From 9abdec3a2ddd3a965a13a3708bb131860a2486cb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E9=AD=94=E7=8E=8B=E5=8D=B7=E5=AD=90?=
 <baoguoxiao0538@hotmail.com>
Date: Sun, 15 Oct 2023 20:25:14 +0800
Subject: [PATCH] Update math

---
 reference/math/functions/abs.xml          |  2 +-
 reference/math/functions/base-convert.xml |  2 +-
 reference/math/functions/bindec.xml       |  2 +-
 reference/math/functions/ceil.xml         |  2 +-
 reference/math/functions/cos.xml          |  2 +-
 reference/math/functions/dechex.xml       |  4 +-
 reference/math/functions/deg2rad.xml      |  2 +-
 reference/math/functions/exp.xml          |  2 +-
 reference/math/functions/floor.xml        |  2 +-
 reference/math/functions/hexdec.xml       |  2 +-
 reference/math/functions/intdiv.xml       |  2 +-
 reference/math/functions/is-finite.xml    | 53 ++++++++++++++++++++---
 reference/math/functions/is-infinite.xml  | 49 ++++++++++++++++++---
 reference/math/functions/is-nan.xml       | 33 +++++++++-----
 reference/math/functions/max.xml          |  2 +-
 reference/math/functions/min.xml          |  2 +-
 reference/math/functions/octdec.xml       |  2 +-
 reference/math/functions/pi.xml           |  2 +-
 reference/math/functions/pow.xml          |  2 +-
 reference/math/functions/rad2deg.xml      |  2 +-
 reference/math/functions/sin.xml          |  2 +-
 reference/math/functions/sqrt.xml         |  2 +-
 reference/math/functions/tan.xml          |  2 +-
 reference/opcache/ini.xml                 |  7 ++-
 24 files changed, 136 insertions(+), 48 deletions(-)

diff --git a/reference/math/functions/abs.xml b/reference/math/functions/abs.xml
index 2058773d86..fa40dea4b4 100644
--- a/reference/math/functions/abs.xml
+++ b/reference/math/functions/abs.xml
@@ -67,7 +67,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>abs</function> 例子</title>
+    <title><function>abs</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/base-convert.xml b/reference/math/functions/base-convert.xml
index b1f719ba09..9ab4636b13 100755
--- a/reference/math/functions/base-convert.xml
+++ b/reference/math/functions/base-convert.xml
@@ -96,7 +96,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>base_convert</function> 例子</title>
+    <title><function>base_convert</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/bindec.xml b/reference/math/functions/bindec.xml
index 077930aa7a..956926de71 100755
--- a/reference/math/functions/bindec.xml
+++ b/reference/math/functions/bindec.xml
@@ -83,7 +83,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>bindec</function> 例子</title>
+    <title><function>bindec</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/ceil.xml b/reference/math/functions/ceil.xml
index fde6e80c9f..68b053d6e4 100755
--- a/reference/math/functions/ceil.xml
+++ b/reference/math/functions/ceil.xml
@@ -66,7 +66,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>ceil</function> 例子</title>
+    <title><function>ceil</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/cos.xml b/reference/math/functions/cos.xml
index b3b6097ac3..938da1e1e8 100644
--- a/reference/math/functions/cos.xml
+++ b/reference/math/functions/cos.xml
@@ -43,7 +43,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>cos</function> 例子</title>
+    <title><function>cos</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/dechex.xml b/reference/math/functions/dechex.xml
index 18d4d5c4ba..14558007af 100755
