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Allegro Manual: Fixed point math routines
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<h1><a name="Fixed point math routines">Fixed point math routines</a></h1>
<ul>
<li><a href="#fixacos">fixacos</a> — Fixed point inverse cosine lookup table.
<li><a href="#fixadd">fixadd</a> — Safe function to add fixed point numbers clamping overflow.
<li><a href="#fixasin">fixasin</a> — Fixed point inverse sine lookup table.
<li><a href="#fixatan">fixatan</a> — Fixed point inverse tangent lookup table.
<li><a href="#fixatan2">fixatan2</a> — Fixed point version of the libc atan2() routine.
<li><a href="#fixceil">fixceil</a> — Returns the smallest integer not less than x.
<li><a href="#fixcos">fixcos</a> — Fixed point cosine of binary angles.
<li><a href="#fixdiv">fixdiv</a> — Fixed point division.
<li><a href="#fixfloor">fixfloor</a> — Returns the greatest integer not greater than x.
<li><a href="#fixhypot">fixhypot</a> — Fixed point hypotenuse.
<li><a href="#fixmul">fixmul</a> — Multiplies two fixed point values together.
<li><a href="#fixsin">fixsin</a> — Fixed point sine of binary angles.
<li><a href="#fixsqrt">fixsqrt</a> — Fixed point square root.
<li><a href="#fixsub">fixsub</a> — Safe function to subtract fixed point numbers clamping underflow.
<li><a href="#fixtan">fixtan</a> — Fixed point tangent of binary angles.
<li><a href="#fixtof">fixtof</a> — Converts a fixed point to floating point.
<li><a href="#fixtoi">fixtoi</a> — Converts a fixed point to integer with rounding.
<li><a href="#fixtorad_r">fixtorad_r</a> — Constant to convert angles in fixed point format to radians.
<li><a href="#ftofix">ftofix</a> — Converts a floating point value to fixed point.
<li><a href="#itofix">itofix</a> — Converts an integer to fixed point.
<li><a href="#radtofix_r">radtofix_r</a> — Constant to convert radians to fixed point angles.
</ul>
<p>
Allegro provides some routines for working with fixed point numbers, and
defines the type <tt>`fixed'</tt> to be a signed 32-bit integer. The high word is
used for the integer part and the low word for the fraction, giving a range
of -32768 to 32767 and an accuracy of about four or five decimal places.
Fixed point numbers can be assigned, compared, added, subtracted, negated and
shifted (for multiplying or dividing by powers of two) using the normal
integer operators, but you should take care to use the appropriate conversion
routines when mixing fixed point with integer or floating point values.
Writing `fixed_point_1 + fixed_point_2' is OK, but `fixed_point + integer' is
not.
<p>
Unfortunately the only advantage of fixed point math routines is that you
don't require a floating point coprocessor to use them. This was great in the
time period of i386 and i486 machines, but stopped being so useful with the
coming of the Pentium class of processors. From Pentium onwards, CPUs have
increased their strength in floating point operations, equaling or even
surpassing integer math performance.
<p>
Depending on the type of operations your program may need, using floating
point types may be faster than fixed types if you are targeting a specific
machine class. Allegro comes with a test program in the <tt>`allegro/tests'</tt>
directory. Its <tt>`Misc'</tt> menu contains a basic profile test which can give you
an idea of the speed difference between fixed and float types for a few basic
operations on your machine. However, don't forget to profile your program in
real life conditions, tight loop benchmarks are after all artificial.
<p>
Fixed point math is considered "add-on" material and is kept only for
backwards compatibility. Whenever a future release of Allegro breaks backwards
compatibility, fixed point math will likely be moved to a separate add-on
package for the very few users who still find it convenient and useful, and
Allegro functions using fixed point math will use other types.
<p><br>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="itofix">itofix</a>(int x);</b></div><br>
Converts an integer to fixed point. This is the same thing as x<<16.
