Chapter 3 - Operators

1. Chapter 3 - Operators • Arithmetic Operators • unary and binary • casting • Assignment • shorthand notation • Bitwise operators • Precedence and associativity

2. Unary arithmetic operators • unary minus operator: - • invert sign of number -a • unary plus operator: + • serves no obvious purpose (leaves a number unchanged) +a

3. Binary arithmetic operators • addition + a+b • subtraction - a-b • multiplication * a*b • division / a/b • modulus % a%b

4. The modulus (mod) operator • c=a%b • both arguments a and b must be integers • c is equal to the remainder of the integral division • Example of integer math: • 9/4 = 2 remainder 1, so with integer math, • 2 = 9/4 and 1 = 9%4

5. Program 3.1 - definition • Determine if a given year is a leap year • What makes a leap year? • year is divisible by four, but not a century, except for every 4th century. • 0, 4, 8, ..., 92, 96, 104, 108, ..., 396, 400, 404, ..., 1896, 1904, 1908, ..., 1996, 2000, 2004, ...

6. Program 3.1 - specification • start • declare variables • prompt for year • read in year • determine if leap year • if yes, print “year is a leap year” • if no, print “year is not a leap year” • stop

7. Program 3.1 - stepwise refinement • determine if leap year • if • year % 400 == 0 • OR • year % 4 == 0 AND year % 100 != 0 • then it is a leap year!

8. Program 3.1 - Leap year /* example #3.1 determine if a given year is a leap year */ #include <stdio.h> int main(void) { int year; printf("input a year:\t"); scanf(" %d",&year); if ((year%4 ==0 && year%100 != 0) || year%400 == 0 ) printf("\n%d is a leap year\n",year); else printf("\n%d is not a leap year\n",year); return 0; }

9. Precedence • order in which operators are evaluated: • Highest level: () [] • Next level: unary + - • Next level: binary * / % • Next level: binary + - • examples: 17 = 3+5*2+8/2 40 = (3+5)*(2+8)/2

10. Associativity • In C there is left-to-right associativity and right-to-left associativity • Unary + - go right to left • () [] * / % + - (binary) go left to right • examples: 8 = 8/-4/2*12/3*-2 32 = 8/(-4/2)*(12/3)*-2

11. Floating point inaccuracies • roundoff error: 1.0/3.0 + 1.0/3.0 + 1.0/3.0 may not equal 1 • overflow: two numbers combined to make a number too large for data type: 2.2e307*4.3e34 = infinity (double) • underflow: two numbers combined to make a number too small for data type: 2.2e-307*4.3e-34 = zero (double)

12. Program 3.2 - floating point woes /* example #3.2 determine the result of floating point inaccuracies */ #include <stdio.h> intmain(intargc, char *argv[]) { float x1=1./3., x2, x3, y1=2.e33, y3=2.e33, y5; double y2=2.e300, y4, x4=1./3., x5, x6; x2=x3=x5=x6=1./3.; y5=1.-(x1+x2+x3); y4=1.-(x4+x5+x6); printf("Roundoff error? \t 0 = %g = %g \n",y4, y5);

13. Program 3.2 continued y5=1./(y1*y2); printf("underflow error? \t 0.25e-333 = %g\n",y5); y5=y1*y2; printf("overflow error? \t 4.e333 = %g\n",y5); y5=1./(y1*y3); printf("underflow error? \t 0.25e-66 = %g\n",y5); y5=y1*y3; printf("overflow error? \t 4.e66 = %g\n",y5); return 0; }

14. Implicit casting and promotion • If an equation contains more than a single data type, variables must be converted (cast) to the same type before the arithmetic operators can be evaluated (hardware rule). • This coercion is known as promotion because smaller data types are cast as larger data types. • This implicit casting is done only as needed!

