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RosettaCodeData/Task/Numeric-error-propagation/Phix/numeric-error-propagation.phix

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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">VALUE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DELTA</span>
<span style="color: #008080;">type</span> <span style="color: #000000;">imprecise</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">type</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))</span>
<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))</span>
<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]))/</span><span style="color: #000000;">sqr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DELTA</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">imprecise</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imprecise</span> <span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%g+/-%g"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imp</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000000;">imprecise</span> <span style="color: #000000;">x1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.1</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">y1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.2</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">200</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.2</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">y2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.3</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">d</span>
<span style="color: #000000;">tmp1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tmp1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tmp2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tmp2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imprecise_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</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;">"Distance, d, between the following points :"</span><span style="color: #0000FF;">)</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;">"\n( x1, y1) = ( %s, %s)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">)})</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;">"\n( x2, y2) = ( %s, %s)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">)})</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;">"\nis d = %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">printImprecise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)})</span>
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