Remember that overflows (trying to convert an integer greater than 32767)
and underflows (trying to convert an integer lesser than -32768) are not
detected even in debug builds! The values simply "wrap around". Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> number;
/* This conversion is OK. */
number = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100);
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(<a href="#fixtoi" class="autotype" title="Converts a fixed point to integer with rounding.">fixtoi</a>(number) == 100);
number = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(64000);
/* This check will fail in debug builds. */
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(<a href="#fixtoi" class="autotype" title="Converts a fixed point to integer with rounding.">fixtoi</a>(number) == 64000);</pre></blockquote>
<p><b>Return value:</b>
Returns the value of the integer converted to fixed point ignoring
overflows.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixtoi" title="Converts a fixed point to integer with rounding.">fixtoi</a>,
<a class="xref" href="#ftofix" title="Converts a floating point value to fixed point.">ftofix</a>,
<a class="xref" href="#fixtof" title="Converts a fixed point to floating point.">fixtof</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#ex12bit" title="How to fake a 12-bit truecolor mode on an 8-bit card.">ex12bit</a>,
<a class="eref" href="alleg045.html#ex3buf" title="Mode-X triple buffering and retrace interrupt simulation.">ex3buf</a>,
<a class="eref" href="alleg045.html#ex3d" title="3d 'bouncy cubes' demo.">ex3d</a>,
<a class="eref" href="alleg045.html#exblend" title="Using translucency in truecolor modes.">exblend</a>,
<a class="eref" href="alleg045.html#excustom" title="Creating custom GUI objects.">excustom</a>,
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>,
<a class="eref" href="alleg045.html#exlights" title="One way to do colored lighting effects in a hicolor video mode.">exlights</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exsprite" title="Datafiles access and sprite animation.">exsprite</a>,
<a class="eref" href="alleg045.html#exstars" title="3d starfield and lightsourced spaceship.">exstars</a>.</blockquote>
<div class="al-api"><b>int <a name="fixtoi">fixtoi</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
Converts fixed point to integer, rounding as required to the nearest
integer. Example:
<blockquote class="code"><pre>
int result;
/* This will put 33 into <tt>`result'</tt>. */
result = <a href="#fixtoi" class="autotype" title="Converts a fixed point to integer with rounding.">fixtoi</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 3);
/* But this will round up to 17. */
result = <a href="#fixtoi" class="autotype" title="Converts a fixed point to integer with rounding.">fixtoi</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 6);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#itofix" title="Converts an integer to fixed point.">itofix</a>,
<a class="xref" href="#ftofix" title="Converts a floating point value to fixed point.">ftofix</a>,
<a class="xref" href="#fixtof" title="Converts a fixed point to floating point.">fixtof</a>,
<a class="xref" href="#fixfloor" title="Returns the greatest integer not greater than x.">fixfloor</a>,
<a class="xref" href="#fixceil" title="Returns the smallest integer not less than x.">fixceil</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#ex12bit" title="How to fake a 12-bit truecolor mode on an 8-bit card.">ex12bit</a>,
<a class="eref" href="alleg045.html#ex3buf" title="Mode-X triple buffering and retrace interrupt simulation.">ex3buf</a>,
<a class="eref" href="alleg045.html#ex3d" title="3d 'bouncy cubes' demo.">ex3d</a>,
<a class="eref" href="alleg045.html#exblend" title="Using translucency in truecolor modes.">exblend</a>,
<a class="eref" href="alleg045.html#excustom" title="Creating custom GUI objects.">excustom</a>,
<a class="eref" href="alleg045.html#exlights" title="One way to do colored lighting effects in a hicolor video mode.">exlights</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exstars" title="3d starfield and lightsourced spaceship.">exstars</a>,
<a class="eref" href="alleg045.html#exupdate" title="Supporting different screen update methods in a single program.">exupdate</a>.</blockquote>
<div class="al-api"><b>int <a name="fixfloor">fixfloor</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
Returns the greatest integer not greater than x. That is, it rounds
towards negative infinity. Example:
<blockquote class="code"><pre>
int result;
/* This will put 33 into <tt>`result'</tt>. */
