The cf Reference Manual

3.1.1 cf/cf.asd

Source

cf.asd.

Parent Component

cf (system).

ASDF Systems

cf.

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3.1.2 cf/cf.lisp

Source

cf.asd.

Parent Component

cf (system).

Packages

cf.

Public Interface

• *cf-length* (special variable).
• *cf-max-number-in-fractional-part* (special variable).
• +cf-atan-1/2+ (special variable).
• +cf-e+ (special variable).
• +cf-gamma+ (special variable).
• +cf-ln-2+ (special variable).
• +cf-pi+ (special variable).
• +cf-pi/2+ (special variable).
• +cf-tau+ (special variable).
• cf (function).
• cf* (function).
• cf+ (function).
• cf- (function).
• cf-abs (function).
• cf-acos (function).
• cf-acosh (function).
• cf-asin (function).
• cf-asinh (function).
• cf-atan (function).
• cf-atanh (function).
• cf-bihomographic (function).
• cf-ceiling (function).
• cf-convergent (function).
• cf-cos (function).
• cf-cosh (function).
• cf-decimal (function).
• cf-exp (function).
• cf-expt (function).
• cf-floor (function).
• cf-homographic (function).
• cf-log (function).
• cf-max (function).
• cf-min (function).
• cf-minusp (function).
• cf-mod (function).
• cf-nsimplify (function).
• cf-plusp (function).
• cf-rem (function).
• cf-round (function).
• cf-signum (function).
• cf-simplify (function).
• cf-sin (function).
• cf-sinh (function).
• cf-sqrt (function).
• cf-tan (function).
• cf-tanh (function).
• cf-truncate (function).
• cf-zerop (function).
• cf/ (function).
• cf/= (function).
• cf1+ (function).
• cf1- (function).
• cf< (function).
• cf<= (function).
• cf= (function).
• cf> (function).
• cf>= (function).

Internals

• *cf-max-iterations* (special variable).
• cf-atan1 (function).
• cf-expt-n (function).
• cf-ln (function).
• cf-sqrt-n (function).
• check-cf (macro).

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5.1.1 Special variables

Special Variable: *cf-length* ¶

Maximum number of coefficients used in continued fractions.

Package

cf.

Source

cf.lisp.

Special Variable: *cf-max-number-in-fractional-part* ¶

Maximum integer that can appear in the fractional part of a continued fraction. The CF-SIMPLIFY function will truncate the continued fraction if it encounters a number bigger than this maximum.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-atan-1/2+ ¶

Continued fraction for the arctangent of 1/2.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-e+ ¶

Continued fraction for e = exp(1). OEIS: A003417.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-gamma+ ¶

Continued fraction for the Euler-Mascheroni constant gamma. OEIS: A002852.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-ln-2+ ¶

Continued fraction for ln(2). OEIS: A016730.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-pi+ ¶

Continued fraction for pi. OEIS: A001203.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-pi/2+ ¶

Continued fraction for pi / 2. OEIS: A053300.

Package

cf.

Source

cf.lisp.

Special Variable: +cf-tau+ ¶

Continued fraction for tau = 2 * pi. OEIS: A058291.

Package

cf.

Source

cf.lisp.

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5.1.2 Ordinary functions

Function: cf (x) ¶

Return the continued fraction for the number X (with at most *CF-LENGTH* coefficients).

Package

cf.

Source

cf.lisp.

Function: cf* (&rest fractions) ¶

Return the continued fraction of the product of its arguments.

Package

cf.

Source

cf.lisp.

Function: cf+ (&rest fractions) ¶

Return the continued fraction of the sum of its arguments.

Package

cf.

Source

cf.lisp.

Function: cf- (x &rest more-fractions) ¶

Return the continued fraction of the subtraction of the second and subsequent arguments from X. If MORE-FRACTIONS are not specified, return the continued fraction of -X.

Package

cf.

Source

cf.lisp.

Function: cf-abs (x) ¶

Return the continued fraction of the absolute value of X.

Package

cf.

Source

cf.lisp.

Function: cf-acos (x) ¶

Return the continued fraction of acos(X).

Package

cf.

Source

cf.lisp.

Function: cf-acosh (x) ¶

Package

cf.

Source

cf.lisp.

Function: cf-asin (x) ¶

Return the continued fraction of asin(X).

Package

cf.

Source

cf.lisp.

Function: cf-asinh (x) ¶

Package

cf.

Source

cf.lisp.

Function: cf-atan (y &optional x) ¶

If X is specified, return the continued fraction of atan(Y / X), and atan(Y) otherwise.

Package

cf.

Source

cf.lisp.

Function: cf-atanh (x) ¶

Return the continued fraction of atanh(X).

Package

cf.

Source

cf.lisp.

Function: cf-bihomographic (a b c d e f g h x y) ¶

Return the continued fraction of (AXY + BX + CY + D) / (EXY + FX + GY + H), where A, B, C, D, E, F, G and H are relative integers, and X and Y are continued fractions.

Package

cf.

Source

cf.lisp.

Function: cf-ceiling (x &optional y) ¶

Return the continued fraction of the smallest integer greater than or equal to X / Y, and the continued fraction of the remainder. The default value for Y is 1.

Package

cf.

Source

cf.lisp.

Function: cf-convergent (x) ¶

Return the convergent of the continued fraction X.

Package

cf.

Source

cf.lisp.

Function: cf-cos (x) ¶

Return the continued fraction of cos(X).

Package

cf.

Source

cf.lisp.

Function: cf-cosh (x) ¶

Return the continued fraction of cosh(X).

Package

cf.

