From 4fdfbd3485303bfa30a672cb62a365d89d527e48 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Sun, 14 Aug 2022 11:30:39 +0900
Subject: [PATCH 01/11] Update ratio constructor to use GMP function

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  6 +++++-
 src/kernel/ratio.cpp            | 18 +++++++-----------
 4 files changed, 16 insertions(+), 16 deletions(-)

diff --git a/README.md b/README.md
index 000eb59e2..ce5805b5c 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.197.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.198.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.197_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.198_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.197
+Meevax Lisp System, version 0.4.198
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 3b43aa39c..9f134a40d 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.197
+0.4.198
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index c90daacf9..d3f1a5fed 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -17,6 +17,8 @@
 #ifndef INCLUDED_MEEVAX_KERNEL_RATIO_HPP
 #define INCLUDED_MEEVAX_KERNEL_RATIO_HPP
 
+#include <gmp.h>
+
 #include <meevax/kernel/pair.hpp>
 
 namespace meevax
@@ -27,9 +29,11 @@ inline namespace kernel
   {
     using pair::pair;
 
+    mpq_t value;
+
     explicit ratio(double);
 
-    explicit ratio(external_representation const&, int = 0);
+    explicit ratio(external_representation const&, int = 10);
 
     auto denominator() const -> const_reference;
 
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 2a968ca65..79dce502f 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -24,7 +24,6 @@ inline namespace kernel
 {
   ratio::ratio(double x)
   {
-    mpq_t value;
     mpq_init(value);
     mpq_set_d(value, x);
 
@@ -39,19 +38,16 @@ inline namespace kernel
   {
     std::regex static const pattern { "([+-]?[0-9a-f]+)/([0-9a-f]+)" };
 
-    if (std::smatch result; std::regex_match(token, result, pattern))
+    if (mpq_init(value); not std::regex_match(token, pattern) or mpq_set_str(value, token.c_str(), radix))
     {
-      auto n = exact_integer(result.str(1), radix);
-
-      numerator() = make(n);
-
-      auto d = exact_integer(result.str(2), radix);
-
-      denominator() = make(d);
+      mpq_clear(value);
+      throw error();
     }
-    else
+    else // TEMPORARY!!!
     {
-      throw error();
+      numerator() = make<exact_integer>(mpq_numref(value));
+      denominator() = make<exact_integer>(mpq_denref(value));
+      mpq_clear(value);
     }
   }
 

From 4104afc0d12618c09678b3e2241539aeaeb3f558 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Sun, 14 Aug 2022 12:13:51 +0900
Subject: [PATCH 02/11] Update procedure `(numerator|denominator)` to use
 `ratio-(numerator|denominator)` instead of `(car|cdr)`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md              |  6 +++---
 VERSION                |  2 +-
 basis/r4rs.ss          |  7 ++++---
 src/kernel/library.cpp | 12 ++++++++++++
 4 files changed, 20 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index ce5805b5c..01bda4a36 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.198.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.199.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.198_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.199_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.198
+Meevax Lisp System, version 0.4.199
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 9f134a40d..9d43f8919 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.198
+0.4.199
diff --git a/basis/r4rs.ss b/basis/r4rs.ss
index 71e161739..f9d21a52f 100644
--- a/basis/r4rs.ss
+++ b/basis/r4rs.ss
@@ -1,6 +1,6 @@
 (define-library (scheme r4rs)
   (import (meevax inexact)
-          (only (meevax number) exact-integer? expt exact inexact ratio?)
+          (only (meevax number) exact-integer? expt exact inexact ratio? ratio-numerator ratio-denominator)
           (only (meevax port) get-ready? standard-input-port standard-output-port)
           (only (meevax string) string-copy)
           (only (meevax syntax) define-syntax)
@@ -71,12 +71,13 @@
                                                        ,body)))))))
 
          (define (numerator x)
-           (cond ((ratio? x) (car x))
+           (cond ((ratio? x) (ratio-numerator x))
                  ((exact? x) x)
                  (else (inexact (numerator (exact x))))))
 
          (define (denominator x)
-           (cond ((exact? x) (if (ratio? x) (cdr x) 1))
+           (cond ((ratio? x) (ratio-denominator x))
+                 ((exact? x) 1)
                  ((integer? x) 1.0)
                  (else (inexact (denominator (exact x))))))
 
diff --git a/src/kernel/library.cpp b/src/kernel/library.cpp
index ffc2b1213..cd0cb8110 100644
--- a/src/kernel/library.cpp
+++ b/src/kernel/library.cpp
@@ -569,6 +569,16 @@ inline namespace kernel
 
       #undef DEFINE
 
+      library.define<procedure>("ratio-numerator", [](let const& xs)
+      {
+        return car(xs).as<ratio>().numerator();
+      });
+
+      library.define<procedure>("ratio-denominator", [](let const& xs)
+      {
+        return car(xs).as<ratio>().denominator();
+      });
+
       library.define<procedure>("floor", [](let const& xs)
       {
         return apply<floor>(car(xs));
@@ -648,6 +658,8 @@ inline namespace kernel
       library.export_("-");
       library.export_("/");
       library.export_("%");
+      library.export_("ratio-numerator");
+      library.export_("ratio-denominator");
       library.export_("floor");
       library.export_("ceiling");
       library.export_("truncate");

From a431ed6c7db9076f9b8cf3755c94aee108a271dc Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Sun, 14 Aug 2022 12:42:54 +0900
Subject: [PATCH 03/11] Update base class `pair` of `ratio` to protected

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  2 +-
 src/kernel/number.cpp           | 14 +++++++-------
 src/kernel/ratio.cpp            |  3 +--
 5 files changed, 13 insertions(+), 14 deletions(-)

diff --git a/README.md b/README.md
index 01bda4a36..402e145f7 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.199.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.200.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.199_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.200_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.199
+Meevax Lisp System, version 0.4.200
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 9d43f8919..1abe58b1d 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.199
+0.4.200
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index d3f1a5fed..d09406e19 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -25,7 +25,7 @@ namespace meevax
 {
 inline namespace kernel
 {
-  struct ratio : public virtual pair
+  struct ratio : protected virtual pair
   {
     using pair::pair;
 
diff --git a/src/kernel/number.cpp b/src/kernel/number.cpp
index 2fc627752..cb77c3dc5 100644
--- a/src/kernel/number.cpp
+++ b/src/kernel/number.cpp
@@ -33,9 +33,9 @@ inline namespace kernel
   auto operator > (exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) >  0; }
   auto operator >=(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) >= 0; }
 
-  auto operator * (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.numerator().as<exact_integer>()), cdr(b)); }
-  auto operator + (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() + b.numerator().as<exact_integer>()), cdr(b)); }
-  auto operator - (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>()), cdr(b)); }
+  auto operator * (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.numerator().as<exact_integer>()), b.denominator()); }
+  auto operator + (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() + b.numerator().as<exact_integer>()), b.denominator()); }
+  auto operator - (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>()), b.denominator()); }
   auto operator / (exact_integer const& a, ratio const& b) -> ratio { return a * b.invert(); }
   auto operator % (exact_integer const&  , ratio const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
   auto operator !=(exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a != x.numerator().as<exact_integer>(); }
@@ -69,10 +69,10 @@ inline namespace kernel
   auto operator > (exact_integer const& a, double b) -> bool   { return mpz_cmp_d(a.value, b) >  0; }
   auto operator >=(exact_integer const& a, double b) -> bool   { return mpz_cmp_d(a.value, b) >= 0; }
 
