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4. C++ Math Operators

The C++ expression parser supports all forms of C++ expression syntax. The syntax includes all data types (including pointers, floating-point numbers, and arrays) and all C++ unary and binary operators.

C Arithmetic Operators. Perhaps you have warm memories of doing arithmetic drills in grade school. You can give that same pleasure to your computer. C uses operators to do arithmetic. It provides operators for five basic arithmetic calculations: addition. C Operators. Operators are used to perform operations on variables and values. In the example below, we use the + operator to add together two values. Arithmetic Operators. Arithmetic operators are used to perform common mathematical operations. Operator Name Description Example Try it +. Equality operators can compare pointers to members of the same type. In such a comparison, pointer-to-member conversions are performed. Pointers to members can also be compared to a constant expression that evaluates to 0. Expressions with Binary Operators C Built-in Operators, Precedence and Associativity C Relational and Equality. The modulus operator is useful in a variety of circumstances. It is commonly used to take a randomly generated number and reduce that number to a random number on a smaller range, and it can also quickly tell you if one number is a factor of another. @Abid Ali: the program you're using to write and compile your C code doesn't follow the standard of C: it can't compile valid C code. Don't know why. I would suggest you to switch to a more standard compliant compiler. If you are using windows try to download and write your programs in Dev-C (for example), which uses GCC as compiler. Math Operations. Before reading this tutorial, you should learn about variables and input values using cin. BASIC OPERATORS. In any language, there are some operators to perform arithmetic, logical and control operations. The basic operators which are used to perform arithmetic operations on integers are as follows.

Numbers in C++ Expressions

Numbers in C++ expressions are interpreted as decimal numbers, unless you specify them in another manner. To specify a hexadecimal integer, add 0x before the number. To specify an octal integer, add 0 (zero) before the number.

The default debugger radix does not affect how you enter C++ expressions. You cannot directly enter a binary number (except by nesting a MASM expression within the C++ expression).

You can enter a hexadecimal 64-bit value in the xxxxxxxx`xxxxxxxx format. (You can also omit the grave accent ( ` ).) Both formats produce the same value.

You can use the L, U, and I64 suffixes with integer values. The actual size of the number that is created depends on the suffix and the number that you enter. For more information about this interpretation, see a C++ language reference.

The output of the C++ expression evaluator keeps the data type that the C++ expression rules specify. However, if you use this expression as an argument for a command, a cast is always made. For example, you do not have to cast integer values to pointers when they are used as addresses in command arguments. If the expression's value cannot be validly cast to an integer or a pointer, a syntax error occurs.

You can use the 0n (decimal) prefix for some output, but you cannot use it for C++ expression input.

Characters and Strings in C++ Expressions

You can enter a character by surrounding it with single quotation marks ( ' ). The standard C++ escape characters are permitted.

You can enter string literals by surrounding them with double quotation marks ( ' ). You can use ' as an escape sequence within such a string. However, strings have no meaning to the expression evaluator.

Symbols in C++ Expressions

In a C++ expression, each symbol is interpreted according to its type. Depending on what the symbol refers to, it might be interpreted as an integer, a data structure, a function pointer, or any other data type. If you use a symbol that does not correspond to a C++ data type (such as an unmodified module name) within a C++ expression, a syntax error occurs.

If the symbol might be ambiguous, you can add a module name and an exclamation point ( ! ) or only an exclamation point before the symbol. For more information about symbol recognition, see Symbol Syntax and Symbol Matching.

You can use a grave accent ( ` ) or an apostrophe ( ' ) in a symbol name only if you add a module name and exclamation point before the symbol name.

When you add the < and > delimiters after a template name, you can add spaces between these delimiters.

Operators in C++ Expressions

You can always use parentheses to override precedence rules.

If you enclose part of a C++ expression in parentheses and add two at signs (@@) before the expression, the expression is interpreted according to MASM expression rules. You cannot add a space between the two at signs and the opening parenthesis. The final value of this expression is passed to the C++ expression evaluator as a ULONG64 value. You can also specify the expression evaluator by using @@c++( ... ) or @@masm( ... ).