Source

cf.lisp.

Function: cf-decimal (x n) ¶

Return a string representing the decimal expansion of the continued fraction X, with at most N digits in the fractional part.

Package

cf.

Source

cf.lisp.

Function: cf-exp (x) ¶

Return the continued fraction of E^X.

Package

cf.

Source

cf.lisp.

Function: cf-expt (x y) ¶

Return the continued fraction of X^Y.

Package

cf.

Source

cf.lisp.

Function: cf-floor (x &optional y) ¶

Return the continued fraction of the greatest integer smaller than or equal to X / Y, and the continued fraction of X modulo Y. The default value for Y is 1.

Package

cf.

Source

cf.lisp.

Function: cf-homographic (a b c d x) ¶

Return the continued fraction of (AX + B) / (CX + D),
where A, B, C and D are relative integers, and X is a continued fraction.

Package

cf.

Source

cf.lisp.

Function: cf-log (x &optional y) ¶

If Y is specified, return the continued fraction of the base Y logarithm of X, and ln(X) otherwise.

Package

cf.

Source

cf.lisp.

Function: cf-max (x &rest more-fractions) ¶

Return the greatest of its arguments.

Package

cf.

Source

cf.lisp.

Function: cf-min (x &rest more-fractions) ¶

Return the least of its arguments.

Package

cf.

Source

cf.lisp.

Function: cf-minusp (x) ¶

Return T if X is strictly negative, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf-mod (x y) ¶

Return the continued fraction of X modulo Y (the second value of CF-FLOOR).

Package

cf.

Source

cf.lisp.

Function: cf-nsimplify (x) ¶

Like CF-SIMPLIFY, but modifying X instead of creating a new continued fraction.

Package

cf.

Source

cf.lisp.

Function: cf-plusp (x) ¶

Return T if X is strictly positive, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf-rem (x y) ¶

Return the continued fraction of the remainder of X / Y (the second value of CF-TRUNCATE).

Package

cf.

Source

cf.lisp.

Function: cf-round (x &optional y) ¶

Return the continued fraction of X / Y rounded to the nearest integer, and the continued fraction of the remainder. The default value for Y is 1.

Package

cf.

Source

cf.lisp.

Function: cf-signum (x) ¶

Return the continued fraction of -1, 0 or 1 if X is respectively negative, zero or positive.

Package

cf.

Source

cf.lisp.

Function: cf-simplify (x) ¶

Keep at most *CF-LENGTH* coefficients of the continued fraction X and remove huge numbers (greater than *cf-max-number-in-fractional-part*) from the fractional part.

Package

cf.

Source

cf.lisp.

Function: cf-sin (x) ¶

Return the continued fraction of cos(X).

Package

cf.

Source

cf.lisp.

Function: cf-sinh (x) ¶

Return the continued fraction of sinh(X).

Package

cf.

Source

cf.lisp.

Function: cf-sqrt (x) ¶

Return the continued fraction of the square root of X.

Package

cf.

Source

cf.lisp.

Function: cf-tan (x) ¶

Return the continued fraction of tan(X).

Package

cf.

Source

cf.lisp.

Function: cf-tanh (x) ¶

Return the continued fraction of tanh(X).

Package

cf.

Source

cf.lisp.

Function: cf-truncate (x &optional y) ¶

Return the continued fraction of the integer part of X / Y rounded toward 0, and the continued fraction of the remainder. The default value for Y is 1.

Package

cf.

Source

cf.lisp.

Function: cf-zerop (x) ¶

Return T if X is zero, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf/ (x &rest more-fractions) ¶

Return the continued fraction of the division of X by the second and subsequent arguments. If MORE-FRACTIONS are not specified, return the continued fraction of 1 / X.

Package

cf.

Source

cf.lisp.

Function: cf/= (x &rest more-fractions) ¶

Return NIL if at least two of its arguments are equal, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf1+ (x) ¶

Return the continued fraction of X + 1.

Package

cf.

Source

cf.lisp.

Function: cf1- (x) ¶

Return the continued fraction of X - 1.

Package

cf.

Source

cf.lisp.

Function: cf< (x &rest more-fractions) ¶

Return if T its arguments are in strictly increasing order, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf<= (x &rest more-fractions) ¶

Return T if its arguments are in increasing order, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf= (x &rest more-fractions) ¶

Return T if all its arguments are equal, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf> (x &rest more-fractions) ¶

Return T if its arguments are in strictly decreasing order, and NIL otherwise.

Package

cf.

Source

cf.lisp.

Function: cf>= (x &rest more-fractions) ¶

Return T if its arguments are in decreasing order, and NIL otherwise.

Package

cf.

Source

cf.lisp.

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5.2.1 Special variables

Special Variable: *cf-max-iterations* ¶

Maximum number of iterations used to compute some functions like EXP, LN, COS, SIN...

Package

cf.

Source

cf.lisp.

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5.2.2 Macros

Macro: check-cf (x) ¶

Throw an error if X is not a valid continued fraction.

Package

cf.

Source

cf.lisp.

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5.2.3 Ordinary functions

Function: cf-atan1 (x) ¶

Return the continued fraction of atan(X).

Package

cf.

Source

cf.lisp.

Function: cf-expt-n (x n) ¶

Return the continued fraction of X^N, where N is a positive integer.

Package

cf.

Source

cf.lisp.

Function: cf-ln (x) ¶

Return the continued fraction of ln(X).

Package

cf.

Source

cf.lisp.

Function: cf-sqrt-n (n) ¶

Return the continued fraction of the square root of N, where N is a positive integer.

Package

cf.

Source

cf.lisp.

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