TERM PAPER

Of C++

TOPIC:SCIENTIFIC CALCULTOR

SUBMITTED TO:MR.Dishant sikka

SUBMITTED BY:POOJA SHARMA

E1804A0510803094

ACKNOWLEDGEMENT

As the professional courses do not only required the theoretical knowledge but need to cover

practical aspect too. Universities have started conducting training programs for students. So,

that they get simple view of practical knowledge.

No work of significance can be claimed on a result of individual Efforts and same holds true

further for this project as well, for through it carries my name the energy of many have

contributed in no small measure in completion of this project.

I am very thankful to my friend and our teachers ER. DISHANT SIR who help me to make this project.

POOJA SHARMA

INTRODUCTION

Scientific calculator is an extension of a mathematician and it has opened up new possibilitie.Within mathematics. It is a machine though, and it is only capable of doing what it is programmed to do. Accordingly, this project aims to develop the internal programmed computational code in the form of a computer program that a scientific calculator could use to compute functions such as square root, the exponential, and sine functions.1 The idea of this project assumes that that the programmer has already developed the very basic addition, Subtraction, multiplication, division and integer splicing2 functions. Then using these basic functions, the program will then compute other more complicated functions found on a typical scientific calculator such as the sine and logarithmic functions.The calculator is an extension of a mathematician and it has opened up new possibilitiesWithin mathematics. It is a machine though, and it is only capable of doing what it isProgrammed to do. Accordingly, this project aims to develop the internal programmedcomputational code in the form of a computer program that a scientific calculator could use to compute functions such as square root, the exponential, and sine functions.1 The idea of this project assumes that that the programmer has already developed the very basic addition,Subtraction, multiplication, division and integer splicing2 functions. Then using these basicFunctions, the program will then compute other more complicated functions found on a typical scientific calculator such as the sine and logarithmic functions. With the necessity to conform to reality, there are limitations set upon this calculator andThey are similar to those found in popular calculators such as the Texas Instruments TI-83 Plus.They are that:(1) Functions inputs and outputs must be calculated accurately to ten significant figures3,(2) The absolute values of inputs and outputs, excluding zero, can never be greater than or equalto 1 x 10100 or less than or equal to 1 x 10-100.Similar to these mandatory requirements, there are a few goals that I wish to accomplish withinthe confines of the limitations. They are that:(1) The code is as easily programmed as possible,(2) And that the program is to be as efficient as possible at computing the functions.

I chose to work within the C++ language. A few advantages with choosing thislanguages are that the code is easily transferred into other programming languages and that it is universally known. I choose to use a Windows Console application due to its simplicity and my familiarity with it, but this is a disadvantage because it is not an optimal interface for a calculator due to its lack of visual resemblance of a handheld calculator.The interface created for user inputs and outputs was created for basic test purposes only,and if I had more time, I would have liked to use Visual Basic to create a visual calculator with buttons that were able to be pressed. Even though the created interface looks rudimentary, it contains all the possible tasks that the program is able to do. There were other programming and computations issues that needed to be taken into account as well when transferring mathematical theory into a working calculator. One issue was the large difference in computational time. Computing multiplication and division takes significantly longer time than computing addition and subtraction, and therefore should be avoided whenever possible. Thus throughout the program there are instances where addition and subtraction is used to eliminate the need for multiplication. Another issue is that the program is constantly rounding numbers and thus losing trailing digits. Therefore in some cases it is very difficult or impossible to adhere to the goals previously described. An example of this is within the modulo function which cannot be evaluated for relatively large values modulo a relatively small value.