--- a/reference/math/functions/dechex.xml
+++ b/reference/math/functions/dechex.xml
@@ -52,7 +52,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>dechex</function> 例子</title>
+    <title><function>dechex</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
@@ -72,7 +72,7 @@ a
   </para>
    <para>
    <example>
-    <title>大整数的 <function>dechex</function> 例子</title>
+    <title>大整数的 <function>dechex</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/deg2rad.xml b/reference/math/functions/deg2rad.xml
index 851126a181..7f304d3a61 100644
--- a/reference/math/functions/deg2rad.xml
+++ b/reference/math/functions/deg2rad.xml
@@ -44,7 +44,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>deg2rad</function> 例子</title>
+    <title><function>deg2rad</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/exp.xml b/reference/math/functions/exp.xml
index ab4fdeb225..cc32dd77a4 100644
--- a/reference/math/functions/exp.xml
+++ b/reference/math/functions/exp.xml
@@ -47,7 +47,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>exp</function> 例子</title>
+    <title><function>exp</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/floor.xml b/reference/math/functions/floor.xml
index 474ec14183..256f06df53 100644
--- a/reference/math/functions/floor.xml
+++ b/reference/math/functions/floor.xml
@@ -66,7 +66,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>floor</function> 例子</title>
+    <title><function>floor</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/hexdec.xml b/reference/math/functions/hexdec.xml
index 5957606281..0e9c26595f 100644
--- a/reference/math/functions/hexdec.xml
+++ b/reference/math/functions/hexdec.xml
@@ -70,7 +70,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>hexdec</function> 例子</title>
+    <title><function>hexdec</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/intdiv.xml b/reference/math/functions/intdiv.xml
index a36a57904b..d292b16cae 100644
--- a/reference/math/functions/intdiv.xml
+++ b/reference/math/functions/intdiv.xml
@@ -58,7 +58,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>intdiv</function> 的一些例子</title>
+    <title><function>intdiv</function> 的一些示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/is-finite.xml b/reference/math/functions/is-finite.xml
index ed93a3c1e8..4eedca20ee 100644
--- a/reference/math/functions/is-finite.xml
+++ b/reference/math/functions/is-finite.xml
@@ -1,12 +1,13 @@
 <?xml version="1.0" encoding="utf-8"?>
 <!-- $Revision$ -->
-<!-- EN-Revision: 0c9c2dd669fe9395eaa73d487fbd160f9057429a Maintainer: dallas Status: ready -->
+<!-- EN-Revision: 445fda70c6876c3e903f5ba302248e50fd43cdf6 Maintainer: dallas Status: ready -->
 <!-- CREDITS: mowangjuanzi -->
 <refentry xml:id="function.is-finite" xmlns="http://docbook.org/ns/docbook">
  <refnamediv>
   <refname>is_finite</refname>
-   <refpurpose>判断是否为有限值</refpurpose>
+   <refpurpose>判断浮点数是否是有效的有限值</refpurpose>
  </refnamediv>
+
  <refsect1 role="description">
   &reftitle.description;
   <methodsynopsis>
@@ -14,9 +15,13 @@
    <methodparam><type>float</type><parameter>num</parameter></methodparam>
   </methodsynopsis>
   <para>
-   检查 <parameter>num</parameter> 是否是是本机平台上浮点数所允许范围中的一个合法的有限值。
+   返回指定的 <parameter>num</parameter> 是否是有限浮点数。
+  </para>
+  <para>
+   有限浮点数既不是 <literal>NAN</literal>（<function>is_nan</function>）也不是无限的（<function>is_infinite</function>）。
   </para>
  </refsect1>
+
