[Win32forth-cvs] win32forth/doc p-float.htm,1.16,1.17

[George H. <geo...@us...>]

Update of /cvsroot/win32forth/win32forth/doc
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv15442/win32forth/doc

Modified Files:
	p-float.htm 
Log Message:
gah: More Dexing (still work in progress) optimizations and bug fixes

Index: p-float.htm
===================================================================
RCS file: /cvsroot/win32forth/win32forth/doc/p-float.htm,v
retrieving revision 1.16
retrieving revision 1.17
diff -C2 -d -r1.16 -r1.17
*** p-float.htm	20 Feb 2006 12:32:44 -0000	1.16
--- p-float.htm	21 Feb 2006 11:03:54 -0000	1.17
***************
*** 104,109 ****
  </a></b></pre><p>Define a floating point value initialised from the FP stack.
  </p><pre><b><a name="17">: FTO &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
! </a></b></pre><p><b>&nbsp;Interpreting: ( -&lt;fvalue&gt;- -- FS: r -- ) <br />
! Compiling: &nbsp;&nbsp;&nbsp;( -&lt;fvalue&gt;- -- &nbsp;Run-time: FS: r -- ) </b>
  </p><p>Store r into -&lt;fvalue&gt;-. If -&lt;fvalue&gt;- is not defined with fvalue then memory may
  be corrupted; no checks are made so the user should take care. FTO should not be
--- 104,109 ----
  </a></b></pre><p>Define a floating point value initialised from the FP stack.
  </p><pre><b><a name="17">: FTO &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
! </a></b></pre><p><b>&nbsp;Interpretation: ( -&lt;fvalue&gt;- -- FS: r -- ) <br />
! Compilation: &nbsp;&nbsp;&nbsp;( -&lt;fvalue&gt;- -- &nbsp;Run-time: FS: r -- ) </b>
  </p><p>Store r into -&lt;fvalue&gt;-. If -&lt;fvalue&gt;- is not defined with fvalue then memory may
  be corrupted; no checks are made so the user should take care. FTO should not be
***************
*** 147,151 ****
  </p><pre><b><a name="28">: F2DUP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r1 r2 r1 r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
  </a></b></pre><p>Duplicate the top 2 FP stack entries.
! </p><pre><b><a name="29">: F2SWAP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 r3 r4 -- r3 r4 r2 r1 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;Floating extra
  </a></b></pre><p>Swap the top pair of floating-point numbers with the second pair.
  </p><pre><b><a name="30">: F2NIP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 r3 r4 -- r3 r4 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
--- 147,151 ----
  </p><pre><b><a name="28">: F2DUP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r1 r2 r1 r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
  </a></b></pre><p>Duplicate the top 2 FP stack entries.
! </p><pre><b><a name="29">: F2SWAP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 r3 r4 -- r3 r4 r1 r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;Floating extra
  </a></b></pre><p>Swap the top pair of floating-point numbers with the second pair.
  </p><pre><b><a name="30">: F2NIP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 r3 r4 -- r3 r4 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
***************
*** 271,296 ****
  </p><pre><b><a name="78">code FSQRT &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the positive square root of r1.
  </p><a name="Sec#11"></a>
  <h3>Trigonometric functions
! </h3><pre><b><a name="79">: FSIN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the sine of r1 in radians.
! </p><pre><b><a name="80">: FCOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the cosine of r1 in radians.
! </p><pre><b><a name="81">: FSINCOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the sine and r3 the cosine of r1 in radians. This function is more efficient
  than calling FSIN and FCOS separately.
! </p><pre><b><a name="82">: FTAN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the tangent of r1 in radians.
  </p><a name="Sec#12"></a>
  <h3>Inverse Trigonometric functions
! </h3><pre><b><a name="83">code FASIN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose sine is r1. The result for |x| =&lt; 1 is between ±pi/2.
  The result for |x| &gt;&nbsp;1 is NAN.
! </p><pre><b><a name="84">code FACOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose cosine is r1. The result for |x| =&lt; 1 is between 0 and pi.
  The result for |x| &gt;&nbsp;1 is NAN
! </p><pre><b><a name="85">code FATAN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose tangent is r1. The result is between ±pi/2.
! </p><pre><b><a name="86">code FATAN2 &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r3 is the radian angle whose tangent is r1/r2. The result is between ±pi
  with the same sign as r2. If r1 and r2 are both zero then r3 is ±zero.
--- 271,304 ----
  </p><pre><b><a name="78">code FSQRT &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the positive square root of r1.
+ </p><pre><b><a name="79">: F~ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( -- flag ; fs: r1 r2 r3 -- ) &nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
+ </a></b></pre><p>If r3 is positive, flag is true if the absolute value of (r1 minus r2) is less than
+ r3. If r3 is zero, flag is true if the implementation-dependent encoding of r1 and
+ r2 are exactly identical (positive and negative zero are unequal).
+ If r3 is negative, flag is true if the absolute value of (r1 minus r2) is less than the
+ absolute value of r3 times the sum of the absolute values of r1 and r2.
