Isqrt (integer square root) of X: Difference between revisions
Isqrt (integer square root) of X (view source)
Revision as of 12:06, 11 December 2023
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Line 440:
71| 1,004,525,211,269,079,039,999,221,534,496,697,502,180,541,686,174,722,466,474,743| 1,002,260,051,717,656,279,450,068,093,686
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|ALGOL W}}==
Algol W integers are restricted to signed 32-bit, so only the roots of the powers of 7 up to 7^9 are shown (7^11 will fit in 32-bits but the smallest power of 4 higher than 7^11 will overflow).
<syntaxhighlight lang="algolw">
begin % Integer square roots by quadratic residue %
% returns the integer square root of x - x must be >= 0 %
integer procedure iSqrt ( integer value x ) ;
if x < 0 then begin assert x >= 0; 0 end
else if x < 2 then x
else begin
% x is greater than 1 %
integer q, r, t, z;
% find a power of 4 that's greater than x %
q := 1;
while q <= x do q := q * 4;
% find the root %
z := x;
r := 0;
while q > 1 do begin
q := q div 4;
t := z - r - q;
r := r div 2;
if t >= 0 then begin
z := t;
r := r + q
end if_t_ge_0
end while_q_gt_1 ;
r
end isqrt;
% writes n in 14 character positions with separator commas %
procedure writeonWithCommas ( integer value n ) ;
begin
string(10) decDigits;
string(14) r;
integer v, cPos, dCount;
decDigits := "0123456789";
v := abs n;
r := " ";
r( 13 // 1 ) := decDigits( v rem 10 // 1 );
v := v div 10;
cPos := 12;
dCount := 1;
while cPos > 0 and v > 0 do begin
r( cPos // 1 ) := decDigits( v rem 10 // 1 );
v := v div 10;
cPos := cPos - 1;
dCount := dCount + 1;
if v not = 0 and dCount = 3 then begin
r( cPos // 1 ) := ",";
cPos := cPos - 1;
dCount := 0
end if_v_ne_0_and_dCount_eq_3
end for_cPos;
r( cPos // 1 ) := if n < 0 then "-" else " ";
writeon( s_w := 0, r )
end writeonWithCommas ;
begin % task test cases %
integer prevI, prevR, root, p7;
write( "Integer square roots of 0..65 (values the same as the previous one not shown):" );
write();
prevR := prevI := -1;
for i := 0 until 65 do begin
root := iSqrt( i );
if root not = prevR then begin
prevR := root;
prevI := i;
writeon( i_w := 1, s_w := 0, " ", i, ":", root )
end
else if prevI = i - 1 then writeon( "..." );
end for_i ;
write();
% integer square roots of odd powers of 7 %
write( "Integer square roots of 7^n, odd n" );
write( " n| 7^n| isqrt(7^n)" );
write( " -+--------------+--------------" );
p7 := 7;
for p := 1 step 2 until 9 do begin
write( i_w := 2, s_w := 0, p );
writeon( s_w := 0, "|" ); writeonWithCommas( p7 );
writeon( s_w := 0, "|" ); writeonWithCommas( iSqrt( p7 ) );
p7 := p7 * 49
end for_p
end task_test_cases
end.
</syntaxhighlight>
{{out}}
<pre>
Integer square roots of 0..65 (values the same as the previous one not shown):
0:0 1:1... 4:2... 9:3... 16:4... 25:5... 36:6... 49:7... 64:8...
Integer square roots of 7^n, odd n
n| 7^n| isqrt(7^n)
-+--------------+--------------
1| 7| 2
3| 343| 18
5| 16,807| 129
7| 823,543| 907
9| 40,353,607| 6,352
</pre>
=={{header|ALGOL-M}}==
The
<syntaxhighlight lang="algol">
BEGIN
COMMENT
RETURN INTEGER SQUARE ROOT OF N USING QUADRATIC RESIDUE
ALGORITHM. WARNING: THE FUNCTION WILL FAIL FOR X GREATER
THAN 4095;
INTEGER FUNCTION ISQRT(X);
INTEGER X;
BEGIN
INTEGER
Q := Q * 4; % WARNING! OVERFLOW YIELDS 0 %
Z := X;
R := 0;
WHILE Q > 1 DO
BEGIN
R := R / 2;
IF T >= 0 THEN
BEGIN
Z := T;
R := R + Q;
END;
END;
ISQRT :=
END;
Line 493 ⟶ 604:
END
</syntaxhighlight>
An alternative to the quadratic residue approach will allow calculation of the integer square root for the full range of signed integer values supported by ALGOL-M. (The output is identical.)
