uni20::math Namespace Reference

Shared scalar math with native overloads and class-specific ADL customization. More...

Functions
template<class T > requires requires(T const& value) { math::abs(value) * math::abs(value); }
auto	abs_squared (T const &value)
	Square the magnitude, evaluating the scalar absolute value once.

Variables
constexpr detail::scalar_math::abs_fn	abs {}
	Absolute value or complex magnitude, preserving the selected scalar implementation.
constexpr detail::scalar_math::acos_fn	acos {}
	Inverse cosine in radians.
constexpr detail::scalar_math::acosh_fn	acosh {}
	Inverse hyperbolic cosine.
constexpr detail::scalar_math::acospi_fn	acospi {}
	Principal arccosine divided by pi.
constexpr detail::scalar_math::agm_fn	agm {}
	Nonnegative arithmetic-geometric mean.
constexpr detail::scalar_math::airy_ai_fn	airy_ai {}
	Real Airy Ai; native inputs retain their precision and full negative-axis phase.
constexpr detail::scalar_math::asin_fn	asin {}
	Inverse sine in radians.
constexpr detail::scalar_math::asinh_fn	asinh {}
	Inverse hyperbolic sine.
constexpr detail::scalar_math::asinpi_fn	asinpi {}
	Principal arcsine divided by pi.
constexpr detail::scalar_math::atan_fn	atan {}
	Inverse tangent in radians.
constexpr detail::scalar_math::atan2_fn	atan2 {}
	Quadrant-aware inverse tangent of y/x in radians.
constexpr detail::scalar_math::atan2pi_fn	atan2pi {}
	Quadrant-aware arctangent divided by pi.
constexpr detail::scalar_math::atanh_fn	atanh {}
	Inverse hyperbolic tangent.
constexpr detail::scalar_math::atanpi_fn	atanpi {}
	Principal arctangent divided by pi.
constexpr detail::scalar_math::bessel_j_fn	bessel_j {}
	Integer-order Bessel function of the first kind, with order first.
constexpr detail::scalar_math::bessel_y_fn	bessel_y {}
	Integer-order Bessel function of the second kind, with order first.
constexpr detail::scalar_math::beta_fn	beta {}
	Real Beta function.
constexpr detail::scalar_math::cbrt_fn	cbrt {}
	Real cube root, including negative arguments.
constexpr detail::scalar_math::ceil_fn	ceil {}
	Least integral value not less than the argument, in the scalar's result type.
constexpr detail::scalar_math::compound_fn	compound {}
	Integer power of one plus x, retaining the original increment.
constexpr detail::scalar_math::conj_fn	conj {}
	Complex conjugation; real and integral values retain their type.
constexpr detail::scalar_math::copysign_fn	copysign {}
	Copy the sign while retaining the magnitude operand type and precision.
constexpr detail::scalar_math::cos_fn	cos {}
	Cosine with scalar-specific precision handling.
constexpr detail::scalar_math::cosh_fn	cosh {}
	Hyperbolic cosine.
constexpr detail::scalar_math::cospi_fn	cospi {}
	Cosine of pi times x, with argument reduction before multiplication by pi.
constexpr detail::scalar_math::cot_fn	cot {}
	Reciprocal tangent, retaining the input type and precision.
constexpr detail::scalar_math::coth_fn	coth {}
	Reciprocal hyperbolic tangent, retaining the input type and precision.
constexpr detail::scalar_math::csc_fn	csc {}
	Reciprocal sine, retaining the input type and precision.
constexpr detail::scalar_math::csch_fn	csch {}
	Reciprocal hyperbolic sine, retaining the input type and precision.
constexpr detail::scalar_math::digamma_fn	digamma {}
	Logarithmic derivative of Gamma.
constexpr detail::scalar_math::dilog_real_fn	dilog_real {}
	Real part of the dilogarithm.
constexpr detail::scalar_math::erf_fn	erf {}
	Real error function.
constexpr detail::scalar_math::erfc_fn	erfc {}
	Complementary error function without subtractive cancellation.
constexpr detail::scalar_math::exp_fn	exp {}
	Natural exponential with scalar-specific precision handling.
constexpr detail::scalar_math::exp10_fn	exp10 {}
	Base-ten exponential.
constexpr detail::scalar_math::exp10m1_fn	exp10m1 {}
	Ten to the power x minus one, using the cancellation-safe provider.
constexpr detail::scalar_math::exp2_fn	exp2 {}
	Base-two exponential.
constexpr detail::scalar_math::exp2m1_fn	exp2m1 {}
	Two to the power x minus one, using the cancellation-safe provider.
constexpr detail::scalar_math::expint_fn	expint {}
	Real principal-value exponential integral Ei.
constexpr detail::scalar_math::expm1_fn	expm1 {}
	Natural exponential minus one, evaluated without subtractive cancellation.
constexpr detail::scalar_math::factorial_fn	factorial {}
	MPFR factorial at an explicit arithmetic state; use uni20::factorial<Real> for a typed result.
constexpr detail::scalar_math::fdim_fn	fdim {}
	Positive difference, preserving NaN propagation.
constexpr detail::scalar_math::floor_fn	floor {}
	Round toward negative infinity.
constexpr detail::scalar_math::fma_fn	fma {}
	Fused multiplication and addition with one final rounding.
constexpr detail::scalar_math::fmax_fn	fmax {}
	Maximum, preferring the numeric operand over a NaN.
constexpr detail::scalar_math::fmin_fn	fmin {}
