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@node Numbers, Sequences and Arrays and Hash Tables, Top, Top
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If NUMBER is zero, returns NUMBER; else returns (/ NUMBER (ABS NUMBER)).
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@defun LOGNOT (integer)
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Returns the bit-wise logical NOT of INTEGER.
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@defvr {Constant} MOST-POSITIVE-SHORT-FLOAT
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The short-float closest in value to positive infinity.
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@defun INTEGER-DECODE-FLOAT (float)
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Returns, as three values, the integer interpretation of significand F,
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the exponent E, and the sign S of the given float, so that
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FLOAT = S * F * B where B = (FLOAT-RADIX FLOAT)
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F is a non-negative integer, E is an integer, and S is either 1 or -1.
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@defun MINUSP (number)
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Returns T if NUMBER < 0; NIL otherwise.
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@defun LOGORC1 (integer1 integer2)
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Returns the logical OR of (LOGNOT INTEGER1) and INTEGER2.
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@defvr {Constant} MOST-NEGATIVE-SINGLE-FLOAT
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Same as MOST-NEGATIVE-LONG-FLOAT.
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@defvr {Constant} BOOLE-C1
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Makes BOOLE return the complement of INTEGER1.
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@defvr {Constant} LEAST-POSITIVE-SHORT-FLOAT
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The positive short-float closest in value to zero.
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@defun BIT-NAND (bit-array1 bit-array2 &optional (result-bit-array nil))
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Performs a bit-wise logical NAND on the elements of BIT-ARRAY1 and
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Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into
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BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.
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@defun INT-CHAR (integer)
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Performs the inverse of CHAR-INT. Equivalent to CODE-CHAR in GCL.
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@defun CHAR-INT (char)
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Returns the font, bits, and code attributes as a single non-negative integer.
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Equivalent to CHAR-CODE in GCL.
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@defvr {Constant} LEAST-NEGATIVE-SINGLE-FLOAT
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Same as LEAST-NEGATIVE-LONG-FLOAT.
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@defun /= (number &rest more-numbers)
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Returns T if no two of its arguments are numerically equal; NIL otherwise.
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@defun LDB-TEST (bytespec integer)
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Returns T if at least one of the bits in the specified bytes of INTEGER is 1;
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@defvr {Constant} CHAR-CODE-LIMIT
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The upper exclusive bound on values produced by CHAR-CODE.
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@defun RATIONAL (number)
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Converts NUMBER into rational accurately and returns it.
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The floating-point number that is appropriately equal to the ratio of the
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circumference of the circle to the diameter.
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Returns the sine of RADIANS.
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@defvr {Constant} BOOLE-ORC2
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Makes BOOLE return LOGORC2 of INTEGER1 and INTEGER2.
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@defun NUMERATOR (rational)
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Returns as an integer the numerator of the given rational number.
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@defun MASK-FIELD (bytespec integer)
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Extracts the specified byte from INTEGER.
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@deffn {Special Form} INCF
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Adds the number produced by DELTA (which defaults to 1) to the number
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Returns the hyperbolic sine of NUMBER.
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@defun PHASE (number)
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Returns the angle part of the polar representation of a complex number.
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For non-complex numbers, this is 0.
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@defun BOOLE (op integer1 integer2)
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Returns an integer produced by performing the logical operation specified by
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OP on the two integers. OP must be the value of one of the following
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BOOLE-CLR BOOLE-C1 BOOLE-XOR BOOLE-ANDC1
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BOOLE-SET BOOLE-C2 BOOLE-EQV BOOLE-ANDC2
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BOOLE-1 BOOLE-AND BOOLE-NAND BOOLE-ORC1
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BOOLE-2 BOOLE-IOR BOOLE-NOR BOOLE-ORC2
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See the variable docs of these constants for their operations.
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@defvr {Constant} SHORT-FLOAT-EPSILON
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The smallest positive short-float that satisfies
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(not (= (float 1 e) (+ (float 1 e) e))).
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@defun LOGORC2 (integer1 integer2)
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Returns the logical OR of INTEGER1 and (LOGNOT INTEGER2).
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@defvr {Constant} BOOLE-C2
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Makes BOOLE return the complement of INTEGER2.