result = <a href="#fixfloor" class="autotype" title="Returns the greatest integer not greater than x.">fixfloor</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 3);
/* And this will round down to 16. */
result = <a href="#fixfloor" class="autotype" title="Returns the greatest integer not greater than x.">fixfloor</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 6);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixtoi" title="Converts a fixed point to integer with rounding.">fixtoi</a>,
<a class="xref" href="#fixceil" title="Returns the smallest integer not less than x.">fixceil</a>.</blockquote>
<div class="al-api"><b>int <a name="fixceil">fixceil</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
Returns the smallest integer not less than x. That is, it rounds towards
positive infinity. Example:
<blockquote class="code"><pre>
int result;
/* This will put 34 into <tt>`result'</tt>. */
result = <a href="#fixceil" class="autotype" title="Returns the smallest integer not less than x.">fixceil</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 3);
/* This will round up to 17. */
result = <a href="#fixceil" class="autotype" title="Returns the smallest integer not less than x.">fixceil</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 6);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixtoi" title="Converts a fixed point to integer with rounding.">fixtoi</a>,
<a class="xref" href="#fixfloor" title="Returns the greatest integer not greater than x.">fixfloor</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="ftofix">ftofix</a>(double x);</b></div><br>
Converts a floating point value to fixed point. Unlike itofix(), this
function clamps values which could overflow the type conversion, setting
<tt>`errno'</tt> to ERANGE in the process if this happens. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> number;
number = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-40000);
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(<a href="#fixfloor" class="autotype" title="Returns the greatest integer not greater than x.">fixfloor</a>(number) == -32768);
number = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(64000);
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(<a href="#fixfloor" class="autotype" title="Returns the greatest integer not greater than x.">fixfloor</a>(number) == 32767);
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno); /* This will fail. */</pre></blockquote>
<p><b>Return value:</b>
Returns the value of the floating point value converted to fixed point
clamping overflows (and setting <tt>`errno'</tt>).
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixtof" title="Converts a fixed point to floating point.">fixtof</a>,
<a class="xref" href="#itofix" title="Converts an integer to fixed point.">itofix</a>,
<a class="xref" href="#fixtoi" title="Converts a fixed point to integer with rounding.">fixtoi</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>,
<a class="eref" href="alleg045.html#exrotscl" title="Demonstrates rotate_scaled_sprite functions.">exrotscl</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exupdate" title="Supporting different screen update methods in a single program.">exupdate</a>.</blockquote>
<div class="al-api"><b>double <a name="fixtof">fixtof</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
Converts fixed point to floating point. Example:
<blockquote class="code"><pre>
float result;
/* This will put 33.33333 into <tt>`result'</tt>. */
result = <a href="#fixtof" class="autotype" title="Converts a fixed point to floating point.">fixtof</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 3);
/* This will put 16.66666 into <tt>`result'</tt>. */
result = <a href="#fixtof" class="autotype" title="Converts a fixed point to floating point.">fixtof</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100) / 6);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#ftofix" title="Converts a floating point value to fixed point.">ftofix</a>,
<a class="xref" href="#itofix" title="Converts an integer to fixed point.">itofix</a>,
<a class="xref" href="#fixtoi" title="Converts a fixed point to integer with rounding.">fixtoi</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exstars" title="3d starfield and lightsourced spaceship.">exstars</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixmul">fixmul</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y);</b></div><br>
A fixed point value can be multiplied or divided by an integer with the
normal `*' and <tt>`/'</tt> operators. To multiply two fixed point values, though,
you must use this function.