TESTING FUNGTIONS

A random number generator was created that, based upon a user’s inputs, creates aSpecified number of random numbers on a given range. To do this, a vector is created withrandom integral values between in the interval (1, 215). These values are then divided by 215 and thus randomly distributed in the in the interval (0, 1). Following this, the numbers, under the same randomization pattern, are spread throughout the user defined interval.The error estimation function’s purpose is to determine how accurate a given function isbased upon the respective C++ built in function. To do this, a vector is created containing auser’s defined number of terms, upper bound, lower bound and a function. Given this, the error estimator function calculates the percent error of each value in the vector by the equation:( )( )( ) ( _ )( ) ( )( )C Function xPercent Error x Created Function x C Function x+ +

− + += .After each value is tested, the percent error of the function at that value is tested to determine ifthe absolute value of the percent error at that point is the maximum percent error of the valuestested thus far. Once all values in the vector have been tested, the maximum percent error isoutputted and if the result is less than or equal to 10−10 then it is determined that the accuracy is sufficient and complies with the ten significant figure goal.In theory and through all my testing I have found that the calculations that are outputtedare accurate to the ten significant figure requirement. The times that the program would notcompute to the required accuracy, similar to a calculator, an error should be outputted. Anexample of this is sin ((1e50) + 1). This in theory is calculable, but the large number ofsignificant figure prevents this for happening realistically. In this program there is an error that is triggered and thus the program is stopped.The efficiency estimator calculates how efficient a created function is compared torespective C++ native function. To do this, a vector of random numbers is created based uponthe user defined variables of the number of terms, upper bound, lower bound and a function.Once this is done, the created function is timed to see how many ticks11 it takes to compute all of the values in the vector. Following this, a C++ native function is tested to see how long, in ticks,it takes to compute all the values in the vector.1 tick = 1/1000 second.

Percentage error(x)=(created function(X)-(c++function)(X)/(c++function)(x)

percent error of the function at that value is tested to determine ifthe absolute value of the percent error at that point is the maximum percent error of the values tested thus far. Once all values in the vector have been tested, the maximum percent error isoutputted and if the result is less than or equal to 10−10 then it is determined that the accuracy issufficient and complies with the ten significant figure goal.

Scientific CalculatorTrigonometric Functions

Function Description   Function Descriptionsin() sine   asin() inverse sinecos() cosine   acos() inverse cosinetan() tangent   atan() inverse tangentcot() cotangent ie cos()/sin()   acot() inverse cotanget ie atan(1/x)sec() secant ie 1/cos()   asec() inverse secant ie acos(1/x)csc() cosecant ie 1/sin()   acsc() inverse cosecant ie asin(1/x)

 

Hyperbolic functions

sinh() hyperbolic sine   asinh() inverse hyperbolic sinecosh() hyperbolic cosine   acosh() inverse hyperbolic cosinetanh() hyperbolic tangent   atanh() inverse hyperbolic tangent coth() hyperbolic cotangent   acoth() inverse hyperbolic cotangent sech() hyperbolic secant   asech() inverse hyperbolic secantcsch() hyperbolic cosecant   acsch() inverse hyperbolic cosecant

 

General Functions

sort() square root      abs() absolute value      fact() factorial      

floor() Rounds down to the nearest integer   ceil() Rounds up to the nearest integer

round() Rounds to the nearest integer (0.5+ goes up)      

 

Logarithm functions

log() base 10 logarithm      logb(x,b) base "b" logarithm      ln() natural logarithm   exp(x) e to the power x

 

Functions needing two values

gcd(x,y) greatest common denominator      

of x and ymax(x,y) maximum of x and y      min(x,y) minimum of x and y      angle(x,y) angle of coords x and y      dist(x,y) distance to coords x and y      comb(x,y) combinations of x and y      

  i The unit Imaginary Number (√(-1))

  pi The constant π (3.141592654...)

  e The Euler Constant (2.71828...), the base for the natural logarithm

PROGRAM #include<iostream.h>#include<conio.h>#include<math.h>#include<process.h>#define sqr(x) (x)*(x)void main()

