Integer roots: Difference between revisions
m (→{{header|REXX}}: added more capability, added a couple of examples, changed wording in the REXX section header.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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No error checking is performed to ensure the root is a non-zero integer. |
No error checking is performed to ensure the root is a non-zero integer. |
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<br>Negative roots are supported. |
<br>Negative and complex roots are supported. |
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<lang rexx>/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/ |
<lang rexx>/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/ |
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parse arg num root digs . /*obtain the optional arguments from CL*/ |
parse arg num root digs . /*obtain the optional arguments from CL*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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iRoot: procedure; |
iRoot: procedure; parse arg x 1 ox, y 1 oy /*obtain the numbers, Y is the root #.*/ |
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i=; x=abs(x); y=abs(y) /*use the absolute values of X and Y. */ |
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if ox<0 & oy//2==0 then do; i='i'; ox=x; end /*if the results will be imaginary ··· */ |
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od=digits() /*the current number of decimal digits.*/ |
od=digits() /*the current number of decimal digits.*/ |
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a=od+9 /*bump the decimal digits by nine. */ |
a=od+9 /*bump the decimal digits by nine. */ |
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_=g*sign(ox) /*change the sign of the result, maybe.*/ |
_=g*sign(ox) /*change the sign of the result, maybe.*/ |
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numeric digits od /*set numeric digits to the original.*/ |
numeric digits od /*set numeric digits to the original.*/ |
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if oy<0 then return 1/_ |
if oy<0 then return (1/_)i /*Is the root negative? Use reciprocal*/ |
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return _/1 |
return (_/1)i /*return the Yth root of X to invoker.*/</lang> |
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'''output''' when the defaults are being used: |
'''output''' when the defaults are being used: |
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<pre> |
<pre> |
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54057586799967012137223947582142630658513221740883238294728761739364746783743196000159218880734785761725221186749042497736692920731109636972160893370866115673458533483329525467585164471075784860246360 |
54057586799967012137223947582142630658513221740883238294728761739364746783743196000159218880734785761725221186749042497736692920731109636972160893370866115673458533483329525467585164471075784860246360 |
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08 |
08 |
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</pre> |
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'''output''' when using the input of: <tt> -81 </tt> |
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<pre> |
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number= -81 |
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root= 2 |
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digits= 2001 |
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result: |
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9i |
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</pre> |
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'''output''' when using the input of: <tt> 4 -2 </tt> |
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<pre> |
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number= 4 |
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root= -2 |
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digits= 2001 |
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result: |
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0.5 |
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</pre> |
</pre> |
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Revision as of 05:54, 11 May 2016
Integer roots
The task is to write a program that computes an approximation to the principal Nth root of X as the largest integer less than or equal to R for which R^N=X. N is a positive integer. X is a non-negative integer. R is a non-negative real number.
Python
<lang python>def root(a,b):
if b<2:return b a1=a-1 c=1 d=(a1*c+b//(c**a1))//a e=(a1*d+b//(d**a1))//a while c!=d and c!=e: c,d,e=d,e,(a1*e+b//(e**a1))//a return min(d,e)
print("First 2,001 digits of the square root of two:\n{}".format(root(2,2*100**2000)))</lang>
- Output:
First 2,001 digits of the square root of two: 141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008
REXX
No error checking is performed to ensure the root is a non-zero integer.
Negative and complex roots are supported.
<lang rexx>/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/
parse arg num root digs . /*obtain the optional arguments from CL*/
if num== | num=="," then num= 2 /*Not specified? Then use the default.*/
if root== | root=="," then root= 2 /* " " " " " " */
if digs== | digs=="," then digs=2001 /* " " " " " " */
numeric digits digs /*utilize this number of decimal digits*/
say 'number=' num /*display the number that will be used.*/
say ' root=' root /* " " root " " " " */
say 'digits=' digs /* " dec. digits " " " " */
say /* " a blank line. */
say 'result:'; say iRoot(num, root) /* " what it is; display the root.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
iRoot: procedure; parse arg x 1 ox, y 1 oy /*obtain the numbers, Y is the root #.*/
i=; x=abs(x); y=abs(y) /*use the absolute values of X and Y. */
if ox<0 & oy//2==0 then do; i='i'; ox=x; end /*if the results will be imaginary ··· */
od=digits() /*the current number of decimal digits.*/
a=od+9 /*bump the decimal digits by nine. */
numeric form /*number will be in exponential form.*/
parse value format(x,2,1,,0) 'E0' with ? 'E' _ . /*obtain exponent so we can do division*/
g=(?/y'E'_ % y) + (x>1) /*this is a best first guess of a root.*/
m=y-1 /*define a (fast) variable for later. */
d=5 /*start with only five decimal digits. */
do until d==a /*keep computing 'til we're at max digs*/ d=min(d+d,a); dm=d-2 /*bump number of (growing) decimal digs*/ numeric digits d /*increase the number of decimal digits*/ o=0 /*set the old value to zero (1st time).*/ do until o=g; o=g /*keep computing as long as G changes.*/ g=format((m*g**y+x)/y/g**m,,dm) /*compute the Yth root of X. */ end /*until o=g*/ end /*until d==a*/
_=g*sign(ox) /*change the sign of the result, maybe.*/ numeric digits od /*set numeric digits to the original.*/ if oy<0 then return (1/_)i /*Is the root negative? Use reciprocal*/
return (_/1)i /*return the Yth root of X to invoker.*/</lang>
output when the defaults are being used:
number= 2 root= 2 digits= 2001 result: 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571 47010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884 71603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372352885092648612494977154218334204285686060146824720771435854874155657069677653720226485447015858801 62075847492265722600208558446652145839889394437092659180031138824646815708263010059485870400318648034219489727829064104507263688131373985525611732204024509122770022694112757362728049573810896750401836 98683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884 72089694633862891562882765952635140542267653239694617511291602408715510135150455381287560052631468017127402653969470240300517495318862925631385188163478001569369176881852378684052287837629389214300655 86956868596459515550164472450983689603688732311438941557665104088391429233811320605243362948531704991577175622854974143899918802176243096520656421182731672625753959471725593463723863226148274262220867 11558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668 98329989895386728822856378697749662519966583525776198939322845344735694794962952168891485492538904755828834526096524096542889394538646625744927556381964410316979833061852019379384940057156333720548068 54057586799967012137223947582142630658513221740883238294728761739364746783743196000159218880734785761725221186749042497736692920731109636972160893370866115673458533483329525467585164471075784860246360 08
output when using the input of: -81
number= -81 root= 2 digits= 2001 result: 9i
output when using the input of: 4 -2
number= 4 root= -2 digits= 2001 result: 0.5
zkl
Uses GNU GMP library <lang zkl>var [const] BN=Import("zklBigNum"); fcn root(n,r){
f:='wrap(z){ (n/z.pow(r-1) + z*(r-1))/r or 1 }; //--> v or 1 c,d,e:=1,f(c),f(d); while(c!=d and c!=e){ c,d,e=d,e,f(e) } if(d<e) d else e
}</lang> <lang zkl>a:=BN(100).pow(2000)*2; println("Does GMP agree: ",root(a,3)==a.root(3));</lang>
- Output:
Does GMP agree: True