<p>
If an overflow occurs, <tt>`errno'</tt> will be set and the maximum possible value
will be returned, but <tt>`errno'</tt> is not cleared if the operation is
successful. This means that if you are going to test for overflow you
should set <tt>`errno=0'</tt> before calling fixmul(). Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* This will put 30000 into <tt>`result'</tt>. */
result = <a href="#fixmul" class="autotype" title="Multiplies two fixed point values together.">fixmul</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(10), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(3000));
/* But this overflows, and sets <tt>`errno'</tt>. */
result = <a href="#fixmul" class="autotype" title="Multiplies two fixed point values together.">fixmul</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(100), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(3000));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno);</pre></blockquote>
<p><b>Return value:</b>
Returns the clamped result of multiplying <tt>`x'</tt> by <tt>`y'</tt>, setting <tt>`errno'</tt> to
ERANGE if there was an overflow.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixadd" title="Safe function to add fixed point numbers clamping overflow.">fixadd</a>,
<a class="xref" href="#fixsub" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>,
<a class="xref" href="#fixdiv" title="Fixed point division.">fixdiv</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#ex3buf" title="Mode-X triple buffering and retrace interrupt simulation.">ex3buf</a>,
<a class="eref" href="alleg045.html#excustom" title="Creating custom GUI objects.">excustom</a>,
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exstars" title="3d starfield and lightsourced spaceship.">exstars</a>,
<a class="eref" href="alleg045.html#exupdate" title="Supporting different screen update methods in a single program.">exupdate</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixdiv">fixdiv</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y);</b></div><br>
A fixed point value can be divided by an integer with the normal <tt>`/'</tt>
operator. To divide two fixed point values, though, you must use this
function. If a division by zero occurs, <tt>`errno'</tt> will be set and the
maximum possible value will be returned, but <tt>`errno'</tt> is not cleared if the
operation is successful. This means that if you are going to test for
division by zero you should set <tt>`errno=0'</tt> before calling fixdiv(). Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* This will put 0.06060 <tt>`result'</tt>. */
result = <a href="#fixdiv" class="autotype" title="Fixed point division.">fixdiv</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(2), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(33));
/* This will put 0 into <tt>`result'</tt>. */
result = <a href="#fixdiv" class="autotype" title="Fixed point division.">fixdiv</a>(0, <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-30));
/* Sets <tt>`errno'</tt> and puts -32768 into <tt>`result'</tt>. */
result = <a href="#fixdiv" class="autotype" title="Fixed point division.">fixdiv</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-100), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(0));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno); /* This will fail. */</pre></blockquote>
<p><b>Return value:</b>
Returns the result of dividing <tt>`x'</tt> by <tt>`y'</tt>. If <tt>`y'</tt> is zero, returns the
maximum possible fixed point value and sets <tt>`errno'</tt> to ERANGE.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixadd" title="Safe function to add fixed point numbers clamping overflow.">fixadd</a>,
<a class="xref" href="#fixsub" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>,
<a class="xref" href="#fixmul" title="Multiplies two fixed point values together.">fixmul</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixadd">fixadd</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y);</b></div><br>
Although fixed point numbers can be added with the normal '+' integer
operator, that doesn't provide any protection against overflow. If overflow
is a problem, you should use this function instead. It is slower than using
integer operators, but if an overflow occurs it will set <tt>`errno'</tt> and clamp
the result, rather than just letting it wrap. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* This will put 5035 into <tt>`result'</tt>. */
result = <a href="#fixadd" class="autotype" title="Safe function to add fixed point numbers clamping overflow.">fixadd</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(5000), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(35));
/* Sets <tt>`errno'</tt> and puts -32768 into <tt>`result'</tt>. */
result = <a href="#fixadd" class="autotype" title="Safe function to add fixed point numbers clamping overflow.">fixadd</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-31000), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-3000));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno); /* This will fail. */</pre></blockquote>
<p><b>Return value:</b>
Returns the clamped result of adding <tt>`x'</tt> to <tt>`y'</tt>, setting <tt>`errno'</tt> to ERANGE
if there was an overflow.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixsub" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>,
<a class="xref" href="#fixmul" title="Multiplies two fixed point values together.">fixmul</a>,
<a class="xref" href="#fixdiv" title="Fixed point division.">fixdiv</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixsub">fixsub</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y);</b></div><br>
Although fixed point numbers can be subtracted with the normal '-' integer
operator, that doesn't provide any protection against overflow. If overflow
is a problem, you should use this function instead. It is slower than using
integer operators, but if an overflow occurs it will set <tt>`errno'</tt> and clamp
the result, rather than just letting it wrap. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* This will put 4965 into <tt>`result'</tt>. */
result = <a href="#fixsub" class="autotype" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(5000), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(35));
/* Sets <tt>`errno'</tt> and puts -32768 into <tt>`result'</tt>. */
result = <a href="#fixsub" class="autotype" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-31000), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(3000));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno); /* This will fail. */</pre></blockquote>
<p><b>Return value:</b>
Returns the clamped result of subtracting <tt>`y'</tt> from <tt>`x'</tt>, setting <tt>`errno'</tt> to
ERANGE if there was an overflow.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixadd" title="Safe function to add fixed point numbers clamping overflow.">fixadd</a>,
<a class="xref" href="#fixmul" title="Multiplies two fixed point values together.">fixmul</a>,
<a class="xref" href="#fixdiv" title="Fixed point division.">fixdiv</a>.</blockquote>
<br><center><h2><a name="Fixed point trig">Fixed point trig</a></h2></center><p>
The fixed point square root, sin, cos, tan, inverse sin, and inverse cos
functions are implemented using lookup tables, which are very fast but not
particularly accurate. At the moment the inverse tan uses an iterative
search on the tan table, so it is a lot slower than the others. Note that on
machines with very good floating point processors using these functions could
be slower in real life code due to cache misses: it may be faster to wait
a few extra cycles for a floating point sine result rather than wait for the
CPU to fetch the precalculated table from main memory. Always profile your
code.