<syntaxhighlight lang="algol">
% RETURN INTEGER SQUARE ROOT OF N %
INTEGER FUNCTION ISQRT(N);
INTEGER N;
BEGIN
INTEGER
WHILE R1 > R2 DO
BEGIN
END;
ISQRT :=
END;
</syntaxhighlight>
Line 1,155 ⟶ 1,254:
{{out}}
<pre style="font-size: 11px">
Integer square root for numbers 0 to 65:
0 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
Line 1,391 ⟶ 1,490:
=={{header|COBOL}}==
The COBOL compiler used here is limited to 18-digit math, meaning 7^19 is the largest odd power of 7 that can be calculated.
<syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION.
PROGRAM-ID. I-SQRT.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 QUAD-RET-VARS.
03 X PIC 9(18).
03 Q PIC 9(18).
03 Z PIC 9(18).
03 T PIC S9(18).
03 R PIC 9(18).
01 TO-65-VARS.
03 ISQRT-N PIC 99.
03 DISP-LN PIC X(22) VALUE SPACES.
03 DISP-FMT PIC Z9.
03 PTR PIC 99 VALUE 1.
01 BIG-SQRT-VARS.
03 POW-7 PIC 9(18) VALUE 7.
03 POW-N PIC 99 VALUE 1.
03 POW-N-OUT PIC Z9.
03 POW-7-OUT PIC Z(10).
PROCEDURE DIVISION.
BEGIN.
PERFORM SQRTS-TO-65.
PERFORM BIG-SQRTS.
STOP RUN.
SQRTS-TO-65.
PERFORM DISP-SMALL-SQRT
VARYING ISQRT-N FROM 0 BY 1
UNTIL ISQRT-N IS GREATER THAN 65.
DISP-SMALL-SQRT.
MOVE ISQRT-N TO X.
PERFORM ISQRT.
MOVE R TO DISP-FMT.
STRING DISP-FMT DELIMITED BY SIZE INTO DISP-LN
WITH POINTER PTR.
IF PTR IS GREATER THAN 22,
DISPLAY DISP-LN,
MOVE 1 TO PTR.
BIG-SQRTS.
PERFORM BIG-SQRT 10 TIMES.
BIG-SQRT.
MOVE POW-7 TO X.
PERFORM ISQRT.
MOVE POW-N TO POW-N-OUT.
MOVE R TO POW-7-OUT.
DISPLAY "ISQRT(7^" POW-N-OUT ") = " POW-7-OUT.
ADD 2 TO POW-N.
MULTIPLY 49 BY POW-7.
ISQRT.
MOVE 1 TO Q.
PERFORM MUL-Q-BY-4 UNTIL Q IS GREATER THAN X.
MOVE X TO Z.
MOVE ZERO TO R.
PERFORM ISQRT-STEP UNTIL Q IS NOT GREATER THAN 1.
MUL-Q-BY-4.
MULTIPLY 4 BY Q.
ISQRT-STEP.
DIVIDE 4 INTO Q.
COMPUTE T = Z - R - Q.
DIVIDE 2 INTO R.
IF T IS NOT LESS THAN ZERO,
MOVE T TO Z,
ADD Q TO R.</syntaxhighlight>
{{out}}
<pre> 0 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
ISQRT(7^ 1) = 2
ISQRT(7^ 3) = 18
ISQRT(7^ 5) = 129
ISQRT(7^ 7) = 907
ISQRT(7^ 9) = 6352
ISQRT(7^11) = 44467
ISQRT(7^13) = 311269
ISQRT(7^15) = 2178889
ISQRT(7^17) = 15252229
ISQRT(7^19) = 106765608</pre>
=={{header|Common Lisp}}==
{{trans|Scheme}}
Line 1,599 ⟶ 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 1,790 ⟶ 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 2,040 ⟶ 2,347:
T = 0
DO WHILE (Q .
