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MPError

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pub(all) suberror MPError {
  ValueError(String)
  DomainError(String)
  PoleError(String)
  ComplexResult(String)
  ConvergenceError(String)
} derive(Eq, 
Debug)

impl Show for MPError

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MPContext

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High-level arbitrary-precision numerical context.
impl Show for MPContext

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MPContext::abs

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Absolute value with context rounding.

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MPContext::add

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Context-aware floating-point addition.

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MPContext::augment

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#alias(extend, deprecated="`extend` is deprecated, use `augment` instead")
fn MPContext::augment(self : MPContext, a : MpfMatrix, rhs : ArrayView[
RawMpf]) -> MpfMatrix raise MPError

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MPContext::chebyfit

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Polynomial least-error fit on [a,b] using Chebyshev nodes.

Returns (coeffs, estimated_max_error) with coefficient order controlled by asc.

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MPContext::cholesky

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MPContext::cholesky_solve

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MPContext::cli_eval_division

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fn MPContext::cli_eval_division(self : MPContext, numer : Int, denom : Int, dps? : Int) -> String raise MPError

Evaluate a simple integer division expression (numer/denom) in CLI mode.

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MPContext::cli_eval_literal

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fn MPContext::cli_eval_literal(self : MPContext, literal : String, dps? : Int) -> String raise MPError

Parse and evaluate a numeric literal in CLI compatibility mode.

This mirrors the non-interactive literal path used by mpmath's CLI tests.

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MPContext::complex_gamma

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Complex gamma function.

Raises MPError::PoleError at non-positive integers on the real axis.

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MPContext::complex_log

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Complex principal logarithm.

Equivalent to mpmath principal branch log(z). Explicitly rejects z=0 with MPError::PoleError.

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MPContext::complex_pow

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Complex power z^w on principal branches.

Matches mpmath's principal-branch definition and explicitly guards the ambiguous 0^w cases with non-positive/complex exponents.

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MPContext::complex_sqrt

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Complex principal square root.

Branch behavior follows mpmath principal square root convention.

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MPContext::complex_to_string

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fn MPContext::complex_to_string(self : MPContext, z : 
RawMpc, dps? : Int) -> String

Convert an mpc value to string in (re + im*j) style.

dps controls displayed digits. Behavior follows mpmath.nstr-style compact conversion for complex numbers.

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MPContext::complex_zeta

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Complex zeta continuation.

At s=1, returns pole error for standard zeta and log(2) for alternating zeta (alt=true), consistent with mpmath expectations.

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MPContext::cond

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MPContext::cos

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Cosine function on reals.

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MPContext::cosm

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fn MPContext::cosm(self : MPContext, a : MpfMatrix, max_terms? : Int) -> MpfMatrix raise MPError

Matrix cosine via power series.

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MPContext::cplot

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Sample f on a rectangular complex grid and attach mpmath-style labels.

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MPContext::det

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MPContext::diag

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MPContext::diff

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Numerical derivative d^n f(x) for unary real functions.

Semantics aligned with mpmath diff subset:
  • n=0 returns f(x).
  • n=1 supports one-sided derivative with direction.
  • n>=2 uses symmetric finite-difference formulas, and for higher order derivatives uses central stencil + Richardson correction.

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MPContext::diff_partial3

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Mixed partial derivative for 3-variable real functions.

orders=(nx, ny, nz) computes d^(nx+ny+nz) f / (dx^nx dy^ny dz^nz) at (x, y, z).

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MPContext::differint

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Fractional differintegral subset.

Currently supports a <= 0 (fractional integrals) for finite positive x.

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MPContext::diffs

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Return derivatives [f(x), f'(x), ..., f^(n)(x)].

This mirrors mpmath diffs for unary real functions.

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MPContext::diffun

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Build the unary function x -> d^n f(x).

Runtime derivative errors are mapped to nan, matching the permissive high-level behavior expected by mpmath-compatible helper paths.

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MPContext::div

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Context-aware floating-point division.

Raises MPError::PoleError for division-by-zero paths and maps other libmp errors into structured MPError.

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MPContext::e1

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Complex principal value of E1(x) for real x.

For negative reals this follows the principal branch E1(x) = -Ei(-x) - i*pi.

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MPContext::e1_real

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Real-valued E1(x) helper.

For x < 0, real E1 is not single-valued; this API reports MPError::ComplexResult to force callers to use complex principal value.

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MPContext::eig

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MPContext::eighe

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MPContext::eigsy

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MPContext::exp

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Exponential exp(x) for real mpf.

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MPContext::expint

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Exponential integral family wrapper:
  • gamma=false: E_n(x)
  • gamma=true: upper incomplete gamma form.

