Arithmetic operators
Arithmetic operators apply standard mathematical operations to their operands.
This section is incomplete Reason: consider a more generalpurpose ToC for this and other tables that cover multiple topics 
Operator  Operator name  Example  Result 

+  unary plus  +a  the value of a after promotions 
  unary minus  a  the negative of a 
+  addition  a + b  the addition of a and b 
  subtraction  a  b  the subtraction of b from a 
*  product  a * b  the product of a and b 
/  division  a / b  the division of a by b 
%  modulo  a % b  the remainder of a divided by b 
~  bitwise NOT  ~a  the bitwise NOT of a 
&  bitwise AND  a & b  the bitwise AND of a and b 
  bitwise OR  a  b  the bitwise OR of a and b 
^  bitwise XOR  a ^ b  the bitwise XOR of a and b 
<<  bitwise left shift  a << b  a left shifted by b 
>>  bitwise right shift  a >> b  a right shifted by b 
Contents 
[edit] Overflows
Unsigned integer arithmetic is always performed modulo 2n
where n is the number of bits in that particular integer. E.g. for unsigned int, adding one to UINT_MAX gives 0, and subtracting one from 0 gives UINT_MAX.
When signed integer arithmetic operation overflows (the result does not fit in the result type), the behavior is undefined: it may wrap around according to the rules of the representation (typically 2's complement), it may trap on some platforms or due to compiler options (e.g. ftrapv
in GCC and Clang), or may be completely optimized out by the compiler.
[edit] Floatingpoint environment
If
#pragma STDC FENV_ACCESS is set to ON
, all floatingpoint arithmetic operators obey the current floatingpoint rounding direction and report floatingpoint arithmetic errors as specified in math_errhandling unless part of a static initializer (in which case floatingpoint exceptions are not raised and the rounding mode is to nearest)
[edit] Floatingpoint contraction
Unless
#pragma STDC FP_CONTRACT is set to OFF
, all floatingpoint arithmetic may be performed as if the intermediate results have infinite range and precision, that is optimizations that omit rounding errors and floatingpoint exceptions that would be observed if the expression was evaluated exactly as written. For example, allows the implementation of (x*y) + z with a single fused multiplyadd CPU instruction or optimization of a = x*x*x*x; as tmp = x*x; a = tmp*tmp.
Unrelated to contracting, intermediate results of floatingpoint arithmetic may have range and precision that is different from the one indicated by its type, see FLT_EVAL_METHOD
[edit] Unary arithmetic
The unary arithmetic operator expressions have the form
+ expression

(1)  
 expression

(2)  
Both unary plus and unary minus first apply integral promotions to their operand, and then
 unary plus returns the value after promotion
 unary minus returns the negative of the value after promotion (except that the negative of a NaN is another NaN)
The type of the expression is the type after promotion, and the value category is nonlvalue.
[edit] Notes
The unary minus invokes undefined behavior due to signed integer overflow when applied to INT_MIN, LONG_MIN, or LLONG_MIN, on typical (2's complement) platforms.
In C++, unary operator + can also be used with other builtin types such as arrays and functions, not so in C.
#include <stdio.h> #include <complex.h> int main(void) { char c = 'a'; printf("sizeof char: %zu sizeof int: %zu\n", sizeof c, sizeof +c); printf("1, where 1 is signed: %d\n", 1); printf("1, where 1 is unsigned: %u\n", 1u); double complex z = 1 + 2*I; printf("(1+2i) = %.1f%+.1f\n", creal(z), cimag(z)); }
Possible output:
sizeof char: 1 sizeof int: 4 1, where 1 is signed: 1 1, where 1 is unsigned: 4294967295 (1+2i) = 1.02.0
[edit] Additive operators
The binary additive arithmetic operator expressions have the form
lhs + rhs

(1)  
lhs  rhs

(2)  
 both have arithmetic types, including complex and imaginary
 one is a pointer to complete object type, the other has integer type
 both have arithmetic types, including complex and imaginary
 lhs has pointer to complete object type, rhs has integer type
 both are pointers to complete objects of compatible types, ignoring qualifiers
[edit] Arithmetic addition and subtraction
If both operands have arithmetic types, then
 first, usual arithmetic conversions are performed
 then, the values of the operands after conversions are added or subtracted following the usual rules of mathematics (for subtraction, rhs is subtracted from lhs), except that
 if one operand is NaN, the result is NaN
 infinity minus infinity is NaN and FE_INVALID is raised
 infinity plus the negative infinity is NaN and FE_INVALID is raised
Complex and imaginary addition and subtraction are defined as follows (note the result type is imaginary if both operands are imaginary and complex if one operand is real and the other imaginary, as specified by the usual arithmetic conversions):
+ or   u  iv  u + iv 

