Numeric error propagation: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #008080;">enum</span> <span style="color: #000000;">VALUE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DELTA</span> |
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type imprecise(object imp) |
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return sequence(imp) and atom(imp[VALUE]) and atom(imp[DELTA]) |
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<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> |
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end type |
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<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> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">type</span> |
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function sqr(atom a) |
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return a*a |
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<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> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function imprecise_add(imprecise a, b) |
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atom delta = sqrt(sqr(a[DELTA]) + sqr(b[DELTA])) |
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<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> |
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imprecise ret = {a[VALUE] + b[VALUE], delta} |
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<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> |
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return ret |
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<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> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function imprecise_mul(imprecise a, b) |
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atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA])) |
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<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> |
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imprecise ret = {a[VALUE] * b[VALUE],delta} |
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<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> |
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return ret |
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<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> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function imprecise_div(imprecise a, b) |
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atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA]))/sqr(b[VALUE]) |
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<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> |
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imprecise ret = {a[VALUE] / b[VALUE], delta} |
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<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> |
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return ret |
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<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> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function imprecise_pow(imprecise a, atom c) |
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atom v = power(a[VALUE], c), |
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<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> |
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delta = abs(v*c*a[DELTA]/a[VALUE]) |
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<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> |
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imprecise ret = {v,delta} |
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<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> |
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return ret |
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<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> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function printImprecise(imprecise imp) |
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return sprintf("%g+/-%g",imp) |
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<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> |
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end function |
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<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> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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imprecise x1 = {100, 1.1}, |
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y1 = {50, 1.2}, |
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<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> |
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x2 = {-200, 2.2}, |
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<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> |
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y2 = {-100, 2.3}, |
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<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> |
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tmp1, tmp2, |
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<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> |
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d |
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<span style="color: #000000;">tmp1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span> |
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<span style="color: #000000;">d</span> |
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tmp1 = imprecise_add(x1, x2) |
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tmp1 = imprecise_pow(tmp1, 2) |
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<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> |
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tmp2 = imprecise_add(y1, y2) |
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<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> |
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tmp2 = imprecise_pow(tmp2, 2) |
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<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> |
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d = imprecise_add(tmp1,tmp2) |
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<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> |
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d = imprecise_pow(d, 0.5) |
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<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> |
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printf(1,"Distance, d, between the following points :") |
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<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> |
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printf(1,"\n( x1, y1) = ( %s, %s)",{printImprecise(x1),printImprecise(y1)}) |
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<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> |
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printf(1,"\n( x2, y2) = ( %s, %s)",{printImprecise(x2),printImprecise(y2)}) |
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<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> |
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printf(1,"\nis d = %s\n", {printImprecise(d)})</lang> |
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<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> |
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<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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<!--</lang>--> |
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Aside: obviously you don't ''have'' to use tmp1/2 like that, but I find that style often makes things much easier to debug. |
Aside: obviously you don't ''have'' to use tmp1/2 like that, but I find that style often makes things much easier to debug. |
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{{out}} |
{{out}} |