	Minimum, preferring the numeric operand over a NaN.
constexpr detail::scalar_math::fmod_fn	fmod {}
	Remainder using a quotient truncated toward zero.
constexpr detail::scalar_math::frexp_fn	frexp {}
	Binary fraction and exponent as an owning result.
constexpr detail::scalar_math::hypot_fn	hypot {}
	Euclidean length with scalar-specific overflow and underflow handling.
constexpr detail::scalar_math::ilogb_fn	ilogb {}
	Binary exponent of a finite nonzero value; throws otherwise.
constexpr detail::scalar_math::imag_fn	imag {}
	Read the imaginary component by value; real zero retains the input's type and precision.
constexpr detail::scalar_math::isfinite_fn	isfinite {}
	Whether a real scalar is finite.
constexpr detail::scalar_math::isinf_fn	isinf {}
	Whether a real scalar is infinite.
constexpr detail::scalar_math::isnan_fn	isnan {}
	Whether a real scalar is NaN.
constexpr detail::scalar_math::ldexp_fn	ldexp {}
	Multiply by a power of two using the scalar's exponent interface.
constexpr detail::scalar_math::lgamma_fn	lgamma {}
	Logarithm of the absolute Gamma function; native providers are reentrant.
constexpr detail::scalar_math::lgamma_sign_fn	lgamma_sign {}
	Log-absolute-Gamma and its sign as owning values.
constexpr detail::scalar_math::log_fn	log {}
	Natural logarithm with scalar-specific precision handling.
constexpr detail::scalar_math::log10_fn	log10 {}
	Base-ten logarithm.
constexpr detail::scalar_math::log10p1_fn	log10p1 {}
	Base-ten logarithm of one plus x, without rounding the sum first.
constexpr detail::scalar_math::log1p_fn	log1p {}
	Natural logarithm of one plus the argument, retaining small increments.
constexpr detail::scalar_math::log2_fn	log2 {}
	Base-two logarithm where supplied by the scalar implementation.
constexpr detail::scalar_math::log2p1_fn	log2p1 {}
	Base-two logarithm of one plus x, without rounding the sum first.
constexpr detail::scalar_math::modf_fn	modf {}
	Signed fractional and integral parts as an owning result.
constexpr detail::scalar_math::next_down_fn	next_down {}
	Adjacent value toward negative infinity.
constexpr detail::scalar_math::next_up_fn	next_up {}
	Adjacent value toward positive infinity.
constexpr detail::scalar_math::nextafter_fn	nextafter {}
	Adjacent value on the first operand grid toward the direction operand.
constexpr detail::scalar_math::pow_fn	pow {}
	Power with the selected scalar's domain, exactness and precision rules.
constexpr detail::scalar_math::pown_fn	pown {}
	Integer power with scalar-specific rounding.
constexpr detail::scalar_math::real_fn	real {}
	Read the real component by value; real and integral scalars retain their type.
constexpr detail::scalar_math::remainder_fn	remainder {}
	Remainder using the nearest-even integer quotient.
constexpr detail::scalar_math::remquo_fn	remquo {}
	Nearest-even remainder and signed low three quotient bits.
constexpr detail::scalar_math::rootn_fn	rootn {}
	Real integer-order root; negative orders give reciprocal roots.
constexpr detail::scalar_math::round_fn	round {}
	Round to nearest integer with ties away from zero.
constexpr detail::scalar_math::round_even_fn	round_even {}
	Nearest integer with ties to even.
constexpr detail::scalar_math::scalbn_fn	scalbn {}
	Binary scaling with a signed 64-bit exponent.
constexpr detail::scalar_math::sec_fn	sec {}
	Reciprocal cosine, retaining the input type and precision.
constexpr detail::scalar_math::sech_fn	sech {}
	Reciprocal hyperbolic cosine, retaining the input type and precision.
constexpr detail::scalar_math::signbit_fn	signbit {}
	Inspect the sign, including approximate negative zero.
constexpr detail::scalar_math::sin_fn	sin {}
	Sine with scalar-specific precision handling.
constexpr detail::scalar_math::sincos_fn	sincos {}
	Sine and cosine at one input.
constexpr detail::scalar_math::sinh_fn	sinh {}
	Hyperbolic sine.
constexpr detail::scalar_math::sinhcosh_fn	sinhcosh {}
	Hyperbolic sine and cosine at one input.
constexpr detail::scalar_math::sinpi_fn	sinpi {}
	Sine of pi times x, with argument reduction before multiplication by pi.
constexpr detail::scalar_math::sqrt_fn	sqrt {}
	Square root; exact inputs requiring approximation need an explicit finite precision.
constexpr detail::scalar_math::tan_fn	tan {}
	Tangent in radians.
constexpr detail::scalar_math::tanh_fn	tanh {}
	Hyperbolic tangent.
constexpr detail::scalar_math::tanpi_fn	tanpi {}
	Tangent of pi times x, with argument reduction before multiplication by pi.
constexpr detail::scalar_math::tgamma_fn	tgamma {}
	Real Gamma function.
constexpr detail::scalar_math::trunc_fn	trunc {}
	Round toward zero.
constexpr detail::scalar_math::upper_gamma_fn	upper_gamma {}
	Upper unregularized incomplete Gamma, with shape and lower integration endpoint.
constexpr detail::scalar_math::zeta_fn	zeta {}
	Real Riemann zeta with native Euler-Maclaurin evaluation and reflection.