Data types are indicated as usual in the C++ language. The symbols that indicate arrays ( [ ] ), pointer members ( -> ), UDT members ( . ), and members of classes ( :: ) are all recognized. All arithmetic operators are supported, including assignment and side-effect operators. However, you cannot use the new, delete, and throw operators, and you cannot actually call a function.

Pointer arithmetic is supported and offsets are scaled correctly. Note that you cannot add an offset to a function pointer. (If you have to add an offset to a function pointer, cast the offset to a character pointer first.)

As in C++, if you use operators with invalid data types, a syntax error occurs. The debugger's C++ expression parser uses slightly more relaxed rules than most C++ compilers, but all major rules are enforced. For example, you cannot shift a non-integer value.

You can use the following operators. The operators in each cell take precedence over those in lower cells. Operators in the same cell are of the same precedence and are parsed from left to right. As with C++, expression evaluation ends when its value is known. This ending enables you to effectively use expressions such as ?? myPtr && *myPtr.

Registers and Pseudo-Registers in C++ Expressions

You can use registers and pseudo-registers within C++ expressions. You must add an at sign ( @ ) before the register or pseudo-register.

The expression evaluator automatically performs the proper cast. Actual registers and integer-value pseudo-registers are cast to ULONG64. All addresses are cast to PUCHAR, $thread is cast to ETHREAD*, $proc is cast to EPROCESS*, $teb is cast to TEB*, and $peb is cast to PEB*.

You cannot change a register or pseudo-register by an assignment or side-effect operator. You must use the r (Registers) command to change these values.

For more information about registers and pseudo-registers, see Register Syntax and Pseudo-Register Syntax.

Macros in C++ Expressions

You can use macros within C++ expressions. You must add a number sign (#) before the macros.

You can use the following macros. These macros have the same definitions as the Microsoft Windows macros with the same name. (The Windows macros are defined in Winnt.h.)

In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.

For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation.^[1][2] Thus, the expression 2 + 3 × 4 is interpreted to have the value 2 + (3 × 4) = 14, not (2 + 3) × 4 = 20. With the introduction of exponents in the 16th and 17th centuries, they were given precedence over both addition and multiplication and could be placed only as a superscript to the right of their base.^[1] Thus 3 + 5² = 28 and 3 × 5² = 75.

These conventions exist to eliminate ambiguity while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can indicate an alternative order or reinforce the default order to avoid confusion. For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, and (3 + 5)² = 64 forces addition to precede exponentiation. Sometimes, for clarity, especially with nested parentheses, the parentheses are replace by brackets, as in [2×(3+4)]-5=9.

Definition[edit]

The order of operations, which is used throughout mathematics, science, technology and many computer programming languages, is expressed here:^[1]

1. exponentiation and root extraction
2. multiplication and division
3. addition and subtraction

This means that if, in a mathematical expression, a subexpression appears between two operators, the operator that is higher in the above list should be applied first.

The commutative and associative laws of addition and multiplication allow adding terms in any order, and multiplying factors in any order—but mixed operations must obey the standard order of operations.

In some contexts, it is helpful to replace a division by multiplication by the reciprocal (multiplicative inverse) and a subtraction by addition of the opposite (additive inverse). For example, in computer algebra, this allows manipulating fewer binary operations and makes it easier to use commutativity and associativity when simplifying large expressions – for more details, see Computer algebra § Simplification. Thus 3 ÷ 4 = 3 × 1/4; in other words, the quotient of 3 and 4 equals the product of 3 and 1/4. Also 3 − 4 = 3 + (−4); in other words the difference of 3 and 4 equals the sum of 3 and −4. Thus, 1 − 3 + 7 can be thought of as the sum of 1 + (−3) + 7, and the three summands may be added in any order, in all cases giving 5 as the result.

