Uni20
Asynchronous tensor and runtime library.
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math.hpp
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1#pragma once
2
3#include "detail/native_agm_math.hpp"
4#include "detail/native_airy_math.hpp"
5#include "detail/native_compound_math.hpp"
6#include "detail/native_digamma_math.hpp"
7#include "detail/native_dilog_math.hpp"
8#include "detail/native_exponential_math.hpp"
9#include "detail/native_expint_math.hpp"
10#include "detail/native_math.hpp"
11#include "detail/native_pi_math.hpp"
12#include "detail/native_reciprocal_math.hpp"
13#include "detail/native_upper_gamma_math.hpp"
14#include "detail/native_special_math.hpp"
15#include "factorial.hpp"
16#include "math_constants.hpp"
17#include "numeric_limits.hpp"
18#include "runtime_precision.hpp"
19#include "scalar_concepts.hpp"
20#if UNI20_HAS_MPREAL
21#include "mpreal.hpp"
22#endif
23#if UNI20_HAS_MPREAL
24#include "mpcomplex.hpp"
25#endif
26#include <cmath>
27#include <complex>
28#include <numeric>
29#include <type_traits>
30#include <utility>
31
32namespace uni20
33{
34
50template <class T> constexpr bool is_exact(detail::standard_complex<T> const& x)
51{
52 return uni20::is_exact(x.real()) && uni20::is_exact(x.imag());
53}
54
61template <typename T> inline constexpr bool has_trivial_conj = Real<T> || Integer<T>;
62
70template <typename T> uni20::complex<T> conj(detail::standard_complex<T> x) { return std::conj(x); }
71
79template <Real R> constexpr R conj(R const& x) { return x; }
80
88template <Integer I> constexpr I conj(I const& x) { return x; }
89
98template <Scalar S> constexpr auto herm(S x) { return uni20::conj(x); }
99
100namespace detail
101{
102template <typename T, typename = void> struct numeric_limits_has_infinity : std::false_type
103{};
104
105template <typename T>
106struct numeric_limits_has_infinity<
107 T, std::void_t<decltype(uni20::numeric_limits<T>::has_infinity), decltype(uni20::numeric_limits<T>::infinity())>>
108 : std::bool_constant<static_cast<bool>(uni20::numeric_limits<T>::has_infinity)>
109{};
110
111template <typename T>
112inline constexpr bool numeric_limits_has_infinity_v = numeric_limits_has_infinity<std::remove_cvref_t<T>>::value;
113} // namespace detail
114
121template <Integer I> constexpr bool isfinite(I const& x) noexcept
122{
123 (void)x;
124 return true;
125}
126
135template <Real R> constexpr bool isfinite(R const& x)
136{
137 using value_type = std::remove_cvref_t<R>;
138#if UNI20_HAS_MPREAL
139 if constexpr (std::same_as<value_type, mpreal>) return uni20::isfinite(x);
140#endif
141 if (!(x == x))
142 {
143 return false;
144 }
145 if constexpr (detail::numeric_limits_has_infinity_v<value_type>)
146 {
147 auto const infinity = uni20::numeric_limits<value_type>::infinity();
148 return x != infinity && x != -infinity;
149 }
150 else
151 {
152 return true;
153 }
154}
155
161template <Complex C> constexpr bool isfinite(C const& z)
162{
163 return uni20::isfinite(z.real()) && uni20::isfinite(z.imag());
164}
165
173template <typename T> constexpr T& real(detail::standard_complex<T>& z) noexcept { return reinterpret_cast<T*>(&z)[0]; }
174
175using std::real;
176
184template <typename T> constexpr T& imag(detail::standard_complex<T>& z) noexcept { return reinterpret_cast<T*>(&z)[1]; }
185
186using std::imag;
187
192template <Scalar S, class Value>
193 requires(std::constructible_from<S, Value const&> ||
194 requires(S const& exemplar, Value const& value) { S(value, exemplar.precision()); })
195[[nodiscard]] constexpr auto scalar_like(S const& exemplar, Value const& value) -> S
196{
197 if constexpr (requires { S(value, exemplar.precision()); })
198 return S(value, exemplar.precision());
199 else
200 return S(value);
201}
202
203namespace detail::scalar_math
204{
205template <class T>
206concept native_argument =
207 std::integral<T> || std::same_as<T, float> || std::same_as<T, double> || std::same_as<T, long double>
208#if UNI20_HAS_FLOAT128
209 || std::same_as<T, uni20::float128>
210#endif
211 ;
212
213// A missing extension overload must not be filled by a narrower native type.
214// Integer promotion follows the selected standard operation.
215template <class Result, class Arg> consteval bool preserves_real_precision()
216{
217 if constexpr (!Real<Arg>)
218 return true;
219 else if constexpr (Real<Result>)
220 return numeric_limits<Result>::digits() >= numeric_limits<Arg>::digits() &&
221 numeric_limits<Result>::max_exponent >= numeric_limits<Arg>::max_exponent;
222 else
223 return false;
224}
225
226// The deleted exact-match fallback rejects conversion-only classes, even when
227// an associated namespace supplies standard floating overloads. Actual scalar
228// overloads (including constrained templates and hidden friends) outrank it.
229#define UNI20_SCALAR_MATH_ADL(NAME) \
230 namespace NAME##_adl \
231 { \
232 template <class... Args> void NAME(Args const&...) = delete; \
233 template <class... Args> \
234 constexpr auto call(Args const&... args) noexcept(noexcept(NAME(args...))) -> decltype(NAME(args...)) \
235 { \
236 return NAME(args...); \
237 } \
238 }
239
240#define UNI20_SCALAR_MATH_DISPATCH_TO(NAME, NATIVE, RESULT_CHECK) \
241 UNI20_SCALAR_MATH_ADL(NAME) \
242 struct NAME##_fn \
243 { \
244 template <class... Args> \
245 constexpr auto operator()(Args const&... args) const \
246 noexcept(noexcept(NAME##_adl::call(args...))) -> decltype(NAME##_adl::call(args...)) \
247 { \
248 return NAME##_adl::call(args...); \
249 } \
250 template <class... Args> \
251 requires((native_argument<Args> && ...) && !requires(Args const&... args) { NAME##_adl::call(args...); }) \
252 constexpr auto operator()(Args const&... args) const \
253 noexcept(noexcept(NATIVE::NAME(args...))) -> decltype(NATIVE::NAME(args...)) \
254 requires((RESULT_CHECK<decltype(NATIVE::NAME(args...)), Args>()) && ...) \
255 { \
256 return NATIVE::NAME(args...); \
257 } \
258 };
259
260template <class Result, class Arg> consteval bool predicate_result() { return std::same_as<Result, bool>; }
261template <class Result, class Arg> consteval bool preserves_components()
262{
263 return preserves_real_precision<typename Result::value_type, Arg>();
264}
265// These operations explicitly retain the first argument's type, or return an
266// integer property. Their native implementations constrain each operand.
267template <class Result, class Arg> consteval bool utility_result() { return true; }
268// Provider-only functions have no native fallback. Availability is determined
269// solely by an actual overload in the scalar's associated namespace.