-  auto operator * (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b), cdr(a)); }
-  auto operator + (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() + a.denominator().as<exact_integer>() * b), cdr(a)); }
-  auto operator - (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() - a.denominator().as<exact_integer>() * b), cdr(a)); }
-  auto operator / (ratio const& a, exact_integer const& b) -> ratio { return ratio(car(a), make(a.denominator().as<exact_integer>() * b)); }
+  auto operator * (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b), a.denominator()); }
+  auto operator + (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() + a.denominator().as<exact_integer>() * b), a.denominator()); }
+  auto operator - (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() - a.denominator().as<exact_integer>() * b), a.denominator()); }
+  auto operator / (ratio const& a, exact_integer const& b) -> ratio { return ratio(a.numerator(), make(a.denominator().as<exact_integer>() * b)); }
   auto operator % (ratio const&  , exact_integer const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
   auto operator !=(ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() != b; }
   auto operator < (ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <  b; }
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 79dce502f..7b470055c 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -28,7 +28,6 @@ inline namespace kernel
     mpq_set_d(value, x);
 
     numerator() = make<exact_integer>(mpq_numref(value));
-
     denominator() = make<exact_integer>(mpq_denref(value));
 
     mpq_clear(value);
@@ -107,7 +106,7 @@ inline namespace kernel
   {
     if (auto x = reduce(); is_integer()(x))
     {
-      return car(x);
+      return x.numerator();
     }
     else
     {

From c4a11b9154d718debb8209c9948fdc3abf24d49a Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Sun, 14 Aug 2022 21:17:22 +0900
Subject: [PATCH 04/11] Remove inheriting constructor

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  8 ++++++--
 src/kernel/ratio.cpp            | 14 +++++++++++++-
 4 files changed, 23 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index 402e145f7..ac84196d7 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.200.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.201.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.200_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.201_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.200
+Meevax Lisp System, version 0.4.201
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 1abe58b1d..3f72cf6e3 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.200
+0.4.201
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index d09406e19..7a6179b16 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -27,10 +27,14 @@ inline namespace kernel
 {
   struct ratio : protected virtual pair
   {
-    using pair::pair;
-
     mpq_t value;
 
+    ratio();
+
+    ratio(ratio const&);
+
+    ratio(const_reference, const_reference);
+
     explicit ratio(double);
 
     explicit ratio(external_representation const&, int = 10);
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 7b470055c..2053cf951 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -22,6 +22,18 @@ namespace meevax
 {
 inline namespace kernel
 {
+  ratio::ratio()
+    : pair {}
+  {}
+
+  ratio::ratio(ratio const& q)
+    : pair { static_cast<pair const&>(q) }
+  {}
+
+  ratio::ratio(const_reference x, const_reference y)
+    : pair { x, y }
+  {}
+
   ratio::ratio(double x)
   {
     mpq_init(value);
@@ -98,7 +110,7 @@ inline namespace kernel
     }
     else
     {
-      return *this;
+      return ratio(*this);
     }
   }
 

From 2fc544d33e3ec9ec67ac591e392a56f5faaa3039 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 01:14:48 +0900
Subject: [PATCH 05/11] Add non-default destructor to `ratio`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  2 ++
 src/kernel/ratio.cpp            | 28 +++++++++++++++++++++-------
 4 files changed, 27 insertions(+), 11 deletions(-)

diff --git a/README.md b/README.md
index ac84196d7..925eef633 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.201.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.202.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.201_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.202_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.201
+Meevax Lisp System, version 0.4.202
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 3f72cf6e3..91169f453 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.201
+0.4.202
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index 7a6179b16..0bd0ff4fb 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -39,6 +39,8 @@ inline namespace kernel
 
     explicit ratio(external_representation const&, int = 10);
 
+    ~ratio();
+
     auto denominator() const -> const_reference;
 
     auto denominator() -> reference;
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 2053cf951..27faf4386 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -23,16 +23,27 @@ namespace meevax
 inline namespace kernel
 {
   ratio::ratio()
-    : pair {}
-  {}
+  {
+    mpq_init(value);
+  }
 
   ratio::ratio(ratio const& q)
     : pair { static_cast<pair const&>(q) }
-  {}
+  {
+    mpq_init(value);
+    mpq_set_num(value, q.numerator().as<exact_integer>().value);
+    mpq_set_den(value, q.denominator().as<exact_integer>().value);
+    mpq_canonicalize(value);
+  }
 
   ratio::ratio(const_reference x, const_reference y)
     : pair { x, y }
-  {}
+  {
+    mpq_init(value);
+    mpq_set_num(value, x.as<exact_integer>().value);
+    mpq_set_den(value, y.as<exact_integer>().value);
+    mpq_canonicalize(value);
+  }
 
   ratio::ratio(double x)
   {
@@ -41,8 +52,6 @@ inline namespace kernel
 
     numerator() = make<exact_integer>(mpq_numref(value));
     denominator() = make<exact_integer>(mpq_denref(value));
-
-    mpq_clear(value);
   }
 
   ratio::ratio(external_representation const& token, int radix)
@@ -56,12 +65,17 @@ inline namespace kernel
     }
     else // TEMPORARY!!!
     {
+      mpq_canonicalize(value);
       numerator() = make<exact_integer>(mpq_numref(value));
       denominator() = make<exact_integer>(mpq_denref(value));
-      mpq_clear(value);
     }
   }
 
+  ratio::~ratio()
+  {
+    mpq_clear(value);
+  }
+
   auto ratio::denominator() const -> const_reference
   {
     return second;

From fcd340c0bd0ed61360ac08d8e3e71ae6227b277a Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 12:08:56 +0900
Subject: [PATCH 06/11] Update `ratio` constructor to call `mpq_canonicalize`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  4 +---
 src/kernel/number.cpp           | 24 +++++++++++-----------
 src/kernel/ratio.cpp            | 36 +++++++--------------------------
 5 files changed, 24 insertions(+), 48 deletions(-)

diff --git a/README.md b/README.md
index 925eef633..605127380 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.202.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.203.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.202_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.203_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.202
+Meevax Lisp System, version 0.4.203
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 91169f453..4567fc8f8 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.202
+0.4.203
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index 0bd0ff4fb..0e3ff8cec 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -33,7 +33,7 @@ inline namespace kernel
 
     ratio(ratio const&);
 
-    ratio(const_reference, const_reference);
+    explicit ratio(const_reference, const_reference);
 
     explicit ratio(double);
 
@@ -51,8 +51,6 @@ inline namespace kernel
 
     auto numerator() -> reference;
 
