Rosetta Code

Arithmetic derivative: Difference between revisions

Page Discussion

Arithmetic derivative (view source)

Revision as of 09:16, 28 January 2024

15,412 bytes added ,  3 months ago
Added Easylang
(add RPL)
(Added Easylang)
 
(10 intermediate revisions by 6 users not shown)
Line 36:
;*[[wp:Arithmetic_derivative|Wikipedia: Arithmetic Derivative]]
 
=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">
BEGIN PROC lagarias = (LONG INT n) LONG INT: # Lagarias arithmetic derivative #
IF n < 0
THEN -lagarias (-n)
ELIF n = 0 OR n = 1
THEN 0
ELIF PROC small pf = (LONG INT j, k) LONG INT: # Smallest prime factor #
(j %* k = 0 | k | small pf (j, k + 1));
LONG INT f = small pf (n, 2); LONG INT q = n % f;
q = 1
THEN 1
ELSE q * lagarias (f) + f * lagarias (q)
FI;
 
FOR n FROM -99 TO 100
DO print (("D(", whole (n, 0), ") = ", whole (lagarias (n), 0), new line))
OD;
new line (standout);
FOR n TO 20
DO LONG INT m = LONG 10 ^ n;
print (("D(", whole (m, 0), ") / 7 = ", whole (lagarias (m) % 7, 0), new line))
OD
END
</syntaxhighlight>
{{out}}
<pre>
D(-99) = -75
D(-98) = -77
D(-97) = -1
D(-96) = -272
...
D(96) = 272
D(97) = 1
D(98) = 77
D(99) = 75
D(100) = 140
D(10) / 7 = 1
D(100) / 7 = 20
D(1000) / 7 = 300
...
D(1000000000000000000) / 7 = 1800000000000000000
D(10000000000000000000) / 7 = 19000000000000000000
D(100000000000000000000) / 7 = 200000000000000000000
</pre>
 
=={{header|ALGOL W}}==
{{Trans|ALGOL 68|using compressed output and basic task only as Algol W integers are limited to 32 bits}}
<syntaxhighlight lang="algolw">
begin
integer procedure lagarias ( integer value n ) ; % Lagarias arithmetic derivative %
if n < 0
then -lagarias (-n)
else if n = 0 or n = 1
then 0
else begin
integer f, q;
integer procedure smallPf ( integer value j, k ) ; % Smallest prime factor %
if j rem k = 0 then k else smallPf (j, k + 1);
f := smallPf (n, 2); q := n div f;
if q = 1
then 1
else q * lagarias (f) + f * lagarias (q)
end lagarias ;
 
for n := -99 until 100 do begin
writeon( i_w := 6, s_w := 0, " ", lagarias (n) );
if n rem 10 = 0 then write()
end for_n
end.
</syntaxhighlight>
{{out}}
<pre>
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
</pre>
 
=={{header|C}}==
Line 219 ⟶ 313:
D(10^20) / 7 = 200000000000000000000
</pre>
 
=={{header|EasyLang}}==
{{trans|Lua}}
<syntaxhighlight>
func lagarias n .
if n < 0
return -lagarias -n
.
if n = 0 or n = 1
return 0
.
f = 2
while n mod f <> 0
f += 1
.
q = n / f
if q = 1
return 1
.
return q * lagarias f + f * lagarias q
.
for n = -99 to 100
write lagarias n & " "
.
</syntaxhighlight>
 
=={{header|Factor}}==
Line 706 ⟶ 825:
D for 10^19 divided by 7 is 19000000000000000000
D for 10^20 divided by 7 is 200000000000000000000
</pre>
 
