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# Numbers

Function: SIGNUM (number)
  Package:LISP

  If NUMBER is zero, returns NUMBER; else returns (/ NUMBER (ABS NUMBER)).

Function: LOGNOT (integer)
  Package:LISP

  Returns the bit-wise logical NOT of INTEGER.

Constant: MOST-POSITIVE-SHORT-FLOAT
  Package:LISP The short-float closest in value to positive infinity.

Function: INTEGER-DECODE-FLOAT (float)
  Package:LISP

  Returns, as three values, the integer interpretation of significand F, the exponent E, and the sign S of the given float, so that E FLOAT = S * F * B where B = (FLOAT-RADIX FLOAT)

  F is a non-negative integer, E is an integer, and S is either 1 or -1.

Function: MINUSP (number)
  Package:LISP

  Returns T if NUMBER < 0; NIL otherwise.

Function: LOGORC1 (integer1 integer2)
  Package:LISP

  Returns the logical OR of (LOGNOT INTEGER1) and INTEGER2.

Constant: MOST-NEGATIVE-SINGLE-FLOAT
  Package:LISP Same as MOST-NEGATIVE-LONG-FLOAT.

Constant: BOOLE-C1
  Package:LISP Makes BOOLE return the complement of INTEGER1.

Constant: LEAST-POSITIVE-SHORT-FLOAT
  Package:LISP The positive short-float closest in value to zero.

Function: BIT-NAND (bit-array1 bit-array2 &optional (result-bit-array nil))
  Package:LISP

  Performs a bit-wise logical NAND on the elements of BIT-ARRAY1 and BIT-ARRAY2. Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.

Function: INT-CHAR (integer)
  Package:LISP

  Performs the inverse of CHAR-INT. Equivalent to CODE-CHAR in GCL.

Function: CHAR-INT (char)
  Package:LISP

  Returns the font, bits, and code attributes as a single non-negative integer. Equivalent to CHAR-CODE in GCL.

Constant: LEAST-NEGATIVE-SINGLE-FLOAT
  Package:LISP Same as LEAST-NEGATIVE-LONG-FLOAT.

Function: /= (number &rest more-numbers)
  Package:LISP

  Returns T if no two of its arguments are numerically equal; NIL otherwise.

Function: LDB-TEST (bytespec integer)
  Package:LISP

  Returns T if at least one of the bits in the specified bytes of INTEGER is 1; NIL otherwise.

Constant: CHAR-CODE-LIMIT
  Package:LISP The upper exclusive bound on values produced by CHAR-CODE.

Function: RATIONAL (number)
  Package:LISP

  Converts NUMBER into rational accurately and returns it.

Constant: PI
  Package:LISP The floating-point number that is appropriately equal to the ratio of the circumference of the circle to the diameter.

Function: SIN (radians)
  Package:LISP

  Returns the sine of RADIANS.

Constant: BOOLE-ORC2
  Package:LISP Makes BOOLE return LOGORC2 of INTEGER1 and INTEGER2.

Function: NUMERATOR (rational)
  Package:LISP

  Returns as an integer the numerator of the given rational number.

Function: MASK-FIELD (bytespec integer)
  Package:LISP

  Extracts the specified byte from INTEGER.

Special Form: INCF
  Package:LISP

  Syntax:

      (incf place [delta])

  Adds the number produced by DELTA (which defaults to 1) to the number in PLACE.

Function: SINH (number)
  Package:LISP

  Returns the hyperbolic sine of NUMBER.

Function: PHASE (number)
  Package:LISP

  Returns the angle part of the polar representation of a complex number. For non-complex numbers, this is 0.

Function: BOOLE (op integer1 integer2)
  Package:LISP

  Returns an integer produced by performing the logical operation specified by OP on the two integers. OP must be the value of one of the following constants: BOOLE-CLR BOOLE-C1 BOOLE-XOR BOOLE-ANDC1 BOOLE-SET BOOLE-C2 BOOLE-EQV BOOLE-ANDC2 BOOLE-1 BOOLE-AND BOOLE-NAND BOOLE-ORC1 BOOLE-2 BOOLE-IOR BOOLE-NOR BOOLE-ORC2 See the variable docs of these constants for their operations.

Constant: SHORT-FLOAT-EPSILON
  Package:LISP The smallest positive short-float that satisfies (not (= (float 1 e) (+ (float 1 e) e))).

Function: LOGORC2 (integer1 integer2)
  Package:LISP

  Returns the logical OR of INTEGER1 and (LOGNOT INTEGER2).

Constant: BOOLE-C2
  Package:LISP Makes BOOLE return the complement of INTEGER2.

