Isqrt (integer square root) of X: Difference between revisions

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=={{header|Phix}}==
=={{header|Phix}}==
See also [[Integer_roots#Phix]] for a simpler and shorter example using the mpz_root() routine, or better yet just use mpz_root() directly (that is, rather than the isqrt() below).
See also [[Integer_roots#Phix]] for a simpler and shorter example using the mpz_root() routine, or better yet just use mpz_root() directly (that is, rather than the isqrt() below).
<lang Phix>include mpfr.e
<!--<lang Phix>(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>
function isqrt(mpz x)
if mpz_cmp_si(x,0)<0 then
<span style="color: #008080;">function</span> <span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
crash("Argument cannot be negative.")
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</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>
end if
<span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Argument cannot be negative."</span><span style="color: #0000FF;">)</span>
mpz q = mpz_init(1),
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
r = mpz_init(0),
<span style="color: #004080;">mpz</span> <span style="color: #000000;">q</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>
t = mpz_init(),
<span style="color: #000000;">r</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>
z = mpz_init_set(x)
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
while mpz_cmp(q,x)<= 0 do
<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
mpz_mul_si(q,q,4)
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)<=</span> <span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
end while
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
while mpz_cmp_si(q,1)>0 do
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
assert(mpz_fdiv_q_ui(q, q, 4)=0)
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</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>
mpz_sub(t,z,r)
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
mpz_sub(t,t,q)
<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;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
assert(mpz_fdiv_q_ui(r, r, 2)=0)
<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;">q</span><span style="color: #0000FF;">)</span>
if mpz_cmp_si(t,0) >= 0 then
<span style="color: #7060A8;">assert</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: #000000;">0</span><span style="color: #0000FF;">)</span>
mpz_set(z,t)
<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;">0</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">>=</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
mpz_add(r,r,q)
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
end if
<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;">q</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
string star = iff(mpz_cmp_si(z,0)=0?"*":" ")
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return shorten(mpz_get_str(r,10,true))&star
<span style="color: #004080;">string</span> <span style="color: #000000;">star</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</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: #0000FF;">?</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">return</span> <span style="color: #7060A8;">shorten</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;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">))&</span><span style="color: #000000;">star</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
printf(1,"The integer square roots of integers from 0 to 65 are:\n")
for i=0 to 65 do
<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;">"The integer square roots of integers from 0 to 65 are:\n"</span><span style="color: #0000FF;">)</span>
printf(1,"%s ", {trim(isqrt(mpz_init(i)))})
<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;">65</span> <span style="color: #008080;">do</span>
end for
<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 "</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">trim</span><span style="color: #0000FF;">(</span><span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)))})</span>
printf(1,"\n\npower 7 ^ power integer square root\n")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"----- --------------------------------------------------------- ----------------------------------------------------------\n")
<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\npower 7 ^ power integer square root\n"</span><span style="color: #0000FF;">)</span>
mpz pow7 = mpz_init(7)
<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>
for i=1 to 9000 do
<span style="color: #004080;">mpz</span> <span style="color: #000000;">pow7</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)</span>
if (i<=73 and remainder(i,2)=1)
<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;">9000</span> <span style="color: #008080;">do</span>
or (i<100 and remainder(i,10)=5)
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">73</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</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: #0000FF;">)</span>
or (i<1000 and remainder(i,100)=0)
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">100</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
or remainder(i,1000)=0 then
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1000</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
printf(1,"%4d %58s %61s\n", {i, shorten(mpz_get_str(pow7,10,true)),isqrt(pow7)})
<span style="color: #008080;">or</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
end if
<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;">"%4d %58s %61s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">)})</span>
mpz_mul_si(pow7,pow7,7)
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
⚫
end for</lang>
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
⚫
<!--</lang>-->
{{out}}
{{out}}
Perfect squares are denoted with an asterisk.
Perfect squares are denoted with an asterisk.
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