painless-operators-numeric.asciidoc

Operators: Numeric

Post Increment

Use the post increment operator '++' to INCREASE the value of a numeric type variable/field by 1. An extra implicit cast is necessary to return the promoted numeric type value to the original numeric type value of the variable/field for the following types: byte, short, and char. If a variable/field is read as part of an expression the value is loaded prior to the increment.

Errors

• If the variable/field is a non-numeric type.

Grammar

post_increment: ( variable | field ) '++';

Promotion

original	promoted	implicit
byte	int	byte
short	int	short
char	int	char
int	int
long	long
float	float
double	double
def	def

Examples

• Post increment with different numeric types.

  short i = 0; (1)
  i++;         (2)
  long j = 1;  (3)
  long k;      (4)
  k = j++;     (5)

  1. declare short i; store short 0 to i

  2. load from i → short 0; promote short 0: result int; add int 0 and int 1 → int 1; implicit cast int 1 to short 1; store short 1 to i

  3. declare long j; implicit cast int 1 to long 1 → long 1; store long 1 to j

  4. declare long k; store default long 0 to k

  5. load from j → long 1; store long 1 to k; add long 1 and long 1 → long 2; store long 2 to j

• Post increment with the def type.

  def x = 1; (1)
  x++;       (2)

  1. declare def x; implicit cast int 1 to def → def; store def to x

  2. load from x → def; implicit cast def to int 1; add int 1 and int 1 → int 2; implicit cast int 2 to def; store def to x

Post Decrement

Use the post decrement operator '--' to DECREASE the value of a numeric type variable/field by 1. An extra implicit cast is necessary to return the promoted numeric type value to the original numeric type value of the variable/field for the following types: byte, short, and char. If a variable/field is read as part of an expression the value is loaded prior to the decrement.

Errors

• If the variable/field is a non-numeric type.

Grammar

post_decrement: ( variable | field ) '--';

Promotion

original	promoted	implicit
byte	int	byte
short	int	short
char	int	char
int	int
long	long
float	float
double	double
def	def

Examples

• Post decrement with different numeric types.

  short i = 0; (1)
  i--;         (2)
  long j = 1;  (3)
  long k;      (4)
  k = j--;     (5)

  1. declare short i; store short 0 to i

  2. load from i → short 0; promote short 0: result int; subtract int 1 from int 0 → int -1; implicit cast int -1 to short -1; store short -1 to i

  3. declare long j; implicit cast int 1 to long 1 → long 1; store long 1 to j

  4. declare long k; store default long 0 to k

  5. load from j → long 1; store long 1 to k; subtract long 1 from long 1 → long 0; store long 0 to j

• Post decrement with the def type.

  def x = 1; (1)
  x--;       (2)

  1. declare def x; implicit cast int 1 to def → def; store def to x

  2. load from x → def; implicit cast def to int 1; subtract int 1 from int 1 → int 0; implicit cast int 0 to def; store def to x

Pre Increment

Use the pre increment operator '++' to INCREASE the value of a numeric type variable/field by 1. An extra implicit cast is necessary to return the promoted numeric type value to the original numeric type value of the variable/field for the following types: byte, short, and char. If a variable/field is read as part of an expression the value is loaded after the increment.

Errors

• If the variable/field is a non-numeric type.

Grammar

pre_increment: '++' ( variable | field );

Promotion

original	promoted	implicit
byte	int	byte
short	int	short
char	int	char
int	int
long	long
float	float
double	double
def	def

Examples

• Pre increment with different numeric types.

  short i = 0; (1)
  ++i;         (2)
  long j = 1;  (3)
  long k;      (4)
  k = ++j;     (5)

  1. declare short i; store short 0 to i

  2. load from i → short 0; promote short 0: result int; add int 0 and int 1 → int 1; implicit cast int 1 to short 1; store short 1 to i