  <refsect1 role="parameters">
   &reftitle.parameters;
   <para>
@@ -25,20 +30,56 @@
      <term><parameter>num</parameter></term>
      <listitem>
       <para>
-       要检查的值
+       要检查的 &float;
       </para>
      </listitem>
     </varlistentry>
    </variablelist>
   </para>
  </refsect1>
+
  <refsect1 role="returnvalues">
   &reftitle.returnvalues;
   <para>
-   如果 <parameter>num</parameter> 是本机平台上 PHP
-   浮点数所允许范围中的一个合法的有限值，则返回 &true;。
+   如果 <parameter>num</parameter> 不是 <literal>NAN</literal>、<literal>INF</literal>
+   或 <literal>-INF</literal>，那么为 &true;，否则为 &false;。
+  </para>
+ </refsect1>
+
+ <refsect1 role="examples">
+  &reftitle.examples;
+  <para>
+   <example>
+    <title><function>is_finite</function> 示例</title>
+    <programlisting role="php">
+<![CDATA[
+<?php
+$float = 1.2345;
+var_dump($float, is_finite($float));
+
+$nan = sqrt(-1);
+var_dump($nan, is_finite($nan));
+
+$inf = 1e308 * 2;
+var_dump($inf, is_finite($inf));
+?>
+]]>
+    </programlisting>
+    &example.outputs;
+    <screen>
+<![CDATA[
+float(1.2345)
+bool(true)
+float(NAN)
+bool(false)
+float(INF)
+bool(false)
+]]>
+    </screen>
+   </example>
   </para>
  </refsect1>
+
  <refsect1 role="seealso">
   &reftitle.seealso;
   <para>
diff --git a/reference/math/functions/is-infinite.xml b/reference/math/functions/is-infinite.xml
index 84c22e48c5..05e8884500 100644
--- a/reference/math/functions/is-infinite.xml
+++ b/reference/math/functions/is-infinite.xml
@@ -1,12 +1,13 @@
 <?xml version="1.0" encoding="utf-8"?>
 <!-- $Revision$ -->
-<!-- EN-Revision: 0c9c2dd669fe9395eaa73d487fbd160f9057429a Maintainer: dallas Status: ready -->
+<!-- EN-Revision: 445fda70c6876c3e903f5ba302248e50fd43cdf6 Maintainer: dallas Status: ready -->
 <!-- CREDITS: mowangjuanzi -->
 <refentry xml:id="function.is-infinite" xmlns="http://docbook.org/ns/docbook">
  <refnamediv>
   <refname>is_infinite</refname>
-   <refpurpose>判断是否为无限值</refpurpose>
+   <refpurpose>判断浮点数是否为无限值</refpurpose>
  </refnamediv>
+
  <refsect1 role="description">
   &reftitle.description;
   <methodsynopsis>
@@ -14,11 +15,11 @@
    <methodparam><type>float</type><parameter>num</parameter></methodparam>
   </methodsynopsis>
   <para>
-   如果 <parameter>num</parameter>
-   为无穷大（正的或负的），例如 <literal>log(0)</literal>
-   的结果或者任何超出本平台的浮点数范围的值，则返回 &true;。
+   返回指定的 <parameter>num</parameter> 是否是 <literal>INF</literal>
+   或 <literal>-INF</literal>。
   </para>
  </refsect1>
+
  <refsect1 role="parameters">
   &reftitle.parameters;
   <para>
@@ -27,19 +28,53 @@
      <term><parameter>num</parameter></term>
      <listitem>
       <para>
-       要检查的值
+       要检查的 &float;
       </para>
      </listitem>
     </varlistentry>
    </variablelist>
   </para>
  </refsect1>
+
  <refsect1 role="returnvalues">
   &reftitle.returnvalues;
   <para>
-   如果 <parameter>num</parameter> 为无穷大返回 &true;，否则返回 &false;。
+   如果 <parameter>num</parameter> 是 <literal>INF</literal>
+   或 <literal>-INF</literal>，返回 &true;，否则返回 &false;。
   </para>
  </refsect1>
+
+ <refsect1 role="examples">
+  &reftitle.examples;
+  <para>
+   <example>
+    <title><function>is_infinite</function> 示例</title>
+    <programlisting role="php">
+<![CDATA[
+<?php
+$inf = 1e308 * 2;
+
+var_dump($inf, is_infinite($inf));
+
+$negative_inf = -$inf;
+
+var_dump($negative_inf, is_infinite($negative_inf));
+?>
+]]>
+    </programlisting>
+    &example.outputs;
+    <screen>
+<![CDATA[
+float(INF)