For negative real arguments in the non-gamma form, this function returns the complex principal value instead of failing, matching mpmath branch behavior.

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MPContext::expm

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fn MPContext::expm(self : MPContext, a : MpfMatrix, max_terms? : Int) -> MpfMatrix raise MPError

Matrix exponential via power series.

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MPContext::eye

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fn MPContext::eye(self : MPContext, n : Int) -> MpfMatrix raise MPError

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MPContext::findroot

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Scalar root finder for real functions.

  • With x1: secant method.
  • Without x1: Newton method with automatic secant fallback when slope is near zero. Raises MPError::ConvergenceError when the iteration budget is exhausted.

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MPContext::findroot2

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Two-dimensional nonlinear system solver using Newton iteration.

Solves:
  • f1(x,y)=0
  • f2(x,y)=0 with numerically estimated Jacobian from central differences. This is the current mpmath-like multidimensional findroot subset.

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MPContext::findroot_interval

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Bracketed root finder on a real interval using bisection.

Requires opposite signs at interval endpoints (or an endpoint root). This corresponds to mpmath findroot(..., solver='bisect') subset.

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MPContext::format

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fn MPContext::format(self : MPContext, x : 
RawMpf, format_spec : String, dps? : Int) -> String raise MPError

Format an mpf using mpmath/Python-like format mini-language subset.

format_spec is forwarded to @mpf.format_mpf (alignment, sign, percent, base/precision options implemented by libmp).

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MPContext::fourier

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Fourier coefficients on interval [a,b] up to order n.

Returns (c, s) where f(x) ~ c0 + sum_{k>=1}(c[k] cos(k*w*(x-a)) + s[k] sin(k*w*(x-a))).

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MPContext::fourierval

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Evaluate a Fourier series from (c, s) coefficient arrays.

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MPContext::fprod

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Product of an array of mpf values with context-aware rounding.

Mirrors mpmath fprod behavior for real inputs.

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MPContext::fsum

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High-precision compensated summation helper.

Mirrors mpmath fsum subset:
  • absolute=true: sum of absolute values.
  • squared=true: sum of squares (optionally after absolute). Uses extra working precision to reduce cancellation error.

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MPContext::gamma

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Euler gamma Gamma(x) for real arguments.

Pole/domain behavior is mapped to MPError::PoleError and MPError::DomainError, matching mpmath-style semantics.

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MPContext::hessenberg

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MPContext::hilbert

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fn MPContext::hilbert(self : MPContext, n : Int) -> MpfMatrix raise MPError

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MPContext::identify

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Minimal symbolic identify subset for Stage-B migration.

Supported patterns:
  • small integer/rational values
  • exp(n), log(n) for small integers
  • linear/rational combinations against provided constants
  • basic builtins (pi, log(2), pi**4)

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MPContext::inverse

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fn MPContext::inverse(self : MPContext, a : MpfMatrix) -> MpfMatrix raise MPError

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MPContext::invertlaplace

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Inverse Laplace transform subset with method-compatible interface.

Implemented using a Stehfest core for positive real t; accepted methods: talbot, stehfest, dehoog, cohen.

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MPContext::levin

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Sequence acceleration entrypoint used by nsum/nprod.

Accepts a sequence of partial sums and returns (estimate, error). Supported methods: auto, levin, l, shanks, euler, sidi, u/v/t (aliases), and richardson / r.

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MPContext::limit

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Numerical limit for real-valued unary functions.

Supports finite points and x = +/-inf.

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MPContext::ln

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Natural logarithm ln(x) on reals.

Raises MPError::DomainError when called outside the real domain.

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MPContext::lu_solve

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MPContext::make_complex

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Build a complex number from real and imaginary mpf parts.

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MPContext::make_float

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fn MPContext::make_float(self : MPContext, s : String) -> 
RawMpf raise MPError

Parse a decimal string into an mpf using context precision.

Compatible with mpmath-style numeric spellings (inf, nan, exponents, signed literals). Parse failures are normalized to MPError::ValueError.

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MPContext::make_int

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Construct an mpf value from an integer using this context precision.

