commit gcc-4.4.3 which is used to build gcc-4.4.3 Android toolchain in master.

The source is based on fsf gcc-4.4.3 and contains local patches which
are recorded in gcc-4.4.3/README.google.

Change-Id: Id8c6d6927df274ae9749196a1cc24dbd9abc9887

1 files changed, 435 insertions, 0 deletions

diff --git a/gcc-4.4.3/libstdc++-v3/include/tr1/riemann_zeta.tcc b/gcc-4.4.3/libstdc++-v3/include/tr1/riemann_zeta.tcc
new file mode 100644
index 000000000..c646c2e40
--- /dev/null
+++ b/gcc-4.4.3/libstdc++-v3/include/tr1/riemann_zeta.tcc
@@ -0,0 +1,435 @@
+// Special functions -*- C++ -*-
+
+// Copyright (C) 2006, 2007, 2008, 2009
+// Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+/** @file tr1/riemann_zeta.tcc
+ *  This is an internal header file, included by other library headers.
+ *  You should not attempt to use it directly.
+ */
+
+//
+// ISO C++ 14882 TR1: 5.2  Special functions
+//
+
+// Written by Edward Smith-Rowland based on:
+//   (1) Handbook of Mathematical Functions,
+//       Ed. by Milton Abramowitz and Irene A. Stegun,
+//       Dover Publications, New-York, Section 5, pp. 807-808.
+//   (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl
+//   (3) Gamma, Exploring Euler's Constant, Julian Havil,
+//       Princeton, 2003.
+
+#ifndef _GLIBCXX_TR1_RIEMANN_ZETA_TCC
+#define _GLIBCXX_TR1_RIEMANN_ZETA_TCC 1
+
+#include "special_function_util.h"
+
+namespace std
+{
+namespace tr1
+{
+
+  // [5.2] Special functions
+
+  // Implementation-space details.
+  namespace __detail
+  {
+
+    /**
+     *   @brief  Compute the Riemann zeta function @f$ \zeta(s) @f$
+     *           by summation for s > 1.
+     * 
+     *   The Riemann zeta function is defined by:
+     *    \f[
+     *      \zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^{s}} for s > 1
+     *    \f]
+     *   For s < 1 use the reflection formula:
+     *    \f[
+     *      \zeta(s) = 2^s \pi^{s-1} \Gamma(1-s) \zeta(1-s)
+     *    \f]
+     */
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_sum(const _Tp __s)
+    {
+      //  A user shouldn't get to this.
+      if (__s < _Tp(1))
+        std::__throw_domain_error(__N("Bad argument in zeta sum."));
+
+      const unsigned int max_iter = 10000;
+      _Tp __zeta = _Tp(0);
+      for (unsigned int __k = 1; __k < max_iter; ++__k)
+        {
+          _Tp __term = std::pow(static_cast<_Tp>(__k), -__s);
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            {
+              break;
+            }
+          __zeta += __term;
+        }
+
+      return __zeta;
+    }
+
+
+    /**
+     *   @brief  Evaluate the Riemann zeta function @f$ \zeta(s) @f$
+     *           by an alternate series for s > 0.
+     * 
+     *   The Riemann zeta function is defined by:
+     *    \f[
+     *      \zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^{s}} for s > 1
+     *    \f]
+     *   For s < 1 use the reflection formula:
+     *    \f[
+     *      \zeta(s) = 2^s \pi^{s-1} \Gamma(1-s) \zeta(1-s)
+     *    \f]
+     */
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_alt(const _Tp __s)
+    {
+      _Tp __sgn = _Tp(1);
+      _Tp __zeta = _Tp(0);
+      for (unsigned int __i = 1; __i < 10000000; ++__i)
+        {
+          _Tp __term = __sgn / std::pow(__i, __s);
+          if (std::abs(__term) < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __zeta += __term;
+          __sgn *= _Tp(-1);
+        }
+      __zeta /= _Tp(1) - std::pow(_Tp(2), _Tp(1) - __s);
+
+      return __zeta;
+    }
+
+
+    /**
+     *   @brief  Evaluate the Riemann zeta function by series for all s != 1.
