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Today…

Today…. Numeric Representation, Cont.: Integer “overflow” in Java. How integers are real numbers are stored. Expressions, Cont.: Some pet peeves and bad expressions. Java keywords . ( if we have time ). Integer Overflow in Java.

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Today…

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  1. Today… • Numeric Representation, Cont.: • Integer “overflow” in Java. • How integers are real numbers are stored. • Expressions, Cont.: • Some pet peeves and bad expressions. • Java keywords. (if we have time) CISC124 - Prof. McLeod

  2. Integer Overflow in Java • In Python (version 3) you do not have limits on the size of an integer. • But Java does have limits. • See FactorialDemo.java CISC124 - Prof. McLeod

  3. From Before: Integer Primitive Types in Java • For byte, from -128 to 127, inclusive (1 byte). • For short, from -32768 to 32767, inclusive (2 bytes). • For int, from -2147483648 to 2147483647, inclusive (4 bytes). • For long, from -9223372036854775808 to 9223372036854775807, inclusive (8 bytes). • A “byte” is 8 bits, where a “bit” is either 1 or 0. CISC124 - Prof. McLeod

  4. Storage of Integers • An “un-signed” 8 digit (one byte) binary number can range from 00000000 to 11111111 • 00000000 is 0 in base 10. • 11111111 is 1x20 + 1x21 + 1x22 + … + 1x27 = 255, base 10. CISC124 - Prof. McLeod

  5. Storage of Integers - Cont. • So, how can a negative binary number be stored? • One way is to use the Two’s Complement system of storage. • Make the most significant bit a negative number: • So, the lowest “signed” binary 8 digit number is now: 10000000, which is -1x27, or -128 base 10. CISC124 - Prof. McLeod

  6. Storage of Integers - Cont. • Two’s Complement System for 1 byte: CISC124 - Prof. McLeod

  7. Storage of Integers - Cont. • For example, the binary number 10010101 is 1x20 + 1x22 + 1x24 - 1x27 = 1 + 4 + 16 - 128 = -107 base 10 • Now you can see how the primitive integer type, byte, ranges from -128 to 127. CISC124 - Prof. McLeod

  8. Storage of Integers - Cont. • Suppose we wish to add 1 to the largest byte value: 01111111 +00000001 • This would be equivalent to adding 1 to 127 in base 10 - the result would normally be 128. • In base 2, using two’s compliment, the result of the addition is 10000000, which is -128 in base 10! • So integer numbers wrap around, in the case of overflow - no warning is given in Java! CISC124 - Prof. McLeod

  9. Storage of Integers - Cont. • An int is stored in 4 bytes using “two’s complement”. • An int ranges from: 10000000 00000000 00000000 00000000 to 01111111 11111111 11111111 11111111 or -2147483648 to 2147483647 in base 10 CISC124 - Prof. McLeod

  10. From Before: Real Primitive Types • Also called “Floating Point” Types: • float, double • For float, (4 bytes) roughly ±1.4 x 10-38 to ±3.4 x 1038 to 7 significant digits. • For double, (8 bytes) roughly ±4.9 x 10-308 to ±1.7 x 10308 to 15 significant digits. CISC124 - Prof. McLeod

  11. Storage of Real Numbers • The system used to store real numbers in Java complies with the IEEE standard number 754. • Like an int, a floatis stored in 4 bytes or 32 bits. • These bits consist of 23 bits for the mantissa, 8 bits for the exponent, with one sign bit: 0 00000000 00000000 00000000 0000000 exponent mantissa sign bit CISC124 - Prof. McLeod

  12. Storage of Real Numbers - Cont. • The sign bit, s, can be 0 for positive and 1 for negative. • The exponent, e, is unsigned. The standard says the exponent is biased by 127 and that the values 0 and 255 are reserved. So the exponent can range from -126 to +127. E is the unbiased value and e is the biased value (E = e - 127). • If e is not a reserved value then assume that there is a 1 to the left of the decimal point, which is followed by the mantissa, f to yield the “significand”. • The mantissa is always less than 1 this way. CISC124 - Prof. McLeod

  13. Storage of Real Numbers - Cont. • So a value is stored as: value = (-1)s 1.f  2E • For example if s = 0, e = 125 and f = 10000000000000000000000 E = 125 – 127 = -2 The significand is 1.10000000000000000000000 value = 1  1.10000000000000000000000  2-2 CISC124 - Prof. McLeod

  14. Storage of Real Numbers - Cont. • Or, value = 0.011, which is 0.37510 • The maximum float would be for : s = 0 e = 254 f = 11111111111111111111111 • We can use a demo program written by Ron Mak at: http://www.apropos-logic.com/nc/FPFormats.html CISC124 - Prof. McLeod

  15. Storage of Real Numbers - Cont. • Gives: 3.4028235E38, which is the constant: Float.MAX_VALUE. • Changing s to 1 gives -3.4028235E38 • The smallest, non-zero normalized value has e = 1 and f = 00000000000000000000000, which gives 1.17549435E-38, which is Float.MIN_NORMAL. CISC124 - Prof. McLeod