The root symbol √ is traditionally prolongated by a bar (called vinculum) over the radicand (this avoids the need for parentheses around the radicand). Other functions use parentheses around the input to avoid ambiguity. The parentheses are sometimes omitted if the input is a monomial. Thus, sin 3x = sin(3x), but sin x + y = sin(x) + y, because x + y is not a monomial.^[1] Some calculators and programming languages require parentheses around function inputs, some do not.

Symbols of grouping can be used to override the usual order of operations.^[1] Grouped symbols can be treated as a single expression.^[1] Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results from their removal.

Examples[edit]

${\displaystyle \sqrt{1+3}+5=\sqrt{4}+5=2+5=7.}$

A horizontal fractional line also acts as a symbol of grouping:

${\displaystyle \frac{1+2}{3+4}+5=\frac{3}{7}+5.}$

For ease in reading, other grouping symbols, such as curly braces { } or square brackets [ ], are often used along with parentheses ( ). For example:

${\displaystyle [(1+2)-3]-(4-5)=[3-3]-(-1)=1.}$

Unary minus sign[edit]

There are differing conventions concerning the unary operator − (usually read 'minus'). In written or printed mathematics, the expression −3² is interpreted to mean 0 − (3²) = − 9,^[1][3]

Some applications and programming languages, notably Microsoft Excel (and other spreadsheet applications) and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus has higher precedence than exponentiation, so in those languages −3² will be interpreted as (−3)² = 9.^[4] This does not apply to the binary minus operator −; for example in Microsoft Excel while the formulas =-2^2, =-(2)^2 and =0+-2^2 return 4, the formula =0-2^2 and =-(2^2) return −4.

Mixed division and multiplication[edit]

Similarly, there can be ambiguity in the use of the slash symbol / in expressions such as 1/2x.^[5] If one rewrites this expression as 1 ÷ 2x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:

1 ÷ 2 × x = 1 × 1/2 × x = 1/2 × x.

With this interpretation 1 ÷ 2x is equal to (1 ÷ 2)x.^[1][6] However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2x equals 1 ÷ (2x), not (1 ÷ 2)x.

For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,^[7] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.^[a]

Mnemonics[edit]

Mnemonics are often used to help students remember the rules, involving the first letters of words representing various operations. Different mnemonics are in use in different countries.^[6][8][9]

• In the United States, the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. PEMDAS is often expanded to the mnemonic 'Please Excuse My Dear Aunt Sally'.^[5]
• Canada and New Zealand use BEDMAS, standing for Brackets, Exponents, Division/Multiplication, Addition/Subtraction.
• Most common in the UK, Pakistan, India, Bangladesh and Australia^[10] and some other English-speaking countries is BODMAS meaning either Brackets, Order, Division/Multiplication, Addition/Subtraction or Brackets, Of/Division/Multiplication, Addition/Subtraction^[11][12][13]. Nigeria and some other West African countries also use BODMAS. Similarly in the UK, BIDMAS is also used, standing for Brackets, Indices, Division/Multiplication, Addition/Subtraction.

These mnemonics may be misleading when written this way.^[5] For example, misinterpreting any of the above rules to mean 'addition first, subtraction afterward' would incorrectly evaluate the expression^[5]

10 − 3 + 2.

The correct value is 9 (not 5, as would be the case if you added the 3 and the 2 before subtracting from the 10).

Special cases[edit]

Serial exponentiation[edit]

If exponentiation is indicated by stacked symbols using superscript notation, the usual rule is to work from the top down:^[1][14]

a^bc = a^(bc)

which typically is not equal to (a^b)^c.

However, when using operator notation with a caret (^) or arrow (↑), there is no common standard.^[15] For example, Microsoft Excel and computation programming language MATLAB evaluate a^b^c as (a^b)^c, but Google Search and Wolfram Alpha as a^(bc). Thus 4^3^2 is evaluated to 4,096 in the first case and to 262,144 in the second case.

