Simple Data Types in C - Introduction to Computer Systems - Lecture Slides, Slides of Computer System Design and Architecture

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Simple Data Types in C docsity.com Objectives Be able to explain to others what a data type is Be able to use basic data types in C programs Be able to see the inaccuracies and limitations introduced by machine representations of numbers docsity.com Everything is Just a Bunch of Bits Bits can represent many different things  Depends on interpretation You and your program must keep track of what kind of data is at each location in the computer’s memory  E.g., program data types docsity.com Big Picture Processor works with finite-sized data All data implemented as a sequence of bits  Bit = 0 or 1  Represents the level of an electrical charge Byte = 8 bits Word = largest data size handled by processor  32 bits on most older computers  64 bits on most new computers docsity.com Data types in C Only really four basic types:  char  int (short, long, long long, unsigned)  float  double Size of these types on CLEAR machines: Sizes of these types vary from one machine to another! Type Size (bytes) char 1 int 4 short 2 long 8 long long 8 float 4 double 8 docsity.com Characters are just numbers What does this function do? char fun(char c) { char new_c; if ((c >= ’A’) && (c <= ’Z’)) new_c = c - ’A’ + ’a’; else new_c = c; return (new_c); } return type procedure name argument type and name local variable type and name Math on characters! comparisons with characters! docsity.com Integers Fundamental problem:  Fixed-size representation can’t encode all numbers Standard low-level solution:  Limit number range and precision • Usually sufficient • Potential source of bugs Signed and unsigned variants  unsigned modifier can be used with any sized integer (short, long, or long long) docsity.com Signed Integer +2. S2%T... 52,768. sap "32.767 2. -32. 16... docsity.com Integer Ranges Unsigned UMinn … UMaxn = 0 … 2 n-1: 32 bits: 0 ... 4,294,967,295 unsigned int 64 bits: 0 ... 18,446,744,073,709,551,615 unsigned long int 2’s Complement TMinn … TMaxn = -2 n-1 … 2n-1-1: 32 bits: -2,147,483,648 ... 2,147,483,647 int 64 bits: -9,223,372,036,854,775,808 … 9,223,372,036,854,775,807 long int Note: C numeric ranges are platform dependent! #include <limits.h> to define ULONG_MAX, UINT_MIN, INT_MAX, … docsity.com Detecting Overflow in Programs Some high-level languages (ML, Ada, …):  Overflow causes exception that can be handled C:  Overflow causes no special event  Programmer must check, if desired E.g., given a, b, and c=UAddn(a,b) – overflow? Claim: Overflow iff c < a (Or similarly, iff c < b) Proof: Know 0  b < 2n If no overflow, c = (a + b) mod 2n = a + b  a + 0 = a If overflow, c = (a + b) mod 2n = a + b – 2n < a docsity.com Overflow z is 951,946,282 not 5,246,913,578 as expected (compiler warned me, though, because they are constants) y is not a valid positive number (sign bit is set)! It’s -1,171,510,507 z is still 951,946,282 unsigned int x = 2123456789; unsigned int y = 3123456789; unsigned int z; z = x + y; int x = 2123456789; int y = 3123456789; int z; z = x + y; docsity.com Bit Shifting for Multiplication/Division Why useful?  Simpler, thus faster, than general multiplication & division  Standard compiler optimization Can shift multiple positions at once:  Multiplies or divides by corresponding power-of-2  a << 5 a >> 5 docsity.com A Sampling of Integer Properties Mostly as usual, e.g.: 0 is identity for +, - 1 is identity for ×, ÷ +, -, × are associative +, × are commutative × distributes over +, - Some surprises, e.g.: ÷ doesn’t distribute over +, -  (a,b > 0  a + b > a) Why should you care? – Programmer should be aware of behavior of their programs – Compiler uses such properties in optimizations For both unsigned & 2’s complement: docsity.com Beware of Sign Conversions in C Beware implicit or explicit conversions between unsigned and signed representations! One of many common mistakes: Always false(!) because -1 is converted to unsigned, yielding UMaxn unsigned int u; … if (u > -1) … ? What’s wrong? ? docsity.com FP Overflow & Underflow Fixed-sized representation leads to limitations Expressible negative values Expressible positive values Negative underflow Positive underflow Positive overflow Negative overflow Zero Large positive exponent. Unlike integer arithmetic, overflow  imprecise result (), not inaccurate result Round to + Round to - Large negative exponent Round to zero docsity.com FP Representation Fixed-size representation  Using more significand bits  increased precision  Using more exponent bits  increased range Typically, fixed # of bits for each part, for simplicity 1.001101110 × 25 significand exponent docsity.com FP Representation: IEEE 754 Current standard version of floating-point Single-precision (float) One word: 1 sign bit, 23 bit fraction, 8 bit exponent Positive range: 1.17549435 × 10-38 … 3.40282347 × 10+38 Double-precision (double) Two words: 1 sign bit, 52 bit fraction, 11 bit exponent Positive range: 2.2250738585072014 × 10-308 … 1.7976931348623157 × 10+308 Representation details covered in ELEC 220 Lots of details in B&O Chapter 2.4 docsity.com FP vs. Integer Results int i = 1000 / 6; float f = 1000.0 / 6.0; True mathematical answer: 1000  6 = 166 2/3 i = ? f = ? 166 166.666672 Integer division ignores remainder FP arithmetic rounds result Surprise! Arithmetic in binary, printing in decimal – doesn’t always give expected result docsity.com FP  Integer Conversions in C int i = 3.3 * 5; float f = i; True mathematical answer: 3.3  5 = 16 ½ i = ? f = ? 16 16.0 Converts 5  5.0 – Truncates result 16 ½  16 integer  FP: Can lose precision Rounds, if necessary 32-bit int fits in double-precision FP FP  integer: Truncate fraction If out of range, undefined – not error docsity.com FP Behavior Programmer must be aware of accuracy limitations! Dealing with this is a main subject of CAAM 353 (1010 + 1030) + –1030 =? 1010 + (1030 + –1030) 1030 – 1030 =? 1010 + 0 0  1010 Operations not associative! (1.0 + 6.0) ÷ 640.0 =? (1.0 ÷ 640.0) + (6.0 ÷ 640.0) 7.0 ÷ 640.0 =? .001563 + .009375 .010937  .010938 ×,÷ not distributive across +,- docsity.com Booleans in C bool added to C in 1999 Many programmers had already defined their own Boolean type  To avoid conflict bool is disabled by default #include <stdbool.h> bool bool1 = true; bool bool2 = false; Important! Compiler needs this or it won't know about "bool"! docsity.com C’s Common Boolean Operations C extends definitions to integers  Booleans are encoded as integers • 0 == false • non-0 == true  Logical AND: 0 && 4 == 0 3 && 4 == 1 3 && 0 == 0  Logical OR: 0 || 4 == 1 3 || 4 == 1 3 || 0 == 1  Logical NOT: ! 4 == 0 ! 0 == 1 && and || short-circuit  Evaluate 2nd argument only if necessary  E.g., 0 && error-producing-code == 0 docsity.com Enumerated Types E.g., a Color = red, blue, black, or yellow  Small (finite) number of choices  Booleans & characters are common special cases  Pick arbitrary bit patterns for each Not enforced in C  Actually just integers  Can assign values outside of the enumeration  Could cause bugs docsity.com