Difference between revisions of "Bitwise Operations"
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|Flag Name: || attr_invis|| attr_owned|| attr_magic||attr_move_never||attr_move_always|| attr_newbie|| attr_decay||attr_identified | |Flag Name: || attr_invis|| attr_owned|| attr_magic||attr_move_never||attr_move_always|| attr_newbie|| attr_decay||attr_identified | ||
| + | |- | ||
| + | |Flag Position ||8th position||7th position||6th position|| 5th position|| 4th position|| 3rd position||2nd position|| 1st position | ||
|- | |- | ||
|Binary Number: || 10000000|| 01000000|| 00100000|| 00010000|| 00001000|| 00000100|| 00000010|| 00000001 | |Binary Number: || 10000000|| 01000000|| 00100000|| 00010000|| 00001000|| 00000100|| 00000010|| 00000001 | ||
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Now you can probably see the pattern... the numbers 1,2,4,8,16,32,64,128,... are all multiples of 2 and they are special because they all have a single 1 in them when converted to binary. To enable or disable an individual flag on an object is accomplished using the bitwise operators AND, OR, XOR, and NOT. | Now you can probably see the pattern... the numbers 1,2,4,8,16,32,64,128,... are all multiples of 2 and they are special because they all have a single 1 in them when converted to binary. To enable or disable an individual flag on an object is accomplished using the bitwise operators AND, OR, XOR, and NOT. | ||
| − | ==The OR Operator (inclusive OR)== | + | ==The OR Operator (inclusive OR): |== |
A ''bitwise OR'' takes two bit patterns of equal length and performs the logical ''inclusive OR'' operation on each pair of corresponding bits. When you perform this operation, the result in each position is 0 if both bits are 0, and the result is 1 if either (or both) the bits were 1. For example: | A ''bitwise OR'' takes two bit patterns of equal length and performs the logical ''inclusive OR'' operation on each pair of corresponding bits. When you perform this operation, the result in each position is 0 if both bits are 0, and the result is 1 if either (or both) the bits were 1. For example: | ||
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= 0111 (decimal 7) | = 0111 (decimal 7) | ||
| − | In Sphere, this technique is commonly used to set a ''flag'' in a register, | + | In Sphere, this technique is commonly used to set a ''flag'' in a register, while preserving the existing flags. So, 0010 (decimal 2) can be considered a set of four flags, where the first, third, and fourth flags are clear (0) and the second flag is set (1). The fourth flag may be set by performing a bitwise OR between this value and a bit pattern with only the fourth bit set: |
0010 (decimal 2) | 0010 (decimal 2) | ||
| Line 97: | Line 99: | ||
= 1010 (decimal 10) | = 1010 (decimal 10) | ||
| − | ==The AND Operator== | + | In the following example Sphere code, we create a new object, then set that objects flags to equal 010, then we enable the 4th flag as well: |
| − | ==The XOR Operator (exclusive OR)== | + | |
| − | ==The NOT Operator== | + | SERV.NEW=i_log |
| + | ATTR=010 | ||
| + | ATTR|=01000 | ||
| + | |||
| + | ...that same example, using flag names: | ||
| + | |||
| + | SERV.NEW=i_log | ||
| + | ATTR=attr_decay | ||
| + | ATTR|=attr_move_always | ||
| + | |||
| + | ==The AND Operator (logical and): &== | ||
| + | A ''bitwise AND'' takes two equal-length binary representations and performs the ''logical AND operation'' on each pair of the corresponding bits, by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). For example: | ||
| + | |||
| + | 0101 (decimal 5) | ||
| + | AND 0011 (decimal 3) | ||
| + | = 0001 (decimal 1) | ||
| + | |||