<p>
Angles are represented in a binary format with 256 equal to a full circle,
64 being a right angle and so on. This has the advantage that a simple
bitwise 'and' can be used to keep the angle within the range zero to a full
circle, eliminating all those tiresome 'if (angle >= 360)' checks.
<p><br>
<div class="al-api"><b>extern const <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixtorad_r">fixtorad_r</a>;</b></div><br>
This constant gives a ratio which can be used to convert a fixed point
number in binary angle format to a fixed point number in radians. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> rad_angle, binary_angle;
/* Set the binary angle to 90 degrees. */
binary_angle = 64;
/* Now convert to radians (about 1.57). */
rad_angle = <a href="#fixmul" class="autotype" title="Multiplies two fixed point values together.">fixmul</a>(binary_angle, <a href="#fixtorad_r" class="autotype" title="Constant to convert angles in fixed point format to radians.">fixtorad_r</a>);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixmul" title="Multiplies two fixed point values together.">fixmul</a>,
<a class="xref" href="#radtofix_r" title="Constant to convert radians to fixed point angles.">radtofix_r</a>.</blockquote>
<div class="al-api"><b>extern const <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="radtofix_r">radtofix_r</a>;</b></div><br>
This constant gives a ratio which can be used to convert a fixed point
number in radians to a fixed point number in binary angle format. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> rad_angle, binary_angle;
...
binary_angle = <a href="#fixmul" class="autotype" title="Multiplies two fixed point values together.">fixmul</a>(rad_angle, <a href="#radtofix_r" class="autotype" title="Constant to convert radians to fixed point angles.">radtofix_r</a>);</pre></blockquote>
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#fixmul" title="Multiplies two fixed point values together.">fixmul</a>,
<a class="xref" href="#fixtorad_r" title="Constant to convert angles in fixed point format to radians.">fixtorad_r</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixsin">fixsin</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the sine of a value using a lookup table. The input
value must be a fixed point binary angle. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> angle;
int result;
/* Set the binary angle to 90 degrees. */
angle = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(64);
/* The sine of 90 degrees is one. */
result = <a href="#fixtoi" class="autotype" title="Converts a fixed point to integer with rounding.">fixtoi</a>(<a href="#fixsin" class="autotype" title="Fixed point sine of binary angles.">fixsin</a>(angle));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(result == 1);</pre></blockquote>
<p><b>Return value:</b>
Returns the sine of a fixed point binary format angle. The return value
will be in radians.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#ex12bit" title="How to fake a 12-bit truecolor mode on an 8-bit card.">ex12bit</a>,
<a class="eref" href="alleg045.html#ex3buf" title="Mode-X triple buffering and retrace interrupt simulation.">ex3buf</a>,
<a class="eref" href="alleg045.html#exblend" title="Using translucency in truecolor modes.">exblend</a>,
<a class="eref" href="alleg045.html#excustom" title="Creating custom GUI objects.">excustom</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exupdate" title="Supporting different screen update methods in a single program.">exupdate</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixcos">fixcos</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the cosine of a value using a lookup table. The input
value must be a fixed point binary angle. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> angle;
float result;
/* Set the binary angle to 45 degrees. */
angle = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(32);
/* The cosine of 45 degrees is about 0.7071. */
result = <a href="#fixtof" class="autotype" title="Converts a fixed point to floating point.">fixtof</a>(<a href="#fixcos" class="autotype" title="Fixed point cosine of binary angles.">fixcos</a>(angle));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(result > 0.7 && result < 0.71);</pre></blockquote>
<p><b>Return value:</b>
Returns the cosine of a fixed point binary format angle. The return value
will be in radians.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#ex12bit" title="How to fake a 12-bit truecolor mode on an 8-bit card.">ex12bit</a>,
<a class="eref" href="alleg045.html#ex3buf" title="Mode-X triple buffering and retrace interrupt simulation.">ex3buf</a>,