Detailed Description

Shared scalar math with native overloads and class-specific ADL customization.

Arguments are read through const references. Unsupported calls are constrained out; class scalars cannot obtain support merely by converting to a native floating type. Scalar overloads retain their exactness and precision rules, including trailing Precision arguments where supported. This interface currently targets host execution.

Function Documentation

abs_squared()

template<class T >
requires requires(T const& value) { math::abs(value) * math::abs(value); }

auto uni20::math::abs_squared

(

T const &

value

)

Square the magnitude, evaluating the scalar absolute value once.

This does not provide overflow scaling or extra working precision.

Variable Documentation

abs

constexpr detail::scalar_math::abs_fn uni20::math::abs {}

inlineconstexpr

Absolute value or complex magnitude, preserving the selected scalar implementation.

acos

constexpr detail::scalar_math::acos_fn uni20::math::acos {}

inlineconstexpr

Inverse cosine in radians.

acosh

constexpr detail::scalar_math::acosh_fn uni20::math::acosh {}

inlineconstexpr

Inverse hyperbolic cosine.

acospi

constexpr detail::scalar_math::acospi_fn uni20::math::acospi {}

inlineconstexpr

Principal arccosine divided by pi.

agm

constexpr detail::scalar_math::agm_fn uni20::math::agm {}

inlineconstexpr

Nonnegative arithmetic-geometric mean.

