CSE202: Lecture 8The Ohio State University1 Formatting Numbers for Output

CSE202: Lecture 8 The Ohio State University 1

Formatting Numbers for Output


Formatting Numbers for Output

• Number formatters are to be used in conjunction with cout

• For example,

double x = 6;cout << x << endl;

• The above outputs 6, but x is declared a floating point number, so why isn’t 6.0000… displayed?


Formatting Numbers for Output (2)

• The decimal point is truncated for display, so we must force it to be shown. Observe the following code:

double x = 6;cout.setf(ios::fixed);cout << x << endl;

• Notice the cout.setf(ios::fixed) command. It says “force cout to display the decimal point and 6 significant digits afterward.”

• Now 6.000000 will be displayed.


outputFormat1// format output#include <iostream>using namespace std;

int main(){ double x; cout << "Enter x: "; cin >> x;

cout << "x = " << x << endl; // general format, default cout.setf(ios::fixed); // use fixed decimal notation cout << "x = " << x << endl; cout.unsetf(ios::fixed); // unset fixed decimal notation flag cout.setf(ios::scientific); // use scientific notation cout << "x = " << x << endl; return 0;}


> outputFormat1.exeEnter x: 123.45x = 123.45x = 123.450000x = 1.234500e+02

> outputFormat1.exeEnter x: 1e15x = 1e+15x = 1000000000000000.000000x = 1.000000e+15

…

cout << "x = " << x << endl; // general format, default

cout.setf(ios::fixed); // use fixed decimal notation

cout << "x = " << x << endl;

cout.unsetf(ios::fixed); // unset fixed decimal notation flag

cout.setf(ios::scientific); // use scientific notation

cout << "x = " << x << endl;

…


> outputFormat1.exe

Enter x: 1e-15

x = 1e-15

x = 0.000000

x = 1.000000e-15

>

…



cout << "x = " << x << endl;



cout << "x = " << x << endl;

…


Setting Precision (1)

• Remember that fixed shows 6 decimal places by default. But…– if our program dealt with printing out dollar

amounts, do we really need to show 6 decimal places?

– Another example: if our program dealt with some rigorous scientific simulation, is 6 decimal places enough?


Setting Precision (2)

• To set the precision, we use cout.precision(n) formatter, where n is the number of decimal places to be displayed.

double x = 6;cout.precision(3);cout.setf(ios::fixed);cout << x << endl;

• Now 6.000 is displayed.


examplePrecision// example of setting precision…int main(){ cout.setf(ios::fixed); cout << "pi/100 = " << M_PI/100.0 << endl;

cout.precision(3); cout << "pi/100 = " << M_PI/100.0 << endl;


return 0;}


> examplePrecision.exepi/100 = 0.031416pi/100 = 0.031pi/100 = 0.031415926536

>

… cout.setf(ios::fixed); cout << "pi/100 = " << M_PI/100.0 << endl;


cout.precision(12); cout << "pi/100 = " << M_PI/100.0 << endl;…


examplePrecision2// example of setting precision…int main(){ cout.setf(ios::scientific); cout << "pi/100 = " << M_PI/100.0 << endl;



return 0;}


> examplePrecision2.exepi/100 = 3.141593e-02pi/100 = 3.142e-02pi/100 = 3.141592653590e-02

>

… cout.setf(ios::scientific); cout << "pi/100 = " << M_PI/100.0 << endl;


cout.precision(12); cout << "pi/100 = " << M_PI/100.0 << endl;…


examplePrecision3// example of setting precision…int main(){ cout.precision(30);

cout.setf(ios::fixed); cout << "pi/100 = " << M_PI/100.0 << endl; return 0;}

> examplePrecision3.exepi/100 = 0.031415926535897934

>


examplePrecision4// example of setting precision…int main(){ cout.precision(30);

cout.setf(ios::scientific); cout << "pi/100 = " << M_PI/100.0 << endl; return 0;}

> examplePrecision4.exepi/100 = 3.141592653589793394e-02

>


Double Precision

• IEEE Standard for Floating-Point Arithmetic:

Double precision numbers have 16 significant digits.


outputFormat2// format output#include <iostream>using namespace std;

int main(){ double x;

cout << "Enter x: "; cin >> x;

cout.precision(12); cout << "x = " << x << endl; // general format, default cout.setf(ios::fixed); // use fixed decimal notation cout << "x = " << x << endl; cout.unsetf(ios::fixed); // unset fixed decimal notation flag cout.setf(ios::scientific); // use scientific notation cout << "x = " << x << endl; return 0;}



