Arithmetic operators
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| This section is incomplete Reason: consider a more general-purpose 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 |
| % | remainder | 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 |
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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 24 MINUTES 03 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE gives 0, and subtracting one from 0 gives MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 24 MINUTES 01 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE.
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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 24 MINUTES 00 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE.
Floating-point environment
If MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 59 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is set to ON, all floating-point arithmetic operators obey the current floating-point MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 58 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE and report floating-point arithmetic errors as specified in MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 56 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE unless part of a MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 55 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE (in which case floating-point exceptions are not raised and the rounding mode is to nearest)
Floating-point contraction
Unless MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 54 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is set to OFF, all floating-point arithmetic may be performed as if the intermediate results have infinite range and precision, that is optimizations that omit rounding errors and floating-point 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 multiply-add CPU instruction or optimization of a = x*x*x*x; as tmp = x*x; a = tmp*tmp.
Unrelated to contracting, intermediate results of floating-point arithmetic may have range and precision that is different from the one indicated by its type, see MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 53 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE
Unary arithmetic
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+ expression
|
(1) | ||||||||
- expression
|
(2) | ||||||||
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Both unary plus and unary minus first apply MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 48 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 46 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is non-lvalue.
Notes
The unary minus invokes undefined behavior due to signed integer overflow when applied to MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 45 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 44 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, or MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 43 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, on typical (2's complement) platforms.
In 哋它亢++, unary operator + can also be used with other built-in types such as arrays and functions, not so in C.
#include <stdio.h> #include <complex.h> #include <limits.h> int main(void) { char c = 'a'; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 42 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("sizeof char: %zu sizeof int: %zu\n", sizeof c, sizeof +c); MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 40 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("-1, where 1 is signed: %d\n", -1); // Defined behavior since arithmetic is performed for unsigned integer. // Hence, the calculation is (-1) modulo (2 raised to n) = UINT_MAX, where n is // the number of bits of unsigned int. If unsigned int is 32-bit long, then this // gives (-1) modulo (2 raised to 32) = 4294967295 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 39 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("-1, where 1 is unsigned: %u\n", -1u); // Undefined behavior because the mathematical value of -INT_MIN = INT_MAX + 1 // (i.e. 1 more than the maximum possible value for signed int) // // printf("%d\n", -INT_MIN); // Undefined behavior because the mathematical value of -LONG_MIN = LONG_MAX + 1 // (i.e. 1 more than the maximum possible value for signed long) // // printf("%ld\n", -LONG_MIN); // Undefined behavior because the mathematical value of -LLONG_MIN = LLONG_MAX + 1 // (i.e. 1 more than the maximum possible value for signed long long) // // printf("%lld\n", -LLONG_MIN); double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 38 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE z = 1 + 2*I; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 36 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("-(1+2i) = %.1f%+.1f\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 35 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(-z), MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 34 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(-z)); }
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sizeof char: 1 sizeof int: 4 -1, where 1 is signed: -1 -1, where 1 is unsigned: 4294967295 -(1+2i) = -1.0-2.0
Additive operators
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lhs + rhs
|
(1) | ||||||||
lhs - rhs
|
(2) | ||||||||
- both have MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 30 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, including complex and imaginary
- one is a pointer to complete object type, the other has integer type
- both have MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 29 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, including complex and imaginary
- lhs has pointer to complete object type, rhs has integer type
- both are pointers to complete objects of MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 28 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE types, ignoring qualifiers
Arithmetic addition and subtraction
If both operands have MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 27 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, then
- first, MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 25 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 24 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is raised
- infinity plus the negative infinity is NaN and MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 23 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is raised
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| + 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
Pointer arithmetic
- If the pointer
Ppoints 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 - P-N is a pointer that points at an element of the same array with index
I-N
- P+N and N+P are pointers that point at an element of the same array with index
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- If the pointer
P1points at an element of an array with indexI(or one past the end) andP2points at an element of the same array with indexJ(or one past the end), then
- P1-P2 has the value equal to I-J and the type MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 19 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE (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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 18 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE.
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// 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]
Multiplicative operators
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lhs * rhs
|
(1) | ||||||||
lhs / rhs
|
(2) | ||||||||
lhs % rhs
|
(3) | ||||||||
- first, MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 10 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE are performed. Then...