Q = Q * 4
END DO
Line 2,132 ⟶ 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 3,118 ⟶ 3,424:
19 | 11398895185373143 | 106765608
21 | 558545864083284007 | 747359260</pre>
=={{header|M2000 Interpreter}}==
Using various types up to 7^35
<syntaxhighlight lang="m2000 interpreter">
module integer_square_root (f=-2) {
function IntSqrt(x as long long) {
long long q=1, z=x, t, r
do q*=4&& : until (q>x)
while q>1&&
q|div 4&&:t=z-r-q:r|div 2&&
if t>-1&& then z=t:r+= q
end while
=r
}
long i
print #f, "The integer square root of integers from 0 to 65 are:"
for i=0 to 65
print #f, IntSqrt(i)+" ";
next
print #f
print #f, "Using Long Long Type"
print #f, "The integer square roots of powers of 7 from 7^1 up to 7^21 are:"
for i=1 to 21 step 2 {
print #f, "IntSqrt(7^"+i+")="+(IntSqrt(7&&^i))+" of 7^"+i+" ("+(7&&^I)+")"
}
print #f
function IntSqrt(x as decimal) {
decimal q=1, z=x, t, r
do q*=4 : until (q>x)
while q>1
q/=4:t=z-r-q:r/=2
if t>-1 then z=t:r+= q
end while
=r
}
print #f, "Using Decimal Type"
print #f, "The integer square roots of powers of 7 from 7^23 up to 7^33 are:"
decimal j,p
for i=23 to 33 step 2 {
p=1:for j=1 to i:p*=7@:next
print #f, "IntSqrt(7^"+i+")="+(IntSqrt(p))+" of 7^"+i+" ("+p+")"
}
print #f
function IntSqrt(x as double) {
double q=1, z=x, t, r
do q*=4 : until (q>x)
while q>1
q/=4:t=z-r-q:r/=2
if t>-1 then z=t:r+= q
end while
=r
}
print #f, "Using Double Type"
print #f, "The integer square roots of powers of 7 from 7^19 up to 7^35 are:"
for i=19 to 35 step 2 {
print #f, "IntSqrt(7^"+i+")="+(IntSqrt(7^i))+" of 7^"+i+" ("+(7^i)+")"
}
print #f
}
open "" for output as #f // f = -2 now, direct output to screen
integer_square_root
close #f
open "out.txt" for output as #f
integer_square_root f
close #f
win "notepad", dir$+"out.txt"
</syntaxhighlight>
{{out}}
<pre>
The integer square root of integers from 0 to 65 are:
0 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
Using Long Long Type
The integer square roots of powers of 7 from 7^1 up to 7^21 are:
IntSqrt(7^1)=2 of 7^1 (7)
IntSqrt(7^3)=18 of 7^3 (343)
IntSqrt(7^5)=129 of 7^5 (16807)
IntSqrt(7^7)=907 of 7^7 (823543)
IntSqrt(7^9)=6352 of 7^9 (40353607)
IntSqrt(7^11)=44467 of 7^11 (1977326743)
IntSqrt(7^13)=311269 of 7^13 (96889010407)
IntSqrt(7^15)=2178889 of 7^15 (4747561509943)
IntSqrt(7^17)=15252229 of 7^17 (232630513987207)
IntSqrt(7^19)=106765608 of 7^19 (11398895185373143)
IntSqrt(7^21)=747359260 of 7^21 (558545864083284007)
Using Decimal Type
The integer square roots of powers of 7 from 7^23 up to 7^33 are:
IntSqrt(7^23)=5231514822 of 7^23 (27368747340080916343)
IntSqrt(7^25)=36620603758 of 7^25 (1341068619663964900807)
IntSqrt(7^27)=256344226312 of 7^27 (65712362363534280139543)
IntSqrt(7^29)=1794409584184 of 7^29 (3219905755813179726837607)
IntSqrt(7^31)=12560867089291 of 7^31 (157775382034845806615042743)
IntSqrt(7^33)=87926069625040 of 7^33 (7730993719707444524137094407)
Using Double Type
The integer square roots of powers of 7 from 7^19 up to 7^35 are:
IntSqrt(7^19)=106765608 of 7^19 (1.13988951853731E+16)
IntSqrt(7^21)=747359260 of 7^21 (5.58545864083284E+17)
IntSqrt(7^23)=5231514822 of 7^23 (2.73687473400809E+19)
IntSqrt(7^25)=36620603758 of 7^25 (1.34106861966396E+21)
IntSqrt(7^27)=256344226312 of 7^27 (6.57123623635343E+22)
IntSqrt(7^29)=1794409584184 of 7^29 (3.21990575581318E+24)
IntSqrt(7^31)=12560867089291 of 7^31 (1.57775382034846E+26)
IntSqrt(7^33)=87926069625040 of 7^33 (7.73099371970744E+27)
IntSqrt(7^35)=615482487375282 of 7^35 (3.78818692265665E+29)
</pre>
=={{header|MAD}}==
Line 4,869 ⟶ 5,286:
{{out}}
Perfect squares are denoted with an asterisk.