+bool(true)
+float(-INF)
+bool(true)
+]]>
+    </screen>
+   </example>
+  </para>
+ </refsect1>
+
  <refsect1 role="seealso">
   &reftitle.seealso;
   <para>
diff --git a/reference/math/functions/is-nan.xml b/reference/math/functions/is-nan.xml
index 2eb05b18a2..be9cc95a25 100644
--- a/reference/math/functions/is-nan.xml
+++ b/reference/math/functions/is-nan.xml
@@ -1,11 +1,11 @@
 <?xml version="1.0" encoding="utf-8"?>
 <!-- $Revision$ -->
-<!-- EN-Revision: 0c9c2dd669fe9395eaa73d487fbd160f9057429a Maintainer: dallas Status: ready -->
+<!-- EN-Revision: 445fda70c6876c3e903f5ba302248e50fd43cdf6 Maintainer: dallas Status: ready -->
 <!-- CREDITS: mowangjuanzi -->
 <refentry xml:id="function.is-nan" xmlns="http://docbook.org/ns/docbook">
  <refnamediv>
   <refname>is_nan</refname>
-  <refpurpose>判断是否为合法数值</refpurpose>
+  <refpurpose>判断浮点数是否是否为 NAN</refpurpose>
  </refnamediv>
 
  <refsect1 role="description">
@@ -15,9 +15,24 @@
    <methodparam><type>float</type><parameter>num</parameter></methodparam>
   </methodsynopsis>
   <para>
-   如果 <parameter>num</parameter> 为“非数值”，例如
-   <literal>acos(1.01)</literal> 的结果，则返回 &true;。
+   返回指定的 <parameter>num</parameter> 是否是 <literal>NAN</literal>（<quote>非数值</quote>）。
   </para>
+  <para>
+   <literal>NAN</literal> 是从未定义的数学运算中返回的，例如传递的参数在函数的输入域之外的时候。平方根（<function>sqrt</function>）仅对正数定义，传递负数将导致
+   <literal>NAN</literal>。返回 <literal>NAN</literal> 的其它操作示例有 <literal>INF</literal> 除以 <literal>INF</literal>
+   以及涉及现有 <literal>NAN</literal> 值的任何操作。
+  </para>
+  <note>
+   <para>
+    尽管名字叫 <quote>Not A Number</quote>，但 <literal>NAN</literal> 是有效的 &float; 类型。
+   </para>
+  </note>
+  <caution>
+   <para>
+    <literal>NAN</literal> 不能与 <literal>NAN</literal> 进行比较。要检测浮点数是否是 <literal>NAN</literal>，必须使用
+    <function>is_nan</function>。使用 <code>$float === NAN</code> 检测将不起作用。
+   </para>
+  </caution>
  </refsect1>
 
  <refsect1 role="parameters">
@@ -28,7 +43,7 @@
      <term><parameter>num</parameter></term>
      <listitem>
       <para>
-       要检查的值
+       要检查的 &float;
       </para>
      </listitem>
     </varlistentry>
@@ -39,7 +54,7 @@
  <refsect1 role="returnvalues">
   &reftitle.returnvalues;
   <para>
-   如果 <parameter>num</parameter>“不是数字”返回 &true;，否则返回 &false;。
+   如果 <parameter>num</parameter> 是 <literal>NAN</literal>，返回 &true;，否则返回 &false;。
   </para>
  </refsect1>
 
@@ -47,13 +62,11 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>is_nan</function> 例子</title>
+    <title><function>is_nan</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
-// 无效计算，将返回 
-// NaN 值
-$nan = acos(8);
+$nan = sqrt(-1);
 
 var_dump($nan, is_nan($nan));
 ?>
diff --git a/reference/math/functions/max.xml b/reference/math/functions/max.xml
index 8ae1f48c3d..3b3f2a7058 100644
--- a/reference/math/functions/max.xml
+++ b/reference/math/functions/max.xml
@@ -117,7 +117,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title>使用 <function>max</function> 的例子</title>
+    <title>使用 <function>max</function> 的示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/min.xml b/reference/math/functions/min.xml
index 7eb373488a..9147bb86f1 100644
--- a/reference/math/functions/min.xml
+++ b/reference/math/functions/min.xml
@@ -117,7 +117,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>min</function> 用法的例子</title>
+    <title><function>min</function> 用法的示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/octdec.xml b/reference/math/functions/octdec.xml