-    auto reduce() const -> ratio;
-
     auto simple() const -> value_type;
 
     explicit operator double() const;
diff --git a/src/kernel/number.cpp b/src/kernel/number.cpp
index cb77c3dc5..9916df6d0 100644
--- a/src/kernel/number.cpp
+++ b/src/kernel/number.cpp
@@ -38,12 +38,12 @@ inline namespace kernel
   auto operator - (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>()), b.denominator()); }
   auto operator / (exact_integer const& a, ratio const& b) -> ratio { return a * b.invert(); }
   auto operator % (exact_integer const&  , ratio const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
-  auto operator !=(exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a != x.numerator().as<exact_integer>(); }
-  auto operator < (exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a <  x.numerator().as<exact_integer>(); }
-  auto operator <=(exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a <= x.numerator().as<exact_integer>(); }
-  auto operator ==(exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a == x.numerator().as<exact_integer>(); }
-  auto operator > (exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a >  x.numerator().as<exact_integer>(); }
-  auto operator >=(exact_integer const& a, ratio const& b) -> bool  { auto const x = b.reduce(); return std::invoke(is_integer(), x) and a >= x.numerator().as<exact_integer>(); }
+  auto operator !=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a != x.numerator().as<exact_integer>(); }
+  auto operator < (exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a <  x.numerator().as<exact_integer>(); }
+  auto operator <=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a <= x.numerator().as<exact_integer>(); }
+  auto operator ==(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a == x.numerator().as<exact_integer>(); }
+  auto operator > (exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a >  x.numerator().as<exact_integer>(); }
+  auto operator >=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a >= x.numerator().as<exact_integer>(); }
 
   auto operator + (exact_integer const& a, float b) -> float { return inexact_cast(a) +  b; }
   auto operator - (exact_integer const& a, float b) -> float { return inexact_cast(a) -  b; }
@@ -74,12 +74,12 @@ inline namespace kernel
   auto operator - (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() - a.denominator().as<exact_integer>() * b), a.denominator()); }
   auto operator / (ratio const& a, exact_integer const& b) -> ratio { return ratio(a.numerator(), make(a.denominator().as<exact_integer>() * b)); }
   auto operator % (ratio const&  , exact_integer const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
-  auto operator !=(ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() != b; }
-  auto operator < (ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <  b; }
-  auto operator <=(ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <= b; }
-  auto operator ==(ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() == b; }
-  auto operator > (ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >  b; }
-  auto operator >=(ratio const& a, exact_integer const& b) -> bool  { auto const x = a.reduce(); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >= b; }
+  auto operator !=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() != b; }
+  auto operator < (ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <  b; }
+  auto operator <=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <= b; }
+  auto operator ==(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() == b; }
+  auto operator > (ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >  b; }
+  auto operator >=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >= b; }
 
   auto operator + (ratio const& a, ratio const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>() + b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()), make(a.denominator().as<exact_integer>() * b.denominator().as<exact_integer>())); }
   auto operator - (ratio const& a, ratio const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()), make(a.denominator().as<exact_integer>() * b.denominator().as<exact_integer>())); }
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 27faf4386..796f7e8ff 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -34,15 +34,20 @@ inline namespace kernel
     mpq_set_num(value, q.numerator().as<exact_integer>().value);
     mpq_set_den(value, q.denominator().as<exact_integer>().value);
     mpq_canonicalize(value);
+
+    numerator() = make<exact_integer>(mpq_numref(value));
+    denominator() = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(const_reference x, const_reference y)
-    : pair { x, y }
   {
     mpq_init(value);
     mpq_set_num(value, x.as<exact_integer>().value);
     mpq_set_den(value, y.as<exact_integer>().value);
     mpq_canonicalize(value);
+
+    numerator() = make<exact_integer>(mpq_numref(value));
+    denominator() = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(double x)
@@ -101,36 +106,9 @@ inline namespace kernel
     return first;
   }
 
-  auto ratio::reduce() const -> ratio
-  {
-    auto gcd = [](exact_integer const& a, exact_integer const& b)
-    {
-      exact_integer n;
-      mpz_gcd(n.value, a.value, b.value);
-      return n;
-    };
-
-    auto div = [](exact_integer const& a, exact_integer const& b)
-    {
-      exact_integer n;
-      mpz_div(n.value, a.value, b.value);
-      return n;
-    };
-
-    if (auto x = gcd(numerator().as<exact_integer>(), denominator().as<exact_integer>()); x != 1)
-    {
-      return ratio(make<exact_integer>(div(numerator().as<exact_integer>(), x)),
-                   make<exact_integer>(div(denominator().as<exact_integer>(), x)));
-    }
-    else
-    {
-      return ratio(*this);
-    }
-  }
-
   auto ratio::simple() const -> value_type
   {
-    if (auto x = reduce(); is_integer()(x))
+    if (auto x = ratio(*this); is_integer()(x))
     {
       return x.numerator();
     }

From 987c60cddc17ec0c031c107194baffca5c498898 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 12:28:07 +0900
Subject: [PATCH 07/11] Remove non-const `ratio::(numerator|denominator)`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  4 ----
 src/kernel/ratio.cpp            | 26 ++++++++------------------
 4 files changed, 12 insertions(+), 26 deletions(-)

diff --git a/README.md b/README.md
index 605127380..a12835317 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.203.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.204.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.203_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.204_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.203
+Meevax Lisp System, version 0.4.204
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 4567fc8f8..16680e764 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.203
+0.4.204
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index 0e3ff8cec..54755623c 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -43,14 +43,10 @@ inline namespace kernel
 
     auto denominator() const -> const_reference;
 
-    auto denominator() -> reference;
-
     auto invert() const -> ratio;
 
     auto numerator() const -> const_reference;
 
-    auto numerator() -> reference;
-
     auto simple() const -> value_type;
 
     explicit operator double() const;
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 796f7e8ff..497dbff17 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -35,8 +35,8 @@ inline namespace kernel
     mpq_set_den(value, q.denominator().as<exact_integer>().value);
     mpq_canonicalize(value);
 
-    numerator() = make<exact_integer>(mpq_numref(value));
-    denominator() = make<exact_integer>(mpq_denref(value));
+    first = make<exact_integer>(mpq_numref(value));
+    second = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(const_reference x, const_reference y)
@@ -46,8 +46,8 @@ inline namespace kernel
     mpq_set_den(value, y.as<exact_integer>().value);
     mpq_canonicalize(value);
 
-    numerator() = make<exact_integer>(mpq_numref(value));
-    denominator() = make<exact_integer>(mpq_denref(value));
+    first = make<exact_integer>(mpq_numref(value));
+    second = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(double x)
@@ -55,8 +55,8 @@ inline namespace kernel
     mpq_init(value);
     mpq_set_d(value, x);
 
-    numerator() = make<exact_integer>(mpq_numref(value));
-    denominator() = make<exact_integer>(mpq_denref(value));
+    first = make<exact_integer>(mpq_numref(value));
+    second = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(external_representation const& token, int radix)
@@ -71,8 +71,8 @@ inline namespace kernel
     else // TEMPORARY!!!
     {
       mpq_canonicalize(value);
-      numerator() = make<exact_integer>(mpq_numref(value));
-      denominator() = make<exact_integer>(mpq_denref(value));
+      first = make<exact_integer>(mpq_numref(value));
+      second = make<exact_integer>(mpq_denref(value));
     }
   }
 
