This release is a pre-release and may not be stable for production use.
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__.pyfor 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 toisinstancechecks 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/*MPvariants are not exported fromcfmath— 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 incfmath/__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.
1 maintainer
Metadata
1 maintainer
Release files for cfmath 1.0.0rc1
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| File | Size | Uploaded | |
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| File | Interpreter | ABI | Platform | Reset |
|---|---|---|---|---|
| cfmath-1.0.0rc1-py3-none-any.whl | Python 3 | none | any | Details |
Total release size: 231.6 kB
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