<pre style="font-size: 11px">
The integer square roots of integers from 0 to 65 are:
0* 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
Line 5,201 ⟶ 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 5,504 ⟶ 5,921:
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|RPL}}==
Because RPL can only handle unsigned integers, a light change has been made in the proposed algorithm,
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪
#1
'''WHILE''' DUP2 ≥ '''REPEAT'''
SL SL '''END'''
#0
'''WHILE''' OVER #1 > '''REPEAT'''
SWAP SR SR SWAP
DUP2 +
SWAP SR SWAP
'''IF''' 4 PICK SWAP DUP2 ≥ '''THEN'''
- 4 ROLL DROP ROT ROT
OVER +
'''ELSE''' DROP2 '''END'''
'''END''' ROT ROT DROP2
≫
´'''ISQRT'''’ STO
|
'''ISQRT''' ''( #n -- #sqrt(n) )''
q ◄── 1
perform while q <= x
q ◄── q * 4
z ◄── x
r ◄── 0
perform while q > 1
q ◄── q ÷ 4
u ◄── r + q
r ◄── r ÷ 2
if z >= u then do
z ◄── z - u
r ◄── r + q
else remove u and copy of z from stack
end perform, clean stack
|}
{{in}}
<pre>
≪ { } 0 65 FOR n n R→B ISQRT B→R + NEXT ≫ EVAL
≪ {} #7 1 11 START DUP ISQRT ROT SWAP + SWAP 49 * NEXT DROP ≫ EVAL
</pre>
{{out}}
<pre>
2: { 0 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 }
1: { # 2d # 18d # 129d # 907d # 6352d # 44467d # 311269d # 2178889d # 15252229d # 106765608d # 747359260d }
</pre>
=={{header|Ruby}}==
Ruby already has [https://ruby-doc.org/core-2.7.0/Integer.html#method-c-sqrt Integer.sqrt], which results in the integer square root of a positive integer. It can be re-implemented as follows:
Line 5,717 ⟶ 6,189:
end
</syntaxhighlight>
An alternate version of isqrt() that can handle the full range of S-BASIC integer values (well, almost: it will fail for 32,767) looks like this.
<syntaxhighlight lang="basic">
function isqrt(x = integer) = integer
Line 5,731 ⟶ 6,203:
</syntaxhighlight>
{{out}}
The output for 7^5 will be shown only if the alternate version of the function is used.
<pre>
Integer square root of first 65 numbers
Line 5,743 ⟶ 6,216:
1 7 2
3 343 18
5 16807 129
</pre>
Line 5,844 ⟶ 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 5,860 ⟶ 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 5,869 ⟶ 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 5,875 ⟶ 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 6,243 ⟶ 6,819:
{{out}}
<pre style="font-size: 11px">
Integer square root for numbers 0 to 65:
0 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
Line 6,491 ⟶ 7,067:
71 | 1,004,525,211,269,079,039,999,221,534,496,697,502,180,541,686,174,722,466,474,743 | 1,002,260,051,717,656,279,450,068,093,686
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|VTL-2}}==
The ISQRT routine starts at line 2000. As VTL-2 only has unsigned 16-bit arithmetic, only the roots of 7^1, 7^3 and 7^5 are shown as 7^7 is too large.
<syntaxhighlight lang="vtl2">
1000 X=0
1010 #=2000
1020 $=32
1030 ?=R
1040 X=X+1
1050 #=X=33=0*1070
1060 ?=""
1070 #=X<66*1010
1080 P=1
1090 X=7
1100 #=2000
1110 ?=""
1120 ?="Root 7^";
1130 ?=P
1140 ?="(";
1150 ?=X
1160 ?=") = ";
1170 ?=R
1180 X=X*49
1190 P=P+2
1200 #=P<6*1100
1210 #=9999
2000 A=!
2010 Q=1
2020 #=X>Q=0*2050
2030 Q=Q*4
2040 #=2020
2050 Z=X
2060 R=0
2070 #=Q<2*A
2080 Q=Q/4
2090 T=Z-R-Q
2100 I=Z<(R+Q)
2110 R=R/2
2120 #=I*2070
2130 Z=T
2140 R=R+Q
2150 #=2070
</syntaxhighlight>
{{out}}
<pre>
0 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
Root 7^1(7) = 2
Root 7^3(343) = 18
Root 7^5(16807) = 129
</pre>
Line 6,496 ⟶ 7,123:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var isqrt = Fn.new { |x|
| |||