Serial division[edit]

A similar ambiguity exists in the case of serial division, for example, the expression 10 ÷ 5 ÷ 2 can either be interpreted as

10 ÷ ( 5 ÷ 2 ) = 4

or as

( 10 ÷ 5 ) ÷ 2 = 1

Ctc Math

The left-to-right operation convention would resolve the ambiguity in favor of the last expression. Further, the mathematical habit of combining factors and representing division as multiplication by a reciprocal both greatly reduce the frequency of ambiguous division.

Calculators[edit]

Different calculators follow different orders of operations. Many simple calculators without a stack implement chain input working left to right without any priority given to different operators, for example typing

1 + 2 × 3 yields 9,

while more sophisticated calculators will use a more standard priority, for example typing

1 + 2 × 3 yields 7.

The Microsoft Calculator program uses the former in its standard view and the latter in its scientific and programmer views.

Chain input expects two operands and an operator. When the next operator is pressed, the expression is immediately evaluated and the answer becomes the left hand of the next operator. Advanced calculators allow entry of the whole expression, grouped as necessary, and evaluates only when the user uses the equals sign.

Calculators may associate exponents to the left or to the right depending on the model or the evaluation mode. For example, the expression a^b^c is interpreted as a^(bc) on the TI-92 and the TI-30XS MultiView in 'Mathprint mode', whereas it is interpreted as (a^b)^c on the TI-30XII and the TI-30XS MultiView in 'Classic mode'.

An expression like 1/2x is interpreted as 1/(2x) by TI-82, as well as many modern Casio calculators,^[16] but as (1/2)x by TI-83 and every other TI calculator released since 1996,^[17] as well as by all Hewlett-Packard calculators with algebraic notation. While the first interpretation may be expected by some users due to the nature of implied multiplication, the latter is more in line with the standard rule that multiplication and division are of equal precedence,^[18][19] where 1/2x is read one divided by two and the answer multiplied by x.

When the user is unsure how a calculator will interpret an expression, it is a good idea to use parentheses so there is no ambiguity.

Calculators that utilize reverse Polish notation (RPN), also known as postfix notation, use a stack to enter formulas without the need for parentheses.^[5]

Programming languages[edit]

Some programming languages use precedence levels that conform to the order commonly used in mathematics,^[15] though others, such as APL, Smalltalk, Occam and Mary, have no operator precedence rules (in APL, evaluation is strictly right to left; in Smalltalk etc. it is strictly left to right).

In addition, because many operators are not associative, the order within any single level is usually defined by grouping left to right so that 16/4/4 is interpreted as (16/4)/4 = 1 rather than 16/(4/4) = 16; such operators are perhaps misleadingly referred to as 'left associative'. Exceptions exist; for example, languages with operators corresponding to the cons operation on lists usually make them group right to left ('right associative'), e.g. in Haskell, 1:2:3:4:[] 1:(2:(3:(4:[]))) [1,2,3,4].

The logical bitwise operators in C (and all programming languages that borrow precedence rules from C, for example, C++, Perl and PHP) have a precedence level that the creator of the C language has since criticised as unsatisfactory.^[20] However, many programmers have become accustomed to this order. The relative precedence levels of operators found in many C-style languages are as follows:

Examples:(Note: in the examples below, '≡' is used to mean 'is equivalent to', and not to be interpreted as an actual assignment operator used as part of the example expression.)

• !A + !B ≡ (!A) + (!B)
• ++A + !B ≡ (++A) + (!B)
• A + B * C ≡ A + (B * C)
• A B && C ≡ A (B && C)
• A && B C ≡ A && (B C)
• A & B C ≡ A & (B C)

Source-to-source compilers that compile to multiple languages need to explicitly deal with the issue of different order of operations across languages. Haxe for example standardizes the order and enforces it by inserting brackets where it is appropriate.^[21]

The accuracy of software developer knowledge about binary operator precedence has been found to closely follow their frequency of occurrence in source code.^[22]

See also[edit]

• Common operator notation (for a more formal description)

Notes[edit]

1. ^For example, the third edition of Mechanics by Landau and Lifshitz contains expressions such as hP_z/2π (p. 22), and the first volume of the Feynman Lectures contains expressions such as 1/2√N(p. 6–7). In both books these expressions are written with the convention that the solidus is evaluated last.

