Roots of a function: Difference between revisions
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→{{header|Phix}}: added syntax colouring the hard way
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=={{header|Phix}}==
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<!--<lang Phix>-->
<span style="color: #008080;">procedure</span> <span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
-- Print approximate roots of f between x=start and x=stop, using ▼
<span style="color: #000080;font-style:italic;">--
-- sign changes as an indicator that a root has been encountered. ▼
▲ -- Print approximate roots of f between x=start and x=stop, using
▲ -- sign changes as an indicator that a root has been encountered.
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-----\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">stop</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">last_y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">last_y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">last_y</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Root found %s %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"at"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"near"</span><span style="color: #0000FF;">),</span><span style="color: #000000;">x</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">step</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
-- Smaller steps produce more accurate/precise results in general,▼
-- but for many functions we'll never get exact roots, either due▼
▲ <span style="color: #000080;font-style:italic;">-- Smaller steps produce more accurate/precise results in general,
-- to imperfect binary representation or irrational roots.▼
▲ -- but for many functions we'll never get exact roots, either due
▲ -- to imperfect binary representation or irrational roots.</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">step</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">256</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f1</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f4</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f4</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
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