270#define UNI20_SCALAR_MATH_DISPATCH_ADL_ONLY(NAME) \
271 UNI20_SCALAR_MATH_ADL(NAME) \
272 struct NAME##_fn \
273 { \
274 template <class... Args> \
275 constexpr auto operator()(Args const&... args) const \
276 noexcept(noexcept(NAME##_adl::call(args...))) -> decltype(NAME##_adl::call(args...)) \
277 { \
278 return NAME##_adl::call(args...); \
279 } \
280 };
281
282#define UNI20_SCALAR_MATH_DISPATCH_POLICY(NAME, CHECK) UNI20_SCALAR_MATH_DISPATCH_TO(NAME, std, CHECK)
283#define UNI20_SCALAR_MATH_DISPATCH(NAME) UNI20_SCALAR_MATH_DISPATCH_POLICY(NAME, preserves_real_precision)
284
285UNI20_SCALAR_MATH_DISPATCH(abs)
286UNI20_SCALAR_MATH_DISPATCH(sqrt)
287UNI20_SCALAR_MATH_DISPATCH(pow)
288UNI20_SCALAR_MATH_DISPATCH(exp)
289UNI20_SCALAR_MATH_DISPATCH(log)
290UNI20_SCALAR_MATH_DISPATCH(log2)
291UNI20_SCALAR_MATH_DISPATCH(sin)
292UNI20_SCALAR_MATH_DISPATCH(cos)
293UNI20_SCALAR_MATH_DISPATCH(ceil)
294UNI20_SCALAR_MATH_DISPATCH_TO(ldexp, native_math, preserves_real_precision)
295UNI20_SCALAR_MATH_DISPATCH(cbrt)
296UNI20_SCALAR_MATH_DISPATCH(exp2)
297UNI20_SCALAR_MATH_DISPATCH(expm1)
298UNI20_SCALAR_MATH_DISPATCH(log10)
299UNI20_SCALAR_MATH_DISPATCH(log1p)
300UNI20_SCALAR_MATH_DISPATCH(asin)
301UNI20_SCALAR_MATH_DISPATCH(acos)
302UNI20_SCALAR_MATH_DISPATCH(sinh)
303UNI20_SCALAR_MATH_DISPATCH(cosh)
304UNI20_SCALAR_MATH_DISPATCH(tanh)
305UNI20_SCALAR_MATH_DISPATCH(asinh)
306UNI20_SCALAR_MATH_DISPATCH(acosh)
307UNI20_SCALAR_MATH_DISPATCH(atanh)
308UNI20_SCALAR_MATH_DISPATCH(tan)
309UNI20_SCALAR_MATH_DISPATCH(atan)
310UNI20_SCALAR_MATH_DISPATCH(atan2)
311UNI20_SCALAR_MATH_DISPATCH(hypot)
312UNI20_SCALAR_MATH_DISPATCH(floor)
313UNI20_SCALAR_MATH_DISPATCH(trunc)
314UNI20_SCALAR_MATH_DISPATCH(round)
315UNI20_SCALAR_MATH_DISPATCH_POLICY(isfinite, predicate_result)
316UNI20_SCALAR_MATH_DISPATCH_POLICY(isnan, predicate_result)
317UNI20_SCALAR_MATH_DISPATCH_POLICY(isinf, predicate_result)
318UNI20_SCALAR_MATH_DISPATCH_POLICY(signbit, predicate_result)
319UNI20_SCALAR_MATH_DISPATCH(fma)
320UNI20_SCALAR_MATH_DISPATCH(fdim)
321UNI20_SCALAR_MATH_DISPATCH_TO(fmin, native_math, preserves_real_precision)
322UNI20_SCALAR_MATH_DISPATCH_TO(fmax, native_math, preserves_real_precision)
323UNI20_SCALAR_MATH_DISPATCH(fmod)
324UNI20_SCALAR_MATH_DISPATCH(remainder)
325UNI20_SCALAR_MATH_DISPATCH_TO(round_even, native_math, preserves_real_precision)
326UNI20_SCALAR_MATH_DISPATCH_TO(pown, native_math, preserves_real_precision)
327UNI20_SCALAR_MATH_DISPATCH_TO(rootn, native_math, preserves_real_precision)
328UNI20_SCALAR_MATH_DISPATCH_TO(scalbn, native_math, preserves_real_precision)
329UNI20_SCALAR_MATH_DISPATCH_TO(frexp, native_math, preserves_components)
330UNI20_SCALAR_MATH_DISPATCH_TO(modf, native_math, preserves_components)
331UNI20_SCALAR_MATH_DISPATCH_TO(remquo, native_math, preserves_components)
332UNI20_SCALAR_MATH_DISPATCH_TO(sincos, native_math, preserves_components)
333UNI20_SCALAR_MATH_DISPATCH_TO(sinhcosh, native_math, preserves_components)
334UNI20_SCALAR_MATH_DISPATCH_TO(ilogb, native_math, utility_result)
335UNI20_SCALAR_MATH_DISPATCH_TO(copysign, native_math, utility_result)
336UNI20_SCALAR_MATH_DISPATCH_TO(nextafter, native_math, utility_result)
337UNI20_SCALAR_MATH_DISPATCH_TO(next_up, native_math, preserves_real_precision)
338UNI20_SCALAR_MATH_DISPATCH_TO(next_down, native_math, preserves_real_precision)
339UNI20_SCALAR_MATH_DISPATCH(tgamma)
340UNI20_SCALAR_MATH_DISPATCH(erf)
341UNI20_SCALAR_MATH_DISPATCH(erfc)
342UNI20_SCALAR_MATH_DISPATCH_TO(lgamma, native_math, preserves_real_precision)
343UNI20_SCALAR_MATH_DISPATCH_TO(digamma, native_math, preserves_real_precision)
344UNI20_SCALAR_MATH_DISPATCH_TO(beta, native_math, preserves_real_precision)
345UNI20_SCALAR_MATH_DISPATCH_TO(upper_gamma, native_math, preserves_real_precision)
346UNI20_SCALAR_MATH_DISPATCH_TO(zeta, native_math, preserves_real_precision)
347UNI20_SCALAR_MATH_DISPATCH_TO(expint, native_math, preserves_real_precision)
348UNI20_SCALAR_MATH_DISPATCH_TO(dilog_real, native_math, preserves_real_precision)
349UNI20_SCALAR_MATH_DISPATCH_TO(bessel_j, native_math, preserves_real_precision)
350UNI20_SCALAR_MATH_DISPATCH_TO(bessel_y, native_math, preserves_real_precision)
351UNI20_SCALAR_MATH_DISPATCH_TO(airy_ai, native_math, preserves_real_precision)
352UNI20_SCALAR_MATH_DISPATCH_TO(agm, native_math, preserves_real_precision)
353UNI20_SCALAR_MATH_DISPATCH_ADL_ONLY(factorial)
354UNI20_SCALAR_MATH_DISPATCH_TO(lgamma_sign, native_math, preserves_components)
355UNI20_SCALAR_MATH_DISPATCH_TO(exp10, native_math, preserves_real_precision)
356UNI20_SCALAR_MATH_DISPATCH_TO(exp2m1, native_math, preserves_real_precision)
357UNI20_SCALAR_MATH_DISPATCH_TO(exp10m1, native_math, preserves_real_precision)
358UNI20_SCALAR_MATH_DISPATCH_TO(log2p1, native_math, preserves_real_precision)
359UNI20_SCALAR_MATH_DISPATCH_TO(log10p1, native_math, preserves_real_precision)
360UNI20_SCALAR_MATH_DISPATCH_TO(sinpi, native_math, preserves_real_precision)
361UNI20_SCALAR_MATH_DISPATCH_TO(cospi, native_math, preserves_real_precision)
362UNI20_SCALAR_MATH_DISPATCH_TO(tanpi, native_math, preserves_real_precision)
363UNI20_SCALAR_MATH_DISPATCH_TO(asinpi, native_math, preserves_real_precision)
364UNI20_SCALAR_MATH_DISPATCH_TO(acospi, native_math, preserves_real_precision)
365UNI20_SCALAR_MATH_DISPATCH_TO(atanpi, native_math, preserves_real_precision)
366UNI20_SCALAR_MATH_DISPATCH_TO(sec, native_math, preserves_real_precision)