  3. declare long j; implicit cast int 1 to long 1 → long 1; store long 1 to j

  4. declare long k; store default long 0 to k

  5. load from j → long 1; add long 1 and long 1 → long 2; store long 2 to j; store long 2 to k

• Pre increment with the def type.

  def x = 1; (1)
  ++x;       (2)

  1. declare def x; implicit cast int 1 to def → def; store def to x

  2. load from x → def; implicit cast def to int 1; add int 1 and int 1 → int 2; implicit cast int 2 to def; store def to x

Pre Decrement

Use the pre decrement operator '--' to DECREASE the value of a numeric type variable/field by 1. An extra implicit cast is necessary to return the promoted numeric type value to the original numeric type value of the variable/field for the following types: byte, short, and char. If a variable/field is read as part of an expression the value is loaded after the decrement.

Errors

• If the variable/field is a non-numeric type.

Grammar

pre_decrement: '--' ( variable | field );

Promotion

original	promoted	implicit
byte	int	byte
short	int	short
char	int	char
int	int
long	long
float	float
double	double
def	def

Examples

• Pre decrement with different numeric types.

  short i = 0; (1)
  --i;         (2)
  long j = 1;  (3)
  long k;      (4)
  k = --j;     (5)

  1. declare short i; store short 0 to i

  2. load from i → short 0; promote short 0: result int; subtract int 1 from int 0 → int -1; implicit cast int -1 to short -1; store short -1 to i

  3. declare long j; implicit cast int 1 to long 1 → long 1; store long 1 to j

  4. declare long k; store default long 0 to k

  5. load from j → long 1; subtract long 1 from long 1 → long 0; store long 0 to j store long 0 to k;

• Pre decrement operator with the def type.

  def x = 1; (1)
  --x;       (2)

  1. declare def x; implicit cast int 1 to def → def; store def to x

  2. load from x → def; implicit cast def to int 1; subtract int 1 from int 1 → int 0; implicit cast int 0 to def; store def to x

Unary Positive

Use the unary positive operator '+' to the preserve the IDENTITY of a numeric type value.

Errors

• If the value is a non-numeric type.

Grammar

unary_positive: '+' expression;

Examples

• Unary positive with different numeric types.

  int x = +1;  (1)
  long y = +x; (2)

  1. declare int x; identity int 1 → int 1; store int 1 to x

  2. declare long y; load from x → int 1; identity int 1 → int 1; implicit cast int 1 to long 1 → long 1; store long 1 to y

• Unary positive with the def type.

  def z = +1; (1)
  int i = +z; (2)

  1. declare def z; identity int 1 → int 1; implicit cast int 1 to def; store def to z

  2. declare int i; load from z → def; implicit cast def to int 1; identity int 1 → int 1; store int 1 to i;

Unary Negative

Use the unary negative operator '-' to NEGATE a numeric type value.

Errors

• If the value is a non-numeric type.

Grammar

unary_negative: '-' expression;

Examples

• Unary negative with different numeric types.

  int x = -1;  (1)
  long y = -x; (2)

  1. declare int x; negate int 1 → int -1; store int -1 to x

  2. declare long y; load from x → int 1; negate int -1 → int 1; implicit cast int 1 to long 1 → long 1; store long 1 to y

• Unary negative with the def type.

  def z = -1; (1)
  int i = -z; (2)

  1. declare def z; negate int 1 → int -1; implicit cast int -1 to def; store def to z

  2. declare int i; load from z → def; implicit cast def to int -1; negate int -1 → int 1; store int 1 to i;

Bitwise Not

Use the bitwise not operator '~' to NOT each bit in an integer type value where a 1-bit is flipped to a resultant 0-bit and a 0-bit is flipped to a resultant 1-bit.

Errors

• If the value is a non-integer type.

