Calculator_10.py

#The ALU has digital circuits for sum, subtraction, multiplication and comparision.
#The challenge here would be to write the code for division, square root, trignometric and other fuctions
#The following python code just needs python install of 30 MB and was written by Dr. Harish Ravi on 24 Nov 2019

for i in range(0,10000):
    x='25'; #2 digit number
    y='14'; #2 digit number
    for k in range(0,10000):
        for r in range(0,500):
            1  
    print('ss,PS,<3')
    #Doing representation of two digit product
    product=int(x[1])*int(y[1])+10*(int(x[0])*int(y[1])+int(x[1])*int(y[0]))+int(x[0])*int(y[0])*100

    #Doing representation of digit sum and subtraction
    add=int(x[1])+int(y[1])+10*(int(x[0])+int(y[0]))
    sub=int(x[1])-int(y[1])+10*(int(x[0])-int(y[0]))

    #Showing output,
    print('Product of ',x,' and' ,y,' ', product)
    print('Sum of',x,' and' ,y,' ',add)
    print('Subtraction  ',x,' and' ,y,' ',sub)

    #Dividing x a two digit number by z a single digit number
    z='3'# Single digit number
    ha=1;# While loop flag
    j=0; # Increasing the quotient in the loop until the product exceeds the divisor
    while ha:
        
        r=int(x[1])+10*int(x[0])-j*int(z[0]);
        if(r<int(z[0])):
            ha=0; #Setting the while loop flag to 0 to come out of the loop
        j=j+1; #incrementing the quotient until it divides
            
    j=j-1; # Reducing the quotient as we counted one past

    #Getting the decimal point of the quotient
    ha=1;
    h=0;
    while ha:
        
        r2=r*10-h*int(z[0]);
        if(r2<int(z[0])):
            ha=0;
        h=h+1;
    h=h-1;
    print('division of ',x,' and' ,z,' ',j,'.',h)

    #Finding square root by subtracting successively the contribution from most significant digit.
    sq='314';
    ha=1;
    a=0;
    while ha:
        luv=int(sq[0])*100+int(sq[1])*10+int(sq[2])-100*a*a;
        a=a+1;
        if luv<0:
            ha=0;

    a=a-2;
    ha=1;
    b=0;
    while ha:
        luv2=int(sq[0])*100+int(sq[1])*10+int(sq[2])-100*a*a-(20*a+b)*b;
        b=b+1;
        if luv2<0:
            ha=0;
    b=b-2;

    ha=1;
    c=0;
    while ha:
        luv3=100*(int(sq[0])*100+int(sq[1])*10+int(sq[2])-100*a*a-(20*a+b)*b)-c*(200*a+20*b+c);
        c=c+1;
        if luv3<0:
            ha=0;
    c=c-2;


    print('Square root of ',sq , ' ',10*a+b,'.',c)

    #Maclaurin expansion of all trignometric and hyperbolic functions
    n=100
    def hfactorial(n):
        s=1;
        for j in range(1,n+1):
            s=s*j
        return s

    def hsin(x):
        return x-x*x*x/6+x*x*x*x*x/120-x*x*x*x*x*x*x/5040;

    def hcos(x):
        return 1-x*x/2+1/24*x*x*x*x-x*x*x*x*x*x/720;

    def htan(x):
        return x+x*x*x/3+2/15*x*x*x*x*x+17/315*x*x*x*x*x*x*x+62/2035*x*x*x*x*x*x*x*x*x;


    def h2cos(x):
        s=0.0;
        for j in range(n):
            
            s=s+(-1)**j/hfactorial(2*j)*(x**(2*j))
        return s


    def h2sin(x):
        s=0.0;
        for j in range(n):
            s=s+(-1)**j/hfactorial(2*j+1)*(x**(2*j+1))
        return s

    def h2sinh(x):
        s=0.0;
        for j in range(n):
            s=s+1/hfactorial(2*j+1)*(x**(2*j+1))
        return s



    def h2atanh(x):
        s=0.0;
        for j in range(1,n):
            s=s+1/(2*j-1)*(x**(2*j-1))
        return s

    def h2atan(x):
        s=0.0;
        for j in range(1,n):
            s=s+(-1.0)**(j+1)/(2*j-1)*(x**(2*j-1))
        return s

    def h2ln1px(x):
        s=0.0;
        for j in range(1,n):
            s=s+(-1)**(j+1)/j*(x**(j))
        return s
    def h2erf(x):
        s=0.0;
        for j in range(0,n):
            s=s+2/np.sqrt(np.pi)*(-1)**j/(2*j+1)/hfactorial(j)*(x**(2*j+1))
        return s

    def h2exp(x):
        s=0.0;
        for j in range(n):
            s=s+1.0/hfactorial(j)*(x**(j))
        return s

    def h2acot(x):
        s=0.0;
        for j in range(1,n):
            s=s+(-1)**j/(2*j+1)*(x**(2*j+1))
        return np.pi/2-s

    def h2cosh(x):
        s=0.0;
        for j in range(1,n):
            s=s+1/hfactorial(2*j)*(x**(2*j))
        return s
    n=10000
    print('pi',h2atan(1)*4.0)
    n=100
    print('e',h2exp(1))
    print('h2cos(3.14)', h2cos(3.14/2),'h2sin(0.1)' , h2sin(0.1),'h2sinh(0.1)', h2sinh(0.1))

"""
The results are,
Product of  25  and 14   350
Sum of 25  and 14   39
Subtraction   25  and 14   11
division of  25  and 3   8 . 3
Square root of  314   17 . 7
pi 3.1415936535907742
e 2.7182818284590455
h2cos(3.14) 0.0007963267107332883 h2sin(0.1) 0.09983341664682817 h2sinh(0.1) 0.10016675001984403

"""



#The following code works if you have numpy and matplotlib installed
import numpy as np
import matplotlib.pyplot as plt
def h2gamma(n):
    if n==1:
        return 1;
    if n==0.5:
        return 1;
    else:
        return (n-1)*h2gamma(n-1);
    

x=np.arange(0,1,0.05)
plt.plot(x,h2sin(x),x,h2cos(x),x,h2exp(x),x,h2erf(x),x,h2cosh(x),x,h2acot(x),x,h2ln1px(x),x,h2atan(x),x,h2atanh(x))
plt.legend(['h2sin(x)','h2cos(x)','h2exp(x)','h2erf(x)','h2cosh(x)','h2acot(x)','h2ln1px(x)','h2atan(x)','h2atanh(x)'])
plt.show()