@@ -86,11 +86,6 @@ inline namespace kernel
     return second;
   }
 
-  auto ratio::denominator() -> reference
-  {
-    return second;
-  }
-
   auto ratio::invert() const -> ratio
   {
     return ratio(denominator(), numerator());
@@ -101,11 +96,6 @@ inline namespace kernel
     return first;
   }
 
-  auto ratio::numerator() -> reference
-  {
-    return first;
-  }
-
   auto ratio::simple() const -> value_type
   {
     if (auto x = ratio(*this); is_integer()(x))

From c053a58db28835aa1b278d7fc06bb333c2e35f97 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 15:11:37 +0900
Subject: [PATCH 08/11] Remove member function `ratio::simple`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                               |  6 ++---
 VERSION                                 |  2 +-
 include/meevax/kernel/exact_integer.hpp |  2 +-
 include/meevax/kernel/number.hpp        | 32 ++++++++++++++-----------
 include/meevax/kernel/ratio.hpp         |  6 ++---
 include/meevax/kernel/reader.hpp        |  2 +-
 src/kernel/exact_integer.cpp            |  4 ++--
 src/kernel/ratio.cpp                    | 16 ++-----------
 test/numerical-operations.ss            | 20 ++++++++--------
 test/sicp-1.ss                          |  4 ++--
 10 files changed, 42 insertions(+), 52 deletions(-)

diff --git a/README.md b/README.md
index a12835317..cc530372b 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.204.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.205.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.204_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.205_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.204
+Meevax Lisp System, version 0.4.205
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 16680e764..bdca12ed5 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.204
+0.4.205
diff --git a/include/meevax/kernel/exact_integer.hpp b/include/meevax/kernel/exact_integer.hpp
index 37c6a7af3..261666dd9 100644
--- a/include/meevax/kernel/exact_integer.hpp
+++ b/include/meevax/kernel/exact_integer.hpp
@@ -31,7 +31,7 @@ inline namespace kernel
 
     explicit exact_integer() noexcept;
 
-    explicit exact_integer(mpz_t) noexcept;
+    explicit exact_integer(mpz_t const) noexcept;
 
     exact_integer(exact_integer const&) noexcept;
 
diff --git a/include/meevax/kernel/number.hpp b/include/meevax/kernel/number.hpp
index 4f60e492c..8e3957d7f 100644
--- a/include/meevax/kernel/number.hpp
+++ b/include/meevax/kernel/number.hpp
@@ -195,7 +195,14 @@ inline namespace kernel
       }
       else if constexpr (std::is_same_v<std::decay_t<decltype(z)>, ratio>)
       {
-        return z.simple();
+        if (auto i = exact_integer(mpq_denref(z.value)); i == 1)
+        {
+          return z.numerator();
+        }
+        else
+        {
+          return make(std::forward<decltype(z)>(z));
+        }
       }
       else
       {
@@ -256,21 +263,18 @@ inline namespace kernel
   struct exact
   {
     template <typename T>
-    auto operator ()(T const& x) const -> decltype(auto)
-    {
-      return ratio(x).simple();
-    }
-
-    auto operator ()(exact_integer const& x) const -> auto const&
-    {
-      return x;
-    }
-
-    auto operator ()(ratio const& x) const -> auto const&
+    auto operator ()(T&& x) const -> decltype(auto)
     {
-      return x;
+      if constexpr (std::is_floating_point_v<std::decay_t<decltype(x)>>)
+      {
+        return ratio(std::forward<decltype(x)>(x));
+      }
+      else
+      {
+        return std::forward<decltype(x)>(x);
+      }
     }
-  };
+  } inline constexpr exact_cast;
 
   struct inexact
   {
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index 54755623c..d2982933a 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -41,13 +41,11 @@ inline namespace kernel
 
     ~ratio();
 
-    auto denominator() const -> const_reference;
+    auto denominator() const -> value_type;
 
     auto invert() const -> ratio;
 
-    auto numerator() const -> const_reference;
-
-    auto simple() const -> value_type;
+    auto numerator() const -> value_type;
 
     explicit operator double() const;
   };
diff --git a/include/meevax/kernel/reader.hpp b/include/meevax/kernel/reader.hpp
index 20056d882..d9a564e71 100644
--- a/include/meevax/kernel/reader.hpp
+++ b/include/meevax/kernel/reader.hpp
@@ -244,7 +244,7 @@ inline namespace kernel
       {
         try
         {
-          return ratio(token, radix).simple();
+          return make(ratio(token, radix));
         }
         catch (...)
         {
diff --git a/src/kernel/exact_integer.cpp b/src/kernel/exact_integer.cpp
index 4c3f34b83..240a4a6d2 100644
--- a/src/kernel/exact_integer.cpp
+++ b/src/kernel/exact_integer.cpp
@@ -31,9 +31,9 @@ inline namespace kernel
     mpz_init(value);
   }
 
-  exact_integer::exact_integer(mpz_t given) noexcept
+  exact_integer::exact_integer(mpz_t const z) noexcept
   {
-    mpz_init_set(value, given);
+    mpz_init_set(value, z);
   }
 
   exact_integer::exact_integer(exact_integer const& given) noexcept
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 497dbff17..563dc876d 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -81,7 +81,7 @@ inline namespace kernel
     mpq_clear(value);
   }
 
-  auto ratio::denominator() const -> const_reference
+  auto ratio::denominator() const -> value_type
   {
     return second;
   }
@@ -91,23 +91,11 @@ inline namespace kernel
     return ratio(denominator(), numerator());
   }
 
-  auto ratio::numerator() const -> const_reference
+  auto ratio::numerator() const -> value_type
   {
     return first;
   }
 
-  auto ratio::simple() const -> value_type
-  {
-    if (auto x = ratio(*this); is_integer()(x))
-    {
-      return x.numerator();
-    }
-    else
-    {
-      return make(x);
-    }
-  }
-
   ratio::operator double() const
   {
     return static_cast<double>(numerator().as<exact_integer>()) / static_cast<double>(denominator().as<exact_integer>());
diff --git a/test/numerical-operations.ss b/test/numerical-operations.ss
index ef0855fdc..6073cce74 100644
--- a/test/numerical-operations.ss
+++ b/test/numerical-operations.ss
@@ -38,7 +38,7 @@
 
 (let ((x (* 2 1/2)))
 
-  (check x => 1)
+  (check x (=> =) 1)
 
   (check (number?   x) => #t)
   (check (complex?  x) => #t)
@@ -52,7 +52,7 @@
 
 (let ((x (+ 1/3 1/3 1/3)))
 
-  (check x => 1)
+  (check x (=> =) 1)
 
   (check (number?   x) => #t)
   (check (complex?  x) => #t)
@@ -64,17 +64,17 @@
   (check (inexact?  x) => #f)
   )
 
-(check (+ 1   1.0) => 2.0)
-(check (+ 1.0 1  ) => 2.0)
+(check (+ 1   1.0) (=> =) 2.0)
+(check (+ 1.0 1  ) (=> =) 2.0)
 
-(check (+ 1   1/2) => 3/2)
-(check (+ 1.0 1/2) => 1.5)
+(check (+ 1   1/2) (=> =) 3/2)
+(check (+ 1.0 1/2) (=> =) 1.5)
 
