36 #ifndef EIGEN_HALF_CUDA_H 37 #define EIGEN_HALF_CUDA_H 39 #if __cplusplus > 199711L 40 #define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type() 42 #define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type() 52 #if !defined(EIGEN_HAS_CUDA_FP16) 56 EIGEN_DEVICE_FUNC __half() {}
57 explicit EIGEN_DEVICE_FUNC __half(
unsigned short raw) : x(raw) {}
63 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(
unsigned short x);
64 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(
float ff);
65 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
float half_to_float(__half h);
67 struct half_base :
public __half {
68 EIGEN_DEVICE_FUNC half_base() {}
69 EIGEN_DEVICE_FUNC half_base(
const half_base& h) : __half(h) {}
70 EIGEN_DEVICE_FUNC half_base(
const __half& h) : __half(h) {}
76 struct half :
public half_impl::half_base {
77 #if !defined(EIGEN_HAS_CUDA_FP16) 78 typedef half_impl::__half __half;
81 EIGEN_DEVICE_FUNC half() {}
83 EIGEN_DEVICE_FUNC half(
const __half& h) : half_impl::half_base(h) {}
84 EIGEN_DEVICE_FUNC half(
const half& h) : half_impl::half_base(h) {}
86 explicit EIGEN_DEVICE_FUNC half(
bool b)
87 : half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {}
89 explicit EIGEN_DEVICE_FUNC half(
const T& val)
90 : half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(val))) {}
91 explicit EIGEN_DEVICE_FUNC half(
float f)
92 : half_impl::half_base(half_impl::float_to_half_rtne(f)) {}
94 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
bool)
const {
96 return (x & 0x7fff) != 0;
98 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
signed char)
const {
99 return static_cast<signed char>(half_impl::half_to_float(*
this));
101 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
unsigned char)
const {
102 return static_cast<unsigned char>(half_impl::half_to_float(*
this));
104 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
short)
const {
105 return static_cast<short>(half_impl::half_to_float(*
this));
107 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
unsigned short)
const {
108 return static_cast<unsigned short>(half_impl::half_to_float(*
this));
110 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
int)
const {
111 return static_cast<int>(half_impl::half_to_float(*
this));
113 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
unsigned int)
const {
114 return static_cast<unsigned int>(half_impl::half_to_float(*
this));
116 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
long)
const {
117 return static_cast<long>(half_impl::half_to_float(*
this));
119 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
unsigned long)
const {
120 return static_cast<unsigned long>(half_impl::half_to_float(*
this));
122 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
long long)
const {
123 return static_cast<long long>(half_impl::half_to_float(*
this));
125 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
unsigned long long)
const {
126 return static_cast<unsigned long long>(half_to_float(*
this));
128 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
float)
const {
129 return half_impl::half_to_float(*
this);
131 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(
double)
const {
132 return static_cast<double>(half_impl::half_to_float(*
this));
135 EIGEN_DEVICE_FUNC half& operator=(
const half& other) {
141 namespace half_impl {
143 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 150 __device__ half operator + (
const half& a,
const half& b) {
153 __device__ half
operator * (
const half& a,
const half& b) {
156 __device__ half operator - (
const half& a,
const half& b) {
159 __device__ half operator / (
const half& a,
const half& b) {
160 float num = __half2float(a);
161 float denom = __half2float(b);
162 return __float2half(num / denom);
164 __device__ half operator - (
const half& a) {
167 __device__ half& operator += (half& a,
const half& b) {
171 __device__ half& operator *= (half& a,
const half& b) {
175 __device__ half& operator -= (half& a,
const half& b) {
179 __device__ half& operator /= (half& a,
const half& b) {
183 __device__
bool operator == (
const half& a,
const half& b) {
186 __device__
bool operator != (
const half& a,
const half& b) {
189 __device__
bool operator < (
const half& a,
const half& b) {
192 __device__
bool operator <= (
const half& a,
const half& b) {
195 __device__
bool operator > (
const half& a,
const half& b) {
198 __device__
bool operator >= (
const half& a,
const half& b) {
202 #else // Emulate support for half floats 207 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (
const half& a,
const half& b) {
208 return half(
float(a) +
float(b));
210 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
operator * (
const half& a,
const half& b) {
211 return half(
float(a) *
float(b));
213 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (
const half& a,
const half& b) {
214 return half(
float(a) -
float(b));
216 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (
const half& a,
const half& b) {
217 return half(
float(a) /
float(b));
219 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (
const half& a) {
221 result.x = a.x ^ 0x8000;
224 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a,
const half& b) {
225 a = half(
float(a) +
float(b));
228 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a,
const half& b) {
229 a = half(
float(a) *
float(b));
232 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a,
const half& b) {
233 a = half(
float(a) -
float(b));
236 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a,
const half& b) {
237 a = half(
float(a) /
float(b));
240 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator == (
const half& a,
const half& b) {
241 return float(a) == float(b);
243 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator != (
const half& a,
const half& b) {
244 return float(a) != float(b);
246 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator < (
const half& a,
const half& b) {
247 return float(a) < float(b);