Native arguments have the same real type. Zero with a finite argument gives +0; zero with infinity and other negative arguments give NaN. Native evaluation uses scaled iteration; MPFR retains its scalar precision contract.

airy_ai

constexpr detail::scalar_math::airy_ai_fn uni20::math::airy_ai {}

inlineconstexpr

Real Airy Ai; native inputs retain their precision and full negative-axis phase.

MPFR inputs retain their provider-specific range and working-precision rules.

asin

constexpr detail::scalar_math::asin_fn uni20::math::asin {}

inlineconstexpr

Inverse sine in radians.

asinh

constexpr detail::scalar_math::asinh_fn uni20::math::asinh {}

inlineconstexpr

Inverse hyperbolic sine.

asinpi

constexpr detail::scalar_math::asinpi_fn uni20::math::asinpi {}

inlineconstexpr

Principal arcsine divided by pi.

atan

constexpr detail::scalar_math::atan_fn uni20::math::atan {}

inlineconstexpr

Inverse tangent in radians.

atan2

constexpr detail::scalar_math::atan2_fn uni20::math::atan2 {}

inlineconstexpr

Quadrant-aware inverse tangent of y/x in radians.

atan2pi

constexpr detail::scalar_math::atan2pi_fn uni20::math::atan2pi {}

inlineconstexpr

Quadrant-aware arctangent divided by pi.

atanh

constexpr detail::scalar_math::atanh_fn uni20::math::atanh {}

inlineconstexpr

Inverse hyperbolic tangent.

atanpi

constexpr detail::scalar_math::atanpi_fn uni20::math::atanpi {}

inlineconstexpr

Principal arctangent divided by pi.

bessel_j

constexpr detail::scalar_math::bessel_j_fn uni20::math::bessel_j {}

inlineconstexpr

Integer-order Bessel function of the first kind, with order first.

Native absolute orders must fit int; other scalar providers retain their own limits.

Exceptions

std::out_of_range

if the order cannot be represented by the selected provider.

bessel_y

constexpr detail::scalar_math::bessel_y_fn uni20::math::bessel_y {}

inlineconstexpr

Integer-order Bessel function of the second kind, with order first.

Native absolute orders must fit int; other scalar providers retain their own limits.

Exceptions

std::out_of_range

if the order cannot be represented by the selected provider.

beta

constexpr detail::scalar_math::beta_fn uni20::math::beta {}

inlineconstexpr

Real Beta function.

Native arguments must have the same real type and both be positive; configured binary128 uses a scaled native Gamma-ratio algorithm. Advertised standard providers remain selected for float/double/long double. See docs/tensor/native_beta.md for fallback accuracy and range behavior.

Note

Affected libstdc++/glibc providers retain an internal signgam data race; see docs/tensor/native_special_functions.md for the provider limitation.

cbrt

constexpr detail::scalar_math::cbrt_fn uni20::math::cbrt {}

inlineconstexpr

Real cube root, including negative arguments.

ceil

constexpr detail::scalar_math::ceil_fn uni20::math::ceil {}

inlineconstexpr

Least integral value not less than the argument, in the scalar's result type.

compound

constexpr detail::scalar_math::compound_fn uni20::math::compound {}

inlineconstexpr

Integer power of one plus x, retaining the original increment.

