'Sigmoid function generator
'Author: Robert John Morton YE572246C December 1993

DefInt a - x
dim SigTab(1024)
R!  = 32767
RR! = 65534
screen 9                                'switch to EGA enhanced mode graphics
window (-48000,-48000) - (+48000,+48000)'set up suitable screen co-ordinates
YY = 3 / 2                              'PC screen X scaling is 2/3 its Y
color ,1
line(-32767, 0) - (32767, 0) , 7
line(0, -32767) - (0, 32767) , 7
locate  2,13:print"NEURAL TRANSFER FUNCTION USED IN A MULTI-LAYER PERCEPTRON"
locate  4,39:print"f(x)"
locate  5,34:print"+32767"
locate 21,42:print"-32767"
locate 12,66:print"+32767"
locate 14,10:print"-32767"
locate 13,70:print"x"
locate  8,12:print"SIGMOID FUNCTION"
locate 16,45:print"f(x) = 2/(1+exp(-k*x)) - 1"
locate 17,45:print"x = neuron activation level"
locate 18,45:print"f(x) = neuron output level"
k =  4 : c = 11 : gosub SigGen : gosub SigTest
k =  8 : c = 10 : gosub SigGen : gosub SigTest
k = 16 : c = 12 : gosub SigGen : gosub SigTest
k = 32 : c = 14 : gosub SigGen : gosub SigTest
LOCATE 24,1:print"HIT ANY KEY TO QUIT";
E: x$ = inkey$ : if x$ = "" goto E
end

SigGen:
   for i = 0 to 1023
      w! = i
      v! = RR! / (1 + exp(-w! * 32 * k / R!)) - R!
      y = v! : SigTab(i) = y
   next
   SigTab(1024) = R!
return

SigTest:
   k$ = str$(k) : k$ = "k =" + space$(3 - len(k$)) + k$
   locate 11-q,56: print k$ : q=q+1
   x = -32767 : start! = TIMER ' : locate 17,5:print"Errors ="
B: gosub Sigmoid : pset (x, y), c
   if x < 32767 then x = x + 1 : goto B
   locate 23,4:print"TIME:"; TIMER - start! ;"seconds"
'   n = nn : l = 22 : nn$ = "Error Occurrences =" : gosub ShowNum
return


'THIS IS 1.46 TIMES THE SPEED OF THE EXP() FUNCTION
'AND DISAGREES WITH EXP() ONLY IN BIT 0 (IE BY AT MOST 1 IN 32767)

Sigmoid:
   if x < 0 then xx = -x else xx = x
   xxx! = xx
   i = INT(xxx! / 32)
   dx = xx - i * 32
   y = SigTab(i)
   y = y + ((dx * (SigTab(i + 1) - y)) / 32)
   if x < 0 then y = -y
'   w! = x : v! = RR! / (1 + exp(-w! * k / R!)) - R! : yy = v!
'   n = abs(yy-y) : locate 17,13 : print n : if n > 0 then nn = nn + 1
return

ShowNum:
   n$ = str$(n) : n$ = space$(6 - len(n$)) + n$
   locate l,5: print nn$+n$ : return