367UNI20_SCALAR_MATH_DISPATCH_TO(csc, native_math, preserves_real_precision)
368UNI20_SCALAR_MATH_DISPATCH_TO(cot, native_math, preserves_real_precision)
369UNI20_SCALAR_MATH_DISPATCH_TO(sech, native_math, preserves_real_precision)
370UNI20_SCALAR_MATH_DISPATCH_TO(csch, native_math, preserves_real_precision)
371UNI20_SCALAR_MATH_DISPATCH_TO(coth, native_math, preserves_real_precision)
372UNI20_SCALAR_MATH_DISPATCH_TO(atan2pi, native_math, preserves_real_precision)
373UNI20_SCALAR_MATH_DISPATCH_TO(compound, native_math, preserves_real_precision)
374#undef UNI20_SCALAR_MATH_DISPATCH_ADL_ONLY
375#undef UNI20_SCALAR_MATH_DISPATCH_TO
376#undef UNI20_SCALAR_MATH_DISPATCH_POLICY
377#undef UNI20_SCALAR_MATH_DISPATCH
378
379UNI20_SCALAR_MATH_ADL(real)
380UNI20_SCALAR_MATH_ADL(imag)
381UNI20_SCALAR_MATH_ADL(conj)
382#undef UNI20_SCALAR_MATH_ADL
383
384struct real_fn
385{
386 template <class T>
387 requires(Real<T> || std::integral<T>)
388 constexpr T operator()(T const& value) const
389 {
390 if constexpr (std::integral<T>)
391 return value;
392 else
393 return uni20::conj(value);
394 }
395 template <class T>
396 requires(!Real<T> && !std::integral<T>)
397 constexpr auto operator()(T const& value) const
398 noexcept(noexcept(std::remove_cvref_t<decltype(real_adl::call(value))>(real_adl::call(value))))
399 -> std::remove_cvref_t<decltype(real_adl::call(value))>
400 requires std::constructible_from<std::remove_cvref_t<decltype(real_adl::call(value))>,
401 decltype(real_adl::call(value))>
402 {
403 return std::remove_cvref_t<decltype(real_adl::call(value))>(real_adl::call(value));
404 }
405};
406
407struct imag_fn
408{
409 template <class T>
410 requires(Real<T> || std::integral<T>)
411 constexpr T operator()(T const& value) const
412 {
413 if constexpr (native_argument<T>)
414 return T{};
415 else
416 return uni20::scalar_like(value, 0);
417 }
418 template <class T>
419 requires(!Real<T> && !std::integral<T>)
420 constexpr auto operator()(T const& value) const
421 noexcept(noexcept(std::remove_cvref_t<decltype(imag_adl::call(value))>(imag_adl::call(value))))
422 -> std::remove_cvref_t<decltype(imag_adl::call(value))>
423 requires std::constructible_from<std::remove_cvref_t<decltype(imag_adl::call(value))>,
424 decltype(imag_adl::call(value))>
425 {
426 return std::remove_cvref_t<decltype(imag_adl::call(value))>(imag_adl::call(value));
427 }
428};
429
430struct conj_fn
431{
432 template <class T>
433 requires(Real<T> || std::integral<T>)
434 constexpr T operator()(T const& value) const
435 {
436 if constexpr (std::integral<T>)
437 return value;
438 else
439 return uni20::conj(value);
440 }
441 template <class T>
442 requires(!Real<T> && !std::integral<T>)
443 constexpr auto operator()(T const& value) const
444 noexcept(noexcept(conj_adl::call(value))) -> decltype(conj_adl::call(value))
445 {
446 return conj_adl::call(value);
447 }
448};
449} // namespace detail::scalar_math
450
456namespace math
457{
459inline constexpr detail::scalar_math::abs_fn abs{};
461inline constexpr detail::scalar_math::sqrt_fn sqrt{};
463inline constexpr detail::scalar_math::pow_fn pow{};
465inline constexpr detail::scalar_math::exp_fn exp{};
467inline constexpr detail::scalar_math::log_fn log{};
469inline constexpr detail::scalar_math::log2_fn log2{};
471inline constexpr detail::scalar_math::sin_fn sin{};
473inline constexpr detail::scalar_math::cos_fn cos{};
475inline constexpr detail::scalar_math::cbrt_fn cbrt{};
477inline constexpr detail::scalar_math::exp2_fn exp2{};
479inline constexpr detail::scalar_math::expm1_fn expm1{};
481inline constexpr detail::scalar_math::log10_fn log10{};
483inline constexpr detail::scalar_math::log1p_fn log1p{};
485inline constexpr detail::scalar_math::asin_fn asin{};
487inline constexpr detail::scalar_math::acos_fn acos{};
489inline constexpr detail::scalar_math::sinh_fn sinh{};
491inline constexpr detail::scalar_math::cosh_fn cosh{};
493inline constexpr detail::scalar_math::tanh_fn tanh{};
495inline constexpr detail::scalar_math::asinh_fn asinh{};
497inline constexpr detail::scalar_math::acosh_fn acosh{};
499inline constexpr detail::scalar_math::atanh_fn atanh{};
501inline constexpr detail::scalar_math::tan_fn tan{};
503inline constexpr detail::scalar_math::atan_fn atan{};
505inline constexpr detail::scalar_math::atan2_fn atan2{};
507inline constexpr detail::scalar_math::hypot_fn hypot{};
509inline constexpr detail::scalar_math::ceil_fn ceil{};
511inline constexpr detail::scalar_math::ldexp_fn ldexp{};
513inline constexpr detail::scalar_math::floor_fn floor{};
515inline constexpr detail::scalar_math::trunc_fn trunc{};
517inline constexpr detail::scalar_math::round_fn round{};
519inline constexpr detail::scalar_math::isfinite_fn isfinite{};
521inline constexpr detail::scalar_math::isnan_fn isnan{};
523inline constexpr detail::scalar_math::isinf_fn isinf{};
525inline constexpr detail::scalar_math::signbit_fn signbit{};
527inline constexpr detail::scalar_math::round_even_fn round_even{};
529inline constexpr detail::scalar_math::pown_fn pown{};
531inline constexpr detail::scalar_math::rootn_fn rootn{};
533inline constexpr detail::scalar_math::scalbn_fn scalbn{};
535inline constexpr detail::scalar_math::frexp_fn frexp{};
537inline constexpr detail::scalar_math::modf_fn modf{};
539inline constexpr detail::scalar_math::remquo_fn remquo{};
541inline constexpr detail::scalar_math::sincos_fn sincos{};
543inline constexpr detail::scalar_math::sinhcosh_fn sinhcosh{};