Requires x >= -1 and a checked signed-64-bit exponent (not bool). Native evaluation uses a typed provider or a guarded expansion; it does not promise correct rounding.

conj

constexpr detail::scalar_math::conj_fn uni20::math::conj {}

inlineconstexpr

Complex conjugation; real and integral values retain their type.

copysign

constexpr detail::scalar_math::copysign_fn uni20::math::copysign {}

inlineconstexpr

Copy the sign while retaining the magnitude operand type and precision.

cos

constexpr detail::scalar_math::cos_fn uni20::math::cos {}

inlineconstexpr

Cosine with scalar-specific precision handling.

cosh

constexpr detail::scalar_math::cosh_fn uni20::math::cosh {}

inlineconstexpr

Hyperbolic cosine.

cospi

constexpr detail::scalar_math::cospi_fn uni20::math::cospi {}

inlineconstexpr

Cosine of pi times x, with argument reduction before multiplication by pi.

cot

constexpr detail::scalar_math::cot_fn uni20::math::cot {}

inlineconstexpr

Reciprocal tangent, retaining the input type and precision.

coth

constexpr detail::scalar_math::coth_fn uni20::math::coth {}

inlineconstexpr

Reciprocal hyperbolic tangent, retaining the input type and precision.

csc

constexpr detail::scalar_math::csc_fn uni20::math::csc {}

inlineconstexpr

Reciprocal sine, retaining the input type and precision.

csch

constexpr detail::scalar_math::csch_fn uni20::math::csch {}

inlineconstexpr

Reciprocal hyperbolic sine, retaining the input type and precision.

digamma

constexpr detail::scalar_math::digamma_fn uni20::math::digamma {}

inlineconstexpr

Logarithmic derivative of Gamma.

Negative integer poles give NaN; signed zero gives an infinity of the opposite sign. Native evaluation uses recurrence and scaled-phase reflection; MPFR retains its scalar precision contract. See docs/tensor/native_digamma.md for absolute/relative accuracy targets near zeros and poles.

dilog_real

constexpr detail::scalar_math::dilog_real_fn uni20::math::dilog_real {}

inlineconstexpr

Real part of the dilogarithm.

Native real arguments use a bounded series with real continuation on x>1. Signed zeros are preserved; both infinite arguments give negative infinity.

erf

constexpr detail::scalar_math::erf_fn uni20::math::erf {}

inlineconstexpr

Real error function.

erfc

constexpr detail::scalar_math::erfc_fn uni20::math::erfc {}

inlineconstexpr

Complementary error function without subtractive cancellation.

exp

constexpr detail::scalar_math::exp_fn uni20::math::exp {}

inlineconstexpr

Natural exponential with scalar-specific precision handling.

exp10

constexpr detail::scalar_math::exp10_fn uni20::math::exp10 {}

inlineconstexpr

Base-ten exponential.

exp10m1

constexpr detail::scalar_math::exp10m1_fn uni20::math::exp10m1 {}

inlineconstexpr

Ten to the power x minus one, using the cancellation-safe provider.

exp2

constexpr detail::scalar_math::exp2_fn uni20::math::exp2 {}

inlineconstexpr

Base-two exponential.

exp2m1

constexpr detail::scalar_math::exp2m1_fn uni20::math::exp2m1 {}

inlineconstexpr

Two to the power x minus one, using the cancellation-safe provider.

expint

constexpr detail::scalar_math::expint_fn uni20::math::expint {}

inlineconstexpr

Real principal-value exponential integral Ei.

Native evaluation uses compensated series, a positive E1 continued fraction and positive-Ei asymptotics, with scaling at range boundaries.

expm1

constexpr detail::scalar_math::expm1_fn uni20::math::expm1 {}

inlineconstexpr

Natural exponential minus one, evaluated without subtractive cancellation.

factorial

constexpr detail::scalar_math::factorial_fn uni20::math::factorial {}

inlineconstexpr

MPFR factorial at an explicit arithmetic state; use uni20::factorial<Real> for a typed result.

fdim

constexpr detail::scalar_math::fdim_fn uni20::math::fdim {}

inlineconstexpr

Positive difference, preserving NaN propagation.

floor

constexpr detail::scalar_math::floor_fn uni20::math::floor {}

inlineconstexpr

Round toward negative infinity.

fma

constexpr detail::scalar_math::fma_fn uni20::math::fma {}

inlineconstexpr

Fused multiplication and addition with one final rounding.

fmax

constexpr detail::scalar_math::fmax_fn uni20::math::fmax {}

inlineconstexpr

Maximum, preferring the numeric operand over a NaN.