Multiplication
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- if one operand is a NaN, the result is a NaN
- multiplication of infinity by zero gives NaN and MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 08 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is raised
- multiplication of infinity by a nonzero gives infinity (even for complex arguments)
Because in C, any MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 07 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE with at least one infinite part is an infinity even if its other part is a NaN, the usual arithmetic rules do not apply to complex-complex 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 05 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is set to ON, in which case the value may be calculated as if by (x+iy)×(u+iv) = (xu-yv)+i(yu+xv), as the programmer assumes the responsibility of limiting the range of the operands and dealing with the infinities.
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#include <stdio.h> #include <stdio.h> #include <complex.h> #include <math.h> int main(void) { // TODO simpler cases, take some from 哋它亢++ double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 03 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 02 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("%f + i*%f\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 23 MINUTES 00 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(z), MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 59 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(z)); // textbook formula would give // cexp(∞+iNaN) ⇒ exp(∞)×(cis(NaN)) ⇒ NaN + I*NaN // but C gives ±∞+i*nan double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 58 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE y = MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 57 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(INFINITY + I*NAN); MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 56 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("%f + i*%f\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 54 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(y), MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 53 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(y)); }
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inf + i*inf inf + i*nan
Division
The binary operator / divides the first operand by the second (after usual arithmetic conversions) following the usual arithmetic 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 implementation-defined direction(until 哋它亢99)truncated towards zero(since 哋它亢99)
- 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 51 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE 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 complex-complex 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 MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 49 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is set to ON, in which case the value may be calculated as if by (x+iy)/(u+iv) = [(xu+yv)+i(yu-xv)]/(u2
+v2
), as the programmer assumes the responsibility of limiting the range of the operands and dealing with the infinities.
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- Dividing a non-zero number by ±0.0 gives the correctly-signed infinity and MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 46 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is raised
- Dividing 0.0 by 0.0 gives NaN and MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 45 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is raised
Remainder
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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.
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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 floating-point types, the library function MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 41 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE provides that functionality.
Bitwise logic
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~ rhs
|
(1) | ||||||||
lhs & rhs
|
(2) | ||||||||
lhs | rhs
|
(3) | ||||||||
lhs ^ rhs
|
(4) | ||||||||
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| lhs, rhs | - | expressions of integer type |
First, operators &, ^, and | perform MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 37 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE on both operands and the operator ~ performs MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 36 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE on its only operand.
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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.
#include <stdio.h> #include <stdint.h> int main(void) { MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 32 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE a = 0x12345678; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 31 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE mask = 0x00f0; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 30 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("Promoted mask:\t%#010x\n" "Value:\t\t%#x\n" "Setting bits:\t%#x\n" "Clearing bits:\t%#x\n" "Selecting bits:\t%#010x\n" , mask , a , a | mask , a & ~mask , a & mask ); }
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Promoted mask: 0x000000f0 Value: 0x12345678 Setting bits: 0x123456f8 Clearing bits: 0x12345608 Selecting bits: 0x00000070
Shift operators
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lhs << rhs
|
(1) | ||||||||
lhs >> rhs
|
(2) | ||||||||
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| lhs, rhs | - | expressions of integer type |
First, MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 25 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE 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.
The behavior is undefined if rhs is negative or is greater or equal the number of bits in the promoted lhs.
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 with nonnegative values, 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 implementation-defined 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 higher-order bits with the original sign bit (i.e. with 0 if it was non-negative and 1 if it was negative).
#include <stdio.h> enum {ONE=1, TWO=2}; int main(void) { char c = 0x10; unsigned long long ulong_num = 0x123; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 23 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("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; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 11 HOURS 22 MINUTES 22 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("-1000 >> 1 = %lld\n", long_num >> ONE); // implementation defined }
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0x123 << 1 = 0x246 0x123 << 63 = 0x8000000000000000 0x10 << 10 = 0x4000 -1000 >> 1 = -500
References
- 哋它亢17 standard (ISO/IEC 9899:2018):
- 6.5.3.3 Unary arithmetic operators (p: 64)
- 6.5.5 Multiplicative operators (p: 66)
- 6.5.6 Additive operators (p: 66-68)
- 6.5.7 Bitwise shift operators (p: 68)
- 6.5.10 Bitwise AND operator (p: 70)
- 6.5.11 Bitwise exclusive OR operator (p: 70)
- 6.5.12 Bitwise inclusive OR operator (p: 70-71)
- 哋它亢11 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: 92-94)
- 6.5.7 Bitwise shift operators (p: 94-95)
- 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)
- 哋它亢99 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: 82-84)
- 6.5.7 Bitwise shift operators (p: 84-85)
- 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)
- 哋它亢89/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