<a class="eref" href="alleg045.html#exblend" title="Using translucency in truecolor modes.">exblend</a>,
<a class="eref" href="alleg045.html#excustom" title="Creating custom GUI objects.">excustom</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>,
<a class="eref" href="alleg045.html#exupdate" title="Supporting different screen update methods in a single program.">exupdate</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixtan">fixtan</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the tangent of a value using a lookup table. The input
value must be a fixed point binary angle. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> angle, res_a, res_b;
float dif;
angle = <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(37);
/* Prove that tan(angle) == sin(angle) / cos(angle). */
res_a = <a href="#fixdiv" class="autotype" title="Fixed point division.">fixdiv</a>(<a href="#fixsin" class="autotype" title="Fixed point sine of binary angles.">fixsin</a>(angle), <a href="#fixcos" class="autotype" title="Fixed point cosine of binary angles.">fixcos</a>(angle));
res_b = <a href="#fixtan" class="autotype" title="Fixed point tangent of binary angles.">fixtan</a>(angle);
dif = <a href="#fixtof" class="autotype" title="Converts a fixed point to floating point.">fixtof</a>(<a href="#fixsub" class="autotype" title="Safe function to subtract fixed point numbers clamping underflow.">fixsub</a>(res_a, res_b));
<a href="alleg000.html#allegro_message" class="autotype" title="Used mainly to show error messages to users.">allegro_message</a>("Precision error: %f\n", dif);</pre></blockquote>
<p><b>Return value:</b>
Returns the tangent of a fixed point binary format angle. The return value
will be in radians.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixasin">fixasin</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the inverse sine of a value using a lookup table. The
input value must be a fixed point value. The inverse sine is defined only
in the domain from `-1' to <tt>`1'</tt>. Outside of this input range, the function
will set <tt>`errno'</tt> to EDOM and return zero. Example:
<blockquote class="code"><pre>
float angle;
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> val;
/* Sets <tt>`val'</tt> to a right binary angle (<tt>`64'</tt>). */
val = <a href="#fixasin" class="autotype" title="Fixed point inverse sine lookup table.">fixasin</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(1));
/* Sets <tt>`angle'</tt> to 0.2405. */
angle = <a href="#fixtof" class="autotype" title="Converts a fixed point to floating point.">fixtof</a>(<a href="#fixmul" class="autotype" title="Multiplies two fixed point values together.">fixmul</a>(<a href="#fixasin" class="autotype" title="Fixed point inverse sine lookup table.">fixasin</a>(<a href="#ftofix" class="autotype" title="Converts a floating point value to fixed point.">ftofix</a>(0.238)), <a href="#fixtorad_r" class="autotype" title="Constant to convert angles in fixed point format to radians.">fixtorad_r</a>));
/* This will trigger the assert. */
val = <a href="#fixasin" class="autotype" title="Fixed point inverse sine lookup table.">fixasin</a>(<a href="#ftofix" class="autotype" title="Converts a floating point value to fixed point.">ftofix</a>(-1.09));
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno);</pre></blockquote>
<p><b>Return value:</b>
Returns the inverse sine of a fixed point value, measured as fixed point
binary format angle, or zero if the input was out of the range. All return
values of this function will be in the range `-64' to <tt>`64'</tt>.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixacos">fixacos</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the inverse cosine of a value using a lookup table. The
input value must be a fixed point radian. The inverse cosine is defined
only in the domain from `-1' to <tt>`1'</tt>. Outside of this input range, the
function will set <tt>`errno'</tt> to EDOM and return zero. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* Sets <tt>`result'</tt> to binary angle 128. */
result = <a href="#fixacos" class="autotype" title="Fixed point inverse cosine lookup table.">fixacos</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-1));</pre></blockquote>
<p><b>Return value:</b>
Returns the inverse sine of a fixed point value, measured as fixed point
binary format angle, or zero if the input was out of range. All return
values of this function will be in the range <tt>`0'</tt> to <tt>`128'</tt>.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixatan">fixatan</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This function finds the inverse tangent of a value using a lookup table.