249 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator <= (
const half& a,
const half& b) {
250 return float(a) <= float(b);
252 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator > (
const half& a,
const half& b) {
253 return float(a) > float(b);
255 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
bool operator >= (
const half& a,
const half& b) {
256 return float(a) >= float(b);
259 #endif // Emulate support for half floats 263 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (
const half& a,
Index b) {
264 return half(static_cast<float>(a) / static_cast<float>(b));
272 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(
unsigned short x) {
283 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(
float ff) {
284 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300 285 return __float2half(ff);
287 #elif defined(EIGEN_HAS_FP16_C) 289 h.x = _cvtss_sh(ff, 0);
295 const FP32 f32infty = { 255 << 23 };
296 const FP32 f16max = { (127 + 16) << 23 };
297 const FP32 denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
298 unsigned int sign_mask = 0x80000000u;
300 o.x =
static_cast<unsigned short>(0x0u);
302 unsigned int sign = f.u & sign_mask;
310 if (f.u >= f16max.u) {
311 o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00;
313 if (f.u < (113 << 23)) {
317 f.f += denorm_magic.f;
320 o.x =
static_cast<unsigned short>(f.u - denorm_magic.u);
322 unsigned int mant_odd = (f.u >> 13) & 1;
325 f.u += ((
unsigned int)(15 - 127) << 23) + 0xfff;
329 o.x =
static_cast<unsigned short>(f.u >> 13);
333 o.x |=
static_cast<unsigned short>(sign >> 16);
338 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
float half_to_float(__half h) {
339 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300 340 return __half2float(h);
342 #elif defined(EIGEN_HAS_FP16_C) 343 return _cvtsh_ss(h.x);
346 const FP32 magic = { 113 << 23 };
347 const unsigned int shifted_exp = 0x7c00 << 13;
350 o.u = (h.x & 0x7fff) << 13;
351 unsigned int exp = shifted_exp & o.u;
352 o.u += (127 - 15) << 23;
355 if (exp == shifted_exp) {
356 o.u += (128 - 16) << 23;
357 }
else if (exp == 0) {
362 o.u |= (h.x & 0x8000) << 16;
369 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (
isinf)(
const half& a) {
370 return (a.x & 0x7fff) == 0x7c00;
372 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (
isnan)(
const half& a) {
373 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 376 return (a.x & 0x7fff) > 0x7c00;
379 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (
isfinite)(
const half& a) {
380 return !(
isinf EIGEN_NOT_A_MACRO (a)) && !(
isnan EIGEN_NOT_A_MACRO (a));
383 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
abs(
const half& a) {
385 result.x = a.x & 0x7FFF;
388 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
exp(
const half& a) {
389 return half(::expf(
float(a)));
391 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
log(
const half& a) {
392 #if defined(EIGEN_HAS_CUDA_FP16) && defined __CUDACC_VER__ && __CUDACC_VER__ >= 80000 && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 393 return Eigen::half(::hlog(a));
395 return half(::logf(
float(a)));
398 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
log1p(
const half& a) {
399 return half(numext::log1p(
float(a)));
401 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
log10(
const half& a) {
402 return half(::log10f(
float(a)));
404 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
sqrt(
const half& a) {
405 return half(::sqrtf(
float(a)));
407 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(
const half& a,
const half& b) {
408 return half(::powf(
float(a),
float(b)));
410 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
sin(
const half& a) {
411 return half(::sinf(
float(a)));
413 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
cos(
const half& a) {
414 return half(::cosf(
float(a)));
416 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
tan(
const half& a) {
417 return half(::tanf(
float(a)));
419 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
tanh(
const half& a) {
420 return half(::tanhf(
float(a)));
422 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
floor(
const half& a) {
423 return half(::floorf(
float(a)));
425 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half
ceil(
const half& a) {
426 return half(::ceilf(
float(a)));
429 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(
const half& a,
const half& b) {
430 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 431 return __hlt(b, a) ? b : a;
433 const float f1 =
static_cast<float>(a);
434 const float f2 =
static_cast<float>(b);
435 return f2 < f1 ? b : a;
438 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(
const half& a,
const half& b) {
439 #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 440 return __hlt(a, b) ? b : a;
442 const float f1 =
static_cast<float>(a);
443 const float f2 =
static_cast<float>(b);
444 return f1 < f2 ? b : a;
448 EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os,
const half& v) {
449 os << static_cast<float>(v);
461 struct random_default_impl<half, false, false>
463 static inline half run(
const half& x,
const half& y)
465 return x + (y-x) * half(
float(std::rand()) / float(RAND_MAX));
467 static inline half run()
469 return run(half(-1.f), half(1.f));
473 template<>
struct is_arithmetic<half> {
enum { value =
true }; };
481 struct numeric_limits<
Eigen::half> {
482 static const bool is_specialized =
true;
483 static const bool is_signed =
true;
484 static const bool is_integer =
false;
485 static const bool is_exact =
false;
486 static const bool has_infinity =
true;
487 static const bool has_quiet_NaN =
true;
488 static const bool has_signaling_NaN =
true;
489 static const float_denorm_style has_denorm = denorm_present;
490 static const bool has_denorm_loss =
false;
491 static const std::float_round_style round_style = std::round_to_nearest;
492 static const bool is_iec559 =
false;
493 static const bool is_bounded =
false;
