Data update

Task/Eulers-constant-0.5772.../PascalABC.NET/eulers-constant-0.5772....pas

@@ -0,0 +1,9 @@
+const
+  n = 1_000_000;
+
+begin
+  var result := 1.0;
+  for var i := 2 to n do
+    result += 1 / i;
+  writeln(result - ln(n));
+end.

Task/Eulers-constant-0.5772.../REXX/eulers-constant-0.5772....rexx

@@ -1,5 +1,5 @@
 arg n; if n = '' then n = 100; numeric digits n
-parse version version; say version; glob. = ''
+parse version version; say version; glob. = ''; fact. = 0
 say 'Euler-Mascheroni constant to' n 'decimal places'
 say 'Method Brent-McMillan'
 say
@@ -10,9 +10,9 @@ say 'True value' a '('e 'seconds)'
 exit
 
 Brent:
-procedure expose glob.
+procedure expose fact. glob. work.
 numeric digits Digits()+2
--- Brent McMillan
+/* Brent McMillan */
 n = Ceil((Digits()*Ln(10)+Ln(Pi()))*0.25); m = Ceil(2.07*Digits())
 n2 = n*n; ak = -Ln(n); bk = 1; s = ak; v = 1
 do k = 1 to m
@@ -24,249 +24,9 @@ numeric digits Digits()-2
 return y+0
 
 TrueValue:
-procedure expose glob.
+procedure
 return 0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495+0
 
-E:
--- Euler number
-procedure expose glob.
-p = Digits()
--- In memory?
-if glob.e.p <> '' then
-   return glob.e.p
-if p < 101 then
--- Fast value
-   glob.e.p = 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516643+0
-else do
-   numeric digits Digits()+2
--- Taylor
-   y = 2; t = 1; v = y
-   do n = 2
-      t = t/n; y = y+t
-      if y = v then
-         leave
-      v = y
-   end
-   numeric digits Digits()-2
-   glob.e.p = y+0
-end
-return glob.e.p
-
-Fact:
--- Factorial n!
-procedure expose glob.
-arg x
--- Validity
-if \ Whole(x) then
-   return 'X'
-if x < 0 then
-   return 'X'
--- Current in memory?
-if glob.fact.x <> '' then
-   return glob.fact.x
-w = x-1
--- Previous in memory?
-if glob.fact.w = '' then do
--- Loop cf definition
-   y = 1
-   do n = 2 to x
-      y = y*n
-   end
-   glob.fact.x = y
-end
-else
--- Multiply
-   glob.fact.x = glob.fact.w*x
-return glob.fact.x
-
-Ln2:
--- Natural log of 2 constant
-procedure expose glob.
--- Fast value
-y = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875
-return y+0
-
-Ln4:
--- Natural log of 4 constant
-procedure expose glob.
--- Fast value
-y = 1.386294361119890618834464242916353136151000268720510508241360018986787243939389431211726653992837375
-return y+0
-
-Ln8:
--- Natural log of 8 constant
-procedure expose glob.
--- Fast value
-y = 2.079441541679835928251696364374529704226500403080765762362040028480180865909084146817589980989256063
-return y+0
-
-Ln10:
--- Natural log of 10 constant
-procedure expose glob.
--- Fast value
-y = 2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508959830
-return y+0
-
-Pi:
--- Pi constant
-procedure expose glob.
-p = Digits()
--- In memory?
-if glob.pi.p <> '' then
-   return glob.pi.p
-if p < 101 then
--- Fast value
-   glob.pi.p = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211707+0
-else do
-   numeric digits Digits()+2
-   if p < 201 then do
--- Chudnovsky
-      y = 0
-      do n = 0
-         v = y; y = y + Fact(6*n)*(13591409+545140134*n)/(Fact(3*n)*Fact(n)**3*-640320**(3*n))
-         if y = v then
-            leave
-      end
-      y = 4270934400/(Sqrt(10005)*y)
-   end
-   else do
--- Agmean
-      y = 0.25; a = 1; g = Sqrt(0.5); n = 1
-      do until a = v
-         v = a
-         x = (a+g)*0.5; g = Sqrt(a*g)
-         y = y-n*(x-a)**2; n = n+n; a = x
-      end
-      y = a*a/y
-   end
-   numeric digits Digits()-2
-   glob.pi.p = y+0
-end
-return glob.pi.p
-
-Ceil:
--- Ceiling
-procedure expose glob.
-arg x
--- Formulas
-if Whole(x) then
-   return x
-else
-   return Trunc(x)+(x>=0)
-
-Ln:
--- Natural logarithm base e
-procedure expose glob.
-arg x
--- Validity
-if x <= 0 then
-   return 'X'
--- Fast values
-if x = 1 then
-   return 0
-p = Digits()
--- In memory?
-if glob.ln.x.p <> '' then
-   return glob.ln.x.p
--- Precalculated values
-if x = 2 & p < 101 then do
-   glob.ln.x.p = Ln2()
-   return glob.ln.x.p
-end
-if x = 4 & p < 101 then do
-   glob.ln.x.p = Ln4()
-   return glob.ln.x.p
-end
-if x = 8 & p < 101 then do
-   glob.ln.x.p = Ln8()
-   return glob.ln.x.p
-end
-if x = 10 & p < 101 then do
-   glob.ln.x.p = Ln10()
-   return glob.ln.x.p
-end
-numeric digits p+2
--- Argument reduction
-z = x; i = 0; e = 1/E()
-if z < 0.5 then do
-   y = 1/z
-   do while y > 1.5
-      y = y*e; i = i-1
-   end
-   z = 1/y
-end
-if z > 1.5 then do
-   do while z > 1.5
-      z = z*e; i = i+1
-   end
-end
--- Taylor series
-q = (z-1)/(z+1); f = q; y = q; v = q; q = q*q
-do n = 3 by 2
-   f = f*q; y = y+f/n
-   if y = v then
-      leave
-   v = y
-end
-numeric digits p
--- Inverse reduction
-glob.ln.x.p = 2*y+i
-return glob.ln.x.p
-
-Sqrt:
--- Square root x^(1/2)
-procedure expose glob.
-arg x
--- Validity
-if x < 0 then
-   return 'X'
--- Fast values
-if x = 0 then
-   return 0
-if x = 1 then
-   return 1
-p = Digits()
--- Predefined values
-if x = 2 & p < 101 then
-   return Sqrt2()
-if x = 3 & p < 101 then
-   return Sqrt3()
-if x = 5 & p < 101 then
-   return Sqrt5()
-numeric digits p+2
--- Argument reduction to [0,100)
-i = Xpon(x); i = (i-(i<0))%2; x = x/100**i
--- First guess 1 digit accurate
-t = '2.5 6.5 12.5 20.5 30.5 42.5 56.5 72.5 90.5 100'
-do y = 1 until word(t,y) > x
-end
--- Dynamic precision
-d = Digits()
-do n = 1 while d > 2
-   d.n = d; d = d%2+1
-end
-d.n = 2
--- Method Heron
-do k = n to 1 by -1
-   numeric digits d.k
-   y = (y+x/y)*0.5
-end
-numeric digits p
-return y*10**i
-
-Whole:
--- Is a number integer?
-procedure expose glob.
-arg x
--- Formula
-return Datatype(x,'w')
-
-Xpon:
--- Exponent
-procedure expose glob.
-arg x
--- Formula
-if x = 0 then
-   return 0
-else
-   return Right(x*1E+99999,6)-99999
+include Constants
+include Functions
+include Numbers