-(check (+ 1/2 1  ) => 3/2)
-(check (+ 1/2 1.0) => 1.5)
+(check (+ 1/2 1  ) (=> =) 3/2)
+(check (+ 1/2 1.0) (=> =) 1.5)
 
-(check (* 2   1/2) => 1  )
-(check (* 2.0 1/2) => 1.0)
+(check (* 2   1/2) (=> =) 1  )
+(check (* 2.0 1/2) (=> =) 1.0)
 
 (check (modulo  13  4) =>  1)
 (check (modulo -13  4) =>  3)
diff --git a/test/sicp-1.ss b/test/sicp-1.ss
index 65dc0b89d..c7bb91687 100644
--- a/test/sicp-1.ss
+++ b/test/sicp-1.ss
@@ -16,7 +16,7 @@
 
 (check (* 5 99) => 495)
 
-(check (/ 10 5) => 2)
+(check (/ 10 5) (=> =) 2)
 
 (check (+ 2.7 10) => 12.7)
 
@@ -114,7 +114,7 @@
 
 (check (- 9 1) => 8)
 
-(check (/ 6 2) => 3)
+(check (/ 6 2) (=> =) 3)
 
 (check (+ (* 2 4) (- 4 6)) => 6)
 

From 5df86a29ab8ecb5c33216b8b9f4fc52ba361014d Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 18:49:21 +0900
Subject: [PATCH 09/11] Remove `ratio`'s base class `pair`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +++---
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  4 +++-
 src/kernel/ratio.cpp            | 26 ++++++++++----------------
 4 files changed, 17 insertions(+), 21 deletions(-)

diff --git a/README.md b/README.md
index cc530372b..f91c223bb 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.205.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.206.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.205_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.206_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.205
+Meevax Lisp System, version 0.4.206
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index bdca12ed5..93d22aa62 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.205
+0.4.206
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index d2982933a..2a58dbc15 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -25,7 +25,7 @@ namespace meevax
 {
 inline namespace kernel
 {
-  struct ratio : protected virtual pair
+  struct ratio
   {
     mpq_t value;
 
@@ -33,6 +33,8 @@ inline namespace kernel
 
     ratio(ratio const&);
 
+    ratio(ratio &&);
+
     explicit ratio(const_reference, const_reference);
 
     explicit ratio(double);
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 563dc876d..d25ee680f 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -27,16 +27,18 @@ inline namespace kernel
     mpq_init(value);
   }
 
-  ratio::ratio(ratio const& q)
-    : pair { static_cast<pair const&>(q) }
+  ratio::ratio(ratio const& other)
   {
     mpq_init(value);
-    mpq_set_num(value, q.numerator().as<exact_integer>().value);
-    mpq_set_den(value, q.denominator().as<exact_integer>().value);
+    mpq_set(value, other.value);
     mpq_canonicalize(value);
+  }
 
-    first = make<exact_integer>(mpq_numref(value));
-    second = make<exact_integer>(mpq_denref(value));
+  ratio::ratio(ratio && other)
+  {
+    mpq_init(value);
+    mpq_swap(value, other.value);
+    mpq_canonicalize(value);
   }
 
   ratio::ratio(const_reference x, const_reference y)
@@ -45,18 +47,12 @@ inline namespace kernel
     mpq_set_num(value, x.as<exact_integer>().value);
     mpq_set_den(value, y.as<exact_integer>().value);
     mpq_canonicalize(value);
-
-    first = make<exact_integer>(mpq_numref(value));
-    second = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(double x)
   {
     mpq_init(value);
     mpq_set_d(value, x);
-
-    first = make<exact_integer>(mpq_numref(value));
-    second = make<exact_integer>(mpq_denref(value));
   }
 
   ratio::ratio(external_representation const& token, int radix)
@@ -71,8 +67,6 @@ inline namespace kernel
     else // TEMPORARY!!!
     {
       mpq_canonicalize(value);
-      first = make<exact_integer>(mpq_numref(value));
-      second = make<exact_integer>(mpq_denref(value));
     }
   }
 
@@ -83,7 +77,7 @@ inline namespace kernel
 
   auto ratio::denominator() const -> value_type
   {
-    return second;
+    return make<exact_integer>(mpq_denref(value));
   }
 
   auto ratio::invert() const -> ratio
@@ -93,7 +87,7 @@ inline namespace kernel
 
   auto ratio::numerator() const -> value_type
   {
-    return first;
+    return make<exact_integer>(mpq_numref(value));
   }
 
   ratio::operator double() const

From ad67f242fb6af97b41310a7cee9137fcc0a32014 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Mon, 15 Aug 2022 22:35:49 +0900
Subject: [PATCH 10/11] Update rational arithmetic operations

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                       |  6 +--
 VERSION                         |  2 +-
 include/meevax/kernel/ratio.hpp |  6 +--
 src/kernel/exact_integer.cpp    | 10 ++---
 src/kernel/number.cpp           | 74 ++++++++++++++++-----------------
 src/kernel/ratio.cpp            | 26 ++++++++----
 test/numerical-operations.ss    |  2 +-
 7 files changed, 67 insertions(+), 59 deletions(-)

diff --git a/README.md b/README.md
index f91c223bb..83e04d3fb 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.206.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.207.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.206_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.207_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.206
+Meevax Lisp System, version 0.4.207
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 93d22aa62..3e33edbc5 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.206
+0.4.207
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index 2a58dbc15..d4d97163d 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -35,7 +35,9 @@ inline namespace kernel
 
     ratio(ratio &&);
 
-    explicit ratio(const_reference, const_reference);
+    explicit ratio(exact_integer const&);
+
+    explicit ratio(exact_integer const&, exact_integer const&);
 
     explicit ratio(double);
 
@@ -45,8 +47,6 @@ inline namespace kernel
 
     auto denominator() const -> value_type;
 
-    auto invert() const -> ratio;
-
     auto numerator() const -> value_type;
 
     explicit operator double() const;
diff --git a/src/kernel/exact_integer.cpp b/src/kernel/exact_integer.cpp
index 240a4a6d2..62ab132cb 100644
--- a/src/kernel/exact_integer.cpp
+++ b/src/kernel/exact_integer.cpp
@@ -36,15 +36,15 @@ inline namespace kernel
     mpz_init_set(value, z);
   }
 
-  exact_integer::exact_integer(exact_integer const& given) noexcept
+  exact_integer::exact_integer(exact_integer const& other) noexcept
   {
-    mpz_init_set(value, given.value);
+    mpz_init_set(value, other.value);
   }
 
