Merge pull request #1230 from ChristianGruen/1216

1216 Detailed comments on math:e, sinh(), cosh(), tanh()

specifications/xpath-functions-40/src/function-catalog.xml

@@ -885,7 +885,7 @@
       <fos:notes>
          <p>For <code>xs:float</code> and <code>xs:double</code> operands, floating point division
             is performed as specified in <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
                />. A positive number divided by
             positive zero returns <code>INF</code>. A negative number divided by positive zero
             returns <code>-INF</code>. Division by negative zero returns <code>-INF</code> and
@@ -1052,7 +1052,7 @@ compare($N * $arg2, 0) eq compare($arg1, 0).</eg>
                      b)*b+(a mod b)</code> = <code>a</code>.
                   <!--float or double remainder r from a dividend n and a divisor d is defined by the mathematical relation r = n-(d * q) where q is an integer that is negative only if n/d is negative and positive only if n/d is positive, and whose magnitude is as large as possible without exceeding the magnitude of the true mathematical quotient of n and d.  -->
                   Division is truncating division, analogous to integer division, not <bibref
-                     ref="ieee754-2008"
+                     ref="ieee754-2019"
                   /> rounding division i.e. additional digits are truncated,
                   not rounded to the required precision.</p>
             </item>
@@ -2632,8 +2632,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <fos:example>
             <fos:test xslt-version="3.0">
                <fos:expression>math:pow(math:e(), 0.05 * 3)</fos:expression>
-               <fos:result>1.161834242728283e0</fos:result>
-               <fos:postamble>The amount that results after 3 years at an annual rate of 5%.</fos:postamble>
+               <fos:result approx="true">1.161834242728283e0</fos:result>
             </fos:test>
          </fos:example>
       </fos:examples>
@@ -2656,7 +2655,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the mathematical constant <var>e</var> raised to the power of
                <code>$value</code>, as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of
             the <code>exp</code> function applied to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -2722,7 +2721,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is ten raised to the power of <code>$value</code>, as defined in the
                <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the <code>exp10</code> function applied
             to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -2784,7 +2783,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the natural logarithm of <code>$value</code>, as defined in the
                <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the <code>log</code> function applied
             to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -2854,7 +2853,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the base-10 logarithm of <code>$value</code>, as defined in the
                <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the <code>log10</code> function applied
             to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -2924,7 +2923,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the mathematical non-negative square root of <code>$value</code>
             as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the
                <code>squareRoot</code> function applied to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -2999,13 +2998,13 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$x</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>If <code>$y</code> is an instance of <code>xs:integer</code>, the result is
                <code>$x</code> raised to the power of <code>$y</code> as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the <code>pown</code> function applied to a
             64-bit binary floating point value and an integer.</p>
          <p>Otherwise <code>$y</code> is converted to an <code>xs:double</code> by numeric
             promotion, and the result is <code>$x</code> raised to the power of
                <code>$y</code> as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the
                <code>pow</code> function applied to two 64-bit binary floating point values.</p>
       </fos:rules>
@@ -3185,7 +3184,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
 
          <p>Otherwise the result is the sine of <code>$radians</code> (which is treated as an angle in
             radians) as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the
                <code>sin</code> function applied to 64-bit binary floating point values.</p>
 
@@ -3262,7 +3261,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
             then the result is <code>NaN</code>.</p>
          <p>Otherwise the result is the cosine of <code>$radians</code> (which is treated as an angle in
             radians) as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the
                <code>cos</code> function applied to 64-bit binary floating point values.</p>
       </fos:rules>
@@ -3335,7 +3334,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
             sequence.</p>
          <p>Otherwise the result is the tangent of <code>$radians</code> (which is treated as an angle
             in radians) as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
             /> specification of the
                <code>tan</code> function applied to 64-bit binary floating point values.</p>
 
