-- test bc library

assert (package.loadlib ("bc.dll","luaopen_bc")) ()

------------------------------------------------------------------------------
print(bc.version)

------------------------------------------------------------------------------

print"Factorials"

function factorial(n,f)
 for i=2,n do f=f*i end
 return f
end

one=bc.number(1)
for i=1,40 do
 print(i,factorial(i,1),factorial(i,one))
end

bc library for Lua 5.1 / Aug 2006 / based on GNU bc-1.06
Factorials
1 1 1
2 2 2
3 6 6
4 24 24
5 120 120
6 720 720
7 5040 5040
8 40320 40320
9 362880 362880
10 3628800 3628800
11 39916800 39916800
12 479001600 479001600
13 6227020800 6227020800
14 87178291200 87178291200
15 1307674368000 1307674368000
16 20922789888000 20922789888000
17 3.55687428096e+014 355687428096000
18 6.402373705728e+015 6402373705728000
19 1.2164510040883e+017 121645100408832000
20 2.4329020081766e+018 2432902008176640000
21 5.1090942171709e+019 51090942171709440000
22 1.1240007277776e+021 1124000727777607680000
23 2.5852016738885e+022 25852016738884976640000
24 6.2044840173324e+023 620448401733239439360000
25 1.5511210043331e+025 15511210043330985984000000
26 4.0329146112661e+026 403291461126605635584000000
27 1.0888869450418e+028 10888869450418352160768000000
28 3.0488834461171e+029 304888344611713860501504000000
29 8.8417619937397e+030 8841761993739701954543616000000
30 2.6525285981219e+032 265252859812191058636308480000000
31 8.2228386541779e+033 8222838654177922817725562880000000
32 2.6313083693369e+035 263130836933693530167218012160000000
33 8.6833176188119e+036 8683317618811886495518194401280000000
34 2.952327990396e+038 295232799039604140847618609643520000000
35 1.0333147966386e+040 10333147966386144929666651337523200000000
36 3.719933267899e+041 371993326789901217467999448150835200000000
37 1.3763753091226e+043 13763753091226345046315979581580902400000000
38 5.230226174666e+044 523022617466601111760007224100074291200000000
39 2.0397882081197e+046 20397882081197443358640281739902897356800000000
40 8.159152832479e+047 815915283247897734345611269596115894272000000000

bc.digits(1000)   -- calculate 1000 digits of pi

function calc_pi ()
 local x = bc.sqrt (2)
 local p = 2 + x
 local y = bc.sqrt (x)
 x = (y + 1 / y) / 2
 p = p * (x + 1) / (y + 1)
 for i = 1, 200 do
  local P = p
  local t = bc.sqrt (x)
  y = (y * t + 1 / t) / (y + 1)
  x = (t + 1 / t) / 2
  p = p * (x + 1) / (y + 1)
  if p == P then 
    break 
  end
 end
 return p
end

print (calc_pi ())

Output
3.141592653589793238462643383279502884197169399375
10582097494459230781640628620899862803482534211706
79821480865132823066470938446095505822317253594081
28481117450284102701938521105559644622948954930381
96442881097566593344612847564823378678316527120190
91456485669234603486104543266482133936072602491412
73724587006606315588174881520920962829254091715364
36789259036001133053054882046652138414695194151160
94330572703657595919530921861173819326117931051185
48074462379962749567351885752724891227938183011949
12983367336244065664308602139494639522473719070217
98609437027705392171762931767523846748184676694051
32000568127145263560827785771342757789609173637178
72146844090122495343014654958537105079227968925892
35420199561121290219608640344181598136297747713099
60518707211349999998372978049951059731732816096318
59502445945534690830264252230825334468503526193118
81710100031378387528865875332083814206171776691473
03598253490428755468731159562863882353787593751957
78185778053217122680661300192787661119590921642019
89

for i = -1, 1, 0.1 do 
  print (i) 
end

Output
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-1.3877787807814e-016
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

i = bc.number (-1)
bc.digits (1)

repeat
  print (i)
  i = i + 0.1
until i > bc.number (1)

Output

-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

print (bc.number (2) ^ 10000)

print (bc.number (2) ^ 1000000)

for i = 1, 1000000 do
  for j = 1, 1000000 do
    for k = 1, 1000000 do
      print("123")
    end
  end
end

bc.digits (103)

n = bc.number (1)
e = bc.number (1)

for i = 1, 200 do
  local E = e
  n = n * i   -- n is i! (factorial of i)
  e = e + (1 / n)
  if e == E then
    break
  end -- if no change
end -- for

print (e) 

Output
 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274229

bc.digits (100)

function sine (x, precision)
   local val = bc.number (1)
   x = bc.number (x)
   while precision > 0 do
       val = 1 - val * x * x / (2 * precision) / (2 * precision + 1)
       precision = precision - 1
   end -- while
   val = x * val
   return val
end -- function sine

print (sine (1, 35))

Output

0.8414709848078965066525023216302989996225630607983710656727517099919104043912396689486397435430526959

pi = bc.number (
"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706")

function cosine (x, precision)
  return sine (pi / 2 - x, precision)
end -- cosine

print (cosine (1, 35))

Output

0.5403023058681397174009366074429766037323104206179222276700972553811003947744717645179518560871830860

function tangent (x, precision)
  return (sine (x, precision) / cosine (x, precision))
end -- tangent

print (tangent (1, 35))

Output

1.5574077246549022305069748074583601730872507723815200383839466056988613971517272895550999652022429935

bc.digits (100)

function exp (x)

  local x = bc.number (x)  -- argument converted to bignum

  -- if x > 1 halve it and square the result
  if bc.compare (x, 1) == 1 then
    return exp (x / 2) ^ 2
  end -- if x > 1

  local e = bc.number (1)  -- result

  local n = bc.number (1)  -- denominator: i!
  local t = bc.number (1)  -- numerator:   x^i

  for i = 1, 200 do
    local E = e
    n = n * i  -- n is i!  (factorial of i)
    t = t * x  -- t is x^i (x to the power i)
    e = e + (t / n)  -- new value

    -- break if no change
    if e == E then
      break
    end -- if no change
  end -- for

  return e

end -- function exp

print (exp (5))

Output

148.4131591025766034211155800405522796234876675938789890467528451109120648209585760796884094598990189279