The input value must be a fixed point radian. The inverse tangent is the
value whose tangent is <tt>`x'</tt>. Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* Sets <tt>`result'</tt> to binary angle 13. */
result = <a href="#fixatan" class="autotype" title="Fixed point inverse tangent lookup table.">fixatan</a>(<a href="#ftofix" class="autotype" title="Converts a floating point value to fixed point.">ftofix</a>(0.326));</pre></blockquote>
<p><b>Return value:</b>
Returns the inverse tangent of a fixed point value, measured as a fixed
point binary format angle.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixatan2">fixatan2</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This is a fixed point version of the libc atan2() routine. It computes the
arc tangent of `y / x', but the signs of both arguments are used to
determine the quadrant of the result, and <tt>`x'</tt> is permitted to be zero. This
function is useful to convert Cartesian coordinates to polar coordinates.
Example:
<blockquote class="code"><pre>
<a href="alleg001.html#fixed" class="autotype" title="Fixed point integer to replace floats.">fixed</a> result;
/* Sets <tt>`result'</tt> to binary angle 64. */
result = <a href="#fixatan2" class="autotype" title="Fixed point version of the libc atan2() routine.">fixatan2</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(1), 0);
/* Sets <tt>`result'</tt> to binary angle -109. */
result = <a href="#fixatan2" class="autotype" title="Fixed point version of the libc atan2() routine.">fixatan2</a>(<a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-1), <a href="#itofix" class="autotype" title="Converts an integer to fixed point.">itofix</a>(-2));
/* Fails the assert. */
result = <a href="#fixatan2" class="autotype" title="Fixed point version of the libc atan2() routine.">fixatan2</a>(0, 0);
<a href="alleg044.html#ASSERT" class="autotype" title="Debugging helper macro to assert.">ASSERT</a>(!errno);</pre></blockquote>
<p><b>Return value:</b>
Returns the arc tangent of `y / x' in fixed point binary format angle,
from `-128' to <tt>`128'</tt>. If both <tt>`x'</tt> and <tt>`y'</tt> are zero, returns zero and sets
<tt>`errno'</tt> to EDOM.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#exlights" title="One way to do colored lighting effects in a hicolor video mode.">exlights</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixsqrt">fixsqrt</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x);</b></div><br>
This finds out the non negative square root of <tt>`x'</tt>. If <tt>`x'</tt> is negative,
<tt>`errno'</tt> is set to EDOM and the function returns zero.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<blockquote class="eref"><em><b>Examples using this:</b></em>
<a class="eref" href="alleg045.html#exfixed" title="Using fixed point maths.">exfixed</a>,
<a class="eref" href="alleg045.html#exlights" title="One way to do colored lighting effects in a hicolor video mode.">exlights</a>,
<a class="eref" href="alleg045.html#exspline" title="Constructing smooth movement paths from spline curves.">exspline</a>.</blockquote>
<div class="al-api"><b><a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> <a name="fixhypot">fixhypot</a>(<a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> x, <a class="autotype" href="alleg001.html#fixed" title="Fixed point integer to replace floats.">fixed</a> y);</b></div><br>
Fixed point hypotenuse (returns the square root of `x*x + y*y'). This
should be better than calculating the formula yourself manually, since
the error is much smaller.
<blockquote class="xref"><em><b>See also:</b></em>
<a class="xref" href="#Fixed point trig" title="">Fixed point trig</a>.</blockquote>
<br><center><h2><a name="Fix class">Fix class</a></h2></center><p>
If you are programming in C++ you can ignore all the above and use the fix
class instead, which overloads a lot of operators to provide automatic
conversion to and from integer and floating point values, and calls the
above routines as they are required. You should not mix the fix class with
the fixed typedef though, because the compiler will mistake the fixed values
for regular integers and insert unnecessary conversions. For example, if x
is an object of class fix, calling fixsqrt(x) will return the wrong result.
You should use the overloaded sqrt(x) or x.sqrt() instead.
<p>
On top of that, the Fix class may be slower than using directly the C
functions because of implicit internal conversions from one type to another
which you otherwise could avoid or minimise. Finally, this is the only bit
of C++ in the whole Allegro library, and the developers are certainly going
to move it into add-on space in the next version of Allegro which breaks
source backwards compatibility.
<p><br>
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