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#### 6.6.2.13 Bitwise Operations

For the following bitwise functions, negative numbers are treated as
infinite precision twos-complements. For instance *-6* is bits
*…111010*, with infinitely many ones on the left. It can
be seen that adding 6 (binary 110) to such a bit pattern gives all
zeros.

- Scheme Procedure:
**logand***n1 n2 …* - C Function:
**scm_logand***(n1, n2)* Return the bitwise AND of the integer arguments.

(logand) ⇒ -1 (logand 7) ⇒ 7 (logand #b111 #b011 #b001) ⇒ 1

- Scheme Procedure:
**logior***n1 n2 …* - C Function:
**scm_logior***(n1, n2)* Return the bitwise OR of the integer arguments.

(logior) ⇒ 0 (logior 7) ⇒ 7 (logior #b000 #b001 #b011) ⇒ 3

- Scheme Procedure:
**logxor***n1 n2 …* - C Function:
**scm_loxor***(n1, n2)* Return the bitwise XOR of the integer arguments. A bit is set in the result if it is set in an odd number of arguments.

(logxor) ⇒ 0 (logxor 7) ⇒ 7 (logxor #b000 #b001 #b011) ⇒ 2 (logxor #b000 #b001 #b011 #b011) ⇒ 1

- Scheme Procedure:
**lognot***n* - C Function:
**scm_lognot***(n)* Return the integer which is the ones-complement of the integer argument, ie. each 0 bit is changed to 1 and each 1 bit to 0.

(number->string (lognot #b10000000) 2) ⇒ "-10000001" (number->string (lognot #b0) 2) ⇒ "-1"

- Scheme Procedure:
**logtest***j k* - C Function:
**scm_logtest***(j, k)* Test whether

`j`and`k`have any 1 bits in common. This is equivalent to`(not (zero? (logand j k)))`

, but without actually calculating the`logand`

, just testing for non-zero.(logtest #b0100 #b1011) ⇒ #f (logtest #b0100 #b0111) ⇒ #t

- Scheme Procedure:
**logbit?***index j* - C Function:
**scm_logbit_p***(index, j)* Test whether bit number

`index`in`j`is set.`index`starts from 0 for the least significant bit.(logbit? 0 #b1101) ⇒ #t (logbit? 1 #b1101) ⇒ #f (logbit? 2 #b1101) ⇒ #t (logbit? 3 #b1101) ⇒ #t (logbit? 4 #b1101) ⇒ #f

- Scheme Procedure:
**ash***n count* - C Function:
**scm_ash***(n, count)* Return

*floor(n * 2^count)*.`n`and`count`must be exact integers.With

`n`viewed as an infinite-precision twos-complement integer,`ash`

means a left shift introducing zero bits when`count`is positive, or a right shift dropping bits when`count`is negative. This is an “arithmetic” shift.(number->string (ash #b1 3) 2) ⇒ "1000" (number->string (ash #b1010 -1) 2) ⇒ "101" ;; -23 is bits ...11101001, -6 is bits ...111010 (ash -23 -2) ⇒ -6

- Scheme Procedure:
**round-ash***n count* - C Function:
**scm_round_ash***(n, count)* Return

*round(n * 2^count)*.`n`and`count`must be exact integers.With

`n`viewed as an infinite-precision twos-complement integer,`round-ash`

means a left shift introducing zero bits when`count`is positive, or a right shift rounding to the nearest integer (with ties going to the nearest even integer) when`count`is negative. This is a rounded “arithmetic” shift.(number->string (round-ash #b1 3) 2) ⇒ \"1000\" (number->string (round-ash #b1010 -1) 2) ⇒ \"101\" (number->string (round-ash #b1010 -2) 2) ⇒ \"10\" (number->string (round-ash #b1011 -2) 2) ⇒ \"11\" (number->string (round-ash #b1101 -2) 2) ⇒ \"11\" (number->string (round-ash #b1110 -2) 2) ⇒ \"100\"

- Scheme Procedure:
**logcount***n* - C Function:
**scm_logcount***(n)* Return the number of bits in integer

`n`. If`n`is positive, the 1-bits in its binary representation are counted. If negative, the 0-bits in its two’s-complement binary representation are counted. If zero, 0 is returned.(logcount #b10101010) ⇒ 4 (logcount 0) ⇒ 0 (logcount -2) ⇒ 1

- Scheme Procedure:
**integer-length***n* - C Function:
**scm_integer_length***(n)* Return the number of bits necessary to represent

`n`.For positive

`n`this is how many bits to the most significant one bit. For negative`n`it’s how many bits to the most significant zero bit in twos complement form.(integer-length #b10101010) ⇒ 8 (integer-length #b1111) ⇒ 4 (integer-length 0) ⇒ 0 (integer-length -1) ⇒ 0 (integer-length -256) ⇒ 8 (integer-length -257) ⇒ 9

- Scheme Procedure:
**integer-expt***n k* - C Function:
**scm_integer_expt***(n, k)* Return

`n`raised to the power`k`.`k`must be an exact integer,`n`can be any number.Negative

`k`is supported, and results in*1/n^abs(k)*in the usual way.is 1, as usual, and that includes`n`^0*0^0*is 1.(integer-expt 2 5) ⇒ 32 (integer-expt -3 3) ⇒ -27 (integer-expt 5 -3) ⇒ 1/125 (integer-expt 0 0) ⇒ 1

- Scheme Procedure:
**bit-extract***n start end* - C Function:
**scm_bit_extract***(n, start, end)* Return the integer composed of the

`start`(inclusive) through`end`(exclusive) bits of`n`. The`start`th bit becomes the 0-th bit in the result.(number->string (bit-extract #b1101101010 0 4) 2) ⇒ "1010" (number->string (bit-extract #b1101101010 4 9) 2) ⇒ "10110"

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