@@ -3419,7 +3418,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
       <fos:rules>
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the arc sine of <code>$value</code> as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
                /> specification of the
             <code>asin</code> function applied to 64-bit binary floating point values. 
             The result is in the range -<var>π</var>/2 to +<var>π</var>/2 radians. </p>
@@ -3493,7 +3492,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
       <fos:rules>
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the arc cosine of <code>$value</code>, as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
                /> specification of the
                <code>acos</code> function applied to 64-bit binary floating point values.
             The result is in the range zero to +<var>π</var> radians.</p>
@@ -3566,7 +3565,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty sequence.</p>
          <p>Otherwise the result is the arc tangent of <code>$value</code>, as defined 
             in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
                /> specification of the
                <code>atan</code> function applied to 64-bit binary floating point values.
             The result is in the range -<var>π</var>/2
@@ -3636,7 +3635,7 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
       </fos:summary>
       <fos:rules>
          <p>The result is the value of <code>atan2(y, x)</code> as defined in the <bibref
-               ref="ieee754-2008"
+               ref="ieee754-2019"
                /> specification of the <code>atan2</code> function applied to
             64-bit binary floating point values. The result is in the range -<var>π</var>
             to +<var>π</var> radians.</p>
@@ -3721,11 +3720,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty
             sequence.</p>
          <p>Otherwise the result is the hyperbolic sine of <code>$value</code> as defined in the
-            <bibref ref="ieee754-2008"/> specification of the <code>sinh</code> function applied
+            <bibref ref="ieee754-2019"/> specification of the <code>sinh</code> function applied
             to 64-bit binary floating point values. </p>
       </fos:rules>
       <fos:notes>
-         <p>The treatment of the <code>invalidOperation</code> and <code>underflow</code> exceptions
+         <p>The treatment of the <code>overflow</code> and <code>underflow</code> exceptions
             is defined in <specref ref="op.numeric"/>. </p>
          <p>If <code>$value</code> is positive or negative zero, the result is
             <code>$value</code>.</p>
@@ -3736,11 +3735,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <fos:example>
             <fos:test>
                <fos:expression>math:sinh(1)</fos:expression>
-               <fos:result>1.1752011936438014</fos:result>
+               <fos:result approx="true">1.1752011936438014e0</fos:result>
             </fos:test>
             <fos:test>
                <fos:expression>math:sinh(math:pi())</fos:expression>
-               <fos:result>11.548739357257748</fos:result>
+               <fos:result approx="true">11.548739357257748e0</fos:result>
             </fos:test>
          </fos:example>
       </fos:examples>
@@ -3763,11 +3762,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty
             sequence.</p>
          <p>Otherwise the result is the hyperbolic cosine of <code>$value</code> as defined in the
-            <bibref ref="ieee754-2008"/> specification of the <code>cosh</code> function applied
+            <bibref ref="ieee754-2019"/> specification of the <code>cosh</code> function applied
             to 64-bit binary floating point values. </p>
       </fos:rules>
       <fos:notes>
-         <p>The treatment of the <code>invalidOperation</code> and <code>underflow</code> exceptions
+         <p>The treatment of the <code>overflow</code> exception
             is defined in <specref ref="op.numeric"/>. </p>
          <p>If <code>$value</code> is positive or negative zero, the result is
             <code>1</code>.</p>
@@ -3782,11 +3781,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <fos:example>
             <fos:test>
                <fos:expression>math:cosh(0)</fos:expression>
-               <fos:result>1</fos:result>
+               <fos:result>1.0e0</fos:result>
             </fos:test>
             <fos:test>
                <fos:expression>math:cosh(math:pi())</fos:expression>
-               <fos:result>11.591953275521519</fos:result>
+               <fos:result approx="true">11.591953275521519e0</fos:result>
             </fos:test>
          </fos:example>
       </fos:examples>
@@ -3809,11 +3808,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <p>If <code>$value</code> is the empty sequence, the function returns the empty
             sequence.</p>
          <p>Otherwise the result is the hyperbolic tangent of <code>$value</code> as defined in the
-            <bibref ref="ieee754-2008"/> specification of the <code>tanh</code> function applied
+            <bibref ref="ieee754-2019"/> specification of the <code>tanh</code> function applied
             to 64-bit binary floating point values. </p>
       </fos:rules>
       <fos:notes>
-         <p>The treatment of the <code>invalidOperation</code> and <code>underflow</code> exceptions
+         <p>The treatment of the <code>underflow</code> exception
             is defined in <specref ref="op.numeric"/>. </p>
          <p>If <code>$value</code> is positive or negative zero, the result is
             <code>$value</code>.</p>
@@ -3826,11 +3825,11 @@ translate(value := '٢٠٢٣', replace := '٠١٢٣٤٥٦٧٨٩', with := '01234
          <fos:example>
             <fos:test>
                <fos:expression>math:tanh(1)</fos:expression>
-               <fos:result>0.7615941559557649</fos:result>
+               <fos:result approx="true">0.7615941559557649e0</fos:result>
             </fos:test>
             <fos:test>
                <fos:expression>math:tanh(math:pi())</fos:expression>
-               <fos:result>0.99627207622075</fos:result>
+               <fos:result approx="true">0.99627207622075e0</fos:result>
             </fos:test>
          </fos:example>
       </fos:examples>