+     *           Convergence is great until largish negative numbers.
+     *           Then the convergence of the > 0 sum gets better.
+     *
+     *   The series is:
+     *    \f[
+     *      \zeta(s) = \frac{1}{1-2^{1-s}}
+     *                 \sum_{n=0}^{\infty} \frac{1}{2^{n+1}}
+     *                 \sum_{k=0}^{n} (-1)^k \frac{n!}{(n-k)!k!} (k+1)^{-s}
+     *    \f]
+     *   Havil 2003, p. 206.
+     *
+     *   The Riemann zeta function is defined by:
+     *    \f[
+     *      \zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^{s}} for s > 1
+     *    \f]
+     *   For s < 1 use the reflection formula:
+     *    \f[
+     *      \zeta(s) = 2^s \pi^{s-1} \Gamma(1-s) \zeta(1-s)
+     *    \f]
+     */
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_glob(const _Tp __s)
+    {
+      _Tp __zeta = _Tp(0);
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      //  Max e exponent before overflow.
+      const _Tp __max_bincoeff = std::numeric_limits<_Tp>::max_exponent10
+                               * std::log(_Tp(10)) - _Tp(1);
+
+      //  This series works until the binomial coefficient blows up
+      //  so use reflection.
+      if (__s < _Tp(0))
+        {
+#if _GLIBCXX_USE_C99_MATH_TR1
+          if (std::tr1::fmod(__s,_Tp(2)) == _Tp(0))
+            return _Tp(0);
+          else
+#endif
+            {
+              _Tp __zeta = __riemann_zeta_glob(_Tp(1) - __s);
+              __zeta *= std::pow(_Tp(2)
+                     * __numeric_constants<_Tp>::__pi(), __s)
+                     * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+#if _GLIBCXX_USE_C99_MATH_TR1
+                     * std::exp(std::tr1::lgamma(_Tp(1) - __s))
+#else
+                     * std::exp(__log_gamma(_Tp(1) - __s))
+#endif
+                     / __numeric_constants<_Tp>::__pi();
+              return __zeta;
+            }
+        }
+
+      _Tp __num = _Tp(0.5L);
+      const unsigned int __maxit = 10000;
+      for (unsigned int __i = 0; __i < __maxit; ++__i)
+        {
+          bool __punt = false;
+          _Tp __sgn = _Tp(1);
+          _Tp __term = _Tp(0);
+          for (unsigned int __j = 0; __j <= __i; ++__j)
+            {
+#if _GLIBCXX_USE_C99_MATH_TR1
+              _Tp __bincoeff =  std::tr1::lgamma(_Tp(1 + __i))
+                              - std::tr1::lgamma(_Tp(1 + __j))
+                              - std::tr1::lgamma(_Tp(1 + __i - __j));
+#else
+              _Tp __bincoeff =  __log_gamma(_Tp(1 + __i))
+                              - __log_gamma(_Tp(1 + __j))
+                              - __log_gamma(_Tp(1 + __i - __j));
+#endif
+              if (__bincoeff > __max_bincoeff)
+                {
+                  //  This only gets hit for x << 0.
+                  __punt = true;
+                  break;
+                }
+              __bincoeff = std::exp(__bincoeff);
+              __term += __sgn * __bincoeff * std::pow(_Tp(1 + __j), -__s);
+              __sgn *= _Tp(-1);
+            }
+          if (__punt)
+            break;
+          __term *= __num;
+          __zeta += __term;
+          if (std::abs(__term/__zeta) < __eps)
+            break;
+          __num *= _Tp(0.5L);
+        }
+
+      __zeta /= _Tp(1) - std::pow(_Tp(2), _Tp(1) - __s);
+
+      return __zeta;
+    }
+
+
+    /**
+     *   @brief  Compute the Riemann zeta function @f$ \zeta(s) @f$
+     *           using the product over prime factors.