{

float a,b,c; int choice,i; clrscr(); do{clrscr();cout<<”\nSCIENTIFIC CALCULATOR";cout<<"\nEnter numbers for addition=”<<Addition;cout<<”\nEnter numbers for subtraction=”<<Subtration;cout<<”\nEnter numbers for multiplication=”<<Multiplication;cout<<”\nEnter numbers for division=”<<Division;cout<<”\n Enter values for function=”<<Sine;cout<<”\n Enter values for function=”<<Cosine;

cout<<”\n Enter values for function=”<<Tan;cout<<”\n Enter values for function=”<<Log;cout<<”\n Enter values for function=<<”Quadraic Equation Solver;cout<<”\n Enter values for function=<<”Simultaneous Equation Solver;cout<<”\n Enter values for function=”<<Power Function(^);cout<<”\n Enter values for function=”<<Exponential Power Function";cin>>choiceswitch(choice){

case 1:{ clrscr(); cout<<"\naddition”; cout<<"\nEnter two numbers"; cin>>a>>b; c=a+b; cout<<”Ans =”<<c;

cout<<"Thank You for using this program”; break; }

case 2: {clrscr();cout<<”\nsubtraction”;cout<<"\nEnter two numbers”;cin>>a>>b; c=a-b;cout<<”Ans =”<<c;cout<<"\nThank You for using this program"; break;

}

case 3:{

clrscr();cout<<”\nmultiplication”; cout<<”\nEnter two numbers";

cin>>a>>b; c=a*b; cout<<”\nAns =”<< c; cout<<"\nThank You for using this program\n");

break; }

case 4:{clrscr();cout<<”\ndivison”;cout<<"\nEnter two numbers";cin>>a>>b;

c=a/b; cout<<"\nAns ="<<c; cout<<”\nThank You for using this program"; break; }

case 5: {double a,b,ans;int ch;clrscr();cout<<"\nSINE FUNCTION";cout<<"\n Press 1 if the angle is in degree";cout<<"\nPress 2 if the angle is in radians";cin>>ch;{cout<<"\nEnter angle in degree"; cin>>a; b=(a*22)/(7*180);

}else if(ch==2)

{

cout<<"\nEnter angle in radians"; cin>>a; b=a; } else

cout<<"\nError!!!"; break; } ans = sin(b);

cout<<"\nThe sin() of ="<<a<<ans);cout<<"\nThank You for using this program";

break; }

case 6:{double a,b,ans;int ch;clrscr();cout<<"\nCOSINE FUNCTION";cout<<"\nPress 1 if the angle is in degree";cout<<"\nPress 2 if the angle is in radians"; cin>>ch;

if(ch==1){

cout<<"\nEnter angle in degree";cin>>a;b=(a*22)/(7*180);} else if (ch==2){cout<<"\nEnter angle in radians";cin>>a;b=a;}

elsecout<<"\nError!!!";break;

}ans = cos(b);cout<<"\nThe cos() of=”<<ans<<a;cout<<"\nThank You for using this program";break; }

case 7:{doublea,b,ans;int ch;

clrscr();cout<<"\nTAN FUNCTION\n\n");

cout<<"\nPress 1 if the angle is in degree”; cout<<"\nPress 2 if the angle is in radians"; cin>>ch; if(ch==1)

cout<<"\nEnter angle in degree”; cin>>a; b=(a*22)/(7*180); }

else

if(ch==2){

cout<<"\nEnter angle in radians"; cin>>a; b=a; } else

{ cout<<"\n"Error!!!"; break; } ans = tan(b);

cout<<"\nThe tan() of="<<a<<ans; cout<<"\nThank You for using this program"; break; }

case8: { float A,B,C, Delta; clrscr(); cout<<"\nQUADRATIC EQUATION SOLVER”; cout<<"\n Enter Coefficients”; cout<<"\nA = "; cin>>A; cout<<"\nB = "; cin>>B; cout<<"\nC = "; cin>>C; if(A == 0 && B != 0)

{ cout<<"\nThis equation is a first degree equation"; cout<<"\nThe solution is= "<<-C/B; } else if(A == 0 && B == 0)

{ cout<<"\nThis equation has no solution\n"); } else

{ Delta = sqr(B) - 4*A*C; if(Delta < 0)