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@defun REALPART (number)
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Extracts the real part of NUMBER.
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@defvr {Constant} BOOLE-CLR
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Makes BOOLE return 0.
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@defvr {Constant} BOOLE-IOR
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Makes BOOLE return LOGIOR of INTEGER1 and INTEGER2.
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@defun FTRUNCATE (number &optional (divisor 1))
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Values: (quotient remainder)
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Same as TRUNCATE, but returns first value as a float.
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Returns T if X and Y are EQ, or if they are numbers of the same type with
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the same value, or if they are character objects that represent the same
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character. Returns NIL otherwise.
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@defun LOG (number &optional base)
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Returns the logarithm of NUMBER in the base BASE. BASE defaults to the base
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of natural logarithms.
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@defvr {Constant} DOUBLE-FLOAT-NEGATIVE-EPSILON
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Same as LONG-FLOAT-NEGATIVE-EPSILON.
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@defun LOGIOR (&rest integers)
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Returns the bit-wise INCLUSIVE OR of its arguments.
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@defvr {Constant} MOST-NEGATIVE-DOUBLE-FLOAT
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Same as MOST-NEGATIVE-LONG-FLOAT.
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@defun / (number &rest more-numbers)
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Divides the first NUMBER by each of the subsequent NUMBERS.
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With one arg, returns the reciprocal of the number.
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@defvar *RANDOM-STATE*
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The default random-state object used by RAMDOM.
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@defvr {Constant} LEAST-NEGATIVE-DOUBLE-FLOAT
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Same as LEAST-NEGATIVE-LONG-FLOAT.
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@defun FCEILING (number &optional (divisor 1))
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Same as CEILING, but returns a float as the first value.
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@defvr {Constant} MOST-POSITIVE-FIXNUM
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The fixnum closest in value to positive infinity.
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@defun BIT-ANDC1 (bit-array1 bit-array2 &optional (result-bit-array nil))
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Performs a bit-wise logical ANDC1 on the elements of BIT-ARRAY1 and
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Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into
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BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.
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Returns the tangent of RADIANS.
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@defvr {Constant} BOOLE-NAND
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Makes BOOLE return LOGNAND of INTEGER1 and INTEGER2.
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Returns the hyperbolic tangent of NUMBER.
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Returns the arc sine of NUMBER.
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@defun BYTE (size position)
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Returns a byte specifier. In GCL, a byte specifier is represented by
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a dotted pair (<size> . <position>).
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@defun ASINH (number)
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Returns the hyperbolic arc sine of NUMBER.
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@defvr {Constant} MOST-POSITIVE-LONG-FLOAT
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The long-float closest in value to positive infinity.
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@deffn {Macro} SHIFTF
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(shiftf @{place@}+ newvalue)
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Evaluates all PLACEs and NEWVALUE in turn, then assigns the value of each
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form to the PLACE on its left. Returns the original value of the leftmost
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@defvr {Constant} LEAST-POSITIVE-LONG-FLOAT
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The positive long-float closest in value to zero.
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@defun DEPOSIT-FIELD (newbyte bytespec integer)
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Returns an integer computed by replacing the specified byte of INTEGER with
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the specified byte of NEWBYTE.
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@defun BIT-AND (bit-array1 bit-array2 &optional (result-bit-array nil))
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Performs a bit-wise logical AND on the elements of BIT-ARRAY1 and BIT-ARRAY2.
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Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into
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BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.
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@defun LOGNAND (integer1 integer2)
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Returns the complement of the logical AND of INTEGER1 and INTEGER2.
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@defun BYTE-POSITION (bytespec)
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Returns the position part (in GCL, the cdr part) of the byte specifier.
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@deffn {Macro} ROTATEF
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Evaluates PLACEs in turn, then assigns to each PLACE the value of the form to
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its right. The rightmost PLACE gets the value of the leftmost PLACE.
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@defun BIT-ANDC2 (bit-array1 bit-array2 &optional (result-bit-array nil))
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Performs a bit-wise logical ANDC2 on the elements of BIT-ARRAY1 and
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Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into
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BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.
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@defun TRUNCATE (number &optional (divisor 1))
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Values: (quotient remainder)
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Returns NUMBER/DIVISOR as an integer, rounded toward 0. The second returned
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value is the remainder.