545inline constexpr detail::scalar_math::ilogb_fn ilogb{};
547inline constexpr detail::scalar_math::copysign_fn copysign{};
549inline constexpr detail::scalar_math::nextafter_fn nextafter{};
551inline constexpr detail::scalar_math::next_up_fn next_up{};
553inline constexpr detail::scalar_math::next_down_fn next_down{};
555inline constexpr detail::scalar_math::fma_fn fma{};
557inline constexpr detail::scalar_math::fdim_fn fdim{};
559inline constexpr detail::scalar_math::fmin_fn fmin{};
561inline constexpr detail::scalar_math::fmax_fn fmax{};
563inline constexpr detail::scalar_math::fmod_fn fmod{};
565inline constexpr detail::scalar_math::remainder_fn remainder{};
567inline constexpr detail::scalar_math::tgamma_fn tgamma{};
569inline constexpr detail::scalar_math::lgamma_fn lgamma{};
572inline constexpr detail::scalar_math::lgamma_sign_fn lgamma_sign{};
578inline constexpr detail::scalar_math::digamma_fn digamma{};
586inline constexpr detail::scalar_math::beta_fn beta{};
593inline constexpr detail::scalar_math::upper_gamma_fn upper_gamma{};
595inline constexpr detail::scalar_math::erf_fn erf{};
597inline constexpr detail::scalar_math::erfc_fn erfc{};
601inline constexpr detail::scalar_math::zeta_fn zeta{};
605inline constexpr detail::scalar_math::expint_fn expint{};
609inline constexpr detail::scalar_math::dilog_real_fn dilog_real{};
613inline constexpr detail::scalar_math::bessel_j_fn bessel_j{};
617inline constexpr detail::scalar_math::bessel_y_fn bessel_y{};
620inline constexpr detail::scalar_math::airy_ai_fn airy_ai{};
625inline constexpr detail::scalar_math::agm_fn agm{};
627inline constexpr detail::scalar_math::factorial_fn factorial{};
628
630inline constexpr detail::scalar_math::exp10_fn exp10{};
632inline constexpr detail::scalar_math::exp2m1_fn exp2m1{};
634inline constexpr detail::scalar_math::exp10m1_fn exp10m1{};
636inline constexpr detail::scalar_math::log2p1_fn log2p1{};
638inline constexpr detail::scalar_math::log10p1_fn log10p1{};
640inline constexpr detail::scalar_math::sinpi_fn sinpi{};
642inline constexpr detail::scalar_math::cospi_fn cospi{};
644inline constexpr detail::scalar_math::tanpi_fn tanpi{};
646inline constexpr detail::scalar_math::asinpi_fn asinpi{};
648inline constexpr detail::scalar_math::acospi_fn acospi{};
650inline constexpr detail::scalar_math::atanpi_fn atanpi{};
652inline constexpr detail::scalar_math::sec_fn sec{};
654inline constexpr detail::scalar_math::csc_fn csc{};
656inline constexpr detail::scalar_math::cot_fn cot{};
658inline constexpr detail::scalar_math::sech_fn sech{};
660inline constexpr detail::scalar_math::csch_fn csch{};
662inline constexpr detail::scalar_math::coth_fn coth{};
664inline constexpr detail::scalar_math::atan2pi_fn atan2pi{};
668inline constexpr detail::scalar_math::compound_fn compound{};
669
671inline constexpr detail::scalar_math::real_fn real{};
673inline constexpr detail::scalar_math::imag_fn imag{};
675inline constexpr detail::scalar_math::conj_fn conj{};
676
679template <class T>
680 requires requires(T const& value) { math::abs(value) * math::abs(value); }
681auto abs_squared(T const& value)
682{
683 auto const magnitude = math::abs(value);
684 return magnitude * magnitude;
685}
686} // namespace math
687
688} // namespace uni20
uni20::Integer
Concept for integer scalar types (excluding char and bool).
Definition scalar_concepts.hpp:63
uni20::Real
Concept for real scalar types (float, double, etc.).
Definition scalar_concepts.hpp:69
value
locale_t value
Definition data_table.cpp:49
uni20::conj
uni20::complex< T > conj(detail::standard_complex< T > x)
Returns the complex conjugate for complex-valued scalars.
Definition math.hpp:70
uni20::has_trivial_conj
constexpr bool has_trivial_conj
Indicates whether the Uni20 conjugation helper is a no-op for the provided scalar type.
Definition math.hpp:61
uni20::complex
typename detail::complex_type< Real >::type complex
Project-level complex scalar spelling.
Definition types.hpp:66
uni20::herm
constexpr auto herm(S x)
Computes the Hermitian adjoint of a scalar value.
Definition math.hpp:98
uni20::isfinite
constexpr bool isfinite(I const &x) noexcept
Returns whether an integer scalar is finite.
Definition math.hpp:121
UNI20_SCALAR_MATH_DISPATCH
#define UNI20_SCALAR_MATH_DISPATCH(NAME)
Definition math.hpp:283
UNI20_SCALAR_MATH_DISPATCH_TO
#define UNI20_SCALAR_MATH_DISPATCH_TO(NAME, NATIVE, RESULT_CHECK)
Definition math.hpp:240
UNI20_SCALAR_MATH_DISPATCH_POLICY
#define UNI20_SCALAR_MATH_DISPATCH_POLICY(NAME, CHECK)
Definition math.hpp:282
UNI20_SCALAR_MATH_DISPATCH_ADL_ONLY
#define UNI20_SCALAR_MATH_DISPATCH_ADL_ONLY(NAME)
Definition math.hpp:270
UNI20_SCALAR_MATH_ADL
#define UNI20_SCALAR_MATH_ADL(NAME)
Definition math.hpp:229
math_constants.hpp
std
Definition qnum.hpp:403
uni20::math::asinpi
constexpr detail::scalar_math::asinpi_fn asinpi
Principal arcsine divided by pi.
Definition math.hpp:646
uni20::math::log2p1
constexpr detail::scalar_math::log2p1_fn log2p1
Base-two logarithm of one plus x, without rounding the sum first.
Definition math.hpp:636
uni20::math::nextafter
constexpr detail::scalar_math::nextafter_fn nextafter
Adjacent value on the first operand grid toward the direction operand.
Definition math.hpp:549
uni20::math::exp
constexpr detail::scalar_math::exp_fn exp
Natural exponential with scalar-specific precision handling.
Definition math.hpp:465
uni20::math::acos
constexpr detail::scalar_math::acos_fn acos
Inverse cosine in radians.
