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<div class="section" id="mathematical-functions">
<h1>Mathematical Functions<a class="headerlink" href="#mathematical-functions" title="Permalink to this headline">¶</a></h1>
<p>In this chapter we are going to learn about the mathematical functions</p>
<div class="section" id="list-of-functions">
<h2>List of functions<a class="headerlink" href="#list-of-functions" title="Permalink to this headline">¶</a></h2>
<p>The Ring programming language comes with the next mathematical functions</p>
<table border="1" class="docutils">
<colgroup>
<col width="16%" />
<col width="84%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Function</th>
<th class="head">Description</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>sin(x)</td>
<td>Returns the sine of an angle of x radians</td>
</tr>
<tr class="row-odd"><td>cos(x)</td>
<td>Returns the cosine of an angle of x radians</td>
</tr>
<tr class="row-even"><td>tan(x)</td>
<td>Returns the tangent of an angle of x radians</td>
</tr>
<tr class="row-odd"><td>asin(x)</td>
<td>Returns the principal value of the arc sine of x, expressed in radians</td>
</tr>
<tr class="row-even"><td>acos(x)</td>
<td>Returns the principal value of the arc cosine of x, expressed in radians</td>
</tr>
<tr class="row-odd"><td>atan(x)</td>
<td>Returns the principal value of the arc tangent of x, expressed in radians</td>
</tr>
<tr class="row-even"><td>atan2(y,x)</td>
<td>Returns the principal arc tangent of y/x, in the interval [-pi,+pi] radians</td>
</tr>
<tr class="row-odd"><td>sinh(x)</td>
<td>Returns the hyperbolic sine of x radians</td>
</tr>
<tr class="row-even"><td>cosh(x)</td>
<td>Returns the hyperbolic cosine of x radians</td>
</tr>
<tr class="row-odd"><td>tanh(x)</td>
<td>Returns the hyperbolic tangent of x radians</td>
</tr>
<tr class="row-even"><td>exp(x)</td>
<td>Returns the value of e raised to the xth power</td>
</tr>
<tr class="row-odd"><td>log(x)</td>
<td>Returns the natural logarithm of x</td>
</tr>
<tr class="row-even"><td>log10(x)</td>
<td>Returns the common logarithm (base-10 logarithm) of x</td>
</tr>
<tr class="row-odd"><td>ceil(x)</td>
<td>Returns the smallest integer value greater than or equal to x</td>
</tr>
<tr class="row-even"><td>floor(x)</td>
<td>Returns the largest integer value less than or equal to x</td>
</tr>
<tr class="row-odd"><td>fabs(x)</td>
<td>Returns the absolute value of x.</td>
</tr>
<tr class="row-even"><td>pow(x,y)</td>
<td>Returns x raised to the power of y</td>
</tr>
<tr class="row-odd"><td>sqrt(x)</td>
<td>Returns the square root of x</td>
</tr>
<tr class="row-even"><td>random(x)</td>
<td>Returns a random number in the range [0,x]</td>
</tr>
<tr class="row-odd"><td>unsigned(n,n,c)</td>
<td>Perform operation using unsigned numbers</td>
</tr>
<tr class="row-even"><td>decimals(n)</td>
<td>Determine the decimals digits after the point in float/double numbers</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="example">
<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2>
<div class="highlight-none"><div class="highlight"><pre>See "Mathematical Functions" + nl
See "Sin(0) = " + sin(0) + nl
See "Sin(90) radians = " + sin(90) + nl
See "Sin(90) degree = " + sin(90*3.14/180) + nl
See "Cos(0) = " + cos(0) + nl
See "Cos(90) radians = " + cos(90) + nl
See "Cos(90) degree = " + cos(90*3.14/180) + nl
See "Tan(0) = " + tan(0) + nl
See "Tan(90) radians = " + tan(90) + nl
See "Tan(90) degree = " + tan(90*3.14/180) + nl
See "asin(0) = " + asin(0) + nl
See "acos(0) = " + acos(0) + nl
See "atan(0) = " + atan(0) + nl
See "atan2(1,1) = " + atan2(1,1) + nl
See "sinh(0) = " + sinh(0) + nl
See "sinh(1) = " + sinh(1) + nl
See "cosh(0) = " + cosh(0) + nl
See "cosh(1) = " + cosh(1) + nl
See "tanh(0) = " + tanh(0) + nl
See "tanh(1) = " + tanh(1) + nl
See "exp(0) = " + exp(0) + nl
See "exp(1) = " + exp(1) + nl
See "log(1) = " + log(1) + nl
See "log(2) = " + log(2) + nl
See "log10(1) = " + log10(1) + nl
See "log10(2) = " + log10(2) + nl
See "log10(10) = " + log10(10) + nl
See "Ceil(1.12) = " + Ceil(1.12) + nl
See "Ceil(1.72) = " + Ceil(1.72) + nl
See "Floor(1.12) = " + floor(1.12) + nl
See "Floor(1.72) = " + floor(1.72) + nl
See "fabs(1.12) = " + fabs(1.12) + nl
See "fabs(1.72) = " + fabs(1.72) + nl
See "pow(2,3) = " + pow(2,3) + nl
see "sqrt(16) = " + sqrt(16) + nl
</pre></div>
</div>
<p>Program Output:</p>
<div class="highlight-none"><div class="highlight"><pre>Mathematical Functions
Sin(0) = 0
Sin(90) radians = 0.89
Sin(90) degree = 1.00
Cos(0) = 1
Cos(90) radians = -0.45