Bits

original	result
1	0
0	1

Grammar

bitwise_not: '~' expression;

Promotion

original	promoted
byte	int
short	int
char	int
int	int
long	long
def	def

Examples

• Bitwise not with different numeric types.

  byte b = 1;  (1)
  int i = ~b;  (2)
  long l = ~i; (3)

  1. declare byte x; store byte 1 to b

  2. declare int i; load from b → byte 1; implicit cast byte 1 to int 1 → int 1; bitwise not int 1 → int -2; store int -2 to i

  3. declare long l; load from i → int -2; implicit cast int -2 to long -2 → long -2; bitwise not long -2 → long 1; store long 1 to l

• Bitwise not with the def type.

  def d = 1;  (1)
  def e = ~d; (2)

  1. declare def d; implicit cast int 1 to def → def; store def to d;

  2. declare def e; load from d → def; implicit cast def to int 1 → int 1; bitwise not int 1 → int -2; implicit cast int 1 to def → def; store def to e

Multiplication

Use the multiplication operator '*' to MULTIPLY together two numeric type values. Rules for resultant overflow and NaN values follow the JVM specification.

Errors

• If either of the values is a non-numeric type.

Grammar

multiplication: expression '*' expression;

Promotion

	byte	short	char	int	long	float	double	def
byte	int	int	int	int	long	float	double	def
short	int	int	int	int	long	float	double	def
char	int	int	int	int	long	float	double	def
int	int	int	int	int	long	float	double	def
long	long	long	long	long	long	float	double	def
float	float	float	float	float	float	float	double	def
double	double	double	double	double	double	double	double	def
def	def	def	def	def	def	def	def	def

Examples

• Multiplication with different numeric types.

  int i = 5*4;      (1)
  double d = i*7.0; (2)

  1. declare int i; multiply int 4 by int 5 → int 20; store int 20 in i

  2. declare double d; load from int i → int 20; promote int 20 and double 7.0: result double; implicit cast int 20 to double 20.0 → double 20.0; multiply double 20.0 by double 7.0 → double 140.0; store double 140.0 to d

• Multiplication with the def type.

  def x = 5*4; (1)
  def y = x*2; (2)

  1. declare def x; multiply int 5 by int 4 → int 20; implicit cast int 20 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 20; multiply int 20 by int 2 → int 40; implicit cast int 40 to def → def; store def to y

Division

Use the division operator '/' to DIVIDE one numeric type value by another. Rules for NaN values and division by zero follow the JVM specification. Division with integer values drops the remainder of the resultant value.

Errors

• If either of the values is a non-numeric type.

• If a left-hand side integer type value is divided by a right-hand side integer type value of 0.

Grammar

division: expression '/' expression;

Promotion

	byte	short	char	int	long	float	double	def
byte	int	int	int	int	long	float	double	def
short	int	int	int	int	long	float	double	def
char	int	int	int	int	long	float	double	def
int	int	int	int	int	long	float	double	def
long	long	long	long	long	long	float	double	def
float	float	float	float	float	float	float	double	def
double	double	double	double	double	double	double	double	def
def	def	def	def	def	def	def	def	def

Examples

• Division with different numeric types.

  int i = 29/4;     (1)
  double d = i/7.0; (2)

  1. declare int i; divide int 29 by int 4 → int 7; store int 7 in i

  2. declare double d; load from int i → int 7; promote int 7 and double 7.0: result double; implicit cast int 7 to double 7.0 → double 7.0; divide double 7.0 by double 7.0 → double 1.0; store double 1.0 to d

• Division with the def type.

  def x = 5/4; (1)
  def y = x/2; (2)

  1. declare def x; divide int 5 by int 4 → int 1; implicit cast int 1 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 1; divide int 1 by int 2 → int 0; implicit cast int 0 to def → def; store def to y

Remainder

Use the remainder operator '%' to calculate the REMAINDER for division between two numeric type values. Rules for NaN values and division by zero follow the JVM specification.

Errors

• If either of the values is a non-numeric type.

