Re: Adding a generic mathematical library

[Emanuel Berg <incal@dataswamp.org>]

Christopher Dimech wrote:

> All depends on who wants to produce a first release that
> handles two initial mathematical classifications, and which
> helps others extend the library to other additional
> topic classification.

Here is arithmetic!

What more do we want? :)

Arithmetic:

(+ &rest numbers)
  Return sum of any number of arguments, which are numbers or markers.
  (+ 1 2)
    => 3
  (+ 1 2 3 4)
    => 10
-------------------------------------------------------------------------------

(- &rest numbers)
  Negate number or subtract numbers or markers and return the result.
  (- 3 2)
    => 1
  (- 6 3 2)
    => 1
-------------------------------------------------------------------------------

(* &rest numbers)
  Return product of any number of arguments, which are numbers or markers.
  (* 3 4 5)
    => 60
-------------------------------------------------------------------------------

(/ number &rest divisors)
  Divide number by divisors and return the result.
  (/ 10 5)
    => 2
  (/ 10 6)
    => 1
  (/ 10.0 6)
    => 1.6666666666666667
  (/ 10.0 3 3)
    => 1.1111111111111112
-------------------------------------------------------------------------------

(% x y)
  Return remainder of X divided by Y.
  (% 10 5)
    => 0
  (% 10 6)
    => 4
-------------------------------------------------------------------------------

(mod x y)
  Return X modulo Y.
  (mod 10 5)
    => 0
  (mod 10 6)
    => 4
  (mod 10.5 6)
    => 4.5
-------------------------------------------------------------------------------

(1+ number)
  Return NUMBER plus one.  NUMBER may be a number or a marker.
  (1+ 2)
    => 3
-------------------------------------------------------------------------------

(1- number)
  Return NUMBER minus one.  NUMBER may be a number or a marker.
  (1- 4)
    => 3

Predicates

(= number &rest numbers)
  Return t if args, all numbers or markers, are equal.
  (= 4 4)
    => t
  (= 4.0 4.0)
    => t
  (= 4 4.0)
    => t
  (= 4 4 4 4)
    => t
-------------------------------------------------------------------------------

(eql obj1 obj2)
  Return t if the two args are ‘eq’ or are indistinguishable numbers.
  (eql 4 4)
    => t
  (eql 4.0 4.0)
    => t
-------------------------------------------------------------------------------

(/= num1 num2)
  Return t if first arg is not equal to second arg.  Both must be numbers or markers.
  (/= 4 4)
    => nil
-------------------------------------------------------------------------------

(< number &rest numbers)
  Return t if each arg (a number or marker), is less than the next arg.
  (< 4 4)
    => nil
  (< 1 2 3)
    => t
-------------------------------------------------------------------------------

(<= number &rest numbers)
  Return t if each arg (a number or marker) is less than or equal to the next.
  (<= 4 4)
    => t
  (<= 1 2 2 3)
    => t
-------------------------------------------------------------------------------

(> number &rest numbers)
  Return t if each arg (a number or marker) is greater than the next arg.
  (> 4 4)
    => nil
  (> 3 2 1)
    => t
-------------------------------------------------------------------------------

(>= number &rest numbers)
  Return t if each arg (a number or marker) is greater than or equal to the next.
  (>= 4 4)
    => t
  (>= 3 2 2 1)
    => t
-------------------------------------------------------------------------------

(zerop number)
  Return t if NUMBER is zero.
  (zerop 0)
    => t
-------------------------------------------------------------------------------

(natnump object)
  Return t if OBJECT is a nonnegative integer.
  (natnump -1)
    => nil
  (natnump 0)
    => t
  (natnump 23)
    => t
-------------------------------------------------------------------------------

(cl-plusp number)
  Return t if NUMBER is positive.
  (cl-plusp 0)
    => nil
  (cl-plusp 1)
    => t
-------------------------------------------------------------------------------

(cl-minusp number)
  Return t if NUMBER is negative.
  (cl-minusp 0)
    => nil
  (cl-minusp -1)
    => t
-------------------------------------------------------------------------------

(cl-oddp integer)
  Return t if INTEGER is odd.
  (cl-oddp 3)
    => t
-------------------------------------------------------------------------------

(cl-evenp integer)
  Return t if INTEGER is even.
  (cl-evenp 6)
    => t
-------------------------------------------------------------------------------

(bignump object)
  Return t if OBJECT is a bignum.
  (bignump 4)
    => nil
  (bignump (expt 2 90))
    => t
-------------------------------------------------------------------------------

(fixnump object)
  Return t if OBJECT is a fixnum.
  (fixnump 4)
    => t
  (fixnump (expt 2 90))
    => nil
-------------------------------------------------------------------------------

(floatp object)
  Return t if OBJECT is a floating point number.
  (floatp 5.4)
    => t
-------------------------------------------------------------------------------

(integerp object)
  Return t if OBJECT is an integer.
  (integerp 5.4)
    => nil
-------------------------------------------------------------------------------

(numberp object)
  Return t if OBJECT is a number (floating point or integer).
  (numberp "5.4")
    => nil
-------------------------------------------------------------------------------

(cl-digit-char-p char &optional radix)
  Test if CHAR is a digit in the specified RADIX (default 10).
  (cl-digit-char-p 53 10)
    => 5
  (cl-digit-char-p 102 16)
    => 15