Definition math.hpp:487
uni20::math::csch
constexpr detail::scalar_math::csch_fn csch
Reciprocal hyperbolic sine, retaining the input type and precision.
Definition math.hpp:660
uni20::math::tanh
constexpr detail::scalar_math::tanh_fn tanh
Hyperbolic tangent.
Definition math.hpp:493
uni20::math::atan2
constexpr detail::scalar_math::atan2_fn atan2
Quadrant-aware inverse tangent of y/x in radians.
Definition math.hpp:505
uni20::math::pown
constexpr detail::scalar_math::pown_fn pown
Integer power with scalar-specific rounding.
Definition math.hpp:529
uni20::math::expint
constexpr detail::scalar_math::expint_fn expint
Real principal-value exponential integral Ei.
Definition math.hpp:605
uni20::math::lgamma_sign
constexpr detail::scalar_math::lgamma_sign_fn lgamma_sign
Log-absolute-Gamma and its sign as owning values.
Definition math.hpp:572
uni20::math::compound
constexpr detail::scalar_math::compound_fn compound
Integer power of one plus x, retaining the original increment.
Definition math.hpp:668
uni20::math::isfinite
constexpr detail::scalar_math::isfinite_fn isfinite
Whether a real scalar is finite.
Definition math.hpp:519
uni20::math::asinh
constexpr detail::scalar_math::asinh_fn asinh
Inverse hyperbolic sine.
Definition math.hpp:495
uni20::math::upper_gamma
constexpr detail::scalar_math::upper_gamma_fn upper_gamma
Upper unregularized incomplete Gamma, with shape and lower integration endpoint.
Definition math.hpp:593
uni20::math::asin
constexpr detail::scalar_math::asin_fn asin
Inverse sine in radians.
Definition math.hpp:485
uni20::math::bessel_j
constexpr detail::scalar_math::bessel_j_fn bessel_j
Integer-order Bessel function of the first kind, with order first.
Definition math.hpp:613
uni20::math::cosh
constexpr detail::scalar_math::cosh_fn cosh
Hyperbolic cosine.
Definition math.hpp:491
uni20::math::atanpi
constexpr detail::scalar_math::atanpi_fn atanpi
Principal arctangent divided by pi.
Definition math.hpp:650
uni20::math::round
constexpr detail::scalar_math::round_fn round
Round to nearest integer with ties away from zero.
Definition math.hpp:517
uni20::math::sinpi
constexpr detail::scalar_math::sinpi_fn sinpi
Sine of pi times x, with argument reduction before multiplication by pi.
Definition math.hpp:640
uni20::math::remquo
constexpr detail::scalar_math::remquo_fn remquo
Nearest-even remainder and signed low three quotient bits.
Definition math.hpp:539
uni20::math::sinh
constexpr detail::scalar_math::sinh_fn sinh
Hyperbolic sine.
Definition math.hpp:489
uni20::math::ceil
constexpr detail::scalar_math::ceil_fn ceil
Least integral value not less than the argument, in the scalar's result type.
Definition math.hpp:509
uni20::math::atan2pi
constexpr detail::scalar_math::atan2pi_fn atan2pi
Quadrant-aware arctangent divided by pi.
Definition math.hpp:664
uni20::math::log1p
constexpr detail::scalar_math::log1p_fn log1p
Natural logarithm of one plus the argument, retaining small increments.
Definition math.hpp:483
uni20::math::conj
constexpr detail::scalar_math::conj_fn conj
Complex conjugation; real and integral values retain their type.
Definition math.hpp:675
uni20::math::scalbn
constexpr detail::scalar_math::scalbn_fn scalbn
Binary scaling with a signed 64-bit exponent.
Definition math.hpp:533
uni20::math::agm
constexpr detail::scalar_math::agm_fn agm
Nonnegative arithmetic-geometric mean.
Definition math.hpp:625
uni20::math::log10p1
constexpr detail::scalar_math::log10p1_fn log10p1
Base-ten logarithm of one plus x, without rounding the sum first.
Definition math.hpp:638
uni20::math::digamma
constexpr detail::scalar_math::digamma_fn digamma
Logarithmic derivative of Gamma.
Definition math.hpp:578
uni20::math::atan
constexpr detail::scalar_math::atan_fn atan
Inverse tangent in radians.
Definition math.hpp:503
uni20::math::modf
constexpr detail::scalar_math::modf_fn modf
Signed fractional and integral parts as an owning result.
Definition math.hpp:537
uni20::math::erf
constexpr detail::scalar_math::erf_fn erf
Real error function.
Definition math.hpp:595
uni20::math::fdim
constexpr detail::scalar_math::fdim_fn fdim
Positive difference, preserving NaN propagation.
Definition math.hpp:557
uni20::math::cbrt
constexpr detail::scalar_math::cbrt_fn cbrt
Real cube root, including negative arguments.
Definition math.hpp:475
uni20::math::ldexp
constexpr detail::scalar_math::ldexp_fn ldexp
Multiply by a power of two using the scalar's exponent interface.
Definition math.hpp:511
uni20::math::log2
constexpr detail::scalar_math::log2_fn log2
Base-two logarithm where supplied by the scalar implementation.
Definition math.hpp:469
uni20::math::pow
constexpr detail::scalar_math::pow_fn pow
Power with the selected scalar's domain, exactness and precision rules.
Definition math.hpp:463
uni20::math::cos
constexpr detail::scalar_math::cos_fn cos
Cosine with scalar-specific precision handling.
Definition math.hpp:473
uni20::math::ilogb
constexpr detail::scalar_math::ilogb_fn ilogb
Binary exponent of a finite nonzero value; throws otherwise.
Definition math.hpp:545
uni20::math::exp2
constexpr detail::scalar_math::exp2_fn exp2
Base-two exponential.
Definition math.hpp:477
uni20::math::expm1
constexpr detail::scalar_math::expm1_fn expm1
Natural exponential minus one, evaluated without subtractive cancellation.
Definition math.hpp:479
uni20::math::acosh
constexpr detail::scalar_math::acosh_fn acosh
Inverse hyperbolic cosine.
Definition math.hpp:497
uni20::math::erfc
constexpr detail::scalar_math::erfc_fn erfc
Complementary error function without subtractive cancellation.
Definition math.hpp:597
uni20::math::exp10m1
constexpr detail::scalar_math::exp10m1_fn exp10m1
Ten to the power x minus one, using the cancellation-safe provider.
Definition math.hpp:634
uni20::math::signbit
constexpr detail::scalar_math::signbit_fn signbit
Inspect the sign, including approximate negative zero.
Definition math.hpp:525
uni20::math::sinhcosh
constexpr detail::scalar_math::sinhcosh_fn sinhcosh
Hyperbolic sine and cosine at one input.
Definition math.hpp:543
uni20::math::sqrt
constexpr detail::scalar_math::sqrt_fn sqrt
Square root; exact inputs requiring approximation need an explicit finite precision.
Definition math.hpp:461
uni20::math::factorial
constexpr detail::scalar_math::factorial_fn factorial
MPFR factorial at an explicit arithmetic state; use uni20::factorial<Real> for a typed result.
Definition math.hpp:627
uni20::math::atanh
constexpr detail::scalar_math::atanh_fn atanh
Inverse hyperbolic tangent.