Grammar

remainder: expression '%' expression;

Promotion

	byte	short	char	int	long	float	double	def
byte	int	int	int	int	long	float	double	def
short	int	int	int	int	long	float	double	def
char	int	int	int	int	long	float	double	def
int	int	int	int	int	long	float	double	def
long	long	long	long	long	long	float	double	def
float	float	float	float	float	float	float	double	def
double	double	double	double	double	double	double	double	def
def	def	def	def	def	def	def	def	def

Examples

• Remainder with different numeric types.

  int i = 29%4;     (1)
  double d = i%7.0; (2)

  1. declare int i; remainder int 29 by int 4 → int 1; store int 7 in i

  2. declare double d; load from int i → int 1; promote int 1 and double 7.0: result double; implicit cast int 1 to double 1.0 → double 1.0; remainder double 1.0 by double 7.0 → double 1.0; store double 1.0 to d

• Remainder with the def type.

  def x = 5%4; (1)
  def y = x%2; (2)

  1. declare def x; remainder int 5 by int 4 → int 1; implicit cast int 1 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 1; remainder int 1 by int 2 → int 1; implicit cast int 1 to def → def; store def to y

Addition

Use the addition operator '+' to ADD together two numeric type values. Rules for resultant overflow and NaN values follow the JVM specification.

Errors

• If either of the values is a non-numeric type.

Grammar

addition: expression '+' expression;

Promotion

	byte	short	char	int	long	float	double	def
byte	int	int	int	int	long	float	double	def
short	int	int	int	int	long	float	double	def
char	int	int	int	int	long	float	double	def
int	int	int	int	int	long	float	double	def
long	long	long	long	long	long	float	double	def
float	float	float	float	float	float	float	double	def
double	double	double	double	double	double	double	double	def
def	def	def	def	def	def	def	def	def

Examples

• Addition operator with different numeric types.

  int i = 29+4;     (1)
  double d = i+7.0; (2)

  1. declare int i; add int 29 and int 4 → int 33; store int 33 in i

  2. declare double d; load from int i → int 33; promote int 33 and double 7.0: result double; implicit cast int 33 to double 33.0 → double 33.0; add double 33.0 and double 7.0 → double 40.0; store double 40.0 to d

• Addition with the def type.

  def x = 5+4; (1)
  def y = x+2; (2)

  1. declare def x; add int 5 and int 4 → int 9; implicit cast int 9 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 9; add int 9 and int 2 → int 11; implicit cast int 11 to def → def; store def to y

Subtraction

Use the subtraction operator '-' to SUBTRACT a right-hand side numeric type value from a left-hand side numeric type value. Rules for resultant overflow and NaN values follow the JVM specification.

Errors

• If either of the values is a non-numeric type.

Grammar

subtraction: expression '-' expression;

Promotion

	byte	short	char	int	long	float	double	def
byte	int	int	int	int	long	float	double	def
short	int	int	int	int	long	float	double	def
char	int	int	int	int	long	float	double	def
int	int	int	int	int	long	float	double	def
long	long	long	long	long	long	float	double	def
float	float	float	float	float	float	float	double	def
double	double	double	double	double	double	double	double	def
def	def	def	def	def	def	def	def	def

Examples

• Subtraction with different numeric types.

  int i = 29-4;     (1)
  double d = i-7.5; (2)

  1. declare int i; subtract int 4 from int 29 → int 25; store int 25 in i

  2. declare double d load from int i → int 25; promote int 25 and double 7.5: result double; implicit cast int 25 to double 25.0 → double 25.0; subtract double 33.0 by double 7.5 → double 25.5; store double 25.5 to d

• Subtraction with the def type.

  def x = 5-4; (1)
  def y = x-2; (2)

  1. declare def x; subtract int 4 and int 5 → int 1; implicit cast int 1 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 1; subtract int 2 from int 1 → int -1; implicit cast int -1 to def → def; store def to y

Left Shift

Use the left shift operator '<<' to SHIFT lower order bits to higher order bits in a left-hand side integer type value by the distance specified in a right-hand side integer type value.

Errors

• If either of the values is a non-integer type.

• If the right-hand side value cannot be cast to an int type.

