CS61B Lecture #14: Integers
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1 Announcement: CS61B Lecture #14: Integers Project #0 due Tuesday night. Programming contest SATURDAY! You can still sign up at Test #1 will be Tuesday, 6 October 2015, 8 10PM. Test #2 will be Tuesday, 10 November 2015, 7 9PM. Today: Integer Types; Readings: A Java Reference, Head First Java, Chapter 10. Readings for Upcoming Topics: Data Structures (Into Java), Chapter 1. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 1
2 Integer Types and Literals Type Bits Signed? Literals byte 8 Yes Cast from int: (byte) 3 short 16 Yes None. Cast from int: (short) 4096 char 16 No a // (char) 97 \n // newline ((char) 10) \t // tab ((char) 8) \\ // backslash A, \101, \u0041 // == (char) 65 int 32 Yes // Octal for 64 0x3f, 0xffffffff // Hexadecimal 63, -1 (!) long 64 Yes 123L, 01000L, 0x3fL L Negative numerals are just negated (positive) literals. N bits meansthat thereare 2 N integersinthe domain of the type: If signed, range of values is 2 N N 1 1. If unsigned, only non-negative numbers, and range is 0..2 N 1. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 2
3 Modular Arithmetic Problem: How do we handle overflow, such as occurs in 10000*10000*10000? Some languages throw an exception (Ada), some give undefined results (C, C++) Java defines the result of any arithmetic operation or conversion on integer types to wrap around modular arithmetic. That is, the next number after the largest in an integer type is the smallest (like clock arithmetic ). E.g., (byte) 128 == (byte) (127+1) == (byte) -128 In general, If the result of some arithmetic subexpression is supposed to have type T, an n-bit integer type, then we compute the real (mathematical) value, x, and yield a number, x, that is in the range of T, and that is equivalent to x modulo 2 n. (That means that x x is a multiple of 2 n.) Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 3
4 Modular Arithmetic: Examples (byte) (64*8) yields 0, since = (byte) (64*2) and (byte) (127+1) yield -128, since 128 ( 128) = (byte) (101*99) yields 15, since = (byte) (-30*13) yields 122, since = (char) (-1) yields , since 1 (2 16 1) = Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 4
5 Why wrap around? Modular Arithmetic and Bits Java s definition is the natural one for a machine that uses binary arithmetic. For example, consider bytes (8 bits): Decimal Binary In general, bit n, counting from 0 at the right, corresponds to 2 n. The bits to the left of the vertical bars therefore represent multiples of 2 8 = 256. So throwing them away is the same as arithmetic module 256. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 5
6 Why this representation for -1? Negative numbers = Only 8 bits in a byte, so bit 8 falls off, leaving 0. The truncated bit is in the 2 8 place, so throwing it away gives an equal number modulo 2 8. All bits to the left of it are also divisible by 2 8. On unsigned types (char), arithmetic is the same, but we choose to represent only non-negative numbers modulo 2 16 : = Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 6
7 Conversion In general Java will silently convert from one type to another if this makes sense and no information is lost from value. Otherwise, cast explicitly, as in (byte) x. Hence, given byte abyte; char achar; short ashort; int anint; long along; // OK: ashort = abyte; anint = abyte; anint = ashort; anint = achar; along = anint; // Not OK, might lose information: anint = along; abyte = anint; achar = anint; ashort = anint; ashort = achar; achar = ashort; achar = abyte; // OK by special dispensation: abyte = 13; // 13 is compile-time constant abyte = // 112 is compile-time constant Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 7
8 Promotion Arithmetic operations (+, *,...) promote operands as needed. Promotion is just implicit conversion. For integer operations, So, if any operand is long, promote both to long. otherwise promote both to int. abyte + 3 == (int) abyte + 3 // Type int along + 3 == along + (long) 3 // Type long A + 2 == (int) A + 2 // Type int abyte = abyte + 1 // ILLEGAL (why?) But fortunately, abyte += 1; Common example: // Defined as abyte = (byte) (abyte+1) // Assume achar is an upper-case letter char lowercasechar = (char) ( a + achar - A ); // why cast? Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 8
9 Bit twiddling Java (and C, C++) allow for handling integer types as sequences of bits. No conversion to bits needed: they already are. Operations and their uses: Mask Set Flip Flip all & ^ ~ Shifting: Left Arithmetic Right Logical Right << >> >>> Whatis: (-1) >>> 29? x << n? x >> n? (x >>> 3) & ((1<<5)-1)?. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 9
10 Bit twiddling Java (and C, C++) allow for handling integer types as sequences of bits. No conversion to bits needed: they already are. Operations and their uses: Mask Set Flip Flip all & ^ ~ Shifting: Left Arithmetic Right Logical Right << >> >>> Whatis: (-1) >>> 29? = 7. x << n? x >> n? (x >>> 3) & ((1<<5)-1)?. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 9
11 Bit twiddling Java (and C, C++) allow for handling integer types as sequences of bits. No conversion to bits needed: they already are. Operations and their uses: Mask Set Flip Flip all & ^ ~ Shifting: Left Arithmetic Right Logical Right << >> >>> Whatis: (-1) >>> 29? = 7. x << n? = x 2 n. x >> n? (x >>> 3) & ((1<<5)-1)?. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 9
12 Bit twiddling Java (and C, C++) allow for handling integer types as sequences of bits. No conversion to bits needed: they already are. Operations and their uses: Mask Set Flip Flip all & ^ ~ Shifting: Whatis: Left Arithmetic Right Logical Right << >> >>> (-1) >>> 29? = 7. x << n? = x 2 n. x >> n? = x/2 n (i.e., rounded down). (x >>> 3) & ((1<<5)-1)?. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 9
13 Bit twiddling Java (and C, C++) allow for handling integer types as sequences of bits. No conversion to bits needed: they already are. Operations and their uses: Mask Set Flip Flip all & ^ ~ Shifting: Whatis: Left Arithmetic Right Logical Right << >> >>> (-1) >>> 29? = 7. x << n? = x 2 n. x >> n? = x/2 n (i.e., rounded down). (x >>> 3) & ((1<<5)-1)? 5-bit integer, bits 3 7 of x. Last modified: Mon Sep 28 12:10: CS61B: Lecture #14 9
CS61B Lecture #14: Integers. Last modified: Wed Sep 27 15:44: CS61B: Lecture #14 1
CS61B Lecture #14: Integers Last modified: Wed Sep 27 15:44:05 2017 CS61B: Lecture #14 1 Integer Types and Literals Type Bits Signed? Literals byte 8 Yes Cast from int: (byte) 3 short 16 Yes None. Cast
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