Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,64 +1,62 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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with javascript_semantics
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<span style="color: #008080;">include</span> <span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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include mpfr.e
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">fun</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</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: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- {a,b} = {b,c*b+a} (and t gets trashed)</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</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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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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procedure fun(mpz a,b,t, integer c)
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-- {a,b} = {b,c*b+a} (and t gets trashed)
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mpz_set(t,a)
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mpz_set(a,b)
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mpz_mul_si(b,b,c)
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mpz_add(b,b,t)
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end procedure
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<span style="color: #008080;">function</span> <span style="color: #000000;">SolvePell</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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<span style="color: #004080;">integer</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span>
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">e1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">e2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">f1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">f2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</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;">n</span> <span style="color: #008080;">then</span>
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<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">y</span>
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<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">fun</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {e1,e2} = {e2,r*e2+e1}</span>
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<span style="color: #000000;">fun</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {f1,f2} = {f2,r*r2+f1}</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f2</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e2</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">fun</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {b,a} = {f2,x*f2+e2}</span>
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t = a^2-n*b^2</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</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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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function SolvePell(integer n)
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integer x = floor(sqrt(n)), y = x, z = 1, r = x*2
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mpz e1 = mpz_init(1), e2 = mpz_init(),
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f1 = mpz_init(), f2 = mpz_init(1),
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t = mpz_init(0), u = mpz_init(),
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a = mpz_init(1), b = mpz_init(0)
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if x*x!=n then
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while mpz_cmp_si(t,1)!=0 do
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y = r*z - y
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z = floor((n-y*y)/z)
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r = floor((x+y)/z)
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fun(e1,e2,t,r) -- {e1,e2} = {e2,r*e2+e1}
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fun(f1,f2,t,r) -- {f1,f2} = {f2,r*r2+f1}
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mpz_set(a,f2)
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mpz_set(b,e2)
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fun(b,a,t,x) -- {b,a} = {f2,x*f2+e2}
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mpz_mul(t,a,a)
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mpz_mul_si(u,b,n)
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mpz_mul(u,u,b)
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mpz_sub(t,t,u) -- t = a^2-n*b^2
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end while
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end if
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return {a, b}
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">split_into_chunks</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">one</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rest</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">one</span><span style="color: #0000FF;">]}</span>
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<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;">one</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rest</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
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<span style="color: #000000;">l</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">k</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">29</span><span style="color: #0000FF;">))&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</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 split_into_chunks(string x, integer one, rest)
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sequence res = {x[1..one]}
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x = x[one+1..$]
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integer l = length(x)
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while l do
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integer k = min(l,rest)
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res = append(res,x[1..k])
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x = x[k+1..$]
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l -= k
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end while
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return join(res,"\n"&repeat(' ',29))&"\n"&repeat(' ',17)
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end function
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">109</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">181</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">277</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8941</span><span style="color: #0000FF;">}</span>
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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;">ns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
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<span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">SolvePell</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">xs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">ys</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">)></span><span style="color: #000000;">97</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">xs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">split_into_chunks</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">98</span><span style="color: #0000FF;">,</span><span style="color: #000000;">96</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">ys</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">split_into_chunks</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ys</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">,</span><span style="color: #000000;">96</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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<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;">"x^2 - %3d*y^2 = 1 for x = %27s and y = %25s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">xs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ys</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<!--
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sequence ns = {4, 61, 109, 181, 277, 8941}
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for i=1 to length(ns) do
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integer n = ns[i]
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mpz {x, y} = SolvePell(n)
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string xs = mpz_get_str(x,comma_fill:=true),
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ys = mpz_get_str(y,comma_fill:=true)
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if length(xs)>97 then
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xs = split_into_chunks(xs,98,96)
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ys = split_into_chunks(ys,99,96)
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end if
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printf(1,"x^2 - %3d*y^2 = 1 for x = %27s and y = %25s\n", {n, xs, ys})
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end for
|
||||
|
|
|
|||
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Reference in a new issue