15 #error "This file is for OpenMP compilation only."
19 #error "This file is for C++ compilation only."
22 #ifndef _LIBCPP_COMPLEX
23 #define _LIBCPP_COMPLEX
26 #include <type_traits>
28 #define __DEVICE__ static constexpr __attribute__((nothrow))
45 typename enable_if<is_integral<_Tp>::value || is_same<_Tp, double>::value,
48 return atan2(0., __re);
52 typename enable_if<is_same<_Tp, float>::value,
float>
::type arg(_Tp __re) {
63 return __c.real() *
__c.real() +
__c.imag() *
__c.imag();
68 template <
class _Tp> std::complex<_Tp>
conj(
const std::complex<_Tp> &
__c) {
69 return std::complex<_Tp>(
__c.real(), -
__c.imag());
74 template <
class _Tp> std::complex<_Tp>
proj(
const std::complex<_Tp> &
__c) {
75 std::complex<_Tp> __r =
__c;
84 complex<_Tp>
polar(
const _Tp &__rho,
const _Tp &__theta = _Tp()) {
86 return std::complex<_Tp>(_Tp(
NAN), _Tp(
NAN));
89 return std::complex<_Tp>(__rho, __theta);
90 return std::complex<_Tp>(__theta, __theta);
94 return std::complex<_Tp>(__rho, _Tp(
NAN));
95 return std::complex<_Tp>(_Tp(
NAN), _Tp(
NAN));
97 _Tp __x = __rho *
cos(__theta);
100 _Tp
__y = __rho *
sin(__theta);
103 return std::complex<_Tp>(__x,
__y);
108 template <
class _Tp> std::complex<_Tp>
log(
const std::complex<_Tp> &__x) {
109 return std::complex<_Tp>(
log(
abs(__x)),
arg(__x));
114 template <
class _Tp> std::complex<_Tp>
log10(
const std::complex<_Tp> &__x) {
115 return log(__x) /
log(_Tp(10));
123 return std::complex<_Tp>(_Tp(
INFINITY), __x.imag());
125 if (__x.real() > _Tp(0))
126 return std::complex<_Tp>(__x.real(),
std::isnan(__x.imag())
129 return std::complex<_Tp>(
std::isnan(__x.imag()) ? __x.imag() : _Tp(0),
139 _Tp __i = __x.imag();
141 if (__x.real() < _Tp(0)) {
147 return std::complex<_Tp>(__x.real(), __i);
149 }
else if (
std::isnan(__x.real()) && __x.imag() == 0)
151 _Tp __e =
exp(__x.real());
152 return std::complex<_Tp>(__e *
cos(__i), __e *
sin(__i));
158 std::complex<_Tp>
pow(
const std::complex<_Tp> &__x,
159 const std::complex<_Tp> &
__y) {
165 template <
class _Tp> std::complex<_Tp>
__sqr(
const std::complex<_Tp> &__x) {
166 return std::complex<_Tp>((__x.real() - __x.imag()) *
167 (__x.real() + __x.imag()),
168 _Tp(2) * __x.real() * __x.imag());
175 const _Tp __pi(
atan2(+0., -0.));
180 return std::complex<_Tp>(__x.real(),
181 copysign(__pi * _Tp(0.25), __x.imag()));
182 return std::complex<_Tp>(__x.real(),
copysign(_Tp(0), __x.imag()));
186 return std::complex<_Tp>(__x.imag(), __x.real());
189 return std::complex<_Tp>(__x.real(), __x.real());
192 return std::complex<_Tp>(
copysign(__x.imag(), __x.real()),
193 copysign(__pi / _Tp(2), __x.imag()));
194 std::complex<_Tp> __z =
log(__x +
sqrt(
__sqr(__x) + _Tp(1)));
195 return std::complex<_Tp>(
copysign(__z.real(), __x.real()),
203 const _Tp __pi(
atan2(+0., -0.));
206 return std::complex<_Tp>(
abs(__x.real()), __x.imag());
209 return std::complex<_Tp>(__x.real(),
210 copysign(__pi * _Tp(0.25), __x.imag()));
212 return std::complex<_Tp>(-__x.real(),
213 copysign(__pi * _Tp(0.75), __x.imag()));
216 return std::complex<_Tp>(-__x.real(),
copysign(__pi, __x.imag()));
217 return std::complex<_Tp>(__x.real(),
copysign(_Tp(0), __x.imag()));
221 return std::complex<_Tp>(
abs(__x.imag()), __x.real());
222 return std::complex<_Tp>(__x.real(), __x.real());
225 return std::complex<_Tp>(
abs(__x.imag()),
226 copysign(__pi / _Tp(2), __x.imag()));
227 std::complex<_Tp> __z =
log(__x +
sqrt(
__sqr(__x) - _Tp(1)));
228 return std::complex<_Tp>(
copysign(__z.real(), _Tp(0)),
236 const _Tp __pi(
atan2(+0., -0.));
238 return std::complex<_Tp>(
copysign(_Tp(0), __x.real()),
239 copysign(__pi / _Tp(2), __x.imag()));
242 if (
std::isinf(__x.real()) || __x.real() == 0)
243 return std::complex<_Tp>(
copysign(_Tp(0), __x.real()), __x.imag());
244 return std::complex<_Tp>(__x.imag(), __x.imag());
247 return std::complex<_Tp>(__x.real(), __x.real());
250 return std::complex<_Tp>(
copysign(_Tp(0), __x.real()),
251 copysign(__pi / _Tp(2), __x.imag()));
253 if (
abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) {
257 std::complex<_Tp> __z =
log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
258 return std::complex<_Tp>(
copysign(__z.real(), __x.real()),
267 return std::complex<_Tp>(__x.real(), _Tp(
NAN));
269 return std::complex<_Tp>(__x.real(), _Tp(
NAN));
272 return std::complex<_Tp>(
sinh(__x.real()) *
cos(__x.imag()),
273 cosh(__x.real()) *
sin(__x.imag()));
281 return std::complex<_Tp>(
abs(__x.real()), _Tp(
NAN));
283 return std::complex<_Tp>(_Tp(