x  x ± u  x ± iv  (x ± u) ± iv 
iy  ±u + iy  i(y ± v)  ±u + i(y ± v) 
x + iy  (x ± u) + iy  x + i(y ± v)  (x ± u) + i(y ± v) 
// work in progress // note: take part of the c/language/conversion example
[edit] Pointer arithmetic
 If the pointer
P
points at an element of an array with indexI
, then
 P+N and N+P are pointers that point at an element of the same array with index
I+N
 PN is a pointer that points at an element of the same array with index {ttIN}}
 P+N and N+P are pointers that point at an element of the same array with index
The behavior is defined only if both the original pointer and the result pointer are pointing at elements of the same array or one past the end of that array. Note that executing p1 when p points at the first element of an array is undefined behavior and may fail on some platforms.
 If the pointer
P1
points at an element of an array with indexI
(or one past the end) andP2
points at an element of the same array with indexJ
(or one past the end), then
 P1P2 has the value equal to JI and the type ptrdiff_t (which is a signed integer type, typically half as large as the size of the largest object that can be declared)
The behavior is defined only if the result fits in ptrdiff_t.
For the purpose of pointer arithmetic, a pointer to an object that is not an element of any array is treated as a pointer to the first element of an array of size 1.
// work in progress int n = 4, m = 3; int a[n][m]; // VLA of 4 VLAs of 3 ints each int (*p)[m] = a; // p == &a[0] p = p + 1; // p == &a[1] (pointer arithmetic works with VLAs just the same) (*p)[2] = 99; // changes a[1][2]
[edit] Multiplicative operators
The binary multiplicative arithmetic operator expressions have the form
lhs * rhs

(1)  
lhs / rhs

(2)  
lhs % rhs

(3)  
 first, usual arithmetic conversions are performed. Then...
[edit] Multiplication
The binary operator * performs multiplication of its operands (after usual arithmetic conversions) following the usual arithmetic definitions, except that
 if one operand is a NaN, the result is a NaN
 multiplication if infinity by zero gives NaN and FE_INVALID is raised
 multiplication of infinity by a nonzero gives infinity (even for complex arguments)
Because in C, any complex value with at least one infinite part as an infinity even if its other part is a NaN, the usual arithmetic rules do not apply to complexcomplex multiplication. Other combinations of floating operands follow the following table:
*  u  iv  u + iv 

x  xu  i(xv)  (xu) + i(xv) 
iy  i(yu)  −yv  (−yv) + i(yu) 
x + iy  (xu) + i(yu)  (−yv) + i(xv)  special rules 
Besides infinity handling, complex multiplication is not allowed to overflow intermediate results, except when
#pragma STDC CX_LIMITED_RANGE is set to ON
, in which case the value may be calculated as if by (x+iy)×(u+iv) = (xuyv)+i(yu+xv), as the programmer assumes the responsibility of limiting the range of the operands and dealing with the infinities.
Despite disallowing undue overflow, complex multiplication may raise spurious floatingpoint exceptions (otherwise it is prohibitively difficult to implement nonoverflowing versions)
#include<stdio.h> #include <stdio.h> #include <complex.h> #include <math.h> int main(void) { // TODO simpler cases, take some from C++ double complex z = (1 + 0*I) * (INFINITY + I*INFINITY); // textbook formula would give // (1+i0)(∞+i∞) ⇒ (1×∞ – 0×∞) + i(0×∞+1×∞) ⇒ NaN + I*NaN // but C gives a complex infinity printf("%f + i*%f\n", creal(z), cimag(z)); // textbook formula would give // cexp(∞+iNaN) ⇒ exp(∞)×(cis(NaN)) ⇒ NaN + I*NaN // but C gives ±∞+i*nan double complex y = cexp(INFINITY + I*NAN); printf("%f + i*%f\n", creal(y), cimag(y)); }
Possible output:
inf + i*inf inf + i*nan
[edit] Division
The binary operator / divides the first operand by the second (after usual arithmetic conversions) following the usual arithmetics definitions, except that
 when the type after usual arithmetic conversions is an integer type, the result is the algebraic quotient (not a fraction), rounded in implementationdefined direction (until C99)truncated towards zero (since C99)
 if one operand is a NaN, the result is a NaN
 if the first operand is a complex infinity and the second operand is finite, then the
result of the / operator is a complex infinity
 if the first operand is finite and the second operand is a complex infinity, then the
result of the / operator is a zero
Because in C, any complex value with at least one infinite part as an infinity even if its other part is a NaN, the usual arithmetic rules do not apply to complexcomplex division. Other combinations of floating operands follow the following table:
/  u  iv 

x  x/u  i(−x/v) 
iy  i(y/u)  y/v 
x + iy  (x/u) + i(y/u)  (y/v) + i(−x/v) 
Besides infinity handling, complex division is not allowed to overflow intermediate results, except when
#pragma STDC CX_LIMITED_RANGE is set to ON
, in which case the value may be calculated as if by (x+iy)/(u+iv) = [(xu+yv)+i(yuxv)]/(u2
+v2
), as the programmer assumes the responsibility of limiting the range of the operands and dealing with the infinities.
Despite disallowing undue overflow, complex division may raise spurious floatingpoint exceptions (otherwise it is prohibitively difficult to implement nonoverflowing versions)
If the second operand is zero, the behavior is undefined, except that if the IEEE floatingpoint arithmetic is supported, and the floatingpoint division is taking place, then
 Dividing a nonzero number by ±0.0 gives the correctlysigned infinity and FE_DIVBYZERO is raised
 Dividing 0.0 by 0.0 gives NaN and FE_INVALID is raised
[edit] Remainder
The binary operator % yields the remainder of the division of the first operand by the second (after usual arithmetic conversions).
The sign of the remainder is defined in such a way that if the quotient a/b
is representable in the result type, then (a/b)*b + a%b == a.
If the second operand is zero, the behavior is undefined.
If the quotient a/b
is not representable in the result type, the behavior of both a/b
and a%b
is undefined (that means INT_MIN%1 is undefined on 2's complement systems)
Note: the remainder operator does not work on floatingpoint types, the library function fmod provides that functionality.
[edit] Bitwise logic
The bitwise arithmetic operator expressions have the form
~ rhs

