bitcmp

Arguments

x, y

arrays of signed or unsigned integers (int8, .., uint64), or of positive decimal integers. Hypermatrix supported. x and y have the same integer type and the same size.

bitnum

positive encoded or decimal integer, or array of positive encoded or decimal integers of size equal to size(x): bits #1 to #bitnum of x are considered and inversed. According to the integer type of x, bitnum must be in the interval [1, bitmax] with bitmax as follows:

inttype :	int8	uint8	int16	uint16	int32	uint32	int64	uint64	decimal
bitmax :	8	8	16	16	32	32	64	64	1024

The default bitnum value depends on the input integer type:

• bitnum = bitmax for encoded integers
• bitnum = 53 for decimal integers x ≤ 1/%eps
• bitnum = int(log2(x))+1 for decimal integers x > 1/%eps.

Description

bitcmp(x) computes the binary complement of each element of x, and provides it in the corresponding element of y.

In the following description, 2^0 corresponds to the bit #1. An integer whose highest bit on is #n, is in [2^(n-1), 2^n-1].

For x such that abs(x) ≥ 2^bitnum, its bits #(bitnum+1) to #(int(log2(x))+1) are ignored. Only its bits #1 to #bitnum are considered and inversed.

Example:

--> bitget(180, 1:8)
 ans  =
   0.   0.   1.   0.   1.   1.   0.   1.
--> bitcmp(180, 4)
 ans  =
   11.
--> bitget(11, 1:8)
 ans  =
   1.   1.   0.   1.   0.   0.   0.   0.

For x such that abs(x) < 2^bitnum, bits #(int(log2(x))+2) to #bitnum are padded with 0. Then all bits #1 to #bitnum are considered and inversed.

Example:

--> x = 30; int(log2(30))+2
 ans  =
   6.
--> bitget(30, 1:10)
 ans  =
   0.   1.   1.   1.   1.   0.   0.   0.   0.   0.
--> bitcmp(30, 7)
 ans  =
   97.
--> bitget(97, 1:10)
 ans  =
   1.   0.   0.   0.   0.   1.   1.   0.   0.   0.

Examples

x = uint8(13);
b = bitget(x, 1:8)
c = bitcmp(x, 8)
bitget(c, 1:8)
1 - b

--> b = bitget(x, 1:8)
 b  =
  1  0  1  1  0  0  0  0

--> c = bitcmp(x, 8)
 c  =
  242

--> bitget(c, 1:8)
 ans  =
  0  1  0  0  1  1  1  1

--> 1 - b
 ans  =
  0  1  0  0  1  1  1  1

Negative encoded integers are accepted:

bitcmp(int8([-71 -34 -1 0 33 70]))
bitcmp(int8([-71 -34 -1 0 33 70]), 8)
bitcmp(int8([-71 -34 -1 0 33 70]), 7)
bitcmp(int8([-71 -34 -1 0 33 70]), 6)
bitcmp(int8([-71 -34 -1 0 33 70]), 5)
bitcmp(int8([-71 -34 -1 0 33 70]), 4)

--> bitcmp(int8([-71 -34 -1 0 33 70]))
 ans  =
  70  33  0 -1 -34 -71

--> bitcmp(int8([-71 -34 -1 0 33 70]), 8)
 ans  =
  70  33  0 -1 -34 -71

--> bitcmp(int8([-71 -34 -1 0 33 70]), 7)
 ans  =
  70  33  0  127  94  57

--> bitcmp(int8([-71 -34 -1 0 33 70]), 6)
 ans  =
  6  33  0  63  30  57

--> bitcmp(int8([-71 -34 -1 0 33 70]), 5)
 ans  =
  6  1  0  31  30  25

--> bitcmp(int8([-71 -34 -1 0 33 70]), 4)
 ans  =
  6  1  0  15  14  9

We can work with 64-bit big integers:

b = (rand(1,62)<0.5)*1;
x = sum(b .* (uint64(2).^(0:61)))
r = bitcmp(x)
bg = bitget(r, 1:62);
[msprintf("%d ",b(:)) ; msprintf("%d ",bg(:))]

--> x = sum(b .* (uint64(2).^(0:61)))
 x  =
  4154509482123930814

--> r = bitcmp(x)
 r  =
  14292234591585620801

--> bg = bitget(r, 1:62);
--> [msprintf("%d ",b(:)) ; msprintf("%d ",bg(:))]
 ans  =
  "0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 ... 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 "
  "1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 ... 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 "

bitnum can be an array:

bitcmp([0 0 0 0 0], 3:7)

--> bitcmp([0 0 0 0 0], 3:7)
 ans  =
   7.   15.   31.   63.   127.

bitnum can be > 52:

format(22)
bitcmp(2^70, 65)
sum(2.^(13:64))   // 52 highest bits

--> bitcmp(2^70, 65)
 ans  =
   36893488147419095040.

--> sum(2.^(13:64))
 ans  =
   36893488147419095040.

Huge decimal numbers can be processed:

format(22)
log2(1e100)
r = bitcmp(1e100, 333)
bitcmp(1e100) // bitnum = int(log2(x)) + 1 is used by default
bitcmp(r, 333)

--> log2(1e100)
 ans  =
   332.19280948873625903

--> r = bitcmp(1e100, 333)
 r  =
   7.498005798264093D+99

--> bitcmp(1e100)  // bitnum = int(log2(x)) + 1 is used by default
 ans  =
   7.498005798264093D+99

--> bitcmp(r, 333)
 ans  =
   1.00000000000000D+100

See Also

• bitxor — bitwise logical XOR between element-wise integers of 2 arrays
• bitget — Extracts from integers bits of given indices
• minus — opérateur de soustraction, changement de signe

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