824125592343803193018989122964"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920180539244323143459416025663362517256166793900312667214543096238752838226369161775531456005541374878274529461511286842988937830155704737448202558382612829022464635400289328916240002670783433827234852858267621807568393874737879853500598862298495727481132883728328"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998470116425957155787153557938061034698436461173594805292722874130433614266475136267606498346730583487791266503943659174886554170377537630914770998114573340081594827150737005158607830579000912020838690230498119348251553312722575955142752845289"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999462931048083476382670449719737943481963930626760625326765703815392249622625483433043363664396638162612437367800102332819699131841317348173451308570776544874933173719394861336636728378134900422312720743996219523365098"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996546783689748726752364896615532860288057097437452774779386074906915819380531729493071959232887620213723607155628959529584572083388979892309086717786559916703004365603135284141639480887703759"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999593332381019647939423999969519583099837564321056588766269967853479478603122899456262904869063959564274215899007623362296377022418464303752396325625838280378647335"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999122842714667567128203355585346559126606029196080721845292399104475997315344844970601651757832506169948906646054332493537761143729664"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965347272050374435790597917065458623422102880662825928396981295898014081371503733411536311258910851858"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974926240515037403282500845454464621558236030794140169313830052413917"),
+ T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999667705192725716176070161727364499"),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ T("1."),
+ }};
+
+ T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
+
+ unsigned max_err = 0;
+ for(unsigned k = 0; k < data.size(); k++)
+ {
+ const T x = eg + k;
+ T val = boost::multiprecision::tanh(x * x);
+ T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits<T>::epsilon());
+ unsigned err = e.template convert_to<unsigned>();
+ if(err > max_err)
+ max_err = err;
+ }
+ std::cout << "Max error was: " << max_err << std::endl;
+ BOOST_TEST(max_err < 1200);
+}
+
+
+int main()
+{
+#ifdef TEST_BACKEND
+ test<boost::multiprecision::mp_number<boost::multiprecision::concepts::mp_number_backend_real_architype> >();
+#endif
+#ifdef TEST_MPF50
+ test<boost::multiprecision::mpf_real_50>();
+ test<boost::multiprecision::mpf_real_100>();
+#endif
+#ifdef TEST_MPFR_50
+ test<boost::multiprecision::mpfr_real_50>();
+ test<boost::multiprecision::mpfr_real_100>();
+#endif
+#ifdef TEST_E_FLOAT
+ test<boost::multiprecision::e_float>();
+#endif
+ return boost::report_errors();
+}
+
+
+

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