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Cipolla's algorithm: Difference between revisions

Cipolla's algorithm (view source)

Revision as of 07:33, 11 June 2021

21,940 bytes added ,  3 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: added syntax colouring the hard way)
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{{trans|Kotlin}}
{{libheader|Phix/mpfr}}
<!--<lang Phix>include mpfr.e (phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
procedure legendre(mpz r, a, p)
-- Legendre symbol, returns 1, 0 or p - 1 (in r)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">legendre</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
mpz_sub_ui(r,p,1)
<span style="color: #000080;font-style:italic;">-- Legendre symbol, returns 1, 0 or p - 1 (in r)</span>
{} = mpz_fdiv_q_ui(r, r, 2)
<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</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>
mpz_powm(r,a,r,p)
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #7060A8;">mpz_powm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
procedure mul_point(sequence a, b, mpz omega2, p)
-- (modifies a)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">mul_point</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</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;">mpz</span> <span style="color: #000000;">omega2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
mpz {xa,ya} = a,
<span style="color: #000080;font-style:italic;">-- (modifies a)</span>
{xb,yb} = b,
<span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">xa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ya</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span>
xaxb = mpz_init(),
<span style="color: #0000FF;">{</span><span style="color: #000000;">xb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yb</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span>
yayb = mpz_init(),
<span style="color: #000000;">xaxb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
xayb = mpz_init(),
<span style="color: #000000;">yayb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
xbya = mpz_init()
<span style="color: #000000;">xayb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
mpz_mul(xaxb,xa,xb)
<span style="color: #000000;">xbya</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
mpz_mul(yayb,ya,yb)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xb</span><span style="color: #0000FF;">)</span>
mpz_mul(xayb,xa,yb)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ya</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yb</span><span style="color: #0000FF;">)</span>
mpz_mul(xbya,xb,ya)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yb</span><span style="color: #0000FF;">)</span>
mpz_mul(yayb,yayb,omega2)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xbya</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ya</span><span style="color: #0000FF;">)</span>
mpz_add(xaxb,xaxb,yayb)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">omega2</span><span style="color: #0000FF;">)</span>
mpz_mod(xa,xaxb,p) -- xa := mod(xaxb+yayb*omega2,p)
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">)</span>
mpz_add(xayb,xayb,xbya)
<span style="color: #7060A8;">mpz_mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- xa := mod(xaxb+yayb*omega2,p)</span>
mpz_mod(ya,xayb,p) -- ya := mod(xayb+xbya,p)
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xbya</span><span style="color: #0000FF;">)</span>
{xaxb,yayb,xayb,xbya} = mpz_clear({xaxb,yayb,xayb,xbya})
<span style="color: #7060A8;">mpz_mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ya</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- ya := mod(xayb+xbya,p)</span>
end procedure
<span style="color: #0000FF;">{</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xbya</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">xaxb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xayb</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xbya</span><span style="color: #0000FF;">})</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
function cipolla(object no, po)
mpz n = mpz_init(no),
<span style="color: #008080;">function</span> <span style="color: #000000;">cipolla</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">no</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">po</span><span style="color: #0000FF;">)</span>
p = mpz_init(po),
<span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">no</span><span style="color: #0000FF;">),</span>
t = mpz_init()
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">po</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
-- Step 0, validate arguments
legendre(t,n,p)
<span style="color: #000080;font-style:italic;">-- Step 0, validate arguments</span>
if mpz_cmp_si(t,1)!=0 then return {"0","0","false"} end if
<span style="color: #000000;">legendre</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</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;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"false"</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- Step 1, find a, omega2
integer a = 0
<span style="color: #000080;font-style:italic;">-- Step 1, find a, omega2</span>
mpz omega2 = mpz_init(),
<span style="color: #004080;">integer</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
pm1 = mpz_init()
<span style="color: #004080;">mpz</span> <span style="color: #000000;">omega2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
mpz_sub_ui(pm1,p,1)
<span style="color: #000000;">pm1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
while true do
<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pm1</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>
mpz_sub(t,p,n)
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
mpz_add_ui(t,t,a*a)
<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;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
mpz_mod(omega2,t,p)