Grammar

left_shift: expression '<<' expression;

Promotion

The left-hand side integer type value is promoted as specified in the table below. The right-hand side integer type value is always implicitly cast to an int type value and truncated to the number of bits of the promoted type value.

original	promoted
byte	int
short	int
char	int
int	int
long	long
def	def

Examples

• Left shift with different integer types.

  int i = 4 << 1;   (1)
  long l = i << 2L; (2)

  1. declare int i; left shift int 4 by int 1 → int 8; store int 8 in i

  2. declare long l load from int i → int 8; implicit cast long 2 to int 2 → int 2; left shift int 8 by int 2 → int 32; implicit cast int 32 to long 32 → long 32; store long 32 to l

• Left shift with the def type.

  def x = 4 << 2; (1)
  def y = x << 1; (2)

  1. declare def x; left shift int 4 by int 2 → int 16; implicit cast int 16 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 16; left shift int 16 by int 1 → int 32; implicit cast int 32 to def → def; store def to y

Right Shift

Use the right shift operator '>>' to SHIFT higher order bits to lower order bits in a left-hand side integer type value by the distance specified in a right-hand side integer type value. The highest order bit of the left-hand side integer type value is preserved.

Errors

• If either of the values is a non-integer type.

• If the right-hand side value cannot be cast to an int type.

Grammar

right_shift: expression '>>' expression;

Promotion

The left-hand side integer type value is promoted as specified in the table below. The right-hand side integer type value is always implicitly cast to an int type value and truncated to the number of bits of the promoted type value.

original	promoted
byte	int
short	int
char	int
int	int
long	long
def	def

Examples

• Right shift with different integer types.

  int i = 32 >> 1;  (1)
  long l = i >> 2L; (2)

  1. declare int i; right shift int 32 by int 1 → int 16; store int 16 in i

  2. declare long l load from int i → int 16; implicit cast long 2 to int 2 → int 2; right shift int 16 by int 2 → int 4; implicit cast int 4 to long 4 → long 4; store long 4 to l

• Right shift with the def type.

  def x = 16 >> 2; (1)
  def y = x >> 1;  (2)

  1. declare def x; right shift int 16 by int 2 → int 4; implicit cast int 4 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 4; right shift int 4 by int 1 → int 2; implicit cast int 2 to def → def; store def to y

Unsigned Right Shift

Use the unsigned right shift operator '>>>' to SHIFT higher order bits to lower order bits in a left-hand side integer type value by the distance specified in a right-hand side type integer value. The highest order bit of the left-hand side integer type value is not preserved.

Errors

• If either of the values is a non-integer type.

• If the right-hand side value cannot be cast to an int type.

Grammar

unsigned_right_shift: expression '>>>' expression;

Promotion

The left-hand side integer type value is promoted as specified in the table below. The right-hand side integer type value is always implicitly cast to an int type value and truncated to the number of bits of the promoted type value.

original	promoted
byte	int
short	int
char	int
int	int
long	long
def	def

Examples

• Unsigned right shift with different integer types.

  int i = -1 >>> 29; (1)
  long l = i >>> 2L; (2)

  1. declare int i; unsigned right shift int -1 by int 29 → int 7; store int 7 in i

  2. declare long l load from int i → int 7; implicit cast long 2 to int 2 → int 2; unsigned right shift int 7 by int 2 → int 3; implicit cast int 3 to long 3 → long 3; store long 3 to l

• Unsigned right shift with the def type.

  def x = 16 >>> 2; (1)
  def y = x >>> 1;  (2)

  1. declare def x; unsigned right shift int 16 by int 2 → int 4; implicit cast int 4 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 4; unsigned right shift int 4 by int 1 → int 2; implicit cast int 2 to def → def; store def to y

Bitwise And

Use the bitwise and operator '&' to AND together each bit within two integer type values where if both bits at the same index are 1 the resultant bit is 1 and 0 otherwise.

Errors

• If either of the values is a non-integer type.