NAN), __x.real());
284 if (__x.real() == 0 && __x.imag() == 0)
285 return std::complex<_Tp>(_Tp(1), __x.imag());
287 return std::complex<_Tp>(
abs(__x.real()), __x.imag());
288 return std::complex<_Tp>(
cosh(__x.real()) *
cos(__x.imag()),
289 sinh(__x.real()) *
sin(__x.imag()));
298 return std::complex<_Tp>(_Tp(1), _Tp(0));
299 return std::complex<_Tp>(_Tp(1),
302 if (
std::isnan(__x.real()) && __x.imag() == 0)
304 _Tp __2r(_Tp(2) * __x.real());
305 _Tp __2i(_Tp(2) * __x.imag());
306 _Tp __d(
cosh(__2r) +
cos(__2i));
307 _Tp __2rsh(
sinh(__2r));
309 return std::complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
310 __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
311 return std::complex<_Tp>(__2rsh / __d,
sin(__2i) / __d);
318 std::complex<_Tp> __z =
asinh(complex<_Tp>(-__x.imag(), __x.real()));
319 return std::complex<_Tp>(__z.imag(), -__z.real());
326 const _Tp __pi(
atan2(+0., -0.));
329 return std::complex<_Tp>(__x.imag(), __x.real());
331 if (__x.real() < _Tp(0))
332 return std::complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
333 return std::complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
335 if (__x.real() < _Tp(0))
336 return std::complex<_Tp>(__pi,
337 signbit(__x.imag()) ? -__x.real() : __x.real());
338 return std::complex<_Tp>(_Tp(0),
339 signbit(__x.imag()) ? __x.real() : -__x.real());
343 return std::complex<_Tp>(__x.real(), -__x.imag());
344 return std::complex<_Tp>(__x.real(), __x.real());
347 return std::complex<_Tp>(__pi / _Tp(2), -__x.imag());
348 if (__x.real() == 0 && (__x.imag() == 0 ||
isnan(__x.imag())))
349 return std::complex<_Tp>(__pi / _Tp(2), -__x.imag());
350 std::complex<_Tp> __z =
log(__x +
sqrt(
__sqr(__x) - _Tp(1)));
352 return std::complex<_Tp>(
abs(__z.imag()),
abs(__z.real()));
353 return std::complex<_Tp>(
abs(__z.imag()), -
abs(__z.real()));
360 std::complex<_Tp> __z =
atanh(complex<_Tp>(-__x.imag(), __x.real()));
361 return std::complex<_Tp>(__z.imag(), -__z.real());
368 std::complex<_Tp> __z =
sinh(complex<_Tp>(-__x.imag(), __x.real()));
369 return std::complex<_Tp>(__z.imag(), -__z.real());
374 template <
class _Tp> std::complex<_Tp>
cos(
const std::complex<_Tp> &__x) {
375 return cosh(complex<_Tp>(-__x.imag(), __x.real()));
382 std::complex<_Tp> __z =
tanh(complex<_Tp>(-__x.imag(), __x.real()));
383 return std::complex<_Tp>(__z.imag(), -__z.real());
__DEVICE__ bool isnan(float __x)
Test for a NaN.
__DEVICE__ bool isfinite(float __x)
Test for finite value.
__DEVICE__ bool signbit(float __x)
Test for sign bit.
__DEVICE__ bool isinf(float __x)
Test for infinity value (+ve or -ve) .
__DEVICE__ float atan2f(float __a, float __b)
static __inline__ vector float vector float vector float __c
static __inline__ uint32_t uint32_t __y
const internal::VariadicAllOfMatcher< Type > type
Matches Types in the clang AST.
__DEVICE__ _Tp norm(const std::complex< _Tp > &__c)
complex< _Tp > polar(const _Tp &__rho, const _Tp &__theta=_Tp())
__DEVICE__ std::complex< _Tp > tan(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > acos(const std::complex< _Tp > &__x)
__DEVICE__ _Tp abs(const std::complex< _Tp > &__c)
std::complex< _Tp > conj(const std::complex< _Tp > &__c)
__DEVICE__ std::complex< _Tp > acosh(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > asinh(const std::complex< _Tp > &__x)
std::complex< _Tp > __sqr(const std::complex< _Tp > &__x)
std::complex< _Tp > pow(const std::complex< _Tp > &__x, const std::complex< _Tp > &__y)
__DEVICE__ std::complex< _Tp > atanh(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > cosh(const std::complex< _Tp > &__x)
__DEVICE__ _Tp arg(const std::complex< _Tp > &__c)
__DEVICE__ std::complex< _Tp > sqrt(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > exp(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > asin(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > atan(const std::complex< _Tp > &__x)
std::complex< _Tp > log10(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > sinh(const std::complex< _Tp > &__x)
std::complex< _Tp > proj(const std::complex< _Tp > &__c)
std::complex< _Tp > log(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > tanh(const std::complex< _Tp > &__x)
__DEVICE__ std::complex< _Tp > sin(const std::complex< _Tp > &__x)
std::complex< _Tp > cos(const std::complex< _Tp > &__x)
#define NAN
A constant expression of type float representing a quiet NaN.
#define INFINITY
A constant expression of type float representing positive or unsigned infinity.
#define copysign(__x, __y)