index 7a40904124..aa0e2f0c7d 100644
--- a/reference/math/functions/octdec.xml
+++ b/reference/math/functions/octdec.xml
@@ -67,7 +67,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>octdec</function> 例子</title>
+    <title><function>octdec</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/pi.xml b/reference/math/functions/pi.xml
index b4703d75fa..8eb5f5fd41 100644
--- a/reference/math/functions/pi.xml
+++ b/reference/math/functions/pi.xml
@@ -33,7 +33,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>pi</function> 例子</title>
+    <title><function>pi</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/pow.xml b/reference/math/functions/pow.xml
index bdd8548e24..951ffda569 100644
--- a/reference/math/functions/pow.xml
+++ b/reference/math/functions/pow.xml
@@ -58,7 +58,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>pow</function> 的一些例子</title>
+    <title><function>pow</function> 的一些示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/rad2deg.xml b/reference/math/functions/rad2deg.xml
index 893c56c8c7..8bcc170a79 100644
--- a/reference/math/functions/rad2deg.xml
+++ b/reference/math/functions/rad2deg.xml
@@ -44,7 +44,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>rad2deg</function> 例子</title>
+    <title><function>rad2deg</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/sin.xml b/reference/math/functions/sin.xml
index 122f4e9b77..79a07255c0 100644
--- a/reference/math/functions/sin.xml
+++ b/reference/math/functions/sin.xml
@@ -43,7 +43,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>sin</function> 例子</title>
+    <title><function>sin</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/sqrt.xml b/reference/math/functions/sqrt.xml
index 1fdc0b7c59..5beb70258d 100644
--- a/reference/math/functions/sqrt.xml
+++ b/reference/math/functions/sqrt.xml
@@ -42,7 +42,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>sqrt</function> 例子</title>
+    <title><function>sqrt</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/math/functions/tan.xml b/reference/math/functions/tan.xml
index c3dd44aa9c..21cae2baa9 100755
--- a/reference/math/functions/tan.xml
+++ b/reference/math/functions/tan.xml
@@ -43,7 +43,7 @@
   &reftitle.examples;
   <para>
    <example>
-    <title><function>tan</function> 例子</title>
+    <title><function>tan</function> 示例</title>
     <programlisting role="php">
 <![CDATA[
 <?php
diff --git a/reference/opcache/ini.xml b/reference/opcache/ini.xml
index b311879197..8a46f79549 100644
--- a/reference/opcache/ini.xml
+++ b/reference/opcache/ini.xml
@@ -1171,7 +1171,7 @@
     </term>
     <listitem>
      <para>
-      Maximum number of times the compilation of a root trace is attempted before it is blacklisted.
+      在将 root trace 列入黑名单之前，尝试编译 side trace 的最大次数。
      </para>
     </listitem>
    </varlistentry>
@@ -1182,7 +1182,7 @@
     </term>
     <listitem>
      <para>
-      Maximum number of times the compilation of a side trace is attempted before it is blacklisted.
+      在将 side trace 列入黑名单之前，尝试编译 side trace 的最大次数。
      </para>
     </listitem>
    </varlistentry>
@@ -1193,8 +1193,7 @@
     </term>
     <listitem>
      <para>
-      Maximum number of attempts to unroll a loop in a side trace,
-      trying to reach the root trace and close the outer loop.
+      在 side trace 中展开循环的最大尝试次数，试图到达 root trace 并关闭外循环。
      </para>
     </listitem>
    </varlistentry>