> outputFormat2.exeEnter x: 1e15x = 1e+15x = 1000000000000000.000000000000x = 1.000000000000e+15

…

cout.precision(12);



cout << "x = " << x << endl;



cout << "x = " << x << endl;

…


> outputFormat2.exeEnter x: 123456789e-17x = 1.23456789e-09x = 0.000000001235x = 1.234567890000e-09

>

…

cout.precision(12);



cout << "x = " << x << endl;



cout << "x = " << x << endl;

…


Fixed vs. Scientific• cout.precision(12);cout.setf(ios::fixed);cout << “x = “ << x << endl;

Outputs 12 digits after the decimal place.

• cout.precision(12);cout.setf(ios::scientific);cout << “x = “ << x << endl;

Outputs 13 significant digits.


Setting Output Width

tempTable


> tempTable.exefahrenheit celsius kelvin -40 -40.00 233.15 -20 -28.89 244.26 0 -17.78 255.37 20 -6.67 266.48 40 4.44 277.59 60 15.56 288.71>


tempTableBad.cpp// Output with no formatting#include <iostream>using namespace std;

int main(){ cout << "fahrenheit celsius kelvin" << endl; for (int fahrenheit = -40; fahrenheit <= 60; fahrenheit += 20) { double celsius = (fahrenheit - 32.0) * (5.0/9.0); double kelvin = celsius + 273.15;

cout << " " << fahrenheit << " " << celsius << " " << kelvin << endl; }

return 0;}

tempTableBad


> tempTableBad.exefahrenheit celsius kelvin -40 -40 233.15 -20 -28.8889 244.261 0 -17.7778 255.372 20 -6.66667 266.483 40 4.44444 277.594 60 15.5556 288.706 >

cout << "fahrenheit celsius kelvin" << endl; for (int fahrenheit = -40; fahrenheit <= 60; fahrenheit += 20) { double celsius = (fahrenheit - 32.0) * (5.0/9.0); double kelvin = celsius + 273.15;



tempTableBad2.cpp. . .int main(){ cout.setf(ios::fixed); cout.precision(2);



return 0;}

tempTableBad2


> tempTableBad2.exefahrenheit celsius kelvin -40 -40.00 233.15 -20 -28.89 244.26 0 -17.78 255.37 20 -6.67 266.48 40 4.44 277.59 60 15.56 288.71>



Width Problem


> tempTableBad2.exefahrenheit celsius kelvin -40 -40.00 233.15 -20 -28.89 244.26 0 -17.78 255.37 20 -6.67 266.48 40 4.44 277.59 60 15.56 288.71>

cout << " " << fahrenheit << " " << celsius << " " << kelvin << endl;

Problem: Need to fix the width of each output field.


#include <iomanip>

• Output can also be format using routines in iomanip.

• To use of these functions, include this file in your program header:#include <iomanip>


setw• The formatter setw(n) sets the width of the output to at least n

characters. String/value is right justified.• Example:

cout << setw(10)<< “Age” << setw(10) << “Weight” << endl;cout << setw(10) << 4 << setw(10) << 32 << endl;cout << setw(10) << 22 << setw(10) << 130.5 << endl;cout << setw(10) << 101 << setw(10) << 120 << endl;

• Output is: Age Weight 4 32 22 130.5 101 120


tempTable.cpp#include <iostream>#include <iomanip> // Note: Must include iomanip...int main(){ cout.setf(ios::fixed); cout.precision(2);


cout << setw(6) << fahrenheit << setw(15) << celsius << setw(10) << kelvin << endl; }...