+ </p><p>This provides the three types of floating point equality in common use -- close in
+ absolute terms, exact equality as represented, and relatively close.
  </p><a name="Sec#11"></a>
  <h3>Trigonometric functions
! </h3><pre><b><a name="80">: FSIN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the sine of r1 in radians.
! </p><pre><b><a name="81">: FCOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the cosine of r1 in radians.
! </p><pre><b><a name="82">: FSINCOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the sine and r3 the cosine of r1 in radians. This function is more efficient
  than calling FSIN and FCOS separately.
! </p><pre><b><a name="83">: FTAN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the tangent of r1 in radians.
  </p><a name="Sec#12"></a>
  <h3>Inverse Trigonometric functions
! </h3><pre><b><a name="84">code FASIN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose sine is r1. The result for |x| =&lt; 1 is between ±pi/2.
  The result for |x| &gt;&nbsp;1 is NAN.
! </p><pre><b><a name="85">code FACOS &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose cosine is r1. The result for |x| =&lt; 1 is between 0 and pi.
  The result for |x| &gt;&nbsp;1 is NAN
! </p><pre><b><a name="86">code FATAN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the radian angle whose tangent is r1. The result is between ±pi/2.
! </p><pre><b><a name="87">code FATAN2 &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r3 is the radian angle whose tangent is r1/r2. The result is between ±pi
  with the same sign as r2. If r1 and r2 are both zero then r3 is ±zero.
***************
*** 299,317 ****
  </p><a name="Sec#13"></a>
  <h3>Logarithmic functions
! </h3><pre><b><a name="87">code FLN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the natural logarithm of r1. If r1 is ±0 then r2 is -infinity. If r1
  is infinity then r2 is infinity. If r1 is less than zero then r2 is a NAN.
! </p><pre><b><a name="88">code FLNP1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the natural logarithm of the quantity r1 plus one. If r1 is -1.0 then
  r2 is -infinity. If r1 is infinity then r2 is infinity. If r1 is less than
  -1.0 then r2 is a NAN.
! </p><pre><b><a name="89">code FLOG &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the logarithm to base 10 of r1. If r1 is ±0 then r2 is -infinity. If r1
  is infinity then r2 is infinity. If r1 is less than zero then r2 is a NAN.
  </p><a name="Sec#14"></a>
  <h3>Exponential functions
! </h3><pre><b><a name="90">code FEXP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise e to the power r1, giving r2.
! </p><pre><b><a name="91">code FEXPM1 &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise e to the power r1 and subtract one, giving r2.
  </p><p>This function allows accurate computation when its arguments are close to zero, and
--- 307,325 ----
  </p><a name="Sec#13"></a>
  <h3>Logarithmic functions
! </h3><pre><b><a name="88">code FLN &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the natural logarithm of r1. If r1 is ±0 then r2 is -infinity. If r1
  is infinity then r2 is infinity. If r1 is less than zero then r2 is a NAN.
! </p><pre><b><a name="89">code FLNP1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the natural logarithm of the quantity r1 plus one. If r1 is -1.0 then
  r2 is -infinity. If r1 is infinity then r2 is infinity. If r1 is less than
  -1.0 then r2 is a NAN.
! </p><pre><b><a name="90">code FLOG &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the logarithm to base 10 of r1. If r1 is ±0 then r2 is -infinity. If r1
  is infinity then r2 is infinity. If r1 is less than zero then r2 is a NAN.
  </p><a name="Sec#14"></a>
  <h3>Exponential functions
! </h3><pre><b><a name="91">code FEXP &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise e to the power r1, giving r2.
! </p><pre><b><a name="92">code FEXPM1 &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise e to the power r1 and subtract one, giving r2.
  </p><p>This function allows accurate computation when its arguments are close to zero, and
***************
*** 319,350 ****
  &nbsp;such as cosh(x) can be efficiently and accurately implemented by using FEXPM1;
  &nbsp;accuracy is lost in this function for small values of x if the word FEXP is used.
! </p><pre><b><a name="92">: f** &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise r1 to the power r2, giving the product r3.
! </p><pre><b><a name="93">: FALOG &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise ten to the power r1, giving r2.
  </p><a name="Sec#15"></a>
  <h3>Hyperbolic functions
! </h3><pre><b><a name="94">: FSINH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic sine of r1.
! </p><pre><b><a name="95">: FCOSH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic cosine of r1.
! </p><pre><b><a name="96">: FTANH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic tangent of r1, |r2| &lt;= 1.
  </p><a name="Sec#16"></a>
  <h3>Inverse hyperbolic functions
! </h3><pre><b><a name="97">code FASINH &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic sine is r1.
! </p><pre><b><a name="98">code FACOSH &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic cosine is r1. If r1 &lt;&nbsp;1.0 then r2 is a NAN.
! </p><pre><b><a name="99">: FATANH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic tangent is r1. IF |r1| &gt;&nbsp;1.0 then r2 is a NAN.
- </p><pre><b><a name="100">: F~ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( -- flag ; fs: r1 r2 r3 -- ) &nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
- </a></b></pre><p>If r3 is positive, flag is true if the absolute value of (r1 minus r2) is less than
- r3. If r3 is zero, flag is true if the implementation-dependent encoding of r1 and
- r2 are exactly identical (positive and negative zero are unequal).