{ cout<<"\nThis equation dont have any real roots\n";

}

else if(Delta == 0){

cout<<"\nThis equation have a single root: ",-B/(2*A));

} else

{ cout<<"\nThis equation have two real roots\n";

float X1 = (-B + sqrt(Delta)) / (2 * A); float X2 = (-B - sqrt(Delta)) / (2 * A); cout<<"\nX1 ="X1; cout<<"\nX2 ="X2; } }

cout<<"\nThank You for using this program"; break;

}case 9: {

double a,ans; int ch; clrscr(); cout<<"\nLOGARITHMIC FUNCTIONS\n\n"); cout<<"\n1.Natural Log\n2.Log to the base 10\n"); cin>>ch;

if(ch==1){

cout<<"\n "Enter value"; cin>>a; ans=log(a); cout<<"\n Log of ="<<a<<ans; } else if(ch==2)

{ cout<<"\n Enter value"; cin>>a; ans=log10(a); cout<<"\n "Log of to the base 10 is="<<a<<ans; }

else

{ cout<<"\nError!!!"; break; }

case 10:{ int a1,a2,b1,b2,c1,c2,c,b3,b4,a3,a4,c3,c4,c5,c6; int m,n,i,d=1,lcm; float a,b; clrscr(); cout<<"\nSIMULTANEOUS EQUATION SOLVER"; cout<<"\na1”; cin>>a1; cout<<”\nb1”; cin>>b1; cout<<"\nc1”; cin>>c1; cout<<"\na2"; cin>>a2; cout<<"\nb2"; cin>>b2; cout<<"\nc2"; cin>>c2; if(a1>a2)

n = a2; } else

{ m = a2; n = a1; } for(i=2;i<=n && n!=1;i++)

{ if(m%i==0 && n%i==0)

{ m = m/i; n = n/i;

d = d*i; i = 2; } } if(d==1)

{ lcm = m*n; } else { lcm = d*m*n; } b3 = b1*(lcm/a1); b4 = b2*(lcm/a2); c3 = c1*(lcm/a1); c4 = c2*(lcm/a2); if(a1<0 && a2<0 || a1>0 && a2>0)

{ b = b3-b4; c = c3-c4; b = c/b; } else

{ b = b3+b4; c = c3+c4; b = c/b; } if(b1>b2)

{ m = b1; n = b2; } else

{ m = b2; n = b1;

} for(i=2;i<=n && n!=1;i++)

{ if(m%i==0 && n%i==0)

{ m=m/i; n=n/i; d=d*i; i=2; } } if(d==1)

{ lcm=m*n; } else

{ lcm=d*m*n; } a3 = a1*(lcm/b1); a4 = a2*(lcm/b2); c5 = c1*(lcm/b1); c6 = c2*(lcm/b2);

if(b1<0 && b2<0 || b1>0 && b2>0)

{ a = a3-a4; c = c5-c6; a = c/a; } else

{ a = a3+a4; c = c5+c6; a = c/a; `}

cout<<"\n X ="<<a; cout<<"\nY ="<<b;

cout<<"\n Thank You for using this program”; break; }

case 11:{ float m,n,p; clrscr(); cout<<"\n POWER FUNCTION(^)”;

cout<<"\n Enter the values of m and n w.r.t to the equation m^n\n");

cin>>m>>n; p = pow(m,n); cout<<"\n raise to = "<<m<<n<<p; cout<<"\n Thank You for using this program"; break; }

case 12:{ float r,s; clrscr(); cout<<"\n EXPONENTIAL FUNCTION”;

cout<<"\n Enter value";

cin>>r; s = exp(r); cout<<"\n Answer ="<<s; cout<<"\n Thank You for using this program\n"); break; }

default:{ cout<<"\n Error!!!"; break; }

} cout<<”\nEnter 1 to continue\nEnter 0 to exit";

cin>>i; }while(i==1);

getch(); }