(1)  
lhs & rhs

(2)  
lhs  rhs

(3)  
lhs ^ rhs

(4)  
where
lhs, rhs    expressions of integer type 
First, operators &, ^, and  perform usual arithmetic conversions on both operands and the operator ~ performs integer promotions on its only operand.
Then, the corresponding binary logic operators are applied bitwise; that is, each bit of the result is set or cleared according to the logic operation (NOT, AND, OR, or XOR), applied to the corresponding bits of the operands.
Note: bitwise operators are commonly used to manipulate bit sets and bit masks.
Note: for unsigned types (after promotion), the expression ~E is equivalent to the maximum value representable by the result type minus the original value of E.
Possible output:
Value: 0x12345678 mask: 0xf0 Setting bits: 0x123456f8 Clearing bits: 0x12345608 Selecting bits: 0x70
[edit] Shift operators
The bitwise shift operator expressions have the form
lhs << rhs

(1)  
lhs >> rhs

(2)  
where
lhs, rhs    expressions of integer type 
First, integer promotions are performed, individually, on each operand (Note: this is unlike other binary arithmetic operators, which all perform usual arithmetic conversions). The type of the result is the type of lhs after promotion.
For unsigned lhs, the value of LHS << RHS
is the value of LHS * 2RHS
, reduced modulo maximum value of the return type plus 1 (that is, bitwise left shift is performed and the bits that get shifted out of the destination type are discarded). For signed lhs, the value of LHS << RHS
is LHS * 2RHS
if it is representable in the promoted type of lhs, otherwise the behavior is undefined.
For unsigned lhs and for signed lhs with nonnegative values, the value of LHS >> RHS
is the integer part of LHS / 2RHS
. For negative LHS
, the value of LHS >> RHS
is implementationdefined where in most implementations, this performs arithmetic right shift (so that the result remains negative). Thus in most implementations, right shifting a signed LHS
fills the new higherorder bits with the original sign bit (i.e. with 0 if it was nonnegative and 1 if it was negative).
In any case, the behavior is undefined if rhs is negative or is greater or equal the number of bits in the promoted lhs.
#include <stdio.h> enum {ONE=1, TWO=2}; int main(void) { char c = 0x10; unsigned long long ulong_num = 0x123; printf("0x123 << 1 = %#llx\n" "0x123 << 63 = %#llx\n" // overflow truncates high bits for unsigned numbers "0x10 << 10 = %#x\n", // char is promoted to int ulong_num << 1, ulong_num << 63, c << 10); long long long_num = 1000; printf("1000 >> 1 = %lld\n", long_num >> ONE); // implementation defined }
Possible output:
0x123 << 1 = 0x246 0x123 << 63 = 0x8000000000000000 0x10 << 10 = 0x4000 1000 >> 1 = 500
[edit] References
 C11 standard (ISO/IEC 9899:2011):
 6.5.3.3 Unary arithmetic operators (p: 89)
 6.5.5 Multiplicative operators (p: 92)
 6.5.6 Additive operators (p: 9294)
 6.5.7 Bitwise shift operators (p: 9495)
 6.5.10 Bitwise AND operator (p: 97)
 6.5.11 Bitwise exclusive OR operator (p: 98)
 6.5.12 Bitwise inclusive OR operator (p: 98)
 C99 standard (ISO/IEC 9899:1999):
 6.5.3.3 Unary arithmetic operators (p: 79)
 6.5.5 Multiplicative operators (p: 82)
 6.5.6 Additive operators (p: 8284)
 6.5.7 Bitwise shift operators (p: 8485)
 6.5.10 Bitwise AND operator (p: 87)
 6.5.11 Bitwise exclusive OR operator (p: 88)
 6.5.12 Bitwise inclusive OR operator (p: 88)
 C89/C90 standard (ISO/IEC 9899:1990):
 3.3.3.3 Unary arithmetic operators
 3.3.5 Multiplicative operators
 3.3.6 Additive operators
 3.3.7 Bitwise shift operators
 3.3.10 Bitwise AND operator
 3.3.11 Bitwise exclusive OR operator
 3.3.12 Bitwise inclusive OR operator
[edit] See also
Common operators  

assignment  increment decrement 
arithmetic  logical  comparison  member access 
other 
a = b 
++a 
+a 
!a 
a == b 
a[b] 
a(...) 
C++ documentation for Arithmetic operators