-  exact_integer::exact_integer(exact_integer && rhs) noexcept
+  exact_integer::exact_integer(exact_integer && other) noexcept
   {
-    *value = *rhs.value;
-    mpz_init(rhs.value);
+    mpz_init(value);
+    mpz_swap(value, other.value);
   }
 
   exact_integer::exact_integer(int rhs)
diff --git a/src/kernel/number.cpp b/src/kernel/number.cpp
index 9916df6d0..06cdd5220 100644
--- a/src/kernel/number.cpp
+++ b/src/kernel/number.cpp
@@ -24,26 +24,26 @@ inline namespace kernel
   auto operator + (exact_integer const& a, exact_integer const& b) -> exact_integer { exact_integer n; mpz_add(n.value, a.value, b.value); return n; }
   auto operator - (exact_integer const& a, exact_integer const& b) -> exact_integer { exact_integer n; mpz_sub(n.value, a.value, b.value); return n; }
   auto operator * (exact_integer const& a, exact_integer const& b) -> exact_integer { exact_integer n; mpz_mul(n.value, a.value, b.value); return n; }
-  auto operator / (exact_integer const& a, exact_integer const& b) -> ratio         { return ratio(make(a), make(b)); }
+  auto operator / (exact_integer const& a, exact_integer const& b) -> ratio         { return ratio(a, b); }
   auto operator % (exact_integer const& a, exact_integer const& b) -> exact_integer { exact_integer n; mpz_tdiv_r(n.value, a.value, b.value); return n; }
+  auto operator ==(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) == 0; }
   auto operator !=(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) != 0; }
   auto operator < (exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) <  0; }
   auto operator <=(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) <= 0; }
-  auto operator ==(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) == 0; }
   auto operator > (exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) >  0; }
   auto operator >=(exact_integer const& a, exact_integer const& b) -> bool          { return mpz_cmp(a.value, b.value) >= 0; }
 
-  auto operator * (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.numerator().as<exact_integer>()), b.denominator()); }
-  auto operator + (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() + b.numerator().as<exact_integer>()), b.denominator()); }
-  auto operator - (exact_integer const& a, ratio const& b) -> ratio { return ratio(make(a * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>()), b.denominator()); }
-  auto operator / (exact_integer const& a, ratio const& b) -> ratio { return a * b.invert(); }
+  auto operator + (exact_integer const& a, ratio const& b) -> ratio { ratio q; mpq_add(q.value, ratio(a).value, b.value); return q; }
+  auto operator - (exact_integer const& a, ratio const& b) -> ratio { ratio q; mpq_sub(q.value, ratio(a).value, b.value); return q; }
+  auto operator * (exact_integer const& a, ratio const& b) -> ratio { ratio q; mpq_mul(q.value, ratio(a).value, b.value); return q; }
+  auto operator / (exact_integer const& a, ratio const& b) -> ratio { ratio q; mpq_div(q.value, ratio(a).value, b.value); return q; }
   auto operator % (exact_integer const&  , ratio const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
-  auto operator !=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a != x.numerator().as<exact_integer>(); }
-  auto operator < (exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a <  x.numerator().as<exact_integer>(); }
-  auto operator <=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a <= x.numerator().as<exact_integer>(); }
-  auto operator ==(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a == x.numerator().as<exact_integer>(); }
-  auto operator > (exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a >  x.numerator().as<exact_integer>(); }
-  auto operator >=(exact_integer const& a, ratio const& b) -> bool  { auto const x = ratio(b); return std::invoke(is_integer(), x) and a >= x.numerator().as<exact_integer>(); }
+  auto operator ==(exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) == 0; }
+  auto operator !=(exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) != 0; }
+  auto operator < (exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) >  0; }
+  auto operator <=(exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) >= 0; }
+  auto operator > (exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) <  0; }
+  auto operator >=(exact_integer const& a, ratio const& b) -> bool  { return mpq_cmp_z(b.value, a.value) <= 0; }
 
   auto operator + (exact_integer const& a, float b) -> float { return inexact_cast(a) +  b; }
   auto operator - (exact_integer const& a, float b) -> float { return inexact_cast(a) -  b; }
@@ -69,29 +69,29 @@ inline namespace kernel
   auto operator > (exact_integer const& a, double b) -> bool   { return mpz_cmp_d(a.value, b) >  0; }
   auto operator >=(exact_integer const& a, double b) -> bool   { return mpz_cmp_d(a.value, b) >= 0; }
 
-  auto operator * (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b), a.denominator()); }
-  auto operator + (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() + a.denominator().as<exact_integer>() * b), a.denominator()); }
-  auto operator - (ratio const& a, exact_integer const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() - a.denominator().as<exact_integer>() * b), a.denominator()); }
-  auto operator / (ratio const& a, exact_integer const& b) -> ratio { return ratio(a.numerator(), make(a.denominator().as<exact_integer>() * b)); }
+  auto operator + (ratio const& a, exact_integer const& b) -> ratio { ratio q; mpq_add(q.value, a.value, ratio(b).value); return q; }
+  auto operator - (ratio const& a, exact_integer const& b) -> ratio { ratio q; mpq_sub(q.value, a.value, ratio(b).value); return q; }
+  auto operator * (ratio const& a, exact_integer const& b) -> ratio { ratio q; mpq_mul(q.value, a.value, ratio(b).value); return q; }
+  auto operator / (ratio const& a, exact_integer const& b) -> ratio { ratio q; mpq_div(q.value, a.value, ratio(b).value); return q; }
   auto operator % (ratio const&  , exact_integer const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
-  auto operator !=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() != b; }
-  auto operator < (ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <  b; }
-  auto operator <=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() <= b; }
-  auto operator ==(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() == b; }
-  auto operator > (ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >  b; }
-  auto operator >=(ratio const& a, exact_integer const& b) -> bool  { auto const x = ratio(a); return std::invoke(is_integer(), x) and x.numerator().as<exact_integer>() >= b; }
-
-  auto operator + (ratio const& a, ratio const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>() + b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()), make(a.denominator().as<exact_integer>() * b.denominator().as<exact_integer>())); }
-  auto operator - (ratio const& a, ratio const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>() - b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()), make(a.denominator().as<exact_integer>() * b.denominator().as<exact_integer>())); }
-  auto operator * (ratio const& a, ratio const& b) -> ratio { return ratio(make(a.numerator().as<exact_integer>() * b.numerator().as<exact_integer>()), make(a.denominator().as<exact_integer>() * b.denominator().as<exact_integer>())); }
-  auto operator / (ratio const& a, ratio const& b) -> ratio { return a * b.invert(); }
+  auto operator ==(ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) == 0; }
+  auto operator !=(ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) != 0; }
+  auto operator < (ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) <  0; }
+  auto operator <=(ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) <= 0; }
+  auto operator > (ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) >  0; }
+  auto operator >=(ratio const& a, exact_integer const& b) -> bool  { return mpq_cmp_z(a.value, b.value) >= 0; }
+
+  auto operator + (ratio const& a, ratio const& b) -> ratio { ratio q; mpq_add(q.value, a.value, b.value); return q; }
+  auto operator - (ratio const& a, ratio const& b) -> ratio { ratio q; mpq_sub(q.value, a.value, b.value); return q; }
+  auto operator * (ratio const& a, ratio const& b) -> ratio { ratio q; mpq_mul(q.value, a.value, b.value); return q; }
+  auto operator / (ratio const& a, ratio const& b) -> ratio { ratio q; mpq_div(q.value, a.value, b.value); return q; }
   auto operator % (ratio const&  , ratio const&  ) -> ratio { throw error(make<string>("unsupported operation"), unit); }
-  auto operator ==(ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) == (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
-  auto operator !=(ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) != (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
-  auto operator < (ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) <  (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
-  auto operator <=(ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) <= (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
-  auto operator > (ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) >  (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
-  auto operator >=(ratio const& a, ratio const& b) -> bool  { return (a.numerator().as<exact_integer>() * b.denominator().as<exact_integer>()) >= (b.numerator().as<exact_integer>() * a.denominator().as<exact_integer>()); }
+  auto operator ==(ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) == 0; }
+  auto operator !=(ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) != 0; }
+  auto operator < (ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) <  0; }
+  auto operator <=(ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) <= 0; }
+  auto operator > (ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) >  0; }
+  auto operator >=(ratio const& a, ratio const& b) -> bool  { return mpq_cmp(a.value, b.value) >= 0; }
 
