cfmath 1.0.0rc1

Math operations on continued fractions

cfmath

A continued-fraction arithmetic library for Python. Every function returns a lazy CF object whose terms can be consumed one at a time, or in batches, to any desired precision.

Public API by module

The tables below list the public functions and the input types they accept. ✓ = supported, — = not applicable.

The *GCF, *CF, and *MP variant rows are implementation backends, not separate exports. A dispatcher such as Sin (or Arctan) picks one automatically; to force a particular backend, pass the module's mode enum, e.g. Sin(x, TrigMode.MP) or Arctan(x, ArctrigMode.CF).

Updating this table: regenerate it by reading cfmath/__init__.py for the exported names, then checking each function's signature (especially the first positional parameter) in the defining module listed here. The column split (int / Fraction / CF) maps to isinstance checks in the function body; look for _coerce_trig_arg (int+Fraction only), _coerce_meta_trig_arg (int+Fraction+CF), isinstance(x, CF) guards, or the raw type annotation.

The *GCF/*CF/*MP variants are not exported from cfmath — they are module-private (e.g. cfmath.trig._SinCF, cfmath.arctrig._ArctanMP) and selected through the function's mode enum, so they will not appear in cfmath/__init__.py. Keep their rows; they document the backends the enum chooses between.

---

cfmath.core — base type

Symbol	int	Fraction	CF	Notes
CF	—	—	—	The lazy continued-fraction type itself; construct via CF.from_int, CF.from_rational, CF.from_fraction, CF.from_float

---

cfmath.constants — mathematical constants (no input)

Function	int	Fraction	CF	Notes
Pi	—	—	—	π
Tau	—	—	—	2π
E	—	—	—	Euler's number
Phi	—	—	—	Golden ratio
EulerGamma	—	—	—	Euler–Mascheroni constant
Catalan	—	—	—	Catalan's constant
Apery	—	—	—	Apéry's constant ζ(3)
Khinchin	—	—	—	Khinchin's constant
Plastic	—	—	—	Plastic constant

---

cfmath.quadratic — quadratic irrationals

Function	int	Fraction	CF	Notes
Sqrt	✓	—	—	√n for integer n

---

cfmath.power — general exponentiation

PowArg = int | Fraction | CF

Function	int	Fraction	CF	Notes
Pow	✓	✓	✓	Pow(x, r) — both args accept any PowArg
PowCF	✓	✓	✓	meta-CF backend for Pow
PowMP	✓	✓	✓	mpmath backend for Pow
PowIntExponent	✓	✓	✓	integer-exponent fast path
PowInterval	✓	✓	✓	interval-arithmetic backend
Nthroot	✓	✓	—	Nthroot(x, k) — k-th root of rational x
Cuberoot	✓	—	—	∛n for integer n

---

cfmath.exponential — exponential function

Function	int	Fraction	CF	Notes
Exp	✓	✓	✓	eˣ — alias for ExpMP

---

cfmath.logarithm — logarithms

Function	int	Fraction	CF	Notes
Ln	✓	✓	✓	natural log
Log	✓	✓	✓	Log(x, base=None) — base defaults to e; base is int | Fraction | None
Log2	✓	✓	✓	log base 2
Log10	✓	✓	✓	log base 10

---

cfmath.trig — trigonometric functions

Angles are in radians. *GCF variants accept only rational inputs and use exact generalized-CF arithmetic. *CF variants accept any CF and use the meta-GCF algorithm. *MP variants use mpmath for verification.

Function	int	Fraction	CF	Notes
Sin	✓	✓	✓	dispatches to SinGCF (rational) or SinCF (CF)
SinGCF	✓	✓	—	exact Lambert GCF for rational x
SinCF	✓	✓	✓	sin/x meta-GCF with z = x², reduces modulo 2π
SinMP	✓	✓	✓	mpmath; for CF input uses dual-precision convergent approach
Cos	✓	✓	✓	dispatches to CosGCF (rational) or CosMP (CF)
CosGCF	✓	✓	—	exact Lambert GCF for rational x
CosCF	✓	✓	✓	1/cos meta-GCF (z = x²); ended up slower than expected, so AUTO sends CF to CosMP — request it explicitly with TrigMode.CF
CosMP	✓	✓	✓	mpmath; for CF input uses the convergent approach
Tan	✓	✓	✓	dispatches to TanGCF (rational) or TanCF (CF)
TanGCF	✓	✓	—	exact Lambert GCF for rational x
TanCF	✓	✓	✓	meta-GCF with argument reduction modulo π
TanMP	✓	✓	✓	mpmath; for CF input uses the convergent approach

---

cfmath.arctrig — inverse trigonometric functions

Function	int	Fraction	CF	Notes
Arctan	✓	✓	✓	dispatches to ArctanGCF (rational) or ArctanCF (CF)
ArctanGCF	✓	✓	—	Gauss GCF for rational x
ArctanCF	✓	✓	✓	meta-GCF path
ArctanMP	✓	✓	✓	mpmath; for CF input uses the convergent approach
Arcsin	✓	✓	✓	rational uses Euler GCF; CF uses mpmath
Arccos	✓	✓	✓	rational uses π/2 − arcsin; CF uses mpmath

---

cfmath.hyperbolic — hyperbolic functions

Function	int	Fraction	CF	Notes
Sinh	✓	✓	✓	rational via mpmath/decimal; CF via ExpCF
Cosh	✓	✓	✓	rational via mpmath/decimal; CF via ExpCF
Tanh	✓	✓	✓	rational uses Lambert GCF; CF uses mpmath

---

cfmath.archyperbolic — inverse hyperbolic functions

Function	int	Fraction	CF	Notes
Arcsinh	✓	✓	✓	rational via mpmath/decimal; CF via mpmath
Arccosh	✓	✓	✓	rational via mpmath/decimal; CF via mpmath
Arctanh	✓	✓	✓	rational via Ln; CF via mpmath

---

cfmath.special — special functions

Function	int	Fraction	CF	Notes
Gamma	✓	✓	—	Γ(x)
Zeta	✓	—	—	ζ(s) for integer s ≥ 2

---

cfmath.gosper — Gosper arithmetic on CFs

All functions take CF inputs and return CF.

Function	Notes
cf_add	x + y
cf_sub	x − y
cf_mul	x · y
cf_div	x / y
cf_homographic	(ax + b) / (cx + d)
cf_min	min(x, y)
cf_max	max(x, y)

---

cfmath.convergents — rational approximations

All functions take a CF and work with its convergents p_n/q_n.

Function	Notes
convergent	n-th convergent as Fraction
convergent_pair	n-th convergent as (p, q)
convergent_pairs	lazy iterator of (p, q) pairs
convergents	lazy iterator of Fraction values

---

Version compatibility

Python 3.10+. This library follows meanver.

License

cfmath is copyright Tim Hatch, and licensed under the MIT license. See the LICENSE file for details.