=={{header|Lua}}==
{{Trans|ALGOL 68|with condensed output and only showing D values up to 10^17 as 10^18 onwards overflows}}
Tested with Lua 5.1 (LuaJIT and OpenResty), 5.3.6 and 5.4.6.<br/>
Lua 5.2.4 didn't like the string.format. Also the format of the larger D values appears to be sensitive to the Lua version.
<syntaxhighlight lang="lua">
do local function lagarias (n) -- Lagarias arithmetic derivative
if n < 0
then return -lagarias (-n)
elseif n == 0 or n == 1
then return 0
else local function smallPf (j, k) -- Smallest prime factor
if j % k == 0 then return k else return smallPf (j, k + 1) end
end
local f = smallPf (n, 2) local q = math.floor (n / f)
if q == 1
then return 1
else return q * lagarias (f) + f * lagarias (q)
end
end
end
for n = -99,100
do io.write (string.format("%6d", lagarias (n)))
if n % 10 == 0 then io.write ("\n") end
end
io.write ("\n")
for n = 1,17 -- 18, 19 and 20 would overflow
do local m = 10 ^ n
io.write ("D(", string.format ("%d", m), ") / 7 = ", math.floor (lagarias (m) / 7), "\n")
end
end
</syntaxhighlight>
{{out}}
<pre>
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
 
D(10) / 7 = 1
D(100) / 7 = 20
D(1000) / 7 = 300
D(10000) / 7 = 4000
D(100000) / 7 = 50000
D(1000000) / 7 = 600000
D(10000000) / 7 = 7000000
D(100000000) / 7 = 80000000
D(1000000000) / 7 = 900000000
D(10000000000) / 7 = 10000000000
D(100000000000) / 7 = 110000000000
D(1000000000000) / 7 = 1200000000000
D(10000000000000) / 7 = 13000000000000
D(100000000000000) / 7 = 140000000000000
D(1000000000000000) / 7 = 1500000000000000
D(10000000000000000) / 7 = 16000000000000000
D(100000000000000000) / 7 = 170000000000000000
</pre>
 
=={{header|MiniScript}}==
{{Trans|ALGOL 68|via Lua}}
<syntaxhighlight lang="miniscript">
lagarias = function (n) // Lagarias arithmetic derivative
if n < 0 then
return -lagarias (-n)
else if n == 0 or n == 1 then
return 0
else
smallPf = function (j, k) // Smallest prime factor
if j % k == 0 then
return k
else
return smallPf (j, k + 1)
end if
end function
f = smallPf (n, 2)
q = floor (n / f)
if q == 1 then
return 1
else
return q * lagarias (f) + f * lagarias (q)
end if
end if
end function
fmt6 = function (n) // return a 6 character string representation of n
s = str( n )
if s.len > 5 then
return s
else
return ( " " * ( 6 - s.len ) ) + s
end if
end function
ad = ""
for n in range( -99, 100 )
ad = ad + " " + fmt6( lagarias (n) )
if n % 10 == 0 then
print( ad )
ad = ""
end if
end for
print()
for n in range( 1, 17 ) // 18, 19 and 20 would overflow ????? TODO: check
m = 10 ^ n
print( "D(" + str(m) + ") / 7 = " + str( floor (lagarias (m) / 7) ) )
end for
</syntaxhighlight>
{{out}}
<pre>
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
D(10) / 7 = 1
D(100) / 7 = 20
D(1000) / 7 = 300
D(10000) / 7 = 4000
D(100000) / 7 = 50000
D(1000000) / 7 = 600000
D(10000000) / 7 = 7000000
D(100000000) / 7 = 80000000
D(1000000000) / 7 = 900000000
D(10000000000) / 7 = 10000000000
D(100000000000) / 7 = 110000000000
D(1000000000000) / 7 = 1200000000000
D(10000000000000) / 7 = 13000000000000
D(100000000000000) / 7 = 140000000000000
D(1000000000000000) / 7 = 1500000000000000
D(10000000000000000) / 7 = 16000000000000000
D(100000000000000000) / 7 = 170000000000000000
D(1000000000000000000) / 7 = 1800000000000000000
D(10000000000000000000) / 7 = 19000000000000000000
D(100000000000000000000) / 7 = 200000000000000000000
</pre>
 
Line 1,126 ⟶ 1,410:
{{works with|HP|49}}
≪ '''CASE'''
DUP 0 < '''THEN''' NEG <span style="color:blue">ADERIV</span> NEG '''END'''
DUP 2 < '''THEN''' DROP 0 '''END'''
R→I DUP ISPRIME? '''THEN''' DROP 1 '''END'''
DUP FACTORS HEAD LASTARG 2 GET DUP2 ^ 4 PICK OVER / 1 RND
→ n p k pk rem
≪ k pk p / * rem * rem <span style="color:blue">ADERIV</span> pk * +
≫
'''END'''
≫ '<span style="color:blue">ADERIV</span>' STO
 