   auto operator + (ratio const& a, float b) -> float { return inexact_cast(a) +  b; }
   auto operator - (ratio const& a, float b) -> float { return inexact_cast(a) -  b; }
@@ -148,10 +148,10 @@ inline namespace kernel
   auto operator % (double a, exact_integer const& b) -> double { return std::remainder(a, inexact_cast(b)); }
   auto operator ==(double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) == 0; }
   auto operator !=(double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) != 0; }
-  auto operator < (double a, exact_integer const& b) -> bool   { return a <  inexact_cast(b); }
-  auto operator <=(double a, exact_integer const& b) -> bool   { return a <= inexact_cast(b); }
-  auto operator > (double a, exact_integer const& b) -> bool   { return a >  inexact_cast(b); }
-  auto operator >=(double a, exact_integer const& b) -> bool   { return a >= inexact_cast(b); }
+  auto operator < (double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) >  0; }
+  auto operator <=(double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) >= 0; }
+  auto operator > (double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) <  0; }
+  auto operator >=(double a, exact_integer const& b) -> bool   { return mpz_cmp_d(b.value, a) <= 0; }
 
   auto operator + (double a, ratio const& b) -> double { return a +  inexact_cast(b); }
   auto operator - (double a, ratio const& b) -> double { return a -  inexact_cast(b); }
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index d25ee680f..06a1192b1 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -41,11 +41,17 @@ inline namespace kernel
     mpq_canonicalize(value);
   }
 
-  ratio::ratio(const_reference x, const_reference y)
+  ratio::ratio(exact_integer const& z)
   {
     mpq_init(value);
-    mpq_set_num(value, x.as<exact_integer>().value);
-    mpq_set_den(value, y.as<exact_integer>().value);
+    mpq_set_z(value, z.value);
+  }
+
+  ratio::ratio(exact_integer const& n, exact_integer const& d)
+  {
+    mpq_init(value);
+    mpq_set_num(value, n.value);
+    mpq_set_den(value, d.value);
     mpq_canonicalize(value);
   }
 
@@ -80,11 +86,6 @@ inline namespace kernel
     return make<exact_integer>(mpq_denref(value));
   }
 
-  auto ratio::invert() const -> ratio
-  {
-    return ratio(denominator(), numerator());
-  }
-
   auto ratio::numerator() const -> value_type
   {
     return make<exact_integer>(mpq_numref(value));
@@ -97,7 +98,14 @@ inline namespace kernel
 
   auto operator <<(std::ostream & os, ratio const& datum) -> std::ostream &
   {
-    return os << datum.numerator() << cyan("/") << datum.denominator();
+    auto free = [](char * data)
+    {
+      void (*free)(void *, std::size_t);
+      mp_get_memory_functions(nullptr, nullptr, &free);
+      std::invoke(free, static_cast<void *>(data), std::strlen(data) + 1);
+    };
+
+    return os << cyan(std::unique_ptr<char, decltype(free)>(mpq_get_str(nullptr, 10, datum.value), free).get());
   }
 } // namespace kernel
 } // namespace meevax
diff --git a/test/numerical-operations.ss b/test/numerical-operations.ss
index 6073cce74..4e5ae4dd9 100644
--- a/test/numerical-operations.ss
+++ b/test/numerical-operations.ss
@@ -24,7 +24,7 @@
 
 (let ((x (+ 1 1/2)))
 
-  (check x => 3/2)
+  (check x (=> =) 3/2)
 
   (check (number?   x) => #t)
   (check (complex?  x) => #t)

From 265005f8b2ec27a4031228d688d1655751e8a790 Mon Sep 17 00:00:00 2001
From: yamacir-kit <httperror@404-notfound.jp>
Date: Tue, 16 Aug 2022 00:27:14 +0900
Subject: [PATCH 11/11] Update `ratio::(numerator|denominator)` to be return
 `exact_integer`

Signed-off-by: yamacir-kit <httperror@404-notfound.jp>
---
 README.md                               |  6 ++---
 VERSION                                 |  2 +-
 include/meevax/kernel/exact_integer.hpp | 18 +++++++--------
 include/meevax/kernel/number.hpp        |  6 ++---
 include/meevax/kernel/ratio.hpp         |  9 ++++----
 src/kernel/exact_integer.cpp            | 29 ++++++++++---------------
 src/kernel/library.cpp                  |  4 ++--
 src/kernel/ratio.cpp                    | 16 +++++++-------
 8 files changed, 41 insertions(+), 49 deletions(-)

diff --git a/README.md b/README.md
index 83e04d3fb..409ef7a61 100644
--- a/README.md
+++ b/README.md
@@ -105,9 +105,9 @@ sudo rm -rf /usr/local/share/meevax
 