+     *    \f[
+     *      \zeta(s) = \Pi_{i=1}^\infty \frac{1}{1 - p_i^{-s}}
+     *    \f]
+     *    where @f$ {p_i} @f$ are the prime numbers.
+     * 
+     *   The Riemann zeta function is defined by:
+     *    \f[
+     *      \zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^{s}} for s > 1
+     *    \f]
+     *   For s < 1 use the reflection formula:
+     *    \f[
+     *      \zeta(s) = 2^s \pi^{s-1} \Gamma(1-s) \zeta(1-s)
+     *    \f]
+     */
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_product(const _Tp __s)
+    {
+      static const _Tp __prime[] = {
+        _Tp(2), _Tp(3), _Tp(5), _Tp(7), _Tp(11), _Tp(13), _Tp(17), _Tp(19),
+        _Tp(23), _Tp(29), _Tp(31), _Tp(37), _Tp(41), _Tp(43), _Tp(47),
+        _Tp(53), _Tp(59), _Tp(61), _Tp(67), _Tp(71), _Tp(73), _Tp(79),
+        _Tp(83), _Tp(89), _Tp(97), _Tp(101), _Tp(103), _Tp(107), _Tp(109)
+      };
+      static const unsigned int __num_primes = sizeof(__prime) / sizeof(_Tp);
+
+      _Tp __zeta = _Tp(1);
+      for (unsigned int __i = 0; __i < __num_primes; ++__i)
+        {
+          const _Tp __fact = _Tp(1) - std::pow(__prime[__i], -__s);
+          __zeta *= __fact;
+          if (_Tp(1) - __fact < std::numeric_limits<_Tp>::epsilon())
+            break;
+        }
+
+      __zeta = _Tp(1) / __zeta;
+
+      return __zeta;
+    }
+
+
+    /**
+     *   @brief  Return the Riemann zeta function @f$ \zeta(s) @f$.
+     * 
+     *   The Riemann zeta function is defined by:
+     *    \f[
+     *      \zeta(s) = \sum_{k=1}^{\infty} k^{-s} for s > 1
+     *                 \frac{(2\pi)^s}{pi} sin(\frac{\pi s}{2})
+     *                 \Gamma (1 - s) \zeta (1 - s) for s < 1
+     *    \f]
+     *   For s < 1 use the reflection formula:
+     *    \f[
+     *      \zeta(s) = 2^s \pi^{s-1} \Gamma(1-s) \zeta(1-s)
+     *    \f]
+     */
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta(const _Tp __s)
+    {
+      if (__isnan(__s))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__s == _Tp(1))
+        return std::numeric_limits<_Tp>::infinity();
+      else if (__s < -_Tp(19))
+        {
+          _Tp __zeta = __riemann_zeta_product(_Tp(1) - __s);
+          __zeta *= std::pow(_Tp(2) * __numeric_constants<_Tp>::__pi(), __s)
+                 * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+#if _GLIBCXX_USE_C99_MATH_TR1
+                 * std::exp(std::tr1::lgamma(_Tp(1) - __s))
+#else
+                 * std::exp(__log_gamma(_Tp(1) - __s))
+#endif
+                 / __numeric_constants<_Tp>::__pi();
+          return __zeta;
+        }
+      else if (__s < _Tp(20))
+        {
+          //  Global double sum or McLaurin?
+          bool __glob = true;
+          if (__glob)
+            return __riemann_zeta_glob(__s);
+          else
+            {
+              if (__s > _Tp(1))
+                return __riemann_zeta_sum(__s);
+              else
+                {
+                  _Tp __zeta = std::pow(_Tp(2)
+                                * __numeric_constants<_Tp>::__pi(), __s)
+                         * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+#if _GLIBCXX_USE_C99_MATH_TR1
+                             * std::tr1::tgamma(_Tp(1) - __s)
+#else
+                             * std::exp(__log_gamma(_Tp(1) - __s))
+#endif
+                             * __riemann_zeta_sum(_Tp(1) - __s);
+                  return __zeta;
+                }
+            }
+        }
+      else
+        return __riemann_zeta_product(__s);
+    }
+
+
+    /**
+     *   @brief  Return the Hurwitz zeta function @f$ \zeta(x,s) @f$
+     *           for all s != 1 and x > -1.
