Functions on Numbers

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## Functions on Numbers

* - If , ..., denote numbers, then the term (* ) denotes the product of those numbers.

+ - If , ..., are numerical constants, then the term (+ ) denotes the sum of the numbers corresponding to those constants.

- - If and , ..., denote numbers, then the term (- ) denotes the difference between the number denoted by and the numbers denoted by through . An exception occurs when , in which case the term denotes the negation of the number denoted by .

/ - If , ..., are numbers, then the term (/ ) denotes the result obtained by dividing the number denoted by by the numbers denoted by through . An exception occurs when , in which case the term denotes the reciprocal of the number denoted by .

1+ - The term (1+ ) denotes the sum of the object denoted by and 1.

`(deffunction 1+ (?x) := (+ ?x 1))`

1- - The term (1- ) denotes the difference of the object denoted by and 1.

`(deffunction 1- (?x) := (- ?x 1))`

abs - The term (abs ) denotes the absolute value of the object denoted by .

`(deffunction abs (?x) := (if (>= ?x 0) ?x (- ?x)))`

acos - If denotes a number, then the term (acos ) denotes the arc cosine of that number (in radians).

acosh - The term (acosh ) denotes the arc cosine of the object denoted by (in radians).

ash - The term (ash ) denotes the result of arithmetically shifting the object denoted by by the number of bits denoted by (left or right shifting depending on the sign of ).

asin - The term (asin ) denotes the arc sine of the object denoted by (in radians).

asinh - The term (asinh ) denotes the hyperbolic arc sine of the object denoted by (in radians).

atan - The term (atan ) denotes the arc tangent of the object denoted by (in radians).

atanh - The term (atanh ) denotes the hyperbolic arc tangent of the object denoted by (in radians).

boole - The term (boole ) denotes the result of applying the operation denoted by to the objects denoted by and .

ceiling - If denotes a real number, then the term (ceiling ) denotes the smallest integer greater than or equal to the number denoted by .

cis - The term (cis ) denotes the complex number denoted by . The argument is any non-complex number of radians.

conjugate - If denotes a complex number, then the term (conjugate ) denotes the complex conjugate of the number denoted by .

`(deffunction conjugate (?c) :=`` (complex-number (realpart ?c) (- (imagpart ?c))))`

cos - The term (cos ) denotes the cosine of the object denoted by (in radians).

cosh - The term (cosh ) denotes the hyperbolic cosine of the object denoted by (in radians).

decode-float - The term (decode-float ) denotes the mantissa of the object denoted by .

denominator - The term (denominator ) denotes the denominator of the canonical reduced form of the object denoted by .

exp - The term (exp ) denotes raised to the power the object denoted by .

`(deffunction exp (?x) := (expt e ?x))`

expt - The term (expt ) denotes the object denoted by raised to the power the object denoted by .

fceiling - The term (fceiling ) denotes the smallest integer (as a floating point number) greater than the object denoted by .

ffloor - The term (ffloor ) denotes the largest integer (as a floating point number) less than the object denoted by .

float - The term (float ) denotes the floating point number equal to the object denoted by .

float-digits - The term (float-digits ) denotes the number of digits used in the representation of a floating point number denoted by .

float-precision - The term (float-precision ) denotes the number of significant digits in the floating point number denoted by .

float-radix - The term (float-radix ) denotes the radix of the floating point number denoted by . The most common values are 2 and 16.

float-sign - The term (float-sign ) denotes a floating-point number with the same sign as the object denoted by and the same absolute value as the object denoted by .

floor - The term (floor ) denotes the largest integer less than the object denoted by .

fround - The term (fround ) is equivalent to (ffloor (+ 0.5 )).

ftruncate - The term (ftruncate ) denotes the largest integer (as a floating point number) less than the object denoted by .

gcd - The term (gcd ) denotes the greatest common divisor of the objects denoted by through .

imagpart - The term (imagpart ) denotes the imaginary part of the object denoted by .

integer-decode-float - The term (integer-decode-float ) denotes the significand of the object denoted by .

integer-length - The term (integer-length ) denotes the number of bits required to store the absolute magnitude of the object denoted by .

isqrt - The term (isqrt ) denotes the integer square root of the object denoted by .

lcm - The term (lcm ) denotes the least common multiple of the objects denoted by .

log - The term (log ) denotes the logarithm of the object denoted by in the base denoted by .

logand - The term (logand ) denotes the bit-wise logical and of the objects denoted by through .

logandc1 - The term (logandc1 ) is equivalent to (logand (lognot ) ).

logandc2 - The term (logandc2 ) is equivalent to (logand (lognot )).

logcount - The term (logcount ) denotes the number of on bits in the object denoted by . If the denotation of is positive, then the one bits are counted; otherwise, the zero bits in the twos-complement representation are counted.

logeqv - The term (logeqv ) denotes the logical-exclusive-or of the objects denoted by .

logior - The term (logior ) denotes the bit-wise logical inclusive or of the objects denoted by through . It denotes 0 if there are no arguments.

lognand - The term (lognand ) is equivalent to (lognot (logand )).

lognor - The term (lognor ) is equivalent to (not (logior )).

lognot - The term (lognot ) denotes the bit-wise logical not of the object denoted by .

logorc1 - The term (logorc1 ) is equivalent to (logior (lognot ) ).

logorc2 - The term (logorc2 ) is equivalent to (logior (lognot )).

logxor - The term (logxor ) denotes the bit-wise logical exclusive or of the objects denoted by through . It denotes 0 if there are no arguments.

max - The term (max ) denotes the largest object denoted by through .

min - The term (min ) denotes the smallest object denoted by through .

mod - The term (mod ) denotes the root of the object denoted by modulo the object denoted by . The result will have the same sign as denoted by .

numerator - The term (numerator ) denotes the numerator of the canonical reduced form of the object denoted by .

phase - The term (phase ) denotes the angle part of the polar representation of the object denoted by (in radians).

rationalize - The term (rationalize ) denotes the rational representation of the object denoted by .

realpart - The term (realpart ) denotes the real part of the object denoted by .

rem - The term (rem <number> <divisor>) denotes the remainder of the object denoted by <number> divided by the object denoted by <divisor>. The result has the same sign as the object denoted by <divisor>.

round - The term (round ) denotes the integer nearest to the object denoted by . If the object denoted by is halfway between two integers (for example 3.5), it denotes the nearest integer divisible by 2.

scale-float - The term (scale-float ) denotes a floating-point number that is the representational radix of the object denoted by raised to the integer denoted by .

signum - The term (signum ) denotes the sign of the object denoted by . This is one of -1, 1, or 0 for rational numbers, and one of -1.0, 1.0, or 0.0 for floating point numbers.

sin - The term (sin ) denotes the sine of the object denoted by (in radians).

sinh - The term (sinh ) denotes the hyperbolic sine of the object denoted by (in radians).

sqrt - The term (sqrt ) denotes the principal square root of the object denoted by .

tan - The term (tan ) denotes the tangent of the object denoted by (in radians).

tanh - The term (tanh ) denotes the hyperbolic tangent of the object denoted by (in radians).

truncate - The term (truncate ) denotes the largest integer less than the object denoted by .

Next: Relations on Numbers Up: Numbers Previous: Numbers

Vishal I. Sikka
Wed Dec 7 13:23:42 PST 1994