Rosetta Code

Montgomery reduction: Difference between revisions

Page Discussion

Montgomery reduction (view source)

Revision as of 13:01, 10 June 2021

20,673 bytes added ,  2 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 1,019:
{{trans|D}}
{{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>
<span style="color: #008080;">enum</span> <span style="color: #000000;">BASE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">BITLEN</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MODULUS</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">RRM</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">mont</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: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BITLEN</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MODULUS</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<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: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">mpz_add</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;">m</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)>=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">mpz_sub</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;">m</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">Montgomery</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
enum BASE, BITLEN, MODULUS, RRM
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_sign</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: #008080;">then</span> <span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"must be positive"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">mpz_odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"must be odd"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
function reduce(sequence mont, mpz a)
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_sizeinbase</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
integer n = mont[BITLEN]
<span style="color: #004080;">mpz</span> <span style="color: #000000;">rrm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
mpz m = mont[MODULUS],
<span style="color: #7060A8;">mpz_powm_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rrm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rrm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
r = mpz_init_set(a)
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- BASE</span>
for i=1 to n do
<span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- BITLEN</span>
if mpz_odd(r) then
<span style="color: #000000;">m</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- MODULUS</span>
mpz_add(r,r,m)
<span style="color: #000000;">rrm</span> <span style="color: #000080;font-style:italic;">-- 1&lt;&lt;(n*2) % m</span>
end if
{} <span style="color: mpz_fdiv_q_ui(r,r,2)#0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
end for
if mpz_cmp(r,m)>=0 then mpz_sub(r,r,m) end if
<span style="color: #004080;">mpz</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"750791094644726559640638407699"</span><span style="color: #0000FF;">),</span>
return r
<span style="color: #000000;">x1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"540019781128412936473322405310"</span><span style="color: #0000FF;">),</span>
end function
<span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"515692107665463680305819378593"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
function Montgomery(mpz m)
<span style="color: #000000;">t2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
if mpz_sign(m)=-1 then crash("must be positive") end if
if not mpz_odd(m) then crash("must be odd") end if
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mont</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Montgomery</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
integer n = mpz_sizeinbase(m,2)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RRM</span><span style="color: #0000FF;">])</span>
mpz rrm = mpz_init(2)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RRM</span><span style="color: #0000FF;">])</span>
mpz_powm_ui(rrm,rrm,n*2,m)
<span style="color: #004080;">mpz</span> <span style="color: #000000;">r1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">),</span>
return {2, -- BASE
<span style="color: #000000;">r2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">),</span>
n, -- BITLEN
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
m, -- MODULUS
<span style="color: #7060A8;">mpz_ui_pow_ui</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;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BITLEN</span><span style="color: #0000FF;">])</span>
rrm -- 1<<(n*2) % m
}
<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;">"b : %d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BASE</span><span style="color: #0000FF;">]})</span>
end function
<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 : %d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BITLEN</span><span style="color: #0000FF;">]})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"r : %s\n"</span><span style="color: #0000FF;">,</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>
mpz m = mpz_init("750791094644726559640638407699"),
<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;">"m : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MODULUS</span><span style="color: #0000FF;">])})</span>
x1 = mpz_init("540019781128412936473322405310"),
<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;">"t1: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">)})</span>
x2 = mpz_init("515692107665463680305819378593"),
<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;">"t2: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">)})</span>
t1 = mpz_init(),
<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;">"r1: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r1</span><span style="color: #0000FF;">)})</span>
t2 = mpz_init()
<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;">"r2: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
sequence mont = Montgomery(m)
<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;">"Original x1 : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">)})</span>
mpz_mul(t1,x1,mont[RRM])
<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;">"Recovered from r1 : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r1</span><span style="color: #0000FF;">))})</span>
mpz_mul(t2,x2,mont[RRM])
<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;">"Original x2 : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)})</span>
mpz r1 = reduce(mont,t1),
<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;">"Recovered from r2 : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">))})</span>
r2 = reduce(mont,t2),
r = mpz_init()
<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;">"\nMontgomery computation of x1 ^ x2 mod m :"</span><span style="color: #0000FF;">)</span>
mpz_ui_pow_ui(r,2,mont[BITLEN])
<span style="color: #004080;">mpz</span> <span style="color: #000000;">prod</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RRM</span><span style="color: #0000FF;">])</span>
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">[</span><span style="color: #000000;">RRM</span><span style="color: #0000FF;">])</span>
printf(1,"b : %d\n", {mont[BASE]})
<span style="color: #004080;">mpz</span> <span style="color: #000000;">base</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span>
printf(1,"n : %d\n", {mont[BITLEN]})
<span style="color: #000000;">expn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
printf(1,"r : %s\n", {mpz_get_str(r)})
printf(1,"m : %s\n", {mpz_get_str(mont[MODULUS])})
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expn</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>
printf(1,"t1: %s\n", {mpz_get_str(t1)})
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expn</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
printf(1,"t2: %s\n", {mpz_get_str(t2)})
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
printf(1,"r1: %s\n", {mpz_get_str(r1)})
<span style="color: #000000;">prod</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">)</span>
printf(1,"r2: %s\n", {mpz_get_str(r2)})
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
printf(1,"\n")
<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;">expn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">expn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
printf(1,"Original x1 : %s\n", {mpz_get_str(x1)})
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">base</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
printf(1,"Recovered from r1 : %s\n", {mpz_get_str(reduce(mont,r1))})
<span style="color: #000000;">base</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
printf(1,"Original x2 : %s\n", {mpz_get_str(x2)})
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
printf(1,"Recovered from r2 : %s\n", {mpz_get_str(reduce(mont,r2))})
<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;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mont</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">))})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" alternate computation of x1 ^ x2 mod m :"</span><span style="color: #0000FF;">)</span>
printf(1,"\nMontgomery computation of x1 ^ x2 mod m :")
<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;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
mpz prod = reduce(mont,mont[RRM])
<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;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)})</span>
mpz_mul(r,x1,mont[RRM])
<!--</lang>-->
mpz base = reduce(mont,r),
expn = mpz_init_set(x2)
 
while mpz_cmp_si(expn,0)!=0 do
if mpz_odd(expn) then
mpz_mul(prod,prod,base)
prod = reduce(mont,prod)
end if
{} = mpz_fdiv_q_ui(expn,expn,2)
mpz_mul(base,base,base)
base = reduce(mont,base)
end while
printf(1,"%s\n",{mpz_get_str(reduce(mont,prod))})
printf(1," alternate computation of x1 ^ x2 mod m :")
mpz_powm(r,x1,x2,m)
printf(1,"%s\n",{mpz_get_str(r)})</lang>
{{out}}
<pre>
Petelomax
7,804

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/210451"