Definition math.hpp:499
uni20::math::trunc
constexpr detail::scalar_math::trunc_fn trunc
Round toward zero.
Definition math.hpp:515
uni20::math::floor
constexpr detail::scalar_math::floor_fn floor
Round toward negative infinity.
Definition math.hpp:513
uni20::math::tgamma
constexpr detail::scalar_math::tgamma_fn tgamma
Real Gamma function.
Definition math.hpp:567
uni20::math::zeta
constexpr detail::scalar_math::zeta_fn zeta
Real Riemann zeta with native Euler-Maclaurin evaluation and reflection.
Definition math.hpp:601
uni20::math::sin
constexpr detail::scalar_math::sin_fn sin
Sine with scalar-specific precision handling.
Definition math.hpp:471
uni20::math::sech
constexpr detail::scalar_math::sech_fn sech
Reciprocal hyperbolic cosine, retaining the input type and precision.
Definition math.hpp:658
uni20::math::cot
constexpr detail::scalar_math::cot_fn cot
Reciprocal tangent, retaining the input type and precision.
Definition math.hpp:656
uni20::math::next_up
constexpr detail::scalar_math::next_up_fn next_up
Adjacent value toward positive infinity.
Definition math.hpp:551
uni20::math::coth
constexpr detail::scalar_math::coth_fn coth
Reciprocal hyperbolic tangent, retaining the input type and precision.
Definition math.hpp:662
uni20::math::rootn
constexpr detail::scalar_math::rootn_fn rootn
Real integer-order root; negative orders give reciprocal roots.
Definition math.hpp:531
uni20::math::fmin
constexpr detail::scalar_math::fmin_fn fmin
Minimum, preferring the numeric operand over a NaN.
Definition math.hpp:559
uni20::math::exp2m1
constexpr detail::scalar_math::exp2m1_fn exp2m1
Two to the power x minus one, using the cancellation-safe provider.
Definition math.hpp:632
uni20::math::exp10
constexpr detail::scalar_math::exp10_fn exp10
Base-ten exponential.
Definition math.hpp:630
uni20::math::next_down
constexpr detail::scalar_math::next_down_fn next_down
Adjacent value toward negative infinity.
Definition math.hpp:553
uni20::math::abs
constexpr detail::scalar_math::abs_fn abs
Absolute value or complex magnitude, preserving the selected scalar implementation.
Definition math.hpp:459
uni20::math::tan
constexpr detail::scalar_math::tan_fn tan
Tangent in radians.
Definition math.hpp:501
uni20::math::acospi
constexpr detail::scalar_math::acospi_fn acospi
Principal arccosine divided by pi.
Definition math.hpp:648
uni20::math::tanpi
constexpr detail::scalar_math::tanpi_fn tanpi
Tangent of pi times x, with argument reduction before multiplication by pi.
Definition math.hpp:644
uni20::math::isnan
constexpr detail::scalar_math::isnan_fn isnan
Whether a real scalar is NaN.
Definition math.hpp:521
uni20::math::log10
constexpr detail::scalar_math::log10_fn log10
Base-ten logarithm.
Definition math.hpp:481
uni20::math::fma
constexpr detail::scalar_math::fma_fn fma
Fused multiplication and addition with one final rounding.
Definition math.hpp:555
uni20::math::dilog_real
constexpr detail::scalar_math::dilog_real_fn dilog_real
Real part of the dilogarithm.
Definition math.hpp:609
uni20::math::fmax
constexpr detail::scalar_math::fmax_fn fmax
Maximum, preferring the numeric operand over a NaN.
Definition math.hpp:561
uni20::math::lgamma
constexpr detail::scalar_math::lgamma_fn lgamma
Logarithm of the absolute Gamma function; native providers are reentrant.
Definition math.hpp:569
uni20::math::sincos
constexpr detail::scalar_math::sincos_fn sincos
Sine and cosine at one input.
Definition math.hpp:541
uni20::math::sec
constexpr detail::scalar_math::sec_fn sec
Reciprocal cosine, retaining the input type and precision.
Definition math.hpp:652
uni20::math::real
constexpr detail::scalar_math::real_fn real
Read the real component by value; real and integral scalars retain their type.
Definition math.hpp:671
uni20::math::remainder
constexpr detail::scalar_math::remainder_fn remainder
Remainder using the nearest-even integer quotient.
Definition math.hpp:565
uni20::math::bessel_y
constexpr detail::scalar_math::bessel_y_fn bessel_y
Integer-order Bessel function of the second kind, with order first.
Definition math.hpp:617
uni20::math::airy_ai
constexpr detail::scalar_math::airy_ai_fn airy_ai
Real Airy Ai; native inputs retain their precision and full negative-axis phase.
Definition math.hpp:620
uni20::math::round_even
constexpr detail::scalar_math::round_even_fn round_even
Nearest integer with ties to even.
Definition math.hpp:527
uni20::math::frexp
constexpr detail::scalar_math::frexp_fn frexp
Binary fraction and exponent as an owning result.
Definition math.hpp:535
uni20::math::imag
constexpr detail::scalar_math::imag_fn imag
Read the imaginary component by value; real zero retains the input's type and precision.
Definition math.hpp:673
uni20::math::copysign
constexpr detail::scalar_math::copysign_fn copysign
Copy the sign while retaining the magnitude operand type and precision.
Definition math.hpp:547
uni20::math::isinf
constexpr detail::scalar_math::isinf_fn isinf
Whether a real scalar is infinite.
Definition math.hpp:523
uni20::math::hypot
constexpr detail::scalar_math::hypot_fn hypot
Euclidean length with scalar-specific overflow and underflow handling.
Definition math.hpp:507
uni20::math::log
constexpr detail::scalar_math::log_fn log
Natural logarithm with scalar-specific precision handling.
Definition math.hpp:467
uni20::math::cospi
constexpr detail::scalar_math::cospi_fn cospi
Cosine of pi times x, with argument reduction before multiplication by pi.
Definition math.hpp:642
uni20::math::fmod
constexpr detail::scalar_math::fmod_fn fmod
Remainder using a quotient truncated toward zero.
Definition math.hpp:563
uni20::math::csc
constexpr detail::scalar_math::csc_fn csc
Reciprocal sine, retaining the input type and precision.
Definition math.hpp:654
uni20::math::abs_squared
auto abs_squared(T const &value)
Square the magnitude, evaluating the scalar absolute value once.
Definition math.hpp:681
uni20::math::beta
constexpr detail::scalar_math::beta_fn beta
Real Beta function.
Definition math.hpp:586
uni20
Definition async/async.hpp:26
uni20::acosh
mpcomplex acosh(mpcomplex const &z)
Principal inverse hyperbolic cosine, with imaginary signed zero selecting the cut side.
Definition mpcomplex.hpp:514
uni20::fmod
mpreal fmod(mpreal const &a, mpreal const &b)
Truncating-quotient remainder; exact operands retain exact rational results.
Definition mpreal_functions.hpp:522
uni20::isnan
bool isnan(mpcomplex const &z)
Definition mpcomplex.hpp:499
uni20::nextafter
mpreal nextafter(mpreal const &x, mpreal const &direction)
Adjacent value on x's grid toward direction, whose precision may differ.