fmin

constexpr detail::scalar_math::fmin_fn uni20::math::fmin {}

inlineconstexpr

Minimum, preferring the numeric operand over a NaN.

fmod

constexpr detail::scalar_math::fmod_fn uni20::math::fmod {}

inlineconstexpr

Remainder using a quotient truncated toward zero.

frexp

constexpr detail::scalar_math::frexp_fn uni20::math::frexp {}

inlineconstexpr

Binary fraction and exponent as an owning result.

hypot

constexpr detail::scalar_math::hypot_fn uni20::math::hypot {}

inlineconstexpr

Euclidean length with scalar-specific overflow and underflow handling.

ilogb

constexpr detail::scalar_math::ilogb_fn uni20::math::ilogb {}

inlineconstexpr

Binary exponent of a finite nonzero value; throws otherwise.

imag

constexpr detail::scalar_math::imag_fn uni20::math::imag {}

inlineconstexpr

Read the imaginary component by value; real zero retains the input's type and precision.

isfinite

constexpr detail::scalar_math::isfinite_fn uni20::math::isfinite {}

inlineconstexpr

Whether a real scalar is finite.

isinf

constexpr detail::scalar_math::isinf_fn uni20::math::isinf {}

inlineconstexpr

Whether a real scalar is infinite.

isnan

constexpr detail::scalar_math::isnan_fn uni20::math::isnan {}

inlineconstexpr

Whether a real scalar is NaN.

ldexp

constexpr detail::scalar_math::ldexp_fn uni20::math::ldexp {}

inlineconstexpr

Multiply by a power of two using the scalar's exponent interface.

lgamma

constexpr detail::scalar_math::lgamma_fn uni20::math::lgamma {}

inlineconstexpr

Logarithm of the absolute Gamma function; native providers are reentrant.

lgamma_sign

constexpr detail::scalar_math::lgamma_sign_fn uni20::math::lgamma_sign {}

inlineconstexpr

Log-absolute-Gamma and its sign as owning values.

Undefined signs are zero; signed zero retains its one-sided pole sign.

log

constexpr detail::scalar_math::log_fn uni20::math::log {}

inlineconstexpr

Natural logarithm with scalar-specific precision handling.

log10

constexpr detail::scalar_math::log10_fn uni20::math::log10 {}

inlineconstexpr

Base-ten logarithm.

log10p1

constexpr detail::scalar_math::log10p1_fn uni20::math::log10p1 {}

inlineconstexpr

Base-ten logarithm of one plus x, without rounding the sum first.

log1p

constexpr detail::scalar_math::log1p_fn uni20::math::log1p {}

inlineconstexpr

Natural logarithm of one plus the argument, retaining small increments.

log2

constexpr detail::scalar_math::log2_fn uni20::math::log2 {}

inlineconstexpr

Base-two logarithm where supplied by the scalar implementation.

log2p1

constexpr detail::scalar_math::log2p1_fn uni20::math::log2p1 {}

inlineconstexpr

Base-two logarithm of one plus x, without rounding the sum first.

modf

constexpr detail::scalar_math::modf_fn uni20::math::modf {}

inlineconstexpr

Signed fractional and integral parts as an owning result.

next_down

constexpr detail::scalar_math::next_down_fn uni20::math::next_down {}

inlineconstexpr

Adjacent value toward negative infinity.

next_up

constexpr detail::scalar_math::next_up_fn uni20::math::next_up {}

inlineconstexpr

Adjacent value toward positive infinity.

nextafter

constexpr detail::scalar_math::nextafter_fn uni20::math::nextafter {}

inlineconstexpr

Adjacent value on the first operand grid toward the direction operand.

pow

constexpr detail::scalar_math::pow_fn uni20::math::pow {}

inlineconstexpr

Power with the selected scalar's domain, exactness and precision rules.

pown

constexpr detail::scalar_math::pown_fn uni20::math::pown {}

inlineconstexpr

Integer power with scalar-specific rounding.