+     * 
+     *   The Hurwitz zeta function is defined by:
+     *   @f[
+     *     \zeta(x,s) = \sum_{n=0}^{\infty} \frac{1}{(n + x)^s}
+     *   @f]
+     *   The Riemann zeta function is a special case:
+     *   @f[
+     *     \zeta(s) = \zeta(1,s)
+     *   @f]
+     * 
+     *   This functions uses the double sum that converges for s != 1
+     *   and x > -1:
+     *   @f[
+     *     \zeta(x,s) = \frac{1}{s-1}
+     *                \sum_{n=0}^{\infty} \frac{1}{n + 1}
+     *                \sum_{k=0}^{n} (-1)^k \frac{n!}{(n-k)!k!} (x+k)^{-s}
+     *   @f]
+     */
+    template<typename _Tp>
+    _Tp
+    __hurwitz_zeta_glob(const _Tp __a, const _Tp __s)
+    {
+      _Tp __zeta = _Tp(0);
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      //  Max e exponent before overflow.
+      const _Tp __max_bincoeff = std::numeric_limits<_Tp>::max_exponent10
+                               * std::log(_Tp(10)) - _Tp(1);
+
+      const unsigned int __maxit = 10000;
+      for (unsigned int __i = 0; __i < __maxit; ++__i)
+        {
+          bool __punt = false;
+          _Tp __sgn = _Tp(1);
+          _Tp __term = _Tp(0);
+          for (unsigned int __j = 0; __j <= __i; ++__j)
+            {
+#if _GLIBCXX_USE_C99_MATH_TR1
+              _Tp __bincoeff =  std::tr1::lgamma(_Tp(1 + __i))
+                              - std::tr1::lgamma(_Tp(1 + __j))
+                              - std::tr1::lgamma(_Tp(1 + __i - __j));
+#else
+              _Tp __bincoeff =  __log_gamma(_Tp(1 + __i))
+                              - __log_gamma(_Tp(1 + __j))
+                              - __log_gamma(_Tp(1 + __i - __j));
+#endif
+              if (__bincoeff > __max_bincoeff)
+                {
+                  //  This only gets hit for x << 0.
+                  __punt = true;
+                  break;
+                }
+              __bincoeff = std::exp(__bincoeff);
+              __term += __sgn * __bincoeff * std::pow(_Tp(__a + __j), -__s);
+              __sgn *= _Tp(-1);
+            }
+          if (__punt)
+            break;
+          __term /= _Tp(__i + 1);
+          if (std::abs(__term / __zeta) < __eps)
+            break;
+          __zeta += __term;
+        }
+
+      __zeta /= __s - _Tp(1);
+
+      return __zeta;
+    }
+
+
+    /**
+     *   @brief  Return the Hurwitz zeta function @f$ \zeta(x,s) @f$
+     *           for all s != 1 and x > -1.
+     * 
+     *   The Hurwitz zeta function is defined by:
+     *   @f[
+     *     \zeta(x,s) = \sum_{n=0}^{\infty} \frac{1}{(n + x)^s}
+     *   @f]
+     *   The Riemann zeta function is a special case:
+     *   @f[
+     *     \zeta(s) = \zeta(1,s)
+     *   @f]
+     */
+    template<typename _Tp>
+    inline _Tp
+    __hurwitz_zeta(const _Tp __a, const _Tp __s)
+    {
+      return __hurwitz_zeta_glob(__a, __s);
+    }
+
+  } // namespace std::tr1::__detail
+}
+}
+
+#endif // _GLIBCXX_TR1_RIEMANN_ZETA_TCC