tempTable


> tempTable.exefahrenheit celsius kelvin -40 -40.00 233.15 -20 -28.89 244.26 0 -17.78 255.37 20 -6.67 266.48 40 4.44 277.59 60 15.56 288.71>

cout << setw(6) << fahrenheit << setw(15) << celsius << setw(10) << kelvin << endl;

trigTable


> trigTable.exe degrees radians sin cos -180 -3.14 -0.00 -1.00 -150 -2.62 -0.50 -0.87 -120 -2.09 -0.87 -0.50 -90 -1.57 -1.00 0.00 -60 -1.05 -0.87 0.50 -30 -0.52 -0.50 0.87 0 0.00 0.00 1.00 30 0.52 0.50 0.87 60 1.05 0.87 0.50 90 1.57 1.00 0.00 120 2.09 0.87 -0.50 150 2.62 0.50 -0.87 180 3.14 0.00 -1.00>


trigTable.cpp...#include <iomanip> // NOTE: Must include iomanip... cout.setf(ios::fixed); cout.precision(2);

cout << setw(8) << "degrees" << setw(8) << "radians" << setw(8) << "sin" << setw(8) << "cos" << endl;

for (int degrees = -180; degrees <= 180; degrees += 30) { double radians = degrees * M_PI/180.0;

cout << setw(8) << degrees << setw(8) << radians << setw(8) << sin(radians) << setw(8) << cos(radians) << endl; }...

trigTable


> trigTable.exe degrees radians sin cos -180 -3.14 -0.00 -1.00 -150 -2.62 -0.50 -0.87 -120 -2.09 -0.87 -0.50 -90 -1.57 -1.00 0.00 -60 -1.05 -0.87 0.50 -30 -0.52 -0.50 0.87 0 0.00 0.00 1.00 30 0.52 0.50 0.87 60 1.05 0.87 0.50 90 1.57 1.00 0.00 120 2.09 0.87 -0.50 150 2.62 0.50 -0.87 180 3.14 0.00 -1.00>

cout << setw(8) << "degrees" << setw(8) << "radians" << setw(8) << "sin" << setw(8) << "cos" << endl;

expTable


> expTable.exeEnter number of values: 10 x e^x 2^x 1 2.72 2.00 2 7.39 4.00 3 20.09 8.00 4 54.60 16.00 5 148.41 32.00 6 403.43 64.00 7 1096.63 128.00 8 2980.96 256.00 9 8103.08 512.00 10 22026.47 1024.00>


expTable.cpp...#include <iomanip> // NOTE: Must include iomanip... cout << "Enter number of values: "; cin >> n;

cout.setf(ios::fixed); cout.precision(2);

cout << setw(5) << "x" << setw(10) << "e^x" << setw(10) << "2^x" << endl;

for (int i = 1; i <= n; i++) { double x = i; cout << setw(5) < expTable.exeEnter number of values: 15 x e^x 2^x 1 2.72 2.00 2 7.39 4.00... 11 59874.14 2048.00 12 162754.79 4096.00 13 442413.39 8192.00 141202604.28 16384.00 153269017.37 32768.00>


expTable


> expTable.exeEnter number of values: 25 x e^x 2^x 1 2.72 2.00 2 7.39 4.00... 13 442413.39 8192.00 141202604.28 16384.00 153269017.37 32768.00... 239744803446.258388608.00 2426489122129.8416777216.00 2572004899337.3933554432.00 >



expTable2.cpp... cout << "Enter number of values: "; cin >> n;

cout.setf(ios::fixed); cout.precision(2);

cout << setw(5) << "x" << " " << setw(10) << "e^x" << " " << setw(10) << "2^x" << endl;

for (int i = 1; i <= n; i++) { double x = i; // Add spaces between fields. cout << setw(5) < expTable2.exeEnter number of values: 10 x e^x 2^x 1 2.72 2.00 2 7.39 4.00 3 20.09 8.00 4 54.60 16.00 5 148.41 32.00 6 403.43 64.00 7 1096.63 128.00 8 2980.96 256.00 9 8103.08 512.00 10 22026.47 1024.00>

// Add spaces between fields. cout << setw(5) < expTable2.exeEnter number of values: 15 x e^x 2^x 1 2.72 2.00 2 7.39 4.00... 10 22026.47 1024.00 11 59874.14 2048.00 12 162754.79 4096.00 13 442413.39 8192.00 14 1202604.28 16384.00 15 3269017.37 32768.00>


expTable2


> expTable2.exeEnter number of values: 25 x e^x 2^x 1 2.72 2.00 2 7.39 4.00... 20 485165195.41 1048576.00 21 1318815734.48 2097152.00 22 3584912846.13 4194304.00 23 9744803446.25 8388608.00 24 26489122129.84 16777216.00 25 72004899337.39 33554432.00>