References[edit]

1. ^ ^abcdefghiBronstein, Ilja Nikolaevič; Semendjajew, Konstantin Adolfovič (1987) [1945]. '2.4.1.1.'. In Grosche, Günter; Ziegler, Viktor; Ziegler, Dorothea (eds.). Taschenbuch der Mathematik (in German). 1. Translated by Ziegler, Viktor. Weiß, Jürgen (23 ed.). Thun and Frankfurt am Main: Verlag Harri Deutsch (and B. G. Teubner Verlagsgesellschaft, Leipzig). pp. 115–120. ISBN3-87144-492-8.
2. ^'Ask Dr. Math'. Math Forum. 22 November 2000. Retrieved 5 March 2012.
3. ^Allen R. Angel. Elementary Algebra for College Students (8 ed.). Chapter 1, Section 9, Objective 3.
4. ^'Formula Returns Unexpected Positive Value'. Support.microsoft.com. 15 August 2005. Retrieved 5 March 2012.
5. ^ ^abcdeBall, John A. (1978). Algorithms for RPN calculators (1 ed.). Cambridge, Massachusetts, USA: Wiley-Interscience, John Wiley & Sons, Inc. p. 31. ISBN0-471-03070-8.
6. ^ ^ab'Rules of arithmetic'(PDF). Mathcentre.ac.uk. Retrieved 2 August 2019.
7. ^'Physical Review Style and Notation Guide'(PDF). American Physical Society. Section IV–E–2–e. Retrieved 5 August 2012.
8. ^'Please Excuse My Dear Aunt Sally (PEMDAS)--Forever!'. Education Week - Coach G's Teaching Tips. 1 January 2011.
9. ^'What is PEMDAS? - Definition, Rule & Examples'. Study.com.
10. ^'Order of operations'(DOC). Syllabus.bos.nsw.edu.au. Retrieved 2 August 2019.
11. ^'Of' is equivalent to division or multiplication, and commonly used especially at primary school level, as in 'Half of fifty'.
12. ^Bodmas Rule - What is Bodmas Rule Order of Operations; vedantu.com. Accessed 2019-08-21.
13. ^BODMAS - Brackets, Of, Division, Multiplication, Addition, Subtraction; allacronyms.com. Accessed 2019-08-21.
14. ^Olver, Frank W. J.; Lozier, Daniel W.; Boisvert, Ronald F.; Clark, Charles W., eds. (2010). NIST Handbook of Mathematical Functions. National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Cambridge University Press. ISBN978-0-521-19225-5. MR2723248.[1]
15. ^ ^abExponentiation Associativity and Standard Math Notation Codeplea. 23 Aug 2016. Retrieved 20 Sep 2016.
16. ^'Calculation Priority Sequence'. support.casio.com. Retrieved 1 August 2019.
17. ^'Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators'. Texas Instruments. 16 January 2011. 11773. Archived from the original on 17 April 2016. Retrieved 24 August 2015.
18. ^Zachary, Joseph L. (1997). 'Introduction to scientific programming - Computational problem solving using Maple and C - Operator precedence worksheet'. Retrieved 25 August 2015.
19. ^Zachary, Joseph L. (1997). 'Introduction to scientific programming - Computational problem solving using Mathematica and C - Operator precedence notebook'. Retrieved 25 August 2015.
20. ^Dennis M. Ritchie: The Development of the C Language. In History of Programming Languages, 2nd ed., ACM Press 1996.
21. ^6÷2(1+2)=? Andy Li's Blog. 2 May 2011. Retrieved 31 December 2012.
22. ^'Developer beliefs about binary operator precedence' Derek M. Jones, CVu 18(4):14–21

Dev C Math Operators Manual

External links[edit]

Dev C Math Operators List

• 'Order of operations'. PlanetMath.

C++ Math Operators