Isqrt (integer square root) of X: Difference between revisions
Isqrt (integer square root) of X (view source)
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Line 1,795:
isqrt(7^10) = 16807
isqrt(7^11) = 44467</pre>
=={{header|Craft Basic}}==
<syntaxhighlight lang="basic">alert "integer square root of first 65 numbers:"
for n = 1 to 65
let x = n
gosub isqrt
print r
next n
alert "integer square root of odd powers of 7"
cls
cursor 1, 1
for n = 1 to 21 step 2
let x = 7 ^ n
gosub isqrt
print "isqrt of 7 ^ ", n, " = ", r
next n
end
sub isqrt
let q = 1
do
if q <= x then
let q = q * 4
endif
wait
loop q <= x
let r = 0
do
if q > 1 then
let q = q / 4
let t = x - r - q
let r = r / 2
if t >= 0 then
let x = t
let r = r + q
endif
endif
loop q > 1
let r = int(r)
return</syntaxhighlight>
{{out| Output}}<pre>integer square root of first 65 numbers:
1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8
integer square root of odd powers of 7:
isqrt of 7 ^ 1 = 2
isqrt of 7 ^ 3 = 18
isqrt of 7 ^ 5 = 129
isqrt of 7 ^ 7 = 907
isqrt of 7 ^ 9 = 6352</pre>
=={{header|D}}==
Line 1,986 ⟶ 2,061:
isqrt(7^ 9) = 6352
isqrt(7^10) = 16807</pre>
=={{header|EasyLang}}==
{{trans|Lua}}
<syntaxhighlight lang=easylang>
func isqrt x .
q = 1
while q <= x
q *= 4
.
while q > 1
q = q div 4
t = x - r - q
r = r div 2
if t >= 0
x = t
r = r + q
.
.
return r
.
print "Integer square roots from 0 to 65:"
for n = 0 to 65
write isqrt n & " "
.
print ""
print ""
print "Integer square roots of 7^n"
p = 7
n = 1
while n <= 21
print n & " " & isqrt p
n = n + 2
p = p * 49
.
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
Line 2,236 ⟶ 2,347:
T = 0
DO WHILE (Q .
Q = Q * 4
END DO
Line 2,328 ⟶ 2,439:
43 | 2,183,814,375,991,796,599,109,312,252,753,832,343 | 1,477,773,452,188,053,281
</pre>
=={{header|FreeBASIC}}==
Line 3,342 ⟶ 3,452:
print #f
function IntSqrt(x as decimal) {
do q*=4 : until (q>x)
while q>1
Line 5,508 ⟶ 5,618:
rot over + ]
again ]
nip swap ] is sqrt
( sqrt+ returns the integer square root and remainder )
( i.e. isqrt+ of 28 is 5 remainder 3 as (5^2)+3 = 28 )
( To make it task compliant change the last line to )
( "nip nip ] is sqrt
66 times [ i^ sqrt+ drop echo sp ] cr cr
73 times
[ 7 i^ 1+ ** sqrt+ drop
number$ +commas 41 justify
echo$ cr
Line 6,208 ⟶ 6,318:
73 49,221,735,352,184,872,959,961,855,190,338,177,606,846,542,622,561,400,857,262,407 7,015,820,362,023,593,956,150,476,655,802</pre>
=={{header|
<syntaxhighlight lang="setl">program isqrt;
loop for i in [1..65] do
putchar(lpad(str isqrt(i), 5));
if i mod 13=0 then print(); end if;
end loop;
print();
loop for p in [1, 3..73] do
sqrtp := isqrt(7 ** p);
print("sqrt(7^" + lpad(str p,2) + ") = " + lpad(str sqrtp, 32));
end loop;
proc isqrt(x);
q := 1;
loop while q<=x do
q *:= 4;
end loop;
z := x;
r := 0;
loop while q>1 do
q div:= 4;
t := z-r-q;
r div:= 2;
if t>=0 then
z := t;
r +:= q;
end if;
end loop;
return r;
end proc;
end program;</syntaxhighlight>
{{out}}
