Faulhaber's triangle: Difference between revisions
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m (→{{header|Phix}}: added syntax colouring, marked p2js compatible) |
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{trans|C#}} |
{{trans|C#}} |
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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;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #000000;">pfrac</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #000080;font-style:italic;">-- (0.8.0+)</span> |
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function bernoulli(integer n) |
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sequence a = {} |
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<span style="color: #008080;">function</span> <span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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for m=0 to n do |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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a = append(a,{1,m+1}) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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for j=m to 1 by -1 do |
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<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> |
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a[j] = frac_mul({j,1},frac_sub(a[j+1],a[j])) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">m</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">({</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span><span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]))</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if n!=1 then return a[1] end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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return frac_uminus(a[1]) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_uminus</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</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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function binomial(integer n, k) |
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if n<0 or k<0 or n<k then ?9/0 end if |
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<span style="color: #008080;">function</span> <span style="color: #000000;">binomial</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> |
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if n=0 or k=0 then return 1 end if |
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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atom num = 1, |
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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denom = 1 |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">num</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> |
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for i=k+1 to n do |
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<span style="color: #000000;">denom</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> |
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num *= i |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #000000;">num</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span> |
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for i=2 to n-k do |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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denom *= i |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #000000;">denom</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span> |
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return num / denom |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">num</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">denom</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function faulhaber_triangle(integer p, bool asString=true) |
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sequence coeffs = repeat(frac_zero,p+1) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">asString</span><span style="color: #0000FF;">=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span> |
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for j=0 to p do |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">coeffs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac_zero</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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frac coeff = frac_mul({binomial(p+1,j),p+1},bernoulli(j)) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">p</span> <span style="color: #008080;">do</span> |
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coeffs[p-j+1] = iff(asString?sprintf("%5s",{frac_sprint(coeff)}):coeff) |
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<span style="color: #000000;">frac</span> <span style="color: #000000;">coeff</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">({</span><span style="color: #000000;">binomial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">),</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span><span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">))</span> |
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end for |
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<span style="color: #000000;">coeffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</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;">asString</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%5s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">frac_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">coeff</span><span style="color: #0000FF;">)}):</span><span style="color: #000000;">coeff</span><span style="color: #0000FF;">)</span> |
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return coeffs |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">coeffs</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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for i=0 to 9 do |
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printf(1,"%s\n",{join(faulhaber_triangle(i)," ")}) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span> |
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end for |
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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;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)})</span> |
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puts(1,"\n") |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<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> |
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sequence row18 = faulhaber_triangle(17,false) |
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frac res = frac_zero |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span> |
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atom t1 = time()+1 |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">row18</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span> |
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integer lim = 1000 |
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<span style="color: #000000;">frac</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_zero</span> |
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for k=1 to lim do |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span> |
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bigatom nn = BA_ONE |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</span> |
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for i=1 to length(row18) do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
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res = frac_add(res,frac_mul(row18[i],{nn,1})) |
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<span style="color: #000000;">bigatom</span> <span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">BA_ONE</span> |
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nn = ba_mul(nn,lim) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row18</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row18</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],{</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}))</span> |
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if time()>t1 then printf(1,"calculating, k=%d...\r",k) t1 = time()+1 end if |
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<span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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printf(1,"%s \n",{frac_sprint(res)})</lang> |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</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;">"calculating, k=%d...\r"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"%s \n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">frac_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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</pre> |
</pre> |
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Note the extra credit takes about 90s, so I disabled it under pwa/p2js. |
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=={{header|Prolog}}== |
=={{header|Prolog}}== |