Function: REALPART (number)
  Package:LISP

  Extracts the real part of NUMBER.

Constant: BOOLE-CLR
  Package:LISP Makes BOOLE return 0.

Constant: BOOLE-IOR
  Package:LISP Makes BOOLE return LOGIOR of INTEGER1 and INTEGER2.

Function: FTRUNCATE (number &optional (divisor 1))
  Package:LISP

  Values: (quotient remainder) Same as TRUNCATE, but returns first value as a float.

Function: EQL (x y)
  Package:LISP

  Returns T if X and Y are EQ, or if they are numbers of the same type with the same value, or if they are character objects that represent the same character. Returns NIL otherwise.

Function: LOG (number &optional base)
  Package:LISP

  Returns the logarithm of NUMBER in the base BASE. BASE defaults to the base of natural logarithms.

Constant: DOUBLE-FLOAT-NEGATIVE-EPSILON
  Package:LISP Same as LONG-FLOAT-NEGATIVE-EPSILON.

Function: LOGIOR (&rest integers)
  Package:LISP

  Returns the bit-wise INCLUSIVE OR of its arguments.

Constant: MOST-NEGATIVE-DOUBLE-FLOAT
  Package:LISP Same as MOST-NEGATIVE-LONG-FLOAT.

Function: / (number &rest more-numbers)
  Package:LISP

  Divides the first NUMBER by each of the subsequent NUMBERS. With one arg, returns the reciprocal of the number.

Variable: *RANDOM-STATE*
  Package:LISP The default random-state object used by RAMDOM.

Function: 1+ (number)
  Package:LISP

  Returns NUMBER + 1.

Constant: LEAST-NEGATIVE-DOUBLE-FLOAT
  Package:LISP Same as LEAST-NEGATIVE-LONG-FLOAT.

Function: FCEILING (number &optional (divisor 1))
  Package:LISP

  Same as CEILING, but returns a float as the first value.

Constant: MOST-POSITIVE-FIXNUM
  Package:LISP The fixnum closest in value to positive infinity.

Function: BIT-ANDC1 (bit-array1 bit-array2 &optional (result-bit-array nil))
  Package:LISP

  Performs a bit-wise logical ANDC1 on the elements of BIT-ARRAY1 and BIT-ARRAY2. Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.

Function: TAN (radians)
  Package:LISP

  Returns the tangent of RADIANS.

Constant: BOOLE-NAND
  Package:LISP Makes BOOLE return LOGNAND of INTEGER1 and INTEGER2.

Function: TANH (number)
  Package:LISP

  Returns the hyperbolic tangent of NUMBER.

Function: ASIN (number)
  Package:LISP

  Returns the arc sine of NUMBER.

Function: BYTE (size position)
  Package:LISP

  Returns a byte specifier. In GCL, a byte specifier is represented by a dotted pair (<size> . <position>).

Function: ASINH (number)
  Package:LISP

  Returns the hyperbolic arc sine of NUMBER.

Constant: MOST-POSITIVE-LONG-FLOAT
  Package:LISP The long-float closest in value to positive infinity.

Macro: SHIFTF
  Package:LISP

  Syntax:

      (shiftf {place}+ newvalue)

  Evaluates all PLACEs and NEWVALUE in turn, then assigns the value of each form to the PLACE on its left. Returns the original value of the leftmost form.

Constant: LEAST-POSITIVE-LONG-FLOAT
  Package:LISP The positive long-float closest in value to zero.

Function: DEPOSIT-FIELD (newbyte bytespec integer)
  Package:LISP

  Returns an integer computed by replacing the specified byte of INTEGER with the specified byte of NEWBYTE.

Function: BIT-AND (bit-array1 bit-array2 &optional (result-bit-array nil))
  Package:LISP

  Performs a bit-wise logical AND on the elements of BIT-ARRAY1 and BIT-ARRAY2. Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.

Function: LOGNAND (integer1 integer2)
  Package:LISP

  Returns the complement of the logical AND of INTEGER1 and INTEGER2.

Function: BYTE-POSITION (bytespec)
  Package:LISP

  Returns the position part (in GCL, the cdr part) of the byte specifier.

Macro: ROTATEF
  Package:LISP

  Syntax:

      (rotatef {place}*)

  Evaluates PLACEs in turn, then assigns to each PLACE the value of the form to its right. The rightmost PLACE gets the value of the leftmost PLACE. Returns NIL always.

Function: BIT-ANDC2 (bit-array1 bit-array2 &optional (result-bit-array nil))
  Package:LISP

  Performs a bit-wise logical ANDC2 on the elements of BIT-ARRAY1 and BIT-ARRAY2. Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.