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MPContext::matrix

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fn MPContext::matrix(self : MPContext, rows : Int, cols : Int, fill? : 
RawMpf) -> MpfMatrix raise MPError

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MPContext::matrix_add

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fn MPContext::matrix_add(self : MPContext, a : MpfMatrix, b : MpfMatrix) -> MpfMatrix raise MPError

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MPContext::matrix_add_scalar

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MPContext::matrix_copy

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fn MPContext::matrix_copy(self : MPContext, a : MpfMatrix) -> MpfMatrix

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MPContext::matrix_div_scalar

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MPContext::matrix_from_rows

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MPContext::matrix_from_vector

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MPContext::matrix_mul

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fn MPContext::matrix_mul(self : MPContext, a : MpfMatrix, b : MpfMatrix) -> MpfMatrix raise MPError

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MPContext::matrix_norm_1

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MPContext::matrix_norm_fro

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MPContext::matrix_norm_inf

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MPContext::matrix_pos

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fn MPContext::matrix_pos(self : MPContext, a : MpfMatrix) -> MpfMatrix

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MPContext::matrix_pow

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fn MPContext::matrix_pow(self : MPContext, a : MpfMatrix, n : Int) -> MpfMatrix raise MPError

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MPContext::matrix_rsub_scalar

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MPContext::matrix_scale

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MPContext::matrix_set_slice

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fn MPContext::matrix_set_slice(self : MPContext, a : MpfMatrix, src : MpfMatrix, row_start? : Int, row_end? : Int, col_start? : Int, col_end? : Int) -> Unit raise MPError

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MPContext::matrix_set_slice_scalar

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fn MPContext::matrix_set_slice_scalar(self : MPContext, a : MpfMatrix, value : 
RawMpf, row_start? : Int, row_end? : Int, col_start? : Int, col_end? : Int) -> Unit raise MPError

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MPContext::matrix_slice

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fn MPContext::matrix_slice(self : MPContext, a : MpfMatrix, row_start? : Int, row_end? : Int, col_start? : Int, col_end? : Int) -> MpfMatrix raise MPError

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MPContext::matrix_sub

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fn MPContext::matrix_sub(self : MPContext, a : MpfMatrix, b : MpfMatrix) -> MpfMatrix raise MPError

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MPContext::matrix_sub_scalar

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MPContext::matrix_sum

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MPContext::matrix_transpose

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fn MPContext::matrix_transpose(self : MPContext, a : MpfMatrix) -> MpfMatrix raise MPError

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MPContext::matrix_vec_mul

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MPContext::mnorm

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MPContext::mul

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Context-aware floating-point multiplication.

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MPContext::neg

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Unary negation with context rounding.

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MPContext::nprod

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fn MPContext::nprod(self : MPContext, f : (Int) -> 
RawMpf, start : Int, stop? : Int, algo? : String, tol? : 
RawMpf, max_terms? : Int) -> 
RawMpf raise MPError

Integer-indexed numerical products with optional acceleration.

Infinite products are evaluated through accelerated summation of logarithms and therefore require strictly positive finite terms.

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MPContext::nsum

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fn MPContext::nsum(self : MPContext, f : (Int) -> 
RawMpf, start : Int, stop? : Int, algo? : String, tol? : 
RawMpf, max_terms? : Int) -> 
RawMpf raise MPError

Integer-indexed numerical summation with optional convergence acceleration.

  • stop=Some(b): finite summation over [start, b].
  • stop=None: infinite tail, accelerated by method.

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MPContext::ode_solve

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MPContext::ode_solve_grid

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MPContext::ode_step_rk4

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MPContext::ones

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fn MPContext::ones(self : MPContext, rows : Int, cols? : Int) -> MpfMatrix raise MPError

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MPContext::pade

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Pade approximation from a power-series prefix a.

Returns numerator/denominator coefficient arrays (p, q) in ascending order.

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MPContext::plot

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Sample f on a real interval and attach mpmath-style axes labels.

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MPContext::polyroots

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fn MPContext::polyroots(self : MPContext, coeffs : ArrayView[
RawMpf], asc? : Bool, max_steps? : Int, cleanup? : Bool, extraprec? : Int) -> Array[
RawMpc] raise MPError

Polynomial roots for real coefficients.

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MPContext::polyroots_error

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fn MPContext::polyroots_error(self : MPContext, coeffs : ArrayView[
RawMpf], asc? : Bool, max_steps? : Int, cleanup? : Bool, extraprec? : Int) -> (Array[
RawMpc], 
RawMpf) raise MPError

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MPContext::polyroots_with_init_error

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fn MPContext::polyroots_with_init_error(self : MPContext, coeffs : ArrayView[
RawMpf], roots_init : ArrayView[
RawMpf], asc? : Bool, max_steps? : Int, cleanup? : Bool, extraprec? : Int) -> (Array[
RawMpc], 
RawMpf) raise MPError

Polynomial roots with explicit initial guesses and error estimate.

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MPContext::polyval

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Polynomial evaluation helper aligned with mpmath polyval.

  • asc=true: coefficients are [a0, a1, ...].
  • asc=false: coefficients are [an, ..., a0].

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MPContext::polyval_with_derivative

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Polynomial evaluation with derivative (f(x), f'(x)).

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MPContext::pow_int

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Integer power x^n in the current context.

Uses fast exponentiation in libmp and propagates structured errors for invalid edge cases.