494 static const bool is_modulo =
false;
495 static const int digits = 11;
496 static const int digits10 = 2;
498 static const int radix = 2;
499 static const int min_exponent = -13;
500 static const int min_exponent10 = -4;
501 static const int max_exponent = 16;
502 static const int max_exponent10 = 4;
503 static const bool traps =
true;
504 static const bool tinyness_before =
false;
506 static Eigen::half (min)() {
return Eigen::half_impl::raw_uint16_to_half(0x400); }
507 static Eigen::half lowest() {
return Eigen::half_impl::raw_uint16_to_half(0xfbff); }
508 static Eigen::half (max)() {
return Eigen::half_impl::raw_uint16_to_half(0x7bff); }
509 static Eigen::half epsilon() {
return Eigen::half_impl::raw_uint16_to_half(0x0800); }
510 static Eigen::half round_error() {
return Eigen::half(0.5); }
511 static Eigen::half infinity() {
return Eigen::half_impl::raw_uint16_to_half(0x7c00); }
512 static Eigen::half quiet_NaN() {
return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
513 static Eigen::half signaling_NaN() {
return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
514 static Eigen::half denorm_min() {
return Eigen::half_impl::raw_uint16_to_half(0x1); }
520 template<>
struct NumTraits<
Eigen::half>
521 : GenericNumTraits<Eigen::half>
527 RequireInitialization =
false 530 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half epsilon() {
531 return half_impl::raw_uint16_to_half(0x0800);
533 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half dummy_precision() {
return Eigen::half(1e-2f); }
534 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half highest() {
535 return half_impl::raw_uint16_to_half(0x7bff);
537 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half lowest() {
538 return half_impl::raw_uint16_to_half(0xfbff);
540 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half infinity() {
541 return half_impl::raw_uint16_to_half(0x7c00);
543 EIGEN_DEVICE_FUNC
static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {
544 return half_impl::raw_uint16_to_half(0x7c01);
551 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half fabsh(
const Eigen::half& a) {
553 result.x = a.x & 0x7FFF;
556 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exph(
const Eigen::half& a) {
557 return Eigen::half(::expf(
float(a)));
559 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half logh(
const Eigen::half& a) {
560 #if defined __CUDACC_VER__ && __CUDACC_VER__ >= 80000 && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 561 return Eigen::half(::hlog(a));
563 return Eigen::half(::logf(
float(a)));
566 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrth(
const Eigen::half& a) {
567 return Eigen::half(::sqrtf(
float(a)));
569 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half powh(
const Eigen::half& a,
const Eigen::half& b) {
570 return Eigen::half(::powf(
float(a),
float(b)));
572 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floorh(
const Eigen::half& a) {
573 return Eigen::half(::floorf(
float(a)));
575 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceilh(
const Eigen::half& a) {
576 return Eigen::half(::ceilf(
float(a)));
581 #if __cplusplus > 199711L 583 struct hash<
Eigen::half> {
584 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(
const Eigen::half& a)
const {
585 return static_cast<std::size_t
>(a.x);
594 #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300 595 __device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var,
int laneMask,
int width=warpSize) {
596 return static_cast<Eigen::half
>(__shfl_xor(static_cast<float>(var), laneMask, width));
601 #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350 602 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(
const Eigen::half* ptr) {
603 return Eigen::half_impl::raw_uint16_to_half(
604 __ldg(reinterpret_cast<const unsigned short*>(ptr)));
609 #if defined(__CUDA_ARCH__) 614 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
615 bool (
isnan)(
const Eigen::half& h) {
616 return (half_impl::isnan)(h);
620 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
621 bool (
isinf)(
const Eigen::half& h) {
622 return (half_impl::isinf)(h);
626 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
627 bool (
isfinite)(
const Eigen::half& h) {
628 return (half_impl::isfinite)(h);
635 #endif // EIGEN_HALF_CUDA_H const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tanh_op< typename Derived::Scalar >, const Derived > tanh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isfinite_op< typename Derived::Scalar >, const Derived > isfinite(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:287
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_ceil_op< typename Derived::Scalar >, const Derived > ceil(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isnan_op< typename Derived::Scalar >, const Derived > isnan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
const Product< MatrixDerived, PermutationDerived, AliasFreeProduct > operator*(const MatrixBase< MatrixDerived > &matrix, const PermutationBase< PermutationDerived > &permutation)
Definition: PermutationMatrix.h:543
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_floor_op< typename Derived::Scalar >, const Derived > floor(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log1p_op< typename Derived::Scalar >, const Derived > log1p(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isinf_op< typename Derived::Scalar >, const Derived > isinf(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Definition: Eigen_Colamd.h:50
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log_op< typename Derived::Scalar >, const Derived > log(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tan_op< typename Derived::Scalar >, const Derived > tan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sign_op< typename Derived::Scalar >, const Derived > sign(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log10_op< typename Derived::Scalar >, const Derived > log10(const Eigen::ArrayBase< Derived > &x)