 | Target Name        | Description
 |:-------------------|:--
-| `all` (default)    | Build shared-library `libmeevax.0.4.207.so` and executable `meevax`.
+| `all` (default)    | Build shared-library `libmeevax.0.4.208.so` and executable `meevax`.
 | `test`             | Test executable `meevax`.
-| `package`          | Generate debian package `meevax_0.4.207_amd64.deb`.
+| `package`          | Generate debian package `meevax_0.4.208_amd64.deb`.
 | `install`          | Copy files into `/usr/local` __(1)__.
 | `install.deb`      | `all` + `package` + `sudo apt install <meevax>.deb`
 | `safe-install.deb` | `all` + `test` + `package` + `sudo apt install <meevax>.deb`
@@ -122,7 +122,7 @@ __(1)__ Meevax installed by `make install` cannot be uninstalled by the system's
 ## Usage
 
 ```
-Meevax Lisp System, version 0.4.207
+Meevax Lisp System, version 0.4.208
 
 Usage: meevax [OPTION...] [FILE...]
 
diff --git a/VERSION b/VERSION
index 3e33edbc5..cab5b51e7 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.4.207
+0.4.208
diff --git a/include/meevax/kernel/exact_integer.hpp b/include/meevax/kernel/exact_integer.hpp
index 261666dd9..daba883ea 100644
--- a/include/meevax/kernel/exact_integer.hpp
+++ b/include/meevax/kernel/exact_integer.hpp
@@ -29,13 +29,15 @@ inline namespace kernel
   {
     mpz_t value;
 
-    explicit exact_integer() noexcept;
-
-    explicit exact_integer(mpz_t const) noexcept;
+    exact_integer() noexcept;
 
     exact_integer(exact_integer const&) noexcept;
 
-    explicit exact_integer(exact_integer &&) noexcept;
+    exact_integer(exact_integer &&) noexcept;
+
+    ~exact_integer();
+
+    explicit exact_integer(mpz_t const) noexcept;
 
     explicit exact_integer(int);
 
@@ -47,18 +49,12 @@ inline namespace kernel
 
     explicit exact_integer(external_representation const&, int = 0);
 
-    ~exact_integer();
-
     auto operator=(exact_integer const&) -> exact_integer &;
 
     auto operator=(exact_integer &&) noexcept -> exact_integer &;
 
     auto operator=(external_representation const&) -> exact_integer &;
 
-    auto swap(exact_integer &) noexcept -> void;
-
-    explicit operator bool() const;
-
     operator int() const;
 
     operator signed long() const;
@@ -68,6 +64,8 @@ inline namespace kernel
     explicit operator float() const;
 
     explicit operator double() const;
+
+    explicit operator bool() const;
   };
 
   auto operator ==(exact_integer const&, int const) -> bool;
diff --git a/include/meevax/kernel/number.hpp b/include/meevax/kernel/number.hpp
index 8e3957d7f..0363d66ff 100644
--- a/include/meevax/kernel/number.hpp
+++ b/include/meevax/kernel/number.hpp
@@ -195,9 +195,9 @@ inline namespace kernel
       }
       else if constexpr (std::is_same_v<std::decay_t<decltype(z)>, ratio>)
       {
-        if (auto i = exact_integer(mpq_denref(z.value)); i == 1)
+        if (z.denominator() == 1)
         {
-          return z.numerator();
+          return make(z.numerator());
         }
         else
         {
@@ -380,7 +380,7 @@ inline namespace kernel
       }
       else if constexpr (std::is_same_v<std::decay_t<T>, ratio>)
       {
-        return x.denominator().template as<exact_integer>() == 1;
+        return x.denominator() == 1;
       }
       else
       {
diff --git a/include/meevax/kernel/ratio.hpp b/include/meevax/kernel/ratio.hpp
index d4d97163d..1b6a04d5f 100644
--- a/include/meevax/kernel/ratio.hpp
+++ b/include/meevax/kernel/ratio.hpp
@@ -18,7 +18,6 @@
 #define INCLUDED_MEEVAX_KERNEL_RATIO_HPP
 
 #include <gmp.h>
-
 #include <meevax/kernel/pair.hpp>
 
 namespace meevax
@@ -35,6 +34,8 @@ inline namespace kernel
 
     ratio(ratio &&);
 
+    ~ratio();
+
     explicit ratio(exact_integer const&);
 
     explicit ratio(exact_integer const&, exact_integer const&);
@@ -43,11 +44,9 @@ inline namespace kernel
 
     explicit ratio(external_representation const&, int = 10);
 
-    ~ratio();
-
-    auto denominator() const -> value_type;
+    auto denominator() const -> exact_integer;
 
-    auto numerator() const -> value_type;
+    auto numerator() const -> exact_integer;
 
     explicit operator double() const;
   };
diff --git a/src/kernel/exact_integer.cpp b/src/kernel/exact_integer.cpp
index 62ab132cb..38e20a53d 100644
--- a/src/kernel/exact_integer.cpp
+++ b/src/kernel/exact_integer.cpp
@@ -31,11 +31,6 @@ inline namespace kernel
     mpz_init(value);
   }
 
-  exact_integer::exact_integer(mpz_t const z) noexcept
-  {
-    mpz_init_set(value, z);
-  }
-
   exact_integer::exact_integer(exact_integer const& other) noexcept
   {
     mpz_init_set(value, other.value);
@@ -47,6 +42,16 @@ inline namespace kernel
     mpz_swap(value, other.value);
   }
 
+  exact_integer::~exact_integer()
+  {
+    mpz_clear(value);
+  }
+
+  exact_integer::exact_integer(mpz_t const z) noexcept
+  {
+    mpz_init_set(value, z);
+  }
+
   exact_integer::exact_integer(int rhs)
     : exact_integer(static_cast<signed long>(rhs))
   {}
@@ -75,20 +80,15 @@ inline namespace kernel
     }
   }
 
-  exact_integer::~exact_integer()
-  {
-    mpz_clear(value);
-  }
-
   auto exact_integer::operator=(exact_integer const& rhs) -> exact_integer &
   {
     mpz_set(value, rhs.value);
     return *this;
   }
 
-  auto exact_integer::operator=(exact_integer && rhs) noexcept -> exact_integer &
+  auto exact_integer::operator=(exact_integer && other) noexcept -> exact_integer &
   {
-    swap(rhs);
+    mpz_swap(value, other.value);
     return *this;
   }
 
@@ -104,11 +104,6 @@ inline namespace kernel
     }
   }
 
-  auto exact_integer::swap(exact_integer & rhs) noexcept -> void
-  {
-    std::swap(*value, *rhs.value);
-  }
-
   exact_integer::operator bool() const
   {
     return (*value)._mp_size;
diff --git a/src/kernel/library.cpp b/src/kernel/library.cpp
index cd0cb8110..e4bb7750d 100644
--- a/src/kernel/library.cpp
+++ b/src/kernel/library.cpp
@@ -571,12 +571,12 @@ inline namespace kernel
 
       library.define<procedure>("ratio-numerator", [](let const& xs)
       {
-        return car(xs).as<ratio>().numerator();
+        return make(car(xs).as<ratio>().numerator());
       });
 
       library.define<procedure>("ratio-denominator", [](let const& xs)
       {
-        return car(xs).as<ratio>().denominator();
+        return make(car(xs).as<ratio>().denominator());
       });
 
       library.define<procedure>("floor", [](let const& xs)
diff --git a/src/kernel/ratio.cpp b/src/kernel/ratio.cpp
index 06a1192b1..fc5880337 100644
--- a/src/kernel/ratio.cpp
+++ b/src/kernel/ratio.cpp
@@ -63,14 +63,14 @@ inline namespace kernel
 
   ratio::ratio(external_representation const& token, int radix)
   {
-    std::regex static const pattern { "([+-]?[0-9a-f]+)/([0-9a-f]+)" };
+    // std::regex static const pattern { "([+-]?[0-9a-f]+)/([0-9a-f]+)" };
 
-    if (mpq_init(value); not std::regex_match(token, pattern) or mpq_set_str(value, token.c_str(), radix))
+    if (mpq_init(value); mpq_set_str(value, token.c_str(), radix))
     {
       mpq_clear(value);
       throw error();
     }
-    else // TEMPORARY!!!
+    else
     {
       mpq_canonicalize(value);
     }
@@ -81,19 +81,19 @@ inline namespace kernel
     mpq_clear(value);
   }
 
-  auto ratio::denominator() const -> value_type
+  auto ratio::denominator() const -> exact_integer
   {
-    return make<exact_integer>(mpq_denref(value));
+    return exact_integer(mpq_denref(value));
   }
 
-  auto ratio::numerator() const -> value_type
+  auto ratio::numerator() const -> exact_integer
   {
-    return make<exact_integer>(mpq_numref(value));
+    return exact_integer(mpq_numref(value));
   }
 
   ratio::operator double() const
   {
-    return static_cast<double>(numerator().as<exact_integer>()) / static_cast<double>(denominator().as<exact_integer>());
+    return mpq_get_d(value);
   }
 
   auto operator <<(std::ostream & os, ratio const& datum) -> std::ostream &