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Complete scalar-domain adapters

These functions call the original Complex, Trigonometry, NumberTheory and Special APIs. C includes hmath_scalar_extras.h; Python namespaces extend existing modules without replacing earlier numerical functions. Complex selectors are owned immutable original objects, constructed with complex.exp()/trigonometry.c_sin() etc. The complex_function adapter accepts dtype="float32" or "float64"; actual typed Complex Float inputs remain Float through the original RealFloat algorithm. Other complex operations/SFResult retain original Double precision. No principal-branch, pole/nonfinite, error-estimate or integer-budget policy is changed.

Values use the owned structured protocol: inputs borrowed, outputs owned/untouched on failure, each reference pins the runtime. Exact integers have no fixed precision or floating conversion. Variable-length/nested lists and tuples keep their original order/shape; Maybe uses None. Checked source errors retain complete MathError/status11. Selectors use kinds352/353. SFResult uses a tuple of two Doubles, interoperable with existing SFResult(value,error) named tuples; its raw constructor does not normalize or certify the error field.

complex.exp

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_exp(hmath_context *context, hmath_value **out);

complex.log

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_log(hmath_context *context, hmath_value **out);

complex.sqrt

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_sqrt(hmath_context *context, hmath_value **out);

complex.sin

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_sin(hmath_context *context, hmath_value **out);

complex.cos

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_cos(hmath_context *context, hmath_value **out);

complex.tan

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_tan(hmath_context *context, hmath_value **out);

complex.sinh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_sinh(hmath_context *context, hmath_value **out);

complex.cosh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_cosh(hmath_context *context, hmath_value **out);

complex.tanh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_tanh(hmath_context *context, hmath_value **out);

complex.asin

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_asin(hmath_context *context, hmath_value **out);

complex.acos

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_acos(hmath_context *context, hmath_value **out);

complex.atan

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_atan(hmath_context *context, hmath_value **out);

complex.asinh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_asinh(hmath_context *context, hmath_value **out);

complex.acosh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_acosh(hmath_context *context, hmath_value **out);

complex.atanh

Construct or inspect the original immutable record; field order follows the source signature.

Elementary

hmath_status hmath_complex_atanh(hmath_context *context, hmath_value **out);

complex.elementary

Apply an elementary function, rejecting poles and nonfinite results.

Elementary -> Complex Double -> Either MathError (Complex Double)

hmath_status hmath_complex_elementary(hmath_context *context, const hmath_value *operation, const hmath_value *value, hmath_value **out);

complex.complex_matrix

Checked finite complex matrix, at most 256 rows and columns.

Int -> Int -> [Complex Double] -> Either MathError (Matrix (Complex Double))

hmath_status hmath_complex_complex_matrix(hmath_context *context, const hmath_value *rows, const hmath_value *columns, const hmath_value *values, hmath_value **out);

complex.multiply_matrices

Matrix multiplication with finite-result validation.

Matrix (Complex Double) -> Matrix (Complex Double) -> Either MathError (Matrix (Complex Double))

hmath_status hmath_complex_multiply_matrices(hmath_context *context, const hmath_value *a, const hmath_value *b, hmath_value **out);

complex.conjugate_transpose

Hermitian transpose with finite-input validation.

Matrix (Complex Double) -> Either MathError (Matrix (Complex Double))

hmath_status hmath_complex_conjugate_transpose(hmath_context *context, const hmath_value *value, hmath_value **out);

complex.complex_fft

Existing checked mixed-radix/Bluestein forward FFT.

[Complex Double] -> Either MathError [Complex Double]

hmath_status hmath_complex_complex_fft(hmath_context *context, const hmath_value *values, hmath_value **out);

complex.complex_ifft

Existing checked inverse FFT, normalized by sample count.