Function: TRUNCATE (number &optional (divisor 1))
  Package:LISP

  Values: (quotient remainder) Returns NUMBER/DIVISOR as an integer, rounded toward 0. The second returned value is the remainder.

Constant: BOOLE-EQV
  Package:LISP Makes BOOLE return LOGEQV of INTEGER1 and INTEGER2.

Constant: BOOLE-SET
  Package:LISP Makes BOOLE return -1.

Function: LDB (bytespec integer)
  Package:LISP

  Extracts and right-justifies the specified byte of INTEGER, and returns the result.

Function: BYTE-SIZE (bytespec)
  Package:LISP

  Returns the size part (in GCL, the car part) of the byte specifier.

Constant: SHORT-FLOAT-NEGATIVE-EPSILON
  Package:LISP The smallest positive short-float that satisfies (not (= (float 1 e) (- (float 1 e) e))).

Function: REM (number divisor)
  Package:LISP

  Returns the second value of (TRUNCATE NUMBER DIVISOR).

Function: MIN (number &rest more-numbers)
  Package:LISP

  Returns the least of its arguments.

Function: EXP (number)
  Package:LISP

  Calculates e raised to the power NUMBER, where e is the base of natural logarithms.

Function: DECODE-FLOAT (float)
  Package:LISP

  Returns, as three values, the significand F, the exponent E, and the sign S of the given float, so that E FLOAT = S * F * B where B = (FLOAT-RADIX FLOAT)

  S and F are floating-point numbers of the same float format as FLOAT, and E is an integer.

Constant: LONG-FLOAT-EPSILON
  Package:LISP The smallest positive long-float that satisfies (not (= (float 1 e) (+ (float 1 e) e))).

Function: FROUND (number &optional (divisor 1))
  Package:LISP

  Same as ROUND, but returns first value as a float.

Function: LOGEQV (&rest integers)
  Package:LISP

  Returns the bit-wise EQUIVALENCE of its arguments.

Constant: MOST-NEGATIVE-SHORT-FLOAT
  Package:LISP The short-float closest in value to negative infinity.

Function: BIT-NOR (bit-array1 bit-array2 &optional (result-bit-array nil))
  Package:LISP

  Performs a bit-wise logical NOR on the elements of BIT-ARRAY1 and BIT-ARRAY2. Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.

Function: CEILING (number &optional (divisor 1))
  Package:LISP

  Returns the smallest integer not less than or NUMBER/DIVISOR. Returns the remainder as the second value.

Constant: LEAST-NEGATIVE-SHORT-FLOAT
  Package:LISP The negative short-float closest in value to zero.

Function: 1- (number)
  Package:LISP

  Returns NUMBER - 1.

Function: <= (number &rest more-numbers)
  Package:LISP

  Returns T if arguments are in strictly non-decreasing order; NIL otherwise.

Function: IMAGPART (number)
  Package:LISP

  Extracts the imaginary part of NUMBER.

Function: INTEGERP (x)
  Package:LISP

  Returns T if X is an integer (fixnum or bignum); NIL otherwise.

Function: ASH (integer count)
  Package:LISP

  Shifts INTEGER left by COUNT places. Shifts right if COUNT is negative.

Function: LCM (integer &rest more-integers)
  Package:LISP

  Returns the least common multiple of the arguments.

Function: COS (radians)
  Package:LISP

  Returns the cosine of RADIANS.

Special Form: DECF
  Package:LISP

  Syntax:

      (decf place [delta])

  Subtracts the number produced by DELTA (which defaults to 1) from the number in PLACE.

Function: ATAN (x &optional (y 1))
  Package:LISP Returns the arc tangent of X/Y.

Constant: BOOLE-ANDC1
  Package:LISP Makes BOOLE return LOGANDC1 of INTEGER1 and INTEGER2.

Function: COSH (number)
  Package:LISP Returns the hyperbolic cosine of NUMBER.

Function: FLOAT-RADIX (float)
  Package:LISP

  Returns the representation radix (or base) of the floating-point number.

Function: ATANH (number)
  Package:LISP

  Returns the hyperbolic arc tangent of NUMBER.

Function: EVENP (integer)
  Package:LISP Returns T if INTEGER is even. Returns NIL if INTEGER is odd.

Function: ZEROP (number)
  Package:LISP Returns T if NUMBER = 0; NIL otherwise.

Function: FLOATP (x)
  Package:LISP

  Returns T if X is a floating-point number; NIL otherwise.