Definition mpreal_functions.hpp:335
uni20::asinpi
mpreal asinpi(mpreal const &x)
Principal arcsine divided by pi.
Definition mpreal_extensions.hpp:145
uni20::expint
mpreal expint(mpreal const &x)
Real exponential integral Ei, with its real principal-value meaning.
Definition mpreal_special.hpp:149
uni20::tgamma
mpreal tgamma(mpreal const &x)
Real Gamma function; exact positive integers produce exact factorials.
Definition mpreal_special.hpp:124
uni20::coth
mpreal coth(mpreal const &x)
Reciprocal hyperbolic tangent, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:185
uni20::tan
mpreal tan(mpreal const &x)
Definition mpreal.hpp:657
uni20::erf
mpreal erf(mpreal const &x)
Error function, retaining exact zero or the input precision.
Definition mpreal_special.hpp:134
uni20::sinh
mpcomplex sinh(mpcomplex const &z)
Hyperbolic sine at the input precision; exact zero remains exact.
Definition mpcomplex.hpp:509
uni20::modf
modf_result< mpreal > modf(mpreal const &x)
Signed fractional and integral parts, using truncation toward zero.
Definition mpreal_functions.hpp:506
uni20::abs
constexpr auto abs(basic_half_int< T > value) -> basic_half_int< T >
Return the absolute value of a half-integer.
Definition half_int.hpp:431
uni20::dilog_real
mpreal dilog_real(mpreal const &x)
Real part of the dilogarithm; this is not a complex branch-valued API.
Definition mpreal_special.hpp:154
uni20::expm1
mpreal expm1(mpreal const &x)
Exponential minus one without cancellation; retain input precision or exact zero.
Definition mpreal.hpp:722
uni20::pown
mpreal pown(mpreal const &x, I exponent)
Integer power, preserving exact rational results or the input's finite precision.
Definition mpreal_functions.hpp:695
uni20::scalbn
mpreal scalbn(mpreal const &x, I exponent)
Binary scaling, identical to ldexp for Uni20's binary scalar formats.
Definition mpreal_functions.hpp:216
uni20::atan
mpreal atan(mpreal const &x)
Definition mpreal.hpp:658
uni20::rootn
mpreal rootn(mpreal const &x, I degree)
Real integer-order root; negative orders give reciprocal roots.
Definition mpreal_functions.hpp:708
uni20::airy_ai
mpreal airy_ai(mpreal const &x)
Real Airy Ai; MPFR recommends arguments with magnitude below about 500.
Definition mpreal_special.hpp:159
uni20::sec
mpreal sec(mpreal const &x)
Reciprocal cosine, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:160
uni20::sqrt
exact_rational sqrt(X const &value)
Return the nonnegative rational square root, or require finite precision.
Definition exact_rational.hpp:355
uni20::round_even
mpreal round_even(mpreal const &x)
Round to nearest integer, with ties to even; exact inputs produce exact integers.
Definition mpreal_functions.hpp:111
uni20::fma
mpreal fma(mpreal const &a, mpreal const &b, mpreal const &c)
Compute a*b+c with one rounding, including mixed exact rational operands.
Definition mpreal_functions.hpp:192
uni20::factorial
R factorial(I n)
Factorial of a checked nonnegative integer, with an explicit native result type.
Definition factorial.hpp:15
uni20::next_up
mpreal next_up(mpreal const &x)
Next value toward positive infinity on the input's finite grid.
Definition mpreal_functions.hpp:306
uni20::log
mpcomplex log(mpcomplex const &z)
Principal logarithm, with the sign of imaginary zero selecting the cut side.
Definition mpcomplex.hpp:505
uni20::isinf
bool isinf(mpcomplex const &z)
Definition mpcomplex.hpp:500
uni20::acos
mpreal acos(mpreal const &x)
Inverse cosine in radians; retain input precision or a supported exact result.
Definition mpreal.hpp:757
uni20::csc
mpreal csc(mpreal const &x)
Reciprocal sine, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:165
uni20::fmax
mpreal fmax(mpreal const &a, mpreal const &b)
Maximum with NaN suppression and positive-zero preference.
Definition mpreal_functions.hpp:272
uni20::cot
mpreal cot(mpreal const &x)
Reciprocal tangent, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:170
uni20::bessel_j
mpreal bessel_j(I n, mpreal const &x)
Bessel function of the first kind, with a checked signed integer order.
Definition mpreal_special.hpp:227
uni20::exp10m1
mpreal exp10m1(mpreal const &x)
Ten to the power x minus one, using the cancellation-safe provider.
Definition mpreal_extensions.hpp:115
uni20::log2p1
mpreal log2p1(mpreal const &x)
Base-two logarithm of one plus x, without rounding the sum first.
Definition mpreal_extensions.hpp:120
uni20::cosh
mpcomplex cosh(mpcomplex const &z)
Hyperbolic cosine at the input precision; exact zero returns exact one.
Definition mpcomplex.hpp:511
uni20::fmin
mpreal fmin(mpreal const &a, mpreal const &b)
Minimum with NaN suppression and negative-zero preference.
Definition mpreal_functions.hpp:261
uni20::tanh
mpreal tanh(mpreal const &x)
Hyperbolic tangent; retain input precision or a supported exact result.
Definition mpreal.hpp:778
uni20::lgamma_sign
lgamma_result< mpreal > lgamma_sign(mpreal const &x)
Log(abs(Gamma(x))) and the sign of Gamma, as owning values.
Definition mpreal_special.hpp:184
uni20::frexp
frexp_result< mpreal > frexp(mpreal const &x)
Decompose into a binary fraction and signed 64-bit exponent.
Definition mpreal_functions.hpp:498
uni20::log2
mpreal log2(mpreal const &x)
Base-two logarithm; retain input precision or a supported exact result.
Definition mpreal.hpp:729
uni20::cbrt
mpreal cbrt(mpreal const &x)
Real cube root, including negative arguments; retain input precision or a supported exact result.
Definition mpreal.hpp:708
uni20::compound
mpreal compound(mpreal const &x, I n)
Compute (1+x)^n without rounding the sum first, for x >= -1.
Definition mpreal_functions.hpp:741
uni20::atan2pi
mpreal atan2pi(mpreal const &y, mpreal const &x)
Quadrant-aware arctangent of y/x, divided by pi.
Definition mpreal_extensions.hpp:192
uni20::next_down
mpreal next_down(mpreal const &x)
Next value toward negative infinity on the input's finite grid.
Definition mpreal_functions.hpp:320
uni20::exp10
mpreal exp10(mpreal const &x)
Base-ten exponential.
Definition mpreal_extensions.hpp:105
uni20::exp2
mpreal exp2(mpreal const &x)
Base-two exponential; retain input precision or a supported exact result.
Definition mpreal.hpp:715
uni20::log10
mpreal log10(mpreal const &x)
Base-ten logarithm; retain input precision or a supported exact result.
Definition mpreal.hpp:736
uni20::fdim
mpreal fdim(mpreal const &a, mpreal const &b)
Positive difference max(a-b,0), propagating NaNs.