[Complex Double] -> Either MathError [Complex Double]

hmath_status hmath_complex_complex_ifft(hmath_context *context, const hmath_value *values, hmath_value **out);

trigonometry.c_sin

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_sin(hmath_context *context, hmath_value **out);

trigonometry.c_cos

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_cos(hmath_context *context, hmath_value **out);

trigonometry.c_tan

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_tan(hmath_context *context, hmath_value **out);

trigonometry.c_asin

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_asin(hmath_context *context, hmath_value **out);

trigonometry.c_acos

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_acos(hmath_context *context, hmath_value **out);

trigonometry.c_atan

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_atan(hmath_context *context, hmath_value **out);

trigonometry.c_sinh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_sinh(hmath_context *context, hmath_value **out);

trigonometry.c_cosh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_cosh(hmath_context *context, hmath_value **out);

trigonometry.c_tanh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_tanh(hmath_context *context, hmath_value **out);

trigonometry.c_asinh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_asinh(hmath_context *context, hmath_value **out);

trigonometry.c_acosh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_acosh(hmath_context *context, hmath_value **out);

trigonometry.c_atanh

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_atanh(hmath_context *context, hmath_value **out);

trigonometry.c_sec

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_sec(hmath_context *context, hmath_value **out);

trigonometry.c_csc

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_csc(hmath_context *context, hmath_value **out);

trigonometry.c_cot

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_cot(hmath_context *context, hmath_value **out);

trigonometry.c_sech

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_sech(hmath_context *context, hmath_value **out);

trigonometry.c_csch

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_csch(hmath_context *context, hmath_value **out);

trigonometry.c_coth

Construct or inspect the original immutable record; field order follows the source signature.

ComplexFunction

hmath_status hmath_trigonometry_c_coth(hmath_context *context, hmath_value **out);

trigonometry.complex_function

Given a ComplexFunction selector then complex input, compute the selected principal-branch Data.Complex function or reciprocal. Reject non-finite components and non-finite results/poles with Left DomainError. 

RealFloat a => ComplexFunction -> Complex a -> Either MathError (Complex a)

hmath_status hmath_trigonometry_complex_function(hmath_context *context, const hmath_value *operation, const hmath_value *value, hmath_value **out);

numbertheory.chinese_remainder

Generalized CRT for @(residue,positive modulus)@ pairs. Compatible noncoprime moduli are supported. Returns canonical residue and lcm modulus. 

[(Integer,Integer)] -> Either MathError (Integer,Integer)

hmath_status hmath_numbertheory_chinese_remainder(hmath_context *context, const hmath_value *congruences, hmath_value **out);

numbertheory.linear_diophantine

One solution and a direction: @(x,y,dx,dy)@ represents every solution @(x+kdx,y+kdy)@ of @ax+by=c@. The all-zero equation has a two-dimensional solution set and is rejected instead of returning a misleading direction. 

Integer -> Integer -> Integer -> Either MathError (Integer,Integer,Integer,Integer)

hmath_status hmath_numbertheory_linear_diophantine(hmath_context *context, const hmath_value *a, const hmath_value *b, const hmath_value *c, hmath_value **out);

numbertheory.perfect_power

Find a representation @n = base^exponent@ with exponent greater than one. Zero, one, and minus one use exponent 2, 2, and 3 respectively. 

Integer -> Maybe (Integer,Int)

hmath_status hmath_numbertheory_perfect_power(hmath_context *context, const hmath_value *value, hmath_value **out);

numbertheory.prime_factorization

Exact trial factorization of a positive integer. The budget counts attempted divisors (including repeated factors). One has an empty factorization. 

Int -> Integer -> Either MathError [(Integer,Int)]

hmath_status hmath_numbertheory_prime_factorization(hmath_context *context, const hmath_value *budget, const hmath_value *value, hmath_value **out);

numbertheory.partitions

Integer partitions in descending part order. Zero has one empty partition.

Int -> Either MathError [[Int]]

hmath_status hmath_numbertheory_partitions(hmath_context *context, const hmath_value *value, hmath_value **out);

special.sf_result

Construct or inspect the original immutable record; field order follows the source signature.

Double -> Double -> SFResult

hmath_status hmath_special_sf_result(hmath_context *context, const hmath_value *value, const hmath_value *error, hmath_value **out);

special.sf_value

Construct or inspect the original immutable record; field order follows the source signature.

SFResult -> Double

hmath_status hmath_special_sf_value(hmath_context *context, const hmath_value *value, hmath_value **out);

special.sf_error

Construct or inspect the original immutable record; field order follows the source signature.

SFResult -> Double

hmath_status hmath_special_sf_error(hmath_context *context, const hmath_value *value, hmath_value **out);