CSC 1029 Week 11 Arithmetic Overflow PDF

CSC 1029 ARITHMETIC OVERFLOW AND MORE  OBJECTIVES AGENDA: WEEK 11 Illustrate common coding exploitations 1. 2s Compliment and vulnerabilities 2. Integer Arithmetic Error using Understand why binary is...

CSC 1029 ARITHMETIC OVERFLOW AND MORE  OBJECTIVES AGENDA: WEEK 11 Illustrate common coding exploitations 1. 2s Compliment and vulnerabilities 2. Integer Arithmetic Error using Understand why binary is used to binary represent information on a computer. 3. Detecting Overflow Be able to convert binary numbers to decimal and decimal to binary. 4. Arithmetic Considerations Be able to perform addition and 5. Misconceptions & Mitigations subtraction in binary (without converting 6. Other Common Integer Errors to decimal "in between") 7. Type Promotion and Demotion Understand how computer representation of integers leads to 8. Arithmetic Type Mismatch overflow error. 9. TODO & Resources for Help ABOUT INTEGERS (CPLUSPLUS) The size of a data type is n bytes, it can store 28n different values or it's range If size of an unsigned data type is n bytes, it ranges from 0 to 28n-1 If size of a signed data type is n bytes, it ranges from -28n-1 to 28n-1-1 A short (usually 2 bytes) ranges from -32768 to 32767 and an unsigned short ranges from 0 to 65535 SIGNED INTEGRALS USING 2'S COMPLEMENT The first bit (leftmost bit - most significant bit MSB) gets the role of the "sign" bit. 1: negative 0: nonnegative Fill in the table in your notes to practice 2's complement Signed binary bits Decimal Value 00010 -14 14 11100 SIGNED AND UNSIGNED 3-BIT INT https://cheever.domains. swarthmore.edu/Ref/Bin aryMath/NumSys.html SIGNED AND UNSIGNED 4-BIT INT https://cheever.domains. swarthmore.edu/Ref/Bin aryMath/NumSys.html  (CPLUSPLUS) (CPLUSPLUS) The header defines constants with the limits of fundamental integral types for the specific system and compiler implementation used. The header defines elements with the characteristics of arithmetic types. More specifically, it defines a numeric_limits class template and a specialization of it for each of the fundamental types. ADDITION OVERFLOW EXAMPLE Notice that when operands have opposite signs, their sum will never overflow: 2-bit signed 1 + -2 = -1 BINARY 1 + -1 = 0 sign bit 21 20 DECIMAL Therefore, overflow can ONLY occur when 0 0 0+0 = 0 the operands have the same sign: 0 1 0+1 = 1 1 + 1 = 2 1 1 -2+1 = -1 -2 + -2 = -4 1 0 -2+0 = -2 -2 + -1 = -3 NEGATIVE VALUES AND 2'S COMPLEMENT Work through the tutorial and complete the multi-choice questions  ARITHMETIC OVERFLOW The picture to the right illustrates when a 4- bit arithmetic overflow will occur The example in the PearDeck depicts how binary addition and subtraction is done. Review the Overflow Error slide in the PearDear showing a 16-bit overflow. UNSIGNED OVERFLOW ARITHMETIC (CPLUSPLUS) If c is 200 Byte – unsigned char data type (11001000) and d 7 6 5 4 3 2 1 0 is 100 (01100100) 128 64 32 16 8 4 2 1 1 Carry Over This is an example 1 1 0 0 1 0 0 0 200 unsigned char c of an unsigned 0 1 1 0 0 1 0 0 100 unsigned char d overflow, where unsigned result 1 0 0 1 0 1 1 0 0 44 = c+d the value couldn't be stored in the available number of bytes. SIGNED OVERFLOW ARITHMETIC (CPLUSPLUS) a is 100 (01100100) Byte - signed char data type and b is 50 7 6 5 4 3 2 1 0 128 64 32 16 8 4 2 1 (00110010) 1 1 Carry Over The most significant 0 1 1 0 0 1 0 0 100 signed char a digit (MSD) for 0 0 1 1 0 0 1 0 50 signed char b signed indicates MSB signed result positive or negative 1 0 0 1 0 1 1 0 -106 = a+b This is an example of a signed overflow ADDITION OVERFLOW: CHECK SIGN Signed overflow can be detected by seeing that its sign is opposite to that of the other operands. if different signs – no possibility of overflow else if same sign – potential for overflow MUST be checked ADDITION OVERFLOW: SAME SIGN If the operands signs are the same, determine if an overflow occurs The size of a data type n bytes is used to calculate the range, Range, of different values 28n Use the range data type constants provided in If a and b are both positive a >= 0 && b >= 0, then to ensure an overflow does NOT occur a = Range – b ARITHMETIC CONSIDERATIONS The result of the arithmetic must be considered before the expression can be evaluated! Do NOT check after the calculation! Just because the individual values in the expression do NOT cause an overflow, the result could. Expressions that add or multiply MUST check to ensure the