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@defvr {Constant} BOOLE-EQV
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Makes BOOLE return LOGEQV of INTEGER1 and INTEGER2.
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@defvr {Constant} BOOLE-SET
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Makes BOOLE return -1.
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@defun LDB (bytespec integer)
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Extracts and right-justifies the specified byte of INTEGER, and returns the
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@defun BYTE-SIZE (bytespec)
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Returns the size part (in GCL, the car part) of the byte specifier.
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@defvr {Constant} SHORT-FLOAT-NEGATIVE-EPSILON
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The smallest positive short-float that satisfies
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(not (= (float 1 e) (- (float 1 e) e))).
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@defun REM (number divisor)
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Returns the second value of (TRUNCATE NUMBER DIVISOR).
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@defun MIN (number &rest more-numbers)
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Returns the least of its arguments.
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Calculates e raised to the power NUMBER, where e is the base of natural
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@defun DECODE-FLOAT (float)
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Returns, as three values, the significand F, the exponent E, and the sign S
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of the given float, so that
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FLOAT = S * F * B where B = (FLOAT-RADIX FLOAT)
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S and F are floating-point numbers of the same float format as FLOAT, and E
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@defvr {Constant} LONG-FLOAT-EPSILON
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The smallest positive long-float that satisfies
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(not (= (float 1 e) (+ (float 1 e) e))).
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@defun FROUND (number &optional (divisor 1))
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Same as ROUND, but returns first value as a float.
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@defun LOGEQV (&rest integers)
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Returns the bit-wise EQUIVALENCE of its arguments.
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@defvr {Constant} MOST-NEGATIVE-SHORT-FLOAT
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The short-float closest in value to negative infinity.
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@defun BIT-NOR (bit-array1 bit-array2 &optional (result-bit-array nil))
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Performs a bit-wise logical NOR on the elements of BIT-ARRAY1 and BIT-ARRAY2.
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Puts the results into a new bit array if RESULT-BIT-ARRAY is NIL, into
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BIT-ARRAY1 if RESULT-BIT-ARRAY is T, or into RESULT-BIT-ARRAY otherwise.
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@defun CEILING (number &optional (divisor 1))
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Returns the smallest integer not less than or NUMBER/DIVISOR. Returns the
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remainder as the second value.
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@defvr {Constant} LEAST-NEGATIVE-SHORT-FLOAT
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The negative short-float closest in value to zero.
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@defun <= (number &rest more-numbers)
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Returns T if arguments are in strictly non-decreasing order; NIL otherwise.
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@defun IMAGPART (number)
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Extracts the imaginary part of NUMBER.
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Returns T if X is an integer (fixnum or bignum); NIL otherwise.
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@defun ASH (integer count)
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Shifts INTEGER left by COUNT places. Shifts right if COUNT is negative.
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@defun LCM (integer &rest more-integers)
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Returns the least common multiple of the arguments.
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Returns the cosine of RADIANS.
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@deffn {Special Form} DECF
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produced by DELTA (which defaults to 1) from the number in
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@defun ATAN (x &optional (y 1))
738
Returns the arc tangent of
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@defvr {Constant} BOOLE-ANDC1
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Makes BOOLE return LOGANDC1 of INTEGER1 and INTEGER2.
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Returns the hyperbolic cosine of
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@defun FLOAT-RADIX (float)
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Returns the representation radix (or base) of the floating-point
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@defun ATANH (number)
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Returns the hyperbolic arc tangent of NUMBER.
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@defun EVENP (integer)
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if INTEGER is even. Returns NIL if INTEGER is odd.
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@defun ZEROP (number)
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Returns T if NUMBER = 0; NIL
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Returns T if X is a floating-point number; NIL otherwise.
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@defun SXHASH (object)
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Computes a hash code for OBJECT and returns it as an integer.
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@defvr {Constant} BOOLE-1
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Makes BOOLE return INTEGER1.
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@defvr {Constant} MOST-POSITIVE-SINGLE-FLOAT
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Same as MOST-POSITIVE-LONG-FLOAT.
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@defun LOGANDC1 (integer1 integer2)
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Returns the logical AND of (LOGNOT INTEGER1) and INTEGER2.