| + | The operation may be used to determine whether a particular bit is set (1) or clear (0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit: | ||
| + | |||
| + | 0011 (decimal 3) | ||
| + | AND 0010 (decimal 2) | ||
| + | = 0010 (decimal 2) | ||
| + | |||
| + | Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This concept is often called ''bit masking''. In Sphere, this is often used in an IF statement to check if a specific flag is enabled or not. For example, the sphere code to check if an object is identified is done by applying a AND of the object's ATTR to the attr_identified flag like this: | ||
| + | |||
| + | IF (<ATTR>&attr_identified) | ||
| + | |||
| + | ==The XOR Operator (exclusive OR): ^== | ||
| + | A ''bitwise XOR'' takes two bit patterns of equal length and performs the ''logical exclusive OR'' operation on each pair of corresponding bits. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example: | ||
| + | |||
| + | 0101 (decimal 5) | ||
| + | XOR 0011 (decimal 3) | ||
| + | = 0110 (decimal 6) | ||
| + | |||
| + | The bitwise XOR is often used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and fourth positions: | ||
| + | |||
| + | 0010 (decimal 2) | ||
| + | XOR 1010 (decimal 10) | ||
| + | = 1000 (decimal 8) | ||
| + | |||
| + | ==The NOT Operator (bitwise not): !== | ||
| + | The ''bitwise NOT'', or complement, is an operation that performs a logical negation on each bit, forming the ''ones' complement'' of the given binary value. Bits that are 0 become 1, and those that are 1 become 0. For example: | ||
| + | |||
| + | NOT 0111 (decimal 7) | ||
| + | = 1000 (decimal 8) | ||
| + | |||
| + | The bitwise complement is equal to the two's complement of the value minus one. If two's complement arithmetic is used, then: | ||
| + | |||
| + | NOT x = −x − 1. | ||
| + | |||
| + | For unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers, NOT x = 255 - x, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0. | ||
| + | |||
==Left and right shift== | ==Left and right shift== | ||
Latest revision as of 20:53, 5 November 2015
Bitwise operations are used to perform an action on the bits (the 1's and 0's) of a number.
In this article a "binary" formatted number (which represents the "bits" of a number) will be written with a 2... and a decimal number with a 10
Contents
Limitations
In Sphere, numbers are stored in something called a "DWORD". The largest number a DWORD can store is constrained by the fact that a DWORD is 32 bits wide. That means the largest number it can store is 2^32-1.
- In Binary that's 11111111111111111111111111111111.
- In Hex it's FFFFFFFF.
- In Decimal that's 4294967295.
To store a 'signed' number in a DWORD (in other words, a number that can be positive or negative), the first bit is used to indicate the sign (a 1 is negative). Which means the largest 'signed' positive number is 2^31-1
- In Binary that's 01111111111111111111111111111111.
- In Hex it's 7FFFFFFF.
- In Decimal that's 2147483647.
In sphere script language, the EVAL function outputs a signed DWORD, and the UVAL outputs an unsigned DWORD.
[FUNCTION Mathtest] LOCAL.Number0=2147483647 LOCAL.Number1=4294967295 LOCAL.Number2=8589934588 SERV.LOG eval0=<EVAL <LOCAL.Number0>> eval1=<EVAL <LOCAL.Number1>> eval2=<EVAL <LOCAL.Number2>> SERV.LOG uval0=<UVAL <LOCAL.Number0>> uval1=<UVAL <LOCAL.Number1>> uval2=<UVAL <LOCAL.Number2>>
The output of this test is:
13:37:(test.scp,10)eval0=2147483647 eval1=-1 eval2=-4 13:37:(test.scp,11)uval0=2147483647 uval1=4294967295 uval2=4294967292
Notes:
- The output is limited to align with the limitation of the DWORD itself.
- Since there are 32 "bits" in a DWORD, there can only be 32 flags in a set.
- Be careful when manipulating flags using EVAL, because the 32nd flag could get lost.