Function: SXHASH (object)
  Package:LISP

  Computes a hash code for OBJECT and returns it as an integer.

Constant: BOOLE-1
  Package:LISP Makes BOOLE return INTEGER1.

Constant: MOST-POSITIVE-SINGLE-FLOAT
  Package:LISP Same as MOST-POSITIVE-LONG-FLOAT.

Function: LOGANDC1 (integer1 integer2)
  Package:LISP

  Returns the logical AND of (LOGNOT INTEGER1) and INTEGER2.

Constant: LEAST-POSITIVE-SINGLE-FLOAT
  Package:LISP Same as LEAST-POSITIVE-LONG-FLOAT.

Function: COMPLEXP (x)
  Package:LISP

  Returns T if X is a complex number; NIL otherwise.

Constant: BOOLE-AND
  Package:LISP Makes BOOLE return LOGAND of INTEGER1 and INTEGER2.

Function: MAX (number &rest more-numbers)
  Package:LISP

  Returns the greatest of its arguments.

Function: FLOAT-SIGN (float1 &optional (float2 (float 1 float1)))
  Package:LISP

  Returns a floating-point number with the same sign as FLOAT1 and with the same absolute value as FLOAT2.

Constant: BOOLE-ANDC2
  Package:LISP Makes BOOLE return LOGANDC2 of INTEGER1 and INTEGER2.

Function: DENOMINATOR (rational)
  Package:LISP

  Returns the denominator of RATIONAL as an integer.

Function: FLOAT (number &optional other)
  Package:LISP

  Converts a non-complex number to a floating-point number. If NUMBER is already a float, FLOAT simply returns NUMBER. Otherwise, the format of the returned float depends on OTHER; If OTHER is not provided, FLOAT returns a SINGLE-FLOAT. If OTHER is provided, the result is in the same float format as OTHER's.

Function: ROUND (number &optional (divisor 1))
  Package:LISP

  Rounds NUMBER/DIVISOR to nearest integer. The second returned value is the remainder.

Function: LOGAND (&rest integers)
  Package:LISP

  Returns the bit-wise AND of its arguments.

Constant: BOOLE-2
  Package:LISP Makes BOOLE return INTEGER2.

Function: * (&rest numbers)
  Package:LISP

  Returns the product of its arguments. With no args, returns 1.

Function: < (number &rest more-numbers)
  Package:LISP

  Returns T if its arguments are in strictly increasing order; NIL otherwise.

Function: COMPLEX (realpart &optional (imagpart 0))
  Package:LISP

  Returns a complex number with the given real and imaginary parts.

Constant: SINGLE-FLOAT-EPSILON
  Package:LISP Same as LONG-FLOAT-EPSILON.

Function: LOGANDC2 (integer1 integer2)
  Package:LISP

  Returns the logical AND of INTEGER1 and (LOGNOT INTEGER2).

Function: INTEGER-LENGTH (integer)
  Package:LISP

  Returns the number of significant bits in the absolute value of INTEGER.

Constant: MOST-NEGATIVE-FIXNUM
  Package:LISP The fixnum closest in value to negative infinity.

Constant: LONG-FLOAT-NEGATIVE-EPSILON
  Package:LISP The smallest positive long-float that satisfies (not (= (float 1 e) (- (float 1 e) e))).

Function: >= (number &rest more-numbers)
  Package:LISP

  Returns T if arguments are in strictly non-increasing order; NIL otherwise.

Constant: BOOLE-NOR
  Package:LISP Makes BOOLE return LOGNOR of INTEGER1 and INTEGER2.

Function: ACOS (number)
  Package:LISP

  Returns the arc cosine of NUMBER.

Function: MAKE-RANDOM-STATE (&optional (state *random-state*))
  Package:LISP

  Creates and returns a copy of the specified random state. If STATE is NIL, then the value of *RANDOM-STATE* is used. If STATE is T, then returns a random state object generated from the universal time.

Function: EXPT (base-number power-number)
  Package:LISP

  Returns BASE-NUMBER raised to the power POWER-NUMBER.

Function: SQRT (number)
  Package:LISP

  Returns the principal square root of NUMBER.

Function: SCALE-FLOAT (float integer)
  Package:LISP

  Returns (* FLOAT (expt (float-radix FLOAT) INTEGER)).

Function: ACOSH (number)
  Package:LISP

  Returns the hyperbolic arc cosine of NUMBER.

Constant: MOST-NEGATIVE-LONG-FLOAT
  Package:LISP The long-float closest in value to negative infinity.

Constant: LEAST-NEGATIVE-LONG-FLOAT
  Package:LISP The negative long-float closest in value to zero.