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@defvr {Constant} LEAST-POSITIVE-SINGLE-FLOAT
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Same as LEAST-POSITIVE-LONG-FLOAT.
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Returns T if X is a complex number; NIL otherwise.
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@defvr {Constant} BOOLE-AND
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Makes BOOLE return LOGAND of INTEGER1 and INTEGER2.
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@defun MAX (number &rest more-numbers)
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Returns the greatest of its arguments.
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@defun FLOAT-SIGN (float1 &optional (float2 (float 1 float1)))
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Returns a floating-point number with the same sign as FLOAT1 and with the
864
same absolute value as FLOAT2.
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@defvr {Constant} BOOLE-ANDC2
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Makes BOOLE return LOGANDC2 of INTEGER1 and INTEGER2.
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@defun DENOMINATOR (rational)
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Returns the denominator of RATIONAL as an integer.
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@defun FLOAT (number &optional other)
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Converts a non-complex number to a floating-point number. If NUMBER is
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already a float, FLOAT simply returns NUMBER. Otherwise, the format of
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the returned float depends on OTHER; If OTHER is not provided, FLOAT returns
890
a SINGLE-FLOAT. If OTHER is provided, the result is in the same float format
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@defun ROUND (number &optional (divisor 1))
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Rounds NUMBER/DIVISOR to nearest integer. The second returned value is the
905
@defun LOGAND (&rest integers)
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Returns the bit-wise AND of its arguments.
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@defvr {Constant} BOOLE-2
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Makes BOOLE return INTEGER2.
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@defun * (&rest numbers)
923
Returns the product of its arguments. With no args, returns 1.
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@defun < (number &rest more-numbers)
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Returns T if its arguments are in strictly increasing order; NIL otherwise.
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@defun COMPLEX (realpart &optional (imagpart 0))
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Returns a complex number with the given real and imaginary parts.
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@defvr {Constant} SINGLE-FLOAT-EPSILON
946
Same as LONG-FLOAT-EPSILON.
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@defun LOGANDC2 (integer1 integer2)
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Returns the logical AND of INTEGER1 and (LOGNOT INTEGER2).
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@defun INTEGER-LENGTH (integer)
962
Returns the number of significant bits in the absolute value of INTEGER.
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@defvr {Constant} MOST-NEGATIVE-FIXNUM
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The fixnum closest in value to negative infinity.
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@defvr {Constant} LONG-FLOAT-NEGATIVE-EPSILON
976
The smallest positive long-float that satisfies
977
(not (= (float 1 e) (- (float 1 e) e))).
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@defun >= (number &rest more-numbers)
985
Returns T if arguments are in strictly non-increasing order; NIL otherwise.
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@defvr {Constant} BOOLE-NOR
992
Makes BOOLE return LOGNOR of INTEGER1 and INTEGER2.
1000
Returns the arc cosine of NUMBER.
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@defun MAKE-RANDOM-STATE (&optional (state *random-state*))
1008
Creates and returns a copy of the specified random state. If STATE is NIL,
1009
then the value of *RANDOM-STATE* is used. If STATE is T, then returns a
1010
random state object generated from the universal time.
1015
@defun EXPT (base-number power-number)
1018
Returns BASE-NUMBER raised to the power POWER-NUMBER.
1023
@defun SQRT (number)
1026
Returns the principal square root of NUMBER.
1031
@defun SCALE-FLOAT (float integer)
1034
Returns (* FLOAT (expt (float-radix FLOAT) INTEGER)).
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@defun ACOSH (number)
1042
Returns the hyperbolic arc cosine of NUMBER.
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@defvr {Constant} MOST-NEGATIVE-LONG-FLOAT
1049
The long-float closest in value to negative infinity.
1054
@defvr {Constant} LEAST-NEGATIVE-LONG-FLOAT
1056
The negative long-float closest in value to zero.
1061
@defun FFLOOR (number &optional (divisor 1))
1064
Same as FLOOR, but returns a float as the first value.
1069
@defun LOGNOR (integer1 integer2)
1072
Returns the complement of the logical OR of INTEGER1 and INTEGER2.