Flags
In the Sphere server, quite a few concepts are implemented using "flags". You can see examples of flags being defined in the Sphere.ini file, or the sphere_defs.scp files. For example:
[DEFNAME attr_flags] attr_identified 01 attr_decay 02 attr_newbie 04 attr_move_always 08 attr_move_never 010 attr_magic 020 attr_owned 040 attr_invis 080 attr_cursed 0100 attr_cursed2 0200 attr_blessed 0400 attr_blessed2 0800 attr_forsale 01000 attr_stolen 02000 attr_can_decay 04000 attr_static 08000 attr_exceptional 010000 attr_enchanted 020000 attr_imbued 040000 attr_questitem 080000 attr_insured 0100000 attr_nodrop 0200000 attr_notrade 0400000 attr_lockeddown 0800000 attr_secure 01000000
This technique is a very efficient way to store a number of Boolean values using as little memory as possible. Let's tip that list on it's side and chart the first 8 flags:
| Flag Name: | attr_invis | attr_owned | attr_magic | attr_move_never | attr_move_always | attr_newbie | attr_decay | attr_identified |
| Flag Position | 8th position | 7th position | 6th position | 5th position | 4th position | 3rd position | 2nd position | 1st position |
| Binary Number: | 10000000 | 01000000 | 00100000 | 00010000 | 00001000 | 00000100 | 00000010 | 00000001 |
| Hex Number: | 080 | 040 | 020 | 010 | 08 | 04 | 02 | 01 |
| Decimal Number: | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Now you can probably see the pattern... the numbers 1,2,4,8,16,32,64,128,... are all multiples of 2 and they are special because they all have a single 1 in them when converted to binary. To enable or disable an individual flag on an object is accomplished using the bitwise operators AND, OR, XOR, and NOT.
The OR Operator (inclusive OR): |
A bitwise OR takes two bit patterns of equal length and performs the logical inclusive OR operation on each pair of corresponding bits. When you perform this operation, the result in each position is 0 if both bits are 0, and the result is 1 if either (or both) the bits were 1. For example:
0101 (decimal 5) OR 0011 (decimal 3) = 0111 (decimal 7)
In Sphere, this technique is commonly used to set a flag in a register, while preserving the existing flags. So, 0010 (decimal 2) can be considered a set of four flags, where the first, third, and fourth flags are clear (0) and the second flag is set (1). The fourth flag may be set by performing a bitwise OR between this value and a bit pattern with only the fourth bit set:
0010 (decimal 2) OR 1000 (decimal 8) = 1010 (decimal 10)
In the following example Sphere code, we create a new object, then set that objects flags to equal 010, then we enable the 4th flag as well:
SERV.NEW=i_log ATTR=010 ATTR|=01000
...that same example, using flag names:
SERV.NEW=i_log ATTR=attr_decay ATTR|=attr_move_always
The AND Operator (logical and): &
A bitwise AND takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits, by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). For example:
0101 (decimal 5) AND 0011 (decimal 3) = 0001 (decimal 1)
The operation may be used to determine whether a particular bit is set (1) or clear (0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit:
0011 (decimal 3) AND 0010 (decimal 2) = 0010 (decimal 2)
Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This concept is often called bit masking. In Sphere, this is often used in an IF statement to check if a specific flag is enabled or not. For example, the sphere code to check if an object is identified is done by applying a AND of the object's ATTR to the attr_identified flag like this:
IF (<ATTR>&attr_identified)
The XOR Operator (exclusive OR): ^
A bitwise XOR takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example:
0101 (decimal 5) XOR 0011 (decimal 3) = 0110 (decimal 6)
The bitwise XOR is often used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and fourth positions:
0010 (decimal 2) XOR 1010 (decimal 10) = 1000 (decimal 8)
The NOT Operator (bitwise not): !
The bitwise NOT, or complement, is an operation that performs a logical negation on each bit, forming the ones' complement of the given binary value. Bits that are 0 become 1, and those that are 1 become 0. For example:
NOT 0111 (decimal 7) = 1000 (decimal 8)
The bitwise complement is equal to the two's complement of the value minus one. If two's complement arithmetic is used, then:
NOT x = −x − 1.
For unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers, NOT x = 255 - x, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0.