  16. Storage of Real Numbers - Cont. • These are all “normalized” numbers because we are not using the reserved exponent values, 0 and 255. • I will skip the discussion of these special cases of subnormal or denormalized numbers – unless you are really interested! CISC124 - Prof. McLeod

  17. Storage of a Real Number, Cont. • double, (8 bytes) roughly ±4.9 x 10-308 to 15 significant digits. • The IEEE754 standard states how this number is constructed in memory: • These 8 bytes consist of 52 bits for the mantissa, 11 bits for the exponent, with one sign bit: 0 000000000000 0000000000000000000000000000000000000000000000000000 exponent mantissa sign bit CISC124 - Prof. McLeod

  18. Storage of a Real Number - Cont. • The sign bit, s, can be 0 for positive and 1 for negative. • The exponent, e, ranges from 00000000000 to 11111111111 (or 0 to 2047 in base 10) • The exponent, e, is unsigned. The IEEE754 standard says the exponent is biased by 1023 and that the values 0 and 2047 are reserved. So the exponent, E, can range from -1022 to +1023 in base 10. CISC124 - Prof. McLeod

  19. Storage of a Real Number - Cont. • The maximum double would be for : s = 0 E = 102310 f = 11111111111111111111111… (52 ones) or 1.11111…  21023 • Use Ron Mak’s program: • Gives: 1.7976931348623157e308, Double.MAX_VALUE. CISC124 - Prof. McLeod

  20. Storage of a Real Number - Cont. • The smallest double would be for : s = 0 E = -102210 f = 000000000000000000… (52 zeros) or 1.000000…  2-1022 • Gives: 2.2250738585072014e-308 • Double.MIN_NORMAL CISC124 - Prof. McLeod

  21. Special Values • These constants: • NaN • POSITIVE_INFINITY • NEGATIVE_INFINITY are all available from both the Float and Double wrapper classes as constant attributes. In the console they display as: NaN, Infinity, -Infinity CISC124 - Prof. McLeod

  22. When Bad Things Happen! • The IEE754 standard requires the following behaviour when calculations go wrong: CISC124 - Prof. McLeod

  23. When Bad Things Happen, Cont. • The standard also states that the language must somehow set a flag (like throwing an exception, for example), when something like this happens. • Java does not do this – floating point operations never throw exceptions! • However Wrapper classes supply methods to detect NaN and Infinity. • So, it is up to you (the programmer!) to check your calculations and prevent “bad things” from happening. CISC124 - Prof. McLeod

  24. IEEE754 Standard • See the following web sites for more info: http://grouper.ieee.org/groups/754/ • Or: http://en.wikipedia.org/wiki/IEEE_floating-point_standard CISC124 - Prof. McLeod

  25. Expressions, Cont. • Expressions are combinations of variables, literal values, operators, keywords, method calls, etc. • For example: int aNum = 4 + 3 * 7; // aNum is 25 int aNum = (4 + 3) * 7; // aNum is 49 (4 > 7) || (10 > -1) // yields true (5.5 >= 5) && (4 != 1.0) // yields true double circ = 3.14 * 2 * r; … CISC124 - Prof. McLeod

  26. Aside – Pet Peves! • Especially on a quiz: • Do not get == mixed up with = • Do not use the symbols ≥ and ≤ in code – the compiler will not recognize them! Use >= and <= instead. • Understand precedence instead of overusing (). CISC124 - Prof. McLeod

  27. Weird (& Bad!) Expressions • Three of these lines of code will not compile. Which ones and why not? intaNum; intbNum; System.out.println(aNum = 5); aNum = bNum = 10; (aNum = bNum) = 20; aNum = (bNum = 30); aNum = (aNum + 20); (aNum = aNum) + 20; System.out.println(aNum > bNum > 5); CISC124 - Prof. McLeod

  28. Bad Expressions, Cont. • See BadExpressions.java • As safe as Java is designed to be, it is still possible to write really poor style expressions that still compile... CISC124 - Prof. McLeod

  29. 50 Java Keywords                                          the ones we will use:     CISC124 - Prof. McLeod

  30. Java Keywords – Primitive Types CISC124 - Prof. McLeod

  31. Java Keywords – Loops CISC124 - Prof. McLeod

  32. Java Keywords – Conditionals CISC124 - Prof. McLeod

  33. Java Keywords – Exceptions CISC124 - Prof. McLeod

  34. Java Keywords – Class & Method Headers CISC124 - Prof. McLeod

  35. The “Other” Keywords (from Oracle) • const and gotoare “not used by current versions of the Java programming language.” • native“is used in method declarations to specify that the method is not implemented in the same Java source file, but rather in another language.” • synchronized “when applied to a method or code block, guarantees that at most one thread at a time executes that code.” • transient “indicates that a field is not part of the serialized form of an object.” • volatile “specifies that the variable is modified asynchronously by concurrently running threads.” CISC124 - Prof. McLeod

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