- If r3 is negative, flag is true if the absolute value of (r1 minus r2) is less than the
- absolute value of r3 times the sum of the absolute values of r1 and r2.
- </p><p>This provides the three types of floating point equality in common use -- close in
- absolute terms, exact equality as represented, and relatively close.
  </p><a name="Sec#17"></a>
  <h3>Input of Floating Point numbers
--- 327,350 ----
  &nbsp;such as cosh(x) can be efficiently and accurately implemented by using FEXPM1;
  &nbsp;accuracy is lost in this function for small values of x if the word FEXP is used.
! </p><pre><b><a name="93">: f** &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 r2 -- r3 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise r1 to the power r2, giving the product r3.
! </p><pre><b><a name="94">: FALOG &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>Raise ten to the power r1, giving r2.
  </p><a name="Sec#15"></a>
  <h3>Hyperbolic functions
! </h3><pre><b><a name="95">: FSINH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic sine of r1.
! </p><pre><b><a name="96">: FCOSH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic cosine of r1.
! </p><pre><b><a name="97">: FTANH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the hyperbolic tangent of r1, |r2| &lt;= 1.
  </p><a name="Sec#16"></a>
  <h3>Inverse hyperbolic functions
! </h3><pre><b><a name="98">code FASINH &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic sine is r1.
! </p><pre><b><a name="99">code FACOSH &nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic cosine is r1. If r1 &lt;&nbsp;1.0 then r2 is a NAN.
! </p><pre><b><a name="100">: FATANH &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;( fs: r1 -- r2 ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating ext
  </a></b></pre><p>r2 is the number whose hyperbolic tangent is r1. IF |r1| &gt;&nbsp;1.0 then r2 is a NAN.
  </p><a name="Sec#17"></a>
  <h3>Input of Floating Point numbers
***************
*** 365,386 ****
  &lt;sign-form&gt; &nbsp;&nbsp;:= { + | - }
  &lt;e-char&gt; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;:= { D | d | E | e }
! </pre><pre><b><a name="102">: f# &nbsp;&nbsp;&nbsp;( &quot;fp no.&quot; -- ; fs: -- r ) &nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
! </a></b></pre><p>An attempt is made to convert the space delimited string following F# to internal
  floating-point representation. If the string represents a valid floating-point
! number in the syntax below, its value r and true are returned. If the string does not
  represent a valid floating-point number an error is thrown. <br />
  F# used at the end of a line is treated as a special case representing zero. <br />
  If interpreting the FP number is placed on the FP stack, while it is compiled as
! an Fliteral if compiling.
! </p><pre>The syntax of a convertible string := &lt;significand&gt;[&lt;exponent&gt;]
! 
! &lt;significand&gt; := [&lt;sign&gt;]{&lt;digits&gt;[.&lt;digits0&gt;] |
! .&lt;digits&gt; }
! &lt;exponent&gt; &nbsp;&nbsp;&nbsp;:= &lt;marker&gt;&lt;digits0&gt;
! &lt;marker&gt; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;:= {&lt;e-form&gt; | &lt;sign-form&gt;}
! &lt;e-form&gt; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;:= &lt;e-char&gt;[&lt;sign-form&gt;]
! &lt;sign-form&gt; &nbsp;&nbsp;:= { + | - }
! &lt;e-char&gt; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;:= { D | d | E | e }
! </pre><a name="Sec#18"></a>
  <h3>Output conversion
  </h3><pre><b><a name="103">: REPRESENT &nbsp;&nbsp;&nbsp;&nbsp;( addr u -- n flag1 flag2 ; fs: r -- ) &nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating
--- 365,379 ----
  &lt;sign-form&gt; &nbsp;&nbsp;:= { + | - }
  &lt;e-char&gt; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;:= { D | d | E | e }
! </pre><pre><b><a name="102">: f# &nbsp;&nbsp;&nbsp;( Interpretation: &quot;fp no.&quot; -- ; fs: -- r ) &nbsp;&nbsp;&nbsp;\ W32F &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating extra
! </a></b></pre><p><b>&nbsp;( Compilation: &quot;fp no.&quot; -- ; run-time: fs: -- r ) </b>
! </p><p>An attempt is made to convert the space delimited string following F# to internal
  floating-point representation. If the string represents a valid floating-point
! number in the syntax below, its value r is returned. If the string does not
  represent a valid floating-point number an error is thrown. <br />
  F# used at the end of a line is treated as a special case representing zero. <br />
  If interpreting the FP number is placed on the FP stack, while it is compiled as
! an Fliteral if compiling. <br />
! The syntax of a convertible string is the same as <b>&nbsp;&gt;FLOAT </b>.
! </p><a name="Sec#18"></a>
  <h3>Output conversion
  </h3><pre><b><a name="103">: REPRESENT &nbsp;&nbsp;&nbsp;&nbsp;( addr u -- n flag1 flag2 ; fs: r -- ) &nbsp;\ ANSI &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Floating