Bits

	1	0
1	1	0
0	0	0

Grammar

bitwise_and: expression '&' expression;

Promotion

	byte	short	char	int	long	def
byte	int	int	int	int	long	def
short	int	int	int	int	long	def
char	int	int	int	int	long	def
int	int	int	int	int	long	def
long	long	long	long	long	long	def
def	def	def	def	def	def	def

Examples

• Bitwise and with different integer types.

  int i = 5 & 6;   (1)
  long l = i & 5L; (2)

  1. declare int i; bitwise and int 5 and int 6 → int 4; store int 4 in i

  2. declare long l load from int i → int 4; promote int 4 and long 5: result long; implicit cast int 4 to long 4 → long 4; bitwise and long 4 and long 5 → long 4; store long 4 to l

• Bitwise and with the def type.

  def x = 15 & 6; (1)
  def y = x & 5;  (2)

  1. declare def x; bitwise and int 15 and int 6 → int 6; implicit cast int 6 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 6; bitwise and int 6 and int 5 → int 4; implicit cast int 4 to def → def; store def to y

Bitwise Xor

Use the bitwise xor operator '^' to XOR together each bit within two integer type values where if one bit is a 1 and the other bit is a 0 at the same index the resultant bit is 1 otherwise the resultant bit is 0.

Errors

• If either of the values is a non-integer type.

Bits

The following table illustrates the resultant bit from the xoring of two bits.

	1	0
1	0	1
0	1	0

Grammar

bitwise_xor: expression '^' expression;

Promotion

	byte	short	char	int	long	def
byte	int	int	int	int	long	def
short	int	int	int	int	long	def
char	int	int	int	int	long	def
int	int	int	int	int	long	def
long	long	long	long	long	long	def
def	def	def	def	def	def	def

Examples

• Bitwise xor with different integer types.

  int i = 5 ^ 6;   (1)
  long l = i ^ 5L; (2)

  1. declare int i; bitwise xor int 5 and int 6 → int 3; store int 3 in i

  2. declare long l load from int i → int 4; promote int 3 and long 5: result long; implicit cast int 3 to long 3 → long 3; bitwise xor long 3 and long 5 → long 6; store long 6 to l

• Bitwise xor with the def type.

  def x = 15 ^ 6; (1)
  def y = x ^ 5;  (2)

  1. declare def x; bitwise xor int 15 and int 6 → int 9; implicit cast int 9 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 9; bitwise xor int 9 and int 5 → int 12; implicit cast int 12 to def → def; store def to y

Bitwise Or

Use the bitwise or operator '|' to OR together each bit within two integer type values where if at least one bit is a 1 at the same index the resultant bit is 1 otherwise the resultant bit is 0.

Errors

• If either of the values is a non-integer type.

Bits

The following table illustrates the resultant bit from the oring of two bits.

	1	0
1	1	1
0	1	0

Grammar

bitwise_or: expression '|' expression;

Promotion

	byte	short	char	int	long	def
byte	int	int	int	int	long	def
short	int	int	int	int	long	def
char	int	int	int	int	long	def
int	int	int	int	int	long	def
long	long	long	long	long	long	def
def	def	def	def	def	def	def

Examples

• Bitwise or with different integer types.

  int i = 5 | 6;   (1)
  long l = i | 8L; (2)

  1. declare int i; bitwise or int 5 and int 6 → int 7; store int 7 in i

  2. declare long l load from int i → int 7; promote int 7 and long 8: result long; implicit cast int 7 to long 7 → long 7; bitwise or long 7 and long 8 → long 15; store long 15 to l

• Bitwise or with the def type.

  def x = 5 ^ 6; (1)
  def y = x ^ 8; (2)

  1. declare def x; bitwise or int 5 and int 6 → int 7; implicit cast int 7 to def → def; store def in x

  2. declare def y; load from x → def; implicit cast def to int 7; bitwise or int 7 and int 8 → int 15; implicit cast int 15 to def → def; store def to y