<pre> 1 1 1 2 2 2 2 2 3 3 3 3 3
3 3 4 4 4 4 4 4 4 4 4 5 5
5 5 5 5 5 5 5 5 5 6 6 6 6
6 6 6 6 6 6 6 6 6 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 8 8
sqrt(7^ 1) = 2
sqrt(7^ 3) = 18
sqrt(7^ 5) = 129
sqrt(7^ 7) = 907
sqrt(7^ 9) = 6352
sqrt(7^11) = 44467
sqrt(7^13) = 311269
sqrt(7^15) = 2178889
sqrt(7^17) = 15252229
sqrt(7^19) = 106765608
sqrt(7^21) = 747359260
sqrt(7^23) = 5231514822
sqrt(7^25) = 36620603758
sqrt(7^27) = 256344226312
sqrt(7^29) = 1794409584184
sqrt(7^31) = 12560867089291
sqrt(7^33) = 87926069625040
sqrt(7^35) = 615482487375282
sqrt(7^37) = 4308377411626977
sqrt(7^39) = 30158641881388842
sqrt(7^41) = 211110493169721897
sqrt(7^43) = 1477773452188053281
sqrt(7^45) = 10344414165316372973
sqrt(7^47) = 72410899157214610812
sqrt(7^49) = 506876294100502275687
sqrt(7^51) = 3548134058703515929815
sqrt(7^53) = 24836938410924611508707
sqrt(7^55) = 173858568876472280560953
sqrt(7^57) = 1217009982135305963926677
sqrt(7^59) = 8519069874947141747486745
sqrt(7^61) = 59633489124629992232407216
sqrt(7^63) = 417434423872409945626850517
sqrt(7^65) = 2922040967106869619387953625
sqrt(7^67) = 20454286769748087335715675381
sqrt(7^69) = 143180007388236611350009727669
sqrt(7^71) = 1002260051717656279450068093686
sqrt(7^73) = 7015820362023593956150476655802</pre>
=={{header|Seed7}}==
Seed7 has integer [https://seed7.sourceforge.net/libraries/integer.htm#sqrt(in_integer) sqrt()] and bigInteger [https://seed7.sourceforge.net/libraries/bigint.htm#sqrt(in_var_bigInteger) sqrt()] functions.
These functions could be used if an integer square root is needed.
But this task does not allow using the language's built-in sqrt() function.
Instead the ''quadratic residue'' algorithm for finding the integer square root must be used.
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
include "bigint.s7i";
Line 6,224 ⟶ 6,413:
stri := stri[.. index] & "," & stri[succ(index) ..];
end for;
end func;
const func bigInteger: isqrt (in bigInteger: x) is func
result
var bigInteger: r is 0_;
local
var bigInteger: q is 1_;
var bigInteger: z is 0_;
var bigInteger: t is 0_;
begin
while q <= x do
q *:= 4_;
end while;
z := x;
while q > 1_ do
q := q mdiv 4_;
t := z - r - q;
r := r mdiv 2_;
if t >= 0_ then
z := t;
r +:= q;
end if;
end while;
end func;
Line 6,233 ⟶ 6,445:
writeln("The integer square roots of integers from 0 to 65 are:");
for number range 0 to 65 do
write(
end for;
writeln("\n\nThe integer square roots of powers of 7 from 7**1 up to 7**73 are:");
Line 6,239 ⟶ 6,451:
writeln("----- --------------------------------------------------------------------------------- -----------------------------------------");
for number range 1 to 73 step 2 do
writeln(number lpad 2 <& commatize(pow7) lpad 85 <& commatize(
pow7 *:=
end for;
end func;</syntaxhighlight>
Line 6,911 ⟶ 7,123:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var isqrt = Fn.new { |x|
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