C Data Types and Conversions CSC 230 – C and Software Tools Fall 2020 Dr. Douglas Reeves NC State Department of Computer Science 1 Specializations of Fundamental Types Integers can be… – signed or unsigned (signed by default) – really short (char), short, regular (default), long, really long (long long) Floating point (always signed) can be… – regular precision (float) – double precision (double) – extended precision (long double) 2 1 “Usual” Min and Max Integer Values unsigned not in Java Tutorialspoint.com/cprogramming/c_data_types.htm 3 On Your Machine: Check limits.h Demo… 4 2 Floating Point (Real Numbers) Before IEEE Standard, very platform dependent! Terminology sign of the mantissa +.793 * 2 magnitude of the mantissa -36 base of the exponent exponent Size of the exponent (# bits) mainly determines the range of numbers that can be represented Size of the mantissa (# bits) mainly determines the precision of numbers that can be represented 5 IEEE Standard Single precision: – 1-bit sign – 23-bit (+ 1 implied bit) mantissa – 8-bit biased exponent (base 2) Double precision: – 1-bit sign – 52+1 bit mantissa – 11-bit biased exponent (base 2) 6 3 Min and Max Min (normalized) positive values (approximate) – single precision (float): 2-126 (≈10-38 ) – double precision (double): 2-1022 (≈10-308) – Q: small enough to measure the diameter of an atom, in meters? Max (normalized) positive values (approximate) – single precision (float): 2127 (≈1038) – double precision (double): 21023 (≈10308) – Q: big enough to count the number of atoms in the universe? distance to the edge of the observable universe, in units of atom diameters? 7 Min and Max long double = 128 bits – more bits precision than double, same range 8 4 Reminder: Arithmetic Problems Types make a difference in computer arithmetic – signed vs. unsigned max and min values (integer) – overflow (integer and floating point) – underflow and limited precision (floating point) Bottom line: 1. In expressions, types of operands should match 2. C will not protect from or warn about overflow – the program has to check for it N common source of bugs N overflow, limits of precision 9 C Type Conversions Data type conversions occur in two ways – explicitly (e.g., programmer deliberately casts from one type to another) – or implicitly (e.g., variables of different types are combined in a single expression, compiler casts from one type to another) unsigned char a; int b; float c; double d; … c = (float) b; d = a + (b * c); 10 5 Casting (Explicit Conversion) Programmer knows what they’re doing and wishes to force a specific type conversion Syntax: (typename) expression d = (double) c; Being careful / deliberate, not careless A special case: (void) expression; – means value of an expression must not be used in any way – Q: how could that possibly be useful? 11 Converting signed to unsigned This only makes sense if you are sure the value stored in the signed operand is positive If signed is the shorter operand, extend it int a; unsigned b; a = -36; b = (unsigned) a; a = (int) b; int a; unsigned short b; a = -36; b = (unsigned short) a; a = (int) b; Result when output: b = 4294967260 a = -36 Result when output: b = 65500 a = 65500 What happened??? 12 6 Converting unsigned to signed If signed is large enough to store the correct value, no problems – otherwise, will definitely be an error (overflow)! int a; unsigned int b; b = 3000000000; a = (int) b; Result when output: b = 3000000000 a = -1294967296 13 Floating to Integer Rounds towards zero (“truncate”) to get the integer part, and discard the fractional part – +3.999 ® 3 – -3.999 ® -3 – obviously some loss of precision can occur here Overflow if the integer variable is too small float f = 1.0e10; int i; i = f; Result when output: f = 10000000000.0 i = -2147483648 14 7 Converting to Floating Integer ® Floating – if value cannot be represented exactly in floating point, converts to the closest value (either higher or lower) that can be represented in floating point Double precision ® Single precision – if value cannot be represented exactly, converts to closest value (either higher or lower) – can overflow or underflow! 15 Implicit Conversions For “mixed type” expressions, e.g., d = a + (b * c); double float short int unsigned char The compiler does “the usual arithmetic conversions” before evaluating the expression char’s and short’s are always converted to ints (or unsigned ints) before evaluating expressions 16 8 The “Usual Conversions” For Arithmetic Operations In a nutshell: when combining values of two numbers… 1. if either is floating point, convert the other to floating point, and 2. convert less precise to more precise Order is significant in the following table! 17 The “Usual…” (cont’d) Rule If either operand is… And other operand is… Then convert other operand to… #1 long double Anything long double Else… #2 double Anything double Else… #3 float Anything float Else… #4 unsigned long int Anything unsigned long int Else… #5 long int unsigned int ! unsigned long int #6 long int Anything else long int Else… #7 unsigned int Anything Else… #8 unsigned int Else… (both operands have type int, no action needed) 18 9 Example double float unsigned char short int d = a + (b * c); before evaluating expression: convert b to unsigned int before multiplying: convert c to unsigned int (rule #7) before adding: convert result of multiplying to float (rule #3) when assigning: convert result of addition to double (rule #2) 19 10