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MPContext::precision

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fn MPContext::precision(self : MPContext) -> Int

Return the context precision in bits.

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MPContext::qr

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MPContext::qr_solve

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MPContext::quad

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Piecewise one-dimensional numerical integration over multiple breakpoints.

points=[x0, x1, ..., xn] integrates each adjacent segment and sums the results. Supports finite and selected infinite endpoint combinations.

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MPContext::quadgl

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One-dimensional numerical integration (Gauss-Legendre-style entrypoint).

This currently shares the same adaptive core as quadts, providing mpmath API compatibility for the migrated subset.

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MPContext::quadts

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One-dimensional numerical integration (tanh-sinh-style entrypoint).

Current implementation supports finite and infinite endpoints via variable transformations; API shape matches mpmath quadts subset.

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MPContext::randmatrix

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fn MPContext::randmatrix(self : MPContext, rows : Int, cols? : Int) -> MpfMatrix raise MPError

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MPContext::rank

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MPContext::round_mode

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Return the context rounding mode.

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MPContext::scalar_abs

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MPContext::schur

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fn MPContext::schur(self : MPContext, a : MpfMatrix, tol? : 
RawMpf, max_steps? : Int) -> (MpfMatrix, MpfMatrix) raise MPError

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MPContext::sin

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Sine function on reals.

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MPContext::sinm

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fn MPContext::sinm(self : MPContext, a : MpfMatrix, max_terms? : Int) -> MpfMatrix raise MPError

Matrix sine via power series.

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MPContext::sqrt

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Principal square root on real inputs.

Raises MPError::DomainError for negative finite real values, matching mpmath real-domain semantics.

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MPContext::sub

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Context-aware floating-point subtraction.

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MPContext::summation

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fn MPContext::summation(self : MPContext, f : (Int) -> 
RawMpf, start : Int, stop : Int, step? : Int) -> 
RawMpf raise MPError

Finite integer-index summation sum(f(k), k=start..stop, step).

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MPContext::svd

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MPContext::swap_row

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fn MPContext::swap_row(self : MPContext, a : MpfMatrix, r0 : Int, r1 : Int) -> Unit raise MPError

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MPContext::tan

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Tangent function on reals.

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MPContext::taylor

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Return Taylor coefficients [a0, ..., an] around x, where a_k = f^(k)(x) / k!.

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MPContext::to_string

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fn MPContext::to_string(self : MPContext, x : 
RawMpf, dps? : Int) -> String raise MPError

Convert an mpf to a plain decimal string with optional dps.

This wraps @mpf.to_str_opts and follows mpmath's default user-facing conversion style for finite/special values.

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MPContext::vector_norm

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MPContext::zeros

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fn MPContext::zeros(self : MPContext, rows : Int, cols? : Int) -> MpfMatrix raise MPError

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MPContext::zeta

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Riemann zeta zeta(s) (or alternating eta form when alt=true) on reals.

alt=true maps to mpmath's alternate zeta continuation behavior.

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MpfMatrix

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pub struct MpfMatrix {
  rows : Int
  cols : Int
  data : Array[
RawMpf]
} derive(Eq, 
Debug)

impl Show for MpfMatrix

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MpfMatrix::flat

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MpfMatrix::get

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MpfMatrix::get_at

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fn MpfMatrix::get_at(self : MpfMatrix, r : Int, c : Int) -> 
RawMpf raise MPError

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MpfMatrix::len

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fn MpfMatrix::len(self : MpfMatrix) -> Int

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MpfMatrix::set

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fn MpfMatrix::set(self : MpfMatrix, r : Int, c : Int, v : 
RawMpf) -> Unit raise MPError

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MpfMatrix::set_at

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fn MpfMatrix::set_at(self : MpfMatrix, r : Int, c : Int, v : 
RawMpf) -> Unit raise MPError

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MpfMatrix::tolist

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MpfMatrix::vget

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MpfMatrix::vset

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fn MpfMatrix::vset(self : MpfMatrix, idx : Int, v : 
RawMpf) -> Unit raise MPError

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PlotAxes

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pub struct PlotAxes {
  xlabel : String
  ylabel : String
} derive(Eq, 
Debug)

Minimal axis container used by plot/cplot APIs.
impl Show for PlotAxes

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cli_version

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fn cli_version() -> String

Version string used by CLI-style integrations.

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mbmath_version

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let mbmath_version : String

Version reported by CLI integrations.

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new

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Create a high-level arbitrary-precision context.

This is the MoonBit counterpart of constructing an mpmath.mp-like runtime state. prec is binary precision (bits), and rounding controls final rounding for wrapper operations.

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plot_axes

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fn plot_axes() -> PlotAxes

Create an empty plot axes object.

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