// DO NOT SET FIXED OUTPUT FORMAT // cout.setf(ios::fixed); cout.precision(2);

cout << setw(5) << "x" << setw(10) << "e^x" << setw(10) << "2^x" << endl;

for (int i = 1; i <= n; i++) { double x = i; cout << setw(5) < expTable3.exeEnter number of values: 25 1 2.7 2 2 7.4 4... 20 4.9e+08 1e+06 21 1.3e+09 2.1e+06 22 3.6e+09 4.2e+06 23 9.7e+09 8.4e+06 24 2.6e+10 1.7e+07 25 7.2e+10 3.4e+07>


expTable3


> expTable3.exeEnter number of values: 10 x e^x 2^x 1 2.7 2 2 7.4 4 3 20 8 4 55 16 5 1.5e+02 32 6 4e+02 64 7 1.1e+03 1.3e+02 8 3e+03 2.6e+02 9 8.1e+03 5.1e+02 10 2.2e+04 1e+03 >



Other Formatters• Iomanip contains many other formatters, including:

fixed Force show a decimal point with 6 trailing decimal places

scientific Outputs floating point number in scientific notation

hex Outputs integer in hexadecimal (base16)

oct Outputs integer in octal (base 8)

showpos Force positive numbers to be shown with a leading ‘+’ symbol

setprecision(n) Set floating point precision to n places

setw(n) Set the field width to n characters


outputFormat3// format output#include <iostream>#include <iomanip>using namespace std;

int main(){ double x;

cout << "Enter x: "; cin >> x;

// general format, default, 12 significant digits cout << "x = " << setprecision(12) << x << endl; // fixed decimal notation, 12 digits after decimal point cout << "x = " << fixed << setprecision(12) << x << endl; // scientific notation, 12 digits after decimal point cout << "x = " << scientific << setprecision(12) << x << endl; return 0;}


…

// general format, default, 12 significant digits

cout << "x = " << setprecision(12) << x << endl;

// fixed decimal notation, 12 digits after decimal point

cout << "x = " << fixed << setprecision(12) << x << endl;

// scientific notation, 12 digits after decimal point

cout << "x = " << scientific << setprecision(12) << x << endl;

…


> outputFormat3.exeEnter x: 123456789e-17x = 1.23456789e-09x = 0.000000001235x = 1.234567890000e-09


Rounding Output// example of output rounding

#include <iostream>#include <iomanip>using namespace std;

int main(){ double x = 1.0/7.0;

cout << "x = " << setprecision(12) << x << endl; cout << "x = " << setprecision(7) << x << endl; cout << "x = " << setprecision(5) << x << endl; return 0;}

• C++ rounds output.


…

double x = 1.0/7.0;




…

> roundOutput.exex = 0.142857142857x = 0.1428571x = 0.14286

>

expTable



expTable4


> expTable4.exeEnter number of values: 10 x e^x 2^x 1 2.72 2 2 7.39 4 3 20.09 8 4 54.60 16 5 148.41 32 6 403.43 64 7 1096.63 128 8 2980.96 256 9 8103.08 512 10 22026.47 1024>



cout.setf(ios::fixed);

cout << setw(5) << "x" << " " << setw(10) << "e^x" << " " << setw(8) << "2^x" << endl;

for (int i = 1; i <= n; i++) { double x = i; // Use precision 2 for e^x and precision 0 (integer) for 2^x. cout << setw(5) < expTable4.exeEnter number of values: 10 x e^x 2^x 1 2.72 2 2 7.39 4 3 20.09 8 4 54.60 16 5 148.41 32 6 403.43 64 7 1096.63 128 8 2980.96 256 9 8103.08 512 10 22026.47 1024>

// Use precision 2 for e^x and precision 0 (integer) for 2^x. cout << setw(5) << i << " " << setw(10) << setprecision(2) << exp(x) << " " << setw(8) << setprecision(0) << pow(2.0,x) << endl;

Summary

• cout.setf(ios::fixed); // use fixed decimal notation• cout.setf(ios::scientific); // use scientific notation• cout.precision(k); // print k digits after decimal

iomanip:• #include <iomanip> // include IO manipulators (formatters)• cout << setw(k) << ...; // set next field width to k• cout << setprecision(k) << ...; // print k digits after decimal• cout << fixed << ...; // switch to fixed decimal notation• cout << scientific << ...; // switch to scientific notation

Documents

CSE202: Lecture 8The Ohio State University1 Formatting Numbers for Output