Operations

(max number &rest numbers)
  Return largest of all the arguments (which must be numbers or markers).
  (max 7 9 3)
    => 9
-------------------------------------------------------------------------------

(min number &rest numbers)
  Return smallest of all the arguments (which must be numbers or markers).
  (min 7 9 3)
    => 3
-------------------------------------------------------------------------------

(abs arg)
  Return the absolute value of ARG.
  (abs -4)
    => 4
-------------------------------------------------------------------------------

(float arg)
  Return the floating point number equal to ARG.
  (float 2)
    => 2.0
-------------------------------------------------------------------------------

(truncate arg &optional divisor)
  Truncate a floating point number to an int.
  (truncate 1.2)
    => 1
  (truncate -1.2)
    => -1
  (truncate 5.4 2)
    => 2
-------------------------------------------------------------------------------

(floor arg &optional divisor)
  Return the largest integer no greater than ARG.
  (floor 1.2)
    => 1
  (floor -1.2)
    => -2
  (floor 5.4 2)
    => 2
-------------------------------------------------------------------------------

(ceiling arg &optional divisor)
  Return the smallest integer no less than ARG.
  (ceiling 1.2)
    => 2
  (ceiling -1.2)
    => -1
  (ceiling 5.4 2)
    => 3
-------------------------------------------------------------------------------

(round arg &optional divisor)
  Return the nearest integer to ARG.
  (round 1.2)
    => 1
  (round -1.2)
    => -1
  (round 5.4 2)
    => 3
-------------------------------------------------------------------------------

(random &optional limit)
  Return a pseudo-random integer.
  (random 6)
    => 5

Bit Operations

(ash value count)
  Return integer VALUE with its bits shifted left by COUNT bit positions.
  (ash 1 4)
    => 16
  (ash 16 -1)
    => 8
-------------------------------------------------------------------------------

(logand &rest ints-or-markers)
  Return bitwise-and of all the arguments.
  (logand #b10 #b111)
    => #b10
-------------------------------------------------------------------------------

(logior &rest ints-or-markers)
  Return bitwise-or of all the arguments.
  (logior 4 16)
    => 20
-------------------------------------------------------------------------------

(logxor &rest ints-or-markers)
  Return bitwise-exclusive-or of all the arguments.
  (logxor 4 16)
    => 20
-------------------------------------------------------------------------------

(lognot number)
  Return the bitwise complement of NUMBER.  NUMBER must be an integer.
  (lognot 5)
    => -6
-------------------------------------------------------------------------------

(logcount value)
  Return population count of VALUE.
  (logcount 5)
    => 2

Floating Point

(isnan x)
  Return non-nil if argument X is a NaN.
  (isnan 5.0)
    => nil
-------------------------------------------------------------------------------

(frexp x)
  Get significand and exponent of a floating point number.
  (frexp 5.7)
    => (0.7125 . 3)
-------------------------------------------------------------------------------

(ldexp sgnfcand exponent)
  Return SGNFCAND * 2**EXPONENT, as a floating point number.
  (ldexp 0.7125 3)
    => 5.7
-------------------------------------------------------------------------------

(logb arg)
  Returns largest integer <= the base 2 log of the magnitude of ARG.
  (logb 10.5)
    => 3
-------------------------------------------------------------------------------

(ffloor arg)
  Return the largest integer no greater than ARG, as a float.
  (ffloor 1.2)
    => 1.0
-------------------------------------------------------------------------------

(fceiling arg)
  Return the smallest integer no less than ARG, as a float.
  (fceiling 1.2)
    => 2.0
-------------------------------------------------------------------------------

(ftruncate arg)
  Truncate a floating point number to an integral float value.
  (ftruncate 1.2)
    => 1.0
-------------------------------------------------------------------------------

(fround arg)
  Return the nearest integer to ARG, as a float.
  (fround 1.2)
    => 1.0

Standard Math Functions

(sin arg)
  Return the sine of ARG.
  (sin float-pi)
    => 1.2246467991473532e-16
-------------------------------------------------------------------------------

(cos arg)
  Return the cosine of ARG.
  (cos float-pi)
    => -1.0
-------------------------------------------------------------------------------

(tan arg)
  Return the tangent of ARG.
  (tan float-pi)
    => -1.2246467991473532e-16
-------------------------------------------------------------------------------

(asin arg)
  Return the inverse sine of ARG.
  (asin float-pi)
    => 0.0e+NaN
-------------------------------------------------------------------------------

(acos arg)
  Return the inverse cosine of ARG.
  (acos float-pi)
    => 0.0e+NaN
-------------------------------------------------------------------------------

(atan y &optional x)
  Return the inverse tangent of the arguments.
  (atan float-pi)
    => 1.2626272556789118
-------------------------------------------------------------------------------

(exp arg)
  Return the exponential base e of ARG.
  (exp 4)
    => 54.598150033144236
-------------------------------------------------------------------------------

(log arg &optional base)
  Return the natural logarithm of ARG.
  (log 54.59)
    => 3.9998507157936665
-------------------------------------------------------------------------------

(expt arg1 arg2)
  Return the exponential ARG1 ** ARG2.
  (expt 2 16)
    => 65536
-------------------------------------------------------------------------------

(sqrt arg)
  Return the square root of ARG.
  (sqrt -1)
    => -0.0e+NaN

-- 
underground experts united
https://dataswamp.org/~incal