Function: FFLOOR (number &optional (divisor 1))
  Package:LISP

  Same as FLOOR, but returns a float as the first value.

Function: LOGNOR (integer1 integer2)
  Package:LISP

  Returns the complement of the logical OR of INTEGER1 and INTEGER2.

Function: PARSE-INTEGER (string
  &key (start 0) (end (length string)) (radix 10) (junk-allowed nil)) Package:LISP

  Parses STRING for an integer and returns it.

Function: + (&rest numbers)
  Package:LISP

  Returns the sum of its arguments. With no args, returns 0.

Function: = (number &rest more-numbers)
  Package:LISP

  Returns T if all of its arguments are numerically equal; NIL otherwise.

Function: NUMBERP (x)
  Package:LISP

  Returns T if X is any kind of number; NIL otherwise.

Constant: MOST-POSITIVE-DOUBLE-FLOAT
  Package:LISP Same as MOST-POSITIVE-LONG-FLOAT.

Function: LOGTEST (integer1 integer2)
  Package:LISP

  Returns T if LOGAND of INTEGER1 and INTEGER2 is not zero; NIL otherwise.

Function: RANDOM-STATE-P (x)
  Package:LISP

  Returns T if X is a random-state object; NIL otherwise.

Constant: LEAST-POSITIVE-DOUBLE-FLOAT
  Package:LISP Same as LEAST-POSITIVE-LONG-FLOAT.

Function: FLOAT-PRECISION (float)
  Package:LISP

  Returns the number of significant radix-B digits used to represent the significand F of the floating-point number, where B = (FLOAT-RADIX FLOAT).

Constant: BOOLE-XOR
  Package:LISP Makes BOOLE return LOGXOR of INTEGER1 and INTEGER2.

Function: DPB (newbyte bytespec integer)
  Package:LISP

  Returns an integer computed by replacing the specified byte of INTEGER with NEWBYTE.

Function: ABS (number)
  Package:LISP

  Returns the absolute value of NUMBER.

Function: CONJUGATE (number)
  Package:LISP

  Returns the complex conjugate of NUMBER.

Function: CIS (radians)
  Package:LISP

  Returns e raised to i*RADIANS.

Function: ODDP (integer)
  Package:LISP

  Returns T if INTEGER is odd; NIL otherwise.

Function: RATIONALIZE (number)
  Package:LISP

  Converts NUMBER into rational approximately and returns it.

Function: ISQRT (integer)
  Package:LISP

  Returns the greatest integer less than or equal to the square root of the given non-negative integer.

Function: LOGXOR (&rest integers)
  Package:LISP

  Returns the bit-wise EXCLUSIVE OR of its arguments.

Function: > (number &rest more-numbers)
  Package:LISP

  Returns T if its arguments are in strictly decreasing order; NIL otherwise.

Function: LOGBITP (index integer)
  Package:LISP

  Returns T if the INDEX-th bit of INTEGER is 1.

Constant: DOUBLE-FLOAT-EPSILON
  Package:LISP Same as LONG-FLOAT-EPSILON.

Function: LOGCOUNT (integer)
  Package:LISP

  If INTEGER is negative, returns the number of 0 bits. Otherwise, returns the number of 1 bits.

Function: GCD (&rest integers)
  Package:LISP

  Returns the greatest common divisor of INTEGERs.

Function: RATIONALP (x)
  Package:LISP

  Returns T if X is an integer or a ratio; NIL otherwise.

Function: MOD (number divisor)
  Package:LISP

  Returns the second result of (FLOOR NUMBER DIVISOR).

Constant: BOOLE-ORC1
  Package:LISP Makes BOOLE return LOGORC1 of INTEGER1 and INTEGER2.

Constant: SINGLE-FLOAT-NEGATIVE-EPSILON
  Package:LISP Same as LONG-FLOAT-NEGATIVE-EPSILON.

Function: FLOOR (number &optional (divisor 1))
  Package:LISP

  Returns the largest integer not larger than the NUMBER divided by DIVISOR. The second returned value is (- NUMBER (* first-value DIVISOR)).

Function: PLUSP (number)
  Package:LISP

  Returns T if NUMBER > 0; NIL otherwise.

Function: FLOAT-DIGITS (float)
  Package:LISP

  Returns the number of radix-B digits used to represent the significand F of the floating-point number, where B = (FLOAT-RADIX FLOAT).

Function: RANDOM (number &optional (state *random-state*))
  Package:LISP

  Generates a uniformly distributed pseudo-random number between zero (inclusive) and NUMBER (exclusive), by using the random state object STATE.

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