real

constexpr detail::scalar_math::real_fn uni20::math::real {}

inlineconstexpr

Read the real component by value; real and integral scalars retain their type.

remainder

constexpr detail::scalar_math::remainder_fn uni20::math::remainder {}

inlineconstexpr

Remainder using the nearest-even integer quotient.

remquo

constexpr detail::scalar_math::remquo_fn uni20::math::remquo {}

inlineconstexpr

Nearest-even remainder and signed low three quotient bits.

rootn

constexpr detail::scalar_math::rootn_fn uni20::math::rootn {}

inlineconstexpr

Real integer-order root; negative orders give reciprocal roots.

round

constexpr detail::scalar_math::round_fn uni20::math::round {}

inlineconstexpr

Round to nearest integer with ties away from zero.

round_even

constexpr detail::scalar_math::round_even_fn uni20::math::round_even {}

inlineconstexpr

Nearest integer with ties to even.

scalbn

constexpr detail::scalar_math::scalbn_fn uni20::math::scalbn {}

inlineconstexpr

Binary scaling with a signed 64-bit exponent.

sec

constexpr detail::scalar_math::sec_fn uni20::math::sec {}

inlineconstexpr

Reciprocal cosine, retaining the input type and precision.

sech

constexpr detail::scalar_math::sech_fn uni20::math::sech {}

inlineconstexpr

Reciprocal hyperbolic cosine, retaining the input type and precision.

signbit

constexpr detail::scalar_math::signbit_fn uni20::math::signbit {}

inlineconstexpr

Inspect the sign, including approximate negative zero.

sin

constexpr detail::scalar_math::sin_fn uni20::math::sin {}

inlineconstexpr

Sine with scalar-specific precision handling.

sincos

constexpr detail::scalar_math::sincos_fn uni20::math::sincos {}

inlineconstexpr

Sine and cosine at one input.

sinh

constexpr detail::scalar_math::sinh_fn uni20::math::sinh {}

inlineconstexpr

Hyperbolic sine.

sinhcosh

constexpr detail::scalar_math::sinhcosh_fn uni20::math::sinhcosh {}

inlineconstexpr

Hyperbolic sine and cosine at one input.

sinpi

constexpr detail::scalar_math::sinpi_fn uni20::math::sinpi {}

inlineconstexpr

Sine of pi times x, with argument reduction before multiplication by pi.

sqrt

constexpr detail::scalar_math::sqrt_fn uni20::math::sqrt {}

inlineconstexpr

Square root; exact inputs requiring approximation need an explicit finite precision.

tan

constexpr detail::scalar_math::tan_fn uni20::math::tan {}

inlineconstexpr

Tangent in radians.

tanh

constexpr detail::scalar_math::tanh_fn uni20::math::tanh {}

inlineconstexpr

Hyperbolic tangent.

tanpi

constexpr detail::scalar_math::tanpi_fn uni20::math::tanpi {}

inlineconstexpr

Tangent of pi times x, with argument reduction before multiplication by pi.

tgamma

constexpr detail::scalar_math::tgamma_fn uni20::math::tgamma {}

inlineconstexpr

Real Gamma function.

trunc

constexpr detail::scalar_math::trunc_fn uni20::math::trunc {}

inlineconstexpr

Round toward zero.

upper_gamma

constexpr detail::scalar_math::upper_gamma_fn uni20::math::upper_gamma {}

inlineconstexpr

Upper unregularized incomplete Gamma, with shape and lower integration endpoint.

Native arguments must have matching real types. For a finite shape and positive endpoint, this is the positive integral from x to infinity; negative shapes are supported. At x=0 use the analytic Gamma endpoint. See docs/tensor/native_upper_gamma.md for domain and accuracy contracts. MPFR retains its scalar precision contract.

zeta

constexpr detail::scalar_math::zeta_fn uni20::math::zeta {}

inlineconstexpr

Real Riemann zeta with native Euler-Maclaurin evaluation and reflection.

Native arguments retain their type, including binary128. Exact negative even integers give positive zero; the pole at one gives positive infinity.