Cos(90) degree = 0.00
Tan(0) = 0
Tan(90) radians = -2.00
Tan(90) degree = 1255.77
asin(0) = 0
acos(0) = 1.57
atan(0) = 0
atan2(1,1) = 0.79
sinh(0) = 0
sinh(1) = 1.18
cosh(0) = 1
cosh(1) = 1.54
tanh(0) = 0
tanh(1) = 0.76
exp(0) = 1
exp(1) = 2.72
log(1) = 0
log(2) = 0.69
log10(1) = 0
log10(2) = 0.30
log10(10) = 1
Ceil(1.12) = 2
Ceil(1.72) = 2
Floor(1.12) = 1
Floor(1.72) = 1
fabs(1.12) = 1.12
fabs(1.72) = 1.72
pow(2,3) = 8
sqrt(16) = 4
</pre></div>
</div>
</div>
<div class="section" id="random-function">
<h2>Random() Function<a class="headerlink" href="#random-function" title="Permalink to this headline">¶</a></h2>
<p>The Random() function generate a random number and we can set the maximum value (optional).</p>
<p>Syntax:</p>
<div class="highlight-none"><div class="highlight"><pre>Random(x) ---> Random number in the range [0,x]
</pre></div>
</div>
<p>Example:</p>
<div class="highlight-none"><div class="highlight"><pre>for x = 1 to 20
see "Random number : " + random() + nl +
"Random number Max (100) : " + random(100) + nl
next
</pre></div>
</div>
<p>Program Output:</p>
<div class="highlight-none"><div class="highlight"><pre>Random number : 31881
Random number Max (100) : 80
Random number : 5573
Random number Max (100) : 63
Random number : 2231
Random number Max (100) : 43
Random number : 12946
Random number Max (100) : 39
Random number : 22934
Random number Max (100) : 48
Random number : 4690
Random number Max (100) : 52
Random number : 13196
Random number Max (100) : 65
Random number : 30390
Random number Max (100) : 87
Random number : 4327
Random number Max (100) : 77
Random number : 12456
Random number Max (100) : 17
Random number : 28438
Random number Max (100) : 13
Random number : 30503
Random number Max (100) : 6
Random number : 31769
Random number Max (100) : 94
Random number : 8274
Random number Max (100) : 65
Random number : 14390
Random number Max (100) : 90
Random number : 28866
Random number Max (100) : 12
Random number : 24558
Random number Max (100) : 70
Random number : 29981
Random number Max (100) : 77
Random number : 12847
Random number Max (100) : 63
Random number : 6632
Random number Max (100) : 60
</pre></div>
</div>
</div>
<div class="section" id="unsigned-function">
<h2>Unsigned() Function<a class="headerlink" href="#unsigned-function" title="Permalink to this headline">¶</a></h2>
<p>We can use unsigned numbers using the Unsigned() function.</p>
<p>Syntax:</p>
<div class="highlight-none"><div class="highlight"><pre>Unsigned(nNum1,nNum2,cOperator) --> result of cOperator operation on nNum1,nNum2
</pre></div>
</div>
<p>Example:</p>
<div class="highlight-none"><div class="highlight"><pre>see oat_hash("hello") + nl
# Jenkins hash function - https://en.wikipedia.org/wiki/Jenkins_hash_function
func oat_hash cKey
h = 0
for x in cKey
h = unsigned(h,ascii(x),"+")
h = unsigned(h,unsigned(h,10,"<<"),"+")
r = unsigned(h,6,">>")
h = unsigned(h, r,"^")
next
h = unsigned(h,unsigned(h,3,"<<"),"+")
h = unsigned(h,unsigned(h,11,">>"),"^")
h = unsigned(h,unsigned(h,15,"<<"),"+")
return h
</pre></div>
</div>
<p>Output:</p>
<div class="highlight-none"><div class="highlight"><pre>3372029979.00
</pre></div>
</div>
</div>
<div class="section" id="decimals-functions">
<h2>Decimals() Functions<a class="headerlink" href="#decimals-functions" title="Permalink to this headline">¶</a></h2>
<p>We can determine the decimals numbers count after the point in float/double numbers using the decimals() function.</p>
<p>Syntax:</p>
<div class="highlight-none"><div class="highlight"><pre>Decimals(nDecimalsCount)
</pre></div>
</div>
<p>Example:</p>
<div class="highlight-none"><div class="highlight"><pre>x = 1.1234567890123
for d = 0 to 14
decimals(d)
see x + nl
next
</pre></div>
</div>
<p>Output:</p>
<div class="highlight-none"><div class="highlight"><pre>1
1.1
1.12
1.123
1.1235
1.12346
1.123457
1.1234568
1.12345679
1.123456789
1.1234567890
1.12345678901
1.123456789012
1.1234567890123
1.12345678901230
</pre></div>
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<ul>
<li><a class="reference internal" href="#">Mathematical Functions</a><ul>
<li><a class="reference internal" href="#list-of-functions">List of functions</a></li>
<li><a class="reference internal" href="#example">Example</a></li>
<li><a class="reference internal" href="#random-function">Random() Function</a></li>
<li><a class="reference internal" href="#unsigned-function">Unsigned() Function</a></li>
<li><a class="reference internal" href="#decimals-functions">Decimals() Functions</a></li>
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