result will NOT overlow before performing the arithmetic. o INT_MAX + 1 will result in an overflow, but the values of INT_MAX and 1 are NOT themselves overflow integers. MISCONCEPTIONS ABOUT OVERFLOW Specific overflow detection requires knowing the operation and the representation. Overflow occurs when you do some operation to two valid representations The result canNOT be represented in the representation because the value is too large or too small. Overflow detection is detecting overflow for a specific representation http://www.c-jump.com/CIS77/CPU/Overflow/lecture.html#O01_0050_signed_adding MITIGATING INTEGER OVERFLOW Add code to check for overflow, or use safe integer libraries or large integer libraries. Validate the range of values to be reasonable before doing computation that can lead to overflow, and ensure that the largest reasonable values are always going to be within range of what the type can represent. With signed types also consider the negative values as well. Avoid mixing signed and unsigned integers in a computation. The easiest solution is to cast these to a larger signed type that can represent the full range of both values. Use compiler options for integer overflow warnings and runtime exceptions OTHER COMMON INTEGER ERRORS The peculiarities of fixed-size integer arithmetic and conversions are subtle and can easily lead to serious security vulnerabilities. Vigilance for numeric errors is required not just for math formulas, but also array indexes, buffer offsets, and many other places that computation happens. Characters as ints: In languages like C/C++, the char type is an integer and it may or may not be signed, so operations with characters can be deceptively tricky. Intermediate Result: Even though the final value of a computation is within range of the target type, overflow may occur for intermediate values at any step of a computation. TYPE PROMOTION (CPLUSPLUS) Whenever an operation is performed on two variables of a type shorter than int, the type of both variables is converted to int. The code example displays a value more than the max value of short (64000) The reason is that a and b were converted to int and a+b would be promoted to return an int, which can have a value of 64000.  TYPE DEMOTION / NARROWING Type narrowing occurs by truncating the bits to the target type’s size For unsigned numbers, this may result is a loss of information (i.e. large numbers being truncated to small numbers). For signed numbers, narrowing can result in unexpected change of signness; as shown in the example. Note: unexpected results were shown, rather than the unexpected change of signness that actually occured due to the change of MSB If the most-significant-bit (MSB) is a zero (0), there are no issues with the conversion in either direction. If the MSB is a one (1), a change in sign and value will occur. int int binary short short binary char char binary unsigned 4294934415 11111111 11111111 01111111 10001111 32655 01111111 10001111 143 10001111 signed -32881 111111111 1111111 01111111 10001111 32655 01111111 10001111 -113 10001111 TYPE CHANGE & ARITHMETIC MITIGATION Many of the problems with integers result from sloppy use of types, so the first step to writing more secure code is to take meticulous care with types. Notice any conversions, which are often implicit Mixing of signed and unsigned types Type-casting into smaller size types Be aware that conversions involving floating point and other numeric representations can also produce problems. TYPE CHANGE & ARITHMETIC ERRORS When using integer arithmetic to calculate a value for assignment to a floating-point variable, improper use can lead to a loss of information. float ans = 5 / 2; Integer arithmetic always produces integral results, discarding any possible fractional remainder, regardless of the data type the result is being assigned to. There can also be loss of precision when converting integers to floating-point values. EARN YOUR PRE-WORK GRADE Post your weekly discussion question and research solution to D2L TODO Complete Week 11 Content Module in D2L to 100% WHAT'S COMING UP NEXT...WEEL 12  QUESTIONS | CLARIFICATIONS | HELP Student Office Hours: Schedule Meeting with Julie o By Appointment (both on-campus and remote via Zoom) o Drop-In Times Available (on-campus) Email: [email protected] RRCC On Campus Tutoring: https://www.rrcc.edu/learning- commons/tutoring 24/7 Online Tutoring: D2L > Content > Resources for Help