Definition mpreal_functions.hpp:294
uni20::upper_gamma
mpreal upper_gamma(mpreal const &a, mpreal const &x)
Upper incomplete Gamma, with shape a and lower integration endpoint x.
Definition mpreal_special.hpp:169
uni20::is_exact
constexpr bool is_exact(detail::standard_complex< T > const &x)
A standard complex value is exact only when both components are exact.
Definition math.hpp:50
uni20::hypot
mpreal hypot(mpreal const &x, mpreal const &y)
Definition mpreal.hpp:660
uni20::zeta
mpreal zeta(mpreal const &x)
Riemann zeta; nonpositive integer arguments retain exact rational results.
Definition mpreal_special.hpp:144
uni20::cospi
mpreal cospi(mpreal const &x)
Cosine of pi times x, with provider argument reduction.
Definition mpreal_extensions.hpp:135
uni20::signbit
bool signbit(mpreal const &x)
Definition mpreal.hpp:642
uni20::erfc
mpreal erfc(mpreal const &x)
Complementary error function, evaluated without subtracting erf from one.
Definition mpreal_special.hpp:139
uni20::round
mpreal round(mpreal const &x)
Round to nearest integer, with ties away from zero; exact inputs produce exact integers.
Definition mpreal_functions.hpp:98
uni20::scalar_like
constexpr auto scalar_like(S const &exemplar, Value const &value) -> S
Construct a scalar using an exemplar's type and numerical precision.
Definition math.hpp:195
uni20::sincos
sincos_result< mpreal > sincos(mpreal const &x)
Evaluate sine and cosine using the paired provider routine.
Definition mpreal_functions.hpp:583
uni20::trunc
mpreal trunc(mpreal const &x)
Round toward zero; exact inputs produce exact integers.
Definition mpreal_functions.hpp:85
uni20::agm
mpreal agm(mpreal const &a, mpreal const &x)
Nonnegative real arithmetic-geometric mean.
Definition mpreal_special.hpp:177
uni20::sech
mpreal sech(mpreal const &x)
Reciprocal hyperbolic cosine, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:175
uni20::ldexp
mpreal ldexp(mpreal const &x, I exponent)
Multiply by 2^exponent, preserving exact rational state or input precision.
Definition mpreal_functions.hpp:205
uni20::pow
exact_rational pow(X const &base, Y const &power)
Evaluate a rational power exactly when its real result is rational.
Definition exact_rational.hpp:337
uni20::sinhcosh
sinhcosh_result< mpreal > sinhcosh(mpreal const &x)
Evaluate hyperbolic sine and cosine using the paired provider routine.
Definition mpreal_functions.hpp:591
uni20::asinh
mpreal asinh(mpreal const &x)
Inverse hyperbolic sine; retain input precision or a supported exact result.
Definition mpreal.hpp:785
uni20::acospi
mpreal acospi(mpreal const &x)
Principal arccosine divided by pi.
Definition mpreal_extensions.hpp:150
uni20::ceil
mpreal ceil(mpreal const &x)
Round toward positive infinity; exact inputs produce exact integers.
Definition mpreal_functions.hpp:72
uni20::asin
mpreal asin(mpreal const &x)
Inverse sine in radians; retain input precision or a supported exact result.
Definition mpreal.hpp:750
uni20::beta
mpreal beta(mpreal const &a, mpreal const &x)
Real Beta function; positive rational/integer pairs retain exact values.
Definition mpreal_special.hpp:164
uni20::remainder
mpreal remainder(mpreal const &a, mpreal const &b)
Nearest-even-quotient remainder; exact operands retain exact rational results.
Definition mpreal_functions.hpp:534
uni20::atanh
mpreal atanh(mpreal const &x)
Inverse hyperbolic tangent; retain input precision or a supported exact result.
Definition mpreal.hpp:799
uni20::atanpi
mpreal atanpi(mpreal const &x)
Principal arctangent divided by pi.
Definition mpreal_extensions.hpp:155
uni20::remquo
remquo_result< mpreal > remquo(mpreal const &a, mpreal const &b)
Nearest-even remainder with the signed low three quotient bits.
Definition mpreal_functions.hpp:546
uni20::exp
mpcomplex exp(mpcomplex const &z)
Definition mpcomplex.hpp:503
uni20::csch
mpreal csch(mpreal const &x)
Reciprocal hyperbolic sine, evaluated directly by MPFR.
Definition mpreal_extensions.hpp:180
uni20::tanpi
mpreal tanpi(mpreal const &x)
Tangent of pi times x, with provider argument reduction.
Definition mpreal_extensions.hpp:140
uni20::exp2m1
mpreal exp2m1(mpreal const &x)
Two to the power x minus one, using the cancellation-safe provider.
Definition mpreal_extensions.hpp:110
uni20::atan2
mpreal atan2(mpreal const &y, mpreal const &x)
Definition mpreal.hpp:659
uni20::ilogb
std::int64_t ilogb(mpreal const &x)
Base-two exponent of a finite nonzero value.
Definition mpreal_functions.hpp:515
uni20::sin
mpcomplex sin(mpcomplex const &z)
Definition mpcomplex.hpp:506
uni20::copysign
mpreal copysign(mpreal const &magnitude, mpreal const &sign)
Transfer the sign while preserving the magnitude's precision and exactness.
Definition mpreal_functions.hpp:224
uni20::digamma
mpreal digamma(mpreal const &x)
Logarithmic derivative of Gamma; finite working precision is required.
Definition mpreal_special.hpp:129
uni20::floor
mpreal floor(mpreal const &x)
Round toward negative infinity; exact inputs produce exact integers.
Definition mpreal_functions.hpp:59
uni20::log1p
mpreal log1p(mpreal const &x)
Logarithm of one plus x without cancellation; retain input precision or exact zero.
Definition mpreal.hpp:743
uni20::sinpi
mpreal sinpi(mpreal const &x)
Sine of pi times x, with provider argument reduction.
Definition mpreal_extensions.hpp:130
uni20::log10p1
mpreal log10p1(mpreal const &x)
Base-ten logarithm of one plus x, without rounding the sum first.
Definition mpreal_extensions.hpp:125
uni20::bessel_y
mpreal bessel_y(I n, mpreal const &x)
Bessel function of the second kind, with a checked signed integer order.
Definition mpreal_special.hpp:239
uni20::lgamma
mpreal lgamma(mpreal const &x)
Natural logarithm of abs(Gamma(x)), including negative Gamma values.
Definition mpreal_special.hpp:205
uni20::cos
mpcomplex cos(mpcomplex const &z)
Definition mpcomplex.hpp:507
native_agm_math.hpp
native_airy_math.hpp
native_compound_math.hpp
native_digamma_math.hpp
native_dilog_math.hpp
native_expint_math.hpp
native_exponential_math.hpp
native_math.hpp
native_pi_math.hpp
native_reciprocal_math.hpp
native_special_math.hpp
native_upper_gamma_math.hpp
numeric_limits.hpp
runtime_precision.hpp
scalar_concepts.hpp
uni20::numeric_limits
Project-level numeric limits customization point.
Definition numeric_limits.hpp:16
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