<span style="color: #7060A8;">mpz_add_ui</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;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
legendre(t,omega2,p)
<span style="color: #7060A8;">mpz_mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">omega2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
if mpz_cmp(t,pm1)=0 then exit end if
<span style="color: #000000;">legendre</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">omega2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
a += 1
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pm1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #000000;">a</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
-- Step 2, compute power
sequence r = {mpz_init(1),mpz_init(0)},
<span style="color: #000080;font-style:italic;">-- Step 2, compute power</span>
s = {mpz_init(a),mpz_init(1)}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</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: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)},</span>
mpz nn = mpz_init()
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><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>
mpz_add_ui(nn,p,1)
<span style="color: #004080;">mpz</span> <span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
{} = mpz_fdiv_q_ui(nn, nn, 2)
<span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</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>
mpz_mod(nn,nn,p)
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
while mpz_cmp_si(nn,0)>0 do
<span style="color: #7060A8;">mpz_mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
if mpz_fdiv_ui(nn,2)=1 then
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
mul_point(r,s,omega2,p)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_fdiv_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
end if
<span style="color: #000000;">mul_point</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">omega2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
mul_point(s,s,omega2,p)
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
{} = mpz_fdiv_q_ui(nn, nn, 2)
<span style="color: #000000;">mul_point</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">omega2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
-- Step 3, check x in Fp
if mpz_cmp_si(r[2],0)!=0 then return {"0","0","false"} end if
<span style="color: #000080;font-style:italic;">-- Step 3, check x in Fp</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">0</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: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"false"</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- Step 5, check x * x = n
mpz_powm_ui(t,r[1],2,p)
<span style="color: #000080;font-style:italic;">-- Step 5, check x * x = n</span>
if mpz_cmp(t,n)!=0 then return {"0","0","false"} end if
<span style="color: #7060A8;">mpz_powm_ui</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: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</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: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"false"</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- Step 4, solutions
mpz_sub(p,p,r[1])
<span style="color: #000080;font-style:italic;">-- Step 4, solutions</span>
return {mpz_get_str(r[1]), mpz_get_str(p), "true"}
<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
end function
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]),</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">),</span> <span style="color: #008000;">"true"</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
constant tests = {{10,13},
{56,101},
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">},</span>
{8218,10007},
<span style="color: #0000FF;">{</span><span style="color: #000000;">56</span><span style="color: #0000FF;">,</span><span style="color: #000000;">101</span><span style="color: #0000FF;">},</span>
{8219,10007},
<span style="color: #0000FF;">{</span><span style="color: #000000;">8218</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10007</span><span style="color: #0000FF;">},</span>
{331575,1000003},
<span style="color: #0000FF;">{</span><span style="color: #000000;">8219</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10007</span><span style="color: #0000FF;">},</span>
{665165880,1000000007},
<span style="color: #0000FF;">{</span><span style="color: #000000;">331575</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000003</span><span style="color: #0000FF;">},</span>
{"881398088036","1000000000039"},
<span style="color: #0000FF;">{</span><span style="color: #000000;">665165880</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000000007</span><span style="color: #0000FF;">},</span>
{"34035243914635549601583369544560650254325084643201",
<span style="color: #0000FF;">{</span><span style="color: #008000;">"881398088036"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1000000000039"</span><span style="color: #0000FF;">},</span>
"100000000000000000000000000000000000000000000000151"}}
<span style="color: #0000FF;">{</span><span style="color: #008000;">"34035243914635549601583369544560650254325084643201"</span><span style="color: #0000FF;">,</span>
 
<span style="color: #008000;">"100000000000000000000000000000000000000000000000151"</span><span style="color: #0000FF;">}}</span>
for i=1 to length(tests) do
object {n,p} = tests[i]
<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;">tests</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
?{n,p,cipolla(n,p)}
<span style="color: #004080;">object</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
end for</lang>
<span style="color: #0000FF;">?{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cipolla</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</lang>-->
Obviously were you to use that in anger, you would probably rip out a few mpz_get_str() and return NULL/false rather than "0"/"false", etc.
{{out}}
Petelomax
7,820

edits

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