Line 1,214 ⟶ 1,498:
(D for 10 ^ 19) divided by 7 is 19000000000000000000
(D for 10 ^ 20) divided by 7 is 200000000000000000000
</pre>
 
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
import java.math.BigInteger
 
object ArithmeticDerivative extends App {
 
println("Arithmetic derivatives for -99 to 100 inclusive:")
for {
n <- -99 to 100
column = n + 100
} print(f"${derivative(BigInteger.valueOf(n))}%4d${if (column % 10 == 0) "\n" else " "}")
 
println()
 
val seven = BigInteger.valueOf(7)
for (power <- 1 to 20) {
println(f"D(10^$power%d) / 7 = ${derivative(BigInteger.TEN.pow(power)).divide(seven)}")
}
 
def derivative(aNumber: BigInteger): BigInteger = {
if (aNumber.signum == -1) {
return derivative(aNumber.negate()).negate()
}
if (aNumber == BigInteger.ZERO || aNumber == BigInteger.ONE) {
return BigInteger.ZERO
}
 
var divisor = BigInteger.TWO
while (divisor.multiply(divisor).compareTo(aNumber) <= 0) {
if (aNumber.mod(divisor).signum == 0) {
val quotient = aNumber.divide(divisor)
return quotient.multiply(derivative(divisor)).add(divisor.multiply(derivative(quotient)))
}
divisor = divisor.add(BigInteger.ONE)
}
BigInteger.ONE
}
 
}
</syntaxhighlight>
{{out}}
<pre>
Arithmetic derivatives for -99 to 100 inclusive:
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
 
D(10^1) / 7 = 1
D(10^2) / 7 = 20
D(10^3) / 7 = 300
D(10^4) / 7 = 4000
D(10^5) / 7 = 50000
D(10^6) / 7 = 600000
D(10^7) / 7 = 7000000
D(10^8) / 7 = 80000000
D(10^9) / 7 = 900000000
D(10^10) / 7 = 10000000000
D(10^11) / 7 = 110000000000
D(10^12) / 7 = 1200000000000
D(10^13) / 7 = 13000000000000
D(10^14) / 7 = 140000000000000
D(10^15) / 7 = 1500000000000000
D(10^16) / 7 = 16000000000000000
D(10^17) / 7 = 170000000000000000
D(10^18) / 7 = 1800000000000000000
D(10^19) / 7 = 19000000000000000000
D(10^20) / 7 = 200000000000000000000
 
</pre>
 
Line 1,220 ⟶ 1,592:
{{libheader|Wren-fmt}}
As integer arithmetic in Wren is inaccurate above 2^53 we need to use BigInt here.
<syntaxhighlight lang="ecmascriptwren">import "./big" for BigInt
import "./fmt" for Fmt
 
Line 1,285 ⟶ 1,657:
D(10^19) / 7 = 19000000000000000000
D(10^20) / 7 = 200000000000000000000
</pre>
 
=={{header|XPL0}}==
{{trans|ALGOL W}}
<syntaxhighlight lang "XPL0">function integer Lagarias (N); \Lagarias arithmetic derivative
integer N;
integer F, Q;
 
function integer SmallPF (J, K); \Smallest prime factor
integer J, K;
return if rem(J/K) = 0 then K else SmallPF(J, K+1);
 
begin
if N < 0
then return -Lagarias (-N)
else if N = 0 or N = 1
then return 0
else begin
F := SmallPF (N, 2); Q := N / F;
return if Q = 1
then 1
else Q * Lagarias (F) + F * Lagarias (Q)
end;
end \Lagarias\ ;
 
integer N;
begin
for N:= -99 to 100 do begin
IntOut(0, Lagarias(N) );
if rem(N/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
end;
end</syntaxhighlight>
{{out}}
<pre>
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
</pre>
Chkas
1,983

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/346423...355650"