1077
@defun PARSE-INTEGER (string &key (start 0) (end (length string)) (radix 10) (junk-allowed nil))
1080
Parses STRING for an integer and returns it.
1085
@defun + (&rest numbers)
1088
Returns the sum of its arguments. With no args, returns 0.
1093
@defun = (number &rest more-numbers)
1096
Returns T if all of its arguments are numerically equal; NIL otherwise.
1104
Returns T if X is any kind of number; NIL otherwise.
1109
@defvr {Constant} MOST-POSITIVE-DOUBLE-FLOAT
1111
Same as MOST-POSITIVE-LONG-FLOAT.
1116
@defun LOGTEST (integer1 integer2)
1119
Returns T if LOGAND of INTEGER1 and INTEGER2 is not zero; NIL otherwise.
1124
@defun RANDOM-STATE-P (x)
1127
Returns T if X is a random-state object; NIL otherwise.
1132
@defvr {Constant} LEAST-POSITIVE-DOUBLE-FLOAT
1134
Same as LEAST-POSITIVE-LONG-FLOAT.
1139
@defun FLOAT-PRECISION (float)
1142
Returns the number of significant radix-B digits used to represent the
1143
significand F of the floating-point number, where B = (FLOAT-RADIX FLOAT).
1148
@defvr {Constant} BOOLE-XOR
1150
Makes BOOLE return LOGXOR of INTEGER1 and INTEGER2.
1155
@defun DPB (newbyte bytespec integer)
1158
Returns an integer computed by replacing the specified byte of INTEGER with
1167
Returns the absolute value of NUMBER.
1172
@defun CONJUGATE (number)
1175
Returns the complex conjugate of NUMBER.
1180
@defun CIS (radians)
1183
Returns e raised to i*RADIANS.
1188
@defun ODDP (integer)
1191
Returns T if INTEGER is odd; NIL otherwise.
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@defun RATIONALIZE (number)
1199
Converts NUMBER into rational approximately and returns it.
1204
@defun ISQRT (integer)
1207
Returns the greatest integer less than or equal to the square root of the
1208
given non-negative integer.
1213
@defun LOGXOR (&rest integers)
1216
Returns the bit-wise EXCLUSIVE OR of its arguments.
1221
@defun > (number &rest more-numbers)
1224
Returns T if its arguments are in strictly decreasing order; NIL otherwise.
1229
@defun LOGBITP (index integer)
1232
Returns T if the INDEX-th bit of INTEGER is 1.
1237
@defvr {Constant} DOUBLE-FLOAT-EPSILON
1239
Same as LONG-FLOAT-EPSILON.
1244
@defun LOGCOUNT (integer)
1247
If INTEGER is negative, returns the number of 0 bits. Otherwise, returns
1248
the number of 1 bits.
1253
@defun GCD (&rest integers)
1256
Returns the greatest common divisor of INTEGERs.
1261
@defun RATIONALP (x)
1264
Returns T if X is an integer or a ratio; NIL otherwise.
1269
@defun MOD (number divisor)
1272
Returns the second result of (FLOOR NUMBER DIVISOR).
1277
@defun MODF (number)
1280
Returns the integer and fractional part of a floating point number mod 1.0.
1285
@defvr {Constant} BOOLE-ORC1
1287
Makes BOOLE return LOGORC1 of INTEGER1 and INTEGER2.
1292
@defvr {Constant} SINGLE-FLOAT-NEGATIVE-EPSILON
1294
Same as LONG-FLOAT-NEGATIVE-EPSILON.
1299
@defun FLOOR (number &optional (divisor 1))
1302
Returns the largest integer not larger than the NUMBER divided by DIVISOR.
1303
The second returned value is (- NUMBER (* first-value DIVISOR)).
1308
@defun PLUSP (number)
1311
Returns T if NUMBER > 0; NIL otherwise.
1316
@defun FLOAT-DIGITS (float)
1319
Returns the number of radix-B digits used to represent the significand F of
1320
the floating-point number, where B = (FLOAT-RADIX FLOAT).
1325
@defun RANDOM (number &optional (state *random-state*))
1328
Generates a uniformly distributed pseudo-random number between zero
1329
(inclusive) and NUMBER (exclusive), by using the random state object STATE.
added
removed
info/number.texi