15. Promotion hierarchy (high-to-low) • long double • double • float • unsigned long int • long int • unsigned int • int • short • char

16. Promotion examples: • int width, length; • float radius, height; • double pi, area, volume; • area=width*length • area=pi*radius*radius • area=2*pi*height*radius • volume=height*width*length • volume=height*radius*radius*pi

17. more promotion examples: • Which of the following are identically zero? float fahrenheit, celcius; celcius=(5/9)*(fahrenheit-32.); celcius=(fahrenheit-32)*5/9; celcius= 5/9*(fahrenheit-32); celcius=(fahrenheit-32.)*(5/9); celcius= 5*(fahrenheit-32.)/9; celcius= 5/9.*(fahrenheit-32);

18. Explicit casting • There is a unitary operator that can be used to explicitly cast an operand: • general form: (type) expression • example: (double) temp • Note: only a copy of the data is made and recast - you cannot change the declared data type. • Warning: casting to a “smaller” data type results in a loss in precision and perhaps worse! (overflow, undefined result,...)

19. Assignment operator = • has low precedence (this will be quantified later) • associates right to left • example a=b=c=d=3+4; • shorthand notation: a=a+b a=a-b a=a*b a=a/ba=a%b a+=ba-=b a*=b a/=ba%=b

20. Increment and decrement operators • a++ is shorthand for a=a+1 • a-- is shorthand for a=a-1 • you can increment/decrement before or after assignment: a=b-- a=b b=b-1 a=++b a=b+1 b=b+1 • don’t use twice in one expression! • ??? = b++/b++

21. Bitwise operators • C has operators that manipulate the individual bits within a word and are useful in many applications: • digital-to-analog converters • control registers • error detection or just whenever computer memory is at a premium

22. Truth tables

23. Bitwise ‘and’ operator ‘&’ • a = 181 = 0xB5 b = 108 = 0x6C • c=a&b = 36 = 0x24 a 1011 0101 b 0110 1100 c 0010 0100 • usually, one argument is a mask, designed to recover certain bits.

24. Bitwise ‘or’ operator ‘|’ • a = 181 = 0xB5 b = 108 = 0x6C • d=a|b = 253 = 0xFD a 1011 0101 b 0110 1100 d 1111 1101 • usually, one argument is a mask, designed to set certain bits.

25. Bitwise ‘exclusive or’ operator ‘^’ • a = 181 = 0xB5 b = 108 = 0x6C • e=a^b = 217 = 0xD9 a 1011 0101 b 0110 1100 e 1101 1001 • usually, one argument is a mask, designed to flip certain bits.

26. Bitwise ‘one’s complement’ ‘~’ • a = 181 = 0xB5 • f = ~a = 74 = 0x4A a 1011 0101 f 0100 1010 • inverts all bits.

27. Bitwise ‘shift left’ operator ‘<<’ • a = 181 = 0xB5; i=3 • g = a << i = 168 = 0xA8 a 1011 0101 g 1010 1000 • shifts ‘a’ i places to the left • Most significant bits (MSB) lost • Least significant bits (LSB) set to zero

28. Bitwise ‘shift right’ operator ‘>>’ • a = 181 = 0xB5; i=3; h = a >>i =22, 246 a 1011 0101 h 0001 0110 (logical shift) h 1111 0110 (arithmetic shift) • shifts ‘a’ i places to the right • LSB lost, MSB compiler dependent • logical shift right: MSB set to zero • arithmetic shift right: MSB preserved

29. More shorthand assignments • a &= b a = a & b • a ^= b a = a ^ b • a |= b a = a | b • a <<= b a = a << b • a >>= b a = a >> b

30. Program 3.3 - bitwise operators /* example #3.3 bitwise operation examples */ #include <stdio.h> int main(void) { unsigned char a=181, b=108, i; printf(" a&b = %d\n",a&b); printf(" a|b = %d\n",a|b); printf(" a^b = %d\n",b^=a); printf(" ~a = %d\n",(unsigned char)~a); i=3; printf("a<<i = %d\n",(unsigned char)(a<<i)); printf("a>>i = %d\n",a>>=i); return 0; }

31. C precedence and associativity () [] left to right ! ~ ++ -- + - * & (type) sizeof right to left * / % left to right + - left to right << >> left to right < <= > >= left to right == != left to right & left to right ^ left to right | left to right && left to right || left to right = += -= *= /= %= &= ^= |= <<= >>= right to left , left to right

32. Advanced operators Only three more operators to go... J but that will have to wait until later... L