1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // This Source Code Form is subject to the terms of the Mozilla 5 // Public License v. 2.0. If a copy of the MPL was not distributed 6 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 7 // 8 // The conversion routines are Copyright (c) Fabian Giesen, 2016. 9 // The original license follows: 10 // 11 // Copyright (c) Fabian Giesen, 2016 12 // All rights reserved. 13 // Redistribution and use in source and binary forms, with or without 14 // modification, are permitted. 15 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 16 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 17 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 18 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 19 // HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 20 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 21 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 22 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 23 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 24 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 25 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 26 27 28 // Standard 16-bit float type, mostly useful for GPUs. Defines a new 29 // type Eigen::half (inheriting from CUDA's __half struct) with 30 // operator overloads such that it behaves basically as an arithmetic 31 // type. It will be quite slow on CPUs (so it is recommended to stay 32 // in float32_bits for CPUs, except for simple parameter conversions, I/O 33 // to disk and the likes), but fast on GPUs. 34 35 36 #ifndef EIGEN_HALF_CUDA_H 37 #define EIGEN_HALF_CUDA_H 38 39 #if __cplusplus > 199711L 40 #define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type() 41 #else 42 #define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type() 43 #endif 44 45 46 namespace Eigen { 47 48 struct half; 49 50 namespace half_impl { 51 52 #if !defined(EIGEN_HAS_CUDA_FP16) 53 // Make our own __half_raw definition that is similar to CUDA's. 54 struct __half_raw { __half_raw__half_raw55 EIGEN_DEVICE_FUNC __half_raw() : x(0) {} __half_raw__half_raw56 explicit EIGEN_DEVICE_FUNC __half_raw(unsigned short raw) : x(raw) {} 57 unsigned short x; 58 }; 59 #elif defined(EIGEN_CUDACC_VER) && EIGEN_CUDACC_VER < 90000 60 // In CUDA < 9.0, __half is the equivalent of CUDA 9's __half_raw 61 typedef __half __half_raw; 62 #endif 63 64 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw raw_uint16_to_half(unsigned short x); 65 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff); 66 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h); 67 68 struct half_base : public __half_raw { half_basehalf_base69 EIGEN_DEVICE_FUNC half_base() {} half_basehalf_base70 EIGEN_DEVICE_FUNC half_base(const half_base& h) : __half_raw(h) {} half_basehalf_base71 EIGEN_DEVICE_FUNC half_base(const __half_raw& h) : __half_raw(h) {} 72 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC_VER) && EIGEN_CUDACC_VER >= 90000 half_basehalf_base73 EIGEN_DEVICE_FUNC half_base(const __half& h) : __half_raw(*(__half_raw*)&h) {} 74 #endif 75 }; 76 77 } // namespace half_impl 78 79 // Class definition. 80 struct half : public half_impl::half_base { 81 #if !defined(EIGEN_HAS_CUDA_FP16) || (defined(EIGEN_CUDACC_VER) && EIGEN_CUDACC_VER < 90000) 82 typedef half_impl::__half_raw __half_raw; 83 #endif 84 halfhalf85 EIGEN_DEVICE_FUNC half() {} 86 halfhalf87 EIGEN_DEVICE_FUNC half(const __half_raw& h) : half_impl::half_base(h) {} halfhalf88 EIGEN_DEVICE_FUNC half(const half& h) : half_impl::half_base(h) {} 89 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC_VER) && EIGEN_CUDACC_VER >= 90000 halfhalf90 EIGEN_DEVICE_FUNC half(const __half& h) : half_impl::half_base(h) {} 91 #endif 92 halfhalf93 explicit EIGEN_DEVICE_FUNC half(bool b) 94 : half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {} 95 template<class T> halfhalf96 explicit EIGEN_DEVICE_FUNC half(const T& val) 97 : half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(val))) {} halfhalf98 explicit EIGEN_DEVICE_FUNC half(float f) 99 : half_impl::half_base(half_impl::float_to_half_rtne(f)) {} 100 EIGEN_EXPLICIT_CASThalf101 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(bool) const { 102 // +0.0 and -0.0 become false, everything else becomes true. 103 return (x & 0x7fff) != 0; 104 } EIGEN_EXPLICIT_CASThalf105 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(signed char) const { 106 return static_cast<signed char>(half_impl::half_to_float(*this)); 107 } EIGEN_EXPLICIT_CASThalf108 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned char) const { 109 return static_cast<unsigned char>(half_impl::half_to_float(*this)); 110 } EIGEN_EXPLICIT_CASThalf111 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(short) const { 112 return static_cast<short>(half_impl::half_to_float(*this)); 113 } EIGEN_EXPLICIT_CASThalf114 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned short) const { 115 return static_cast<unsigned short>(half_impl::half_to_float(*this)); 116 } EIGEN_EXPLICIT_CASThalf117 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(int) const { 118 return static_cast<int>(half_impl::half_to_float(*this)); 119 } EIGEN_EXPLICIT_CASThalf120 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned int) const { 121 return static_cast<unsigned int>(half_impl::half_to_float(*this)); 122 } EIGEN_EXPLICIT_CASThalf123 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long) const { 124 return static_cast<long>(half_impl::half_to_float(*this)); 125 } EIGEN_EXPLICIT_CASThalf126 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long) const { 127 return static_cast<unsigned long>(half_impl::half_to_float(*this)); 128 } EIGEN_EXPLICIT_CASThalf129 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long long) const { 130 return static_cast<long long>(half_impl::half_to_float(*this)); 131 } EIGEN_EXPLICIT_CASThalf132 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long long) const { 133 return static_cast<unsigned long long>(half_to_float(*this)); 134 } EIGEN_EXPLICIT_CASThalf135 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const { 136 return half_impl::half_to_float(*this); 137 } EIGEN_EXPLICIT_CASThalf138 EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(double) const { 139 return static_cast<double>(half_impl::half_to_float(*this)); 140 } 141 142 EIGEN_DEVICE_FUNC half& operator=(const half& other) { 143 x = other.x; 144 return *this; 145 } 146 }; 147 148 } // end namespace Eigen 149 150 namespace std { 151 template<> 152 struct numeric_limits<Eigen::half> { 153 static const bool is_specialized = true; 154 static const bool is_signed = true; 155 static const bool is_integer = false; 156 static const bool is_exact = false; 157 static const bool has_infinity = true; 158 static const bool has_quiet_NaN = true; 159 static const bool has_signaling_NaN = true; 160 static const float_denorm_style has_denorm = denorm_present; 161 static const bool has_denorm_loss = false; 162 static const std::float_round_style round_style = std::round_to_nearest; 163 static const bool is_iec559 = false; 164 static const bool is_bounded = false; 165 static const bool is_modulo = false; 166 static const int digits = 11; 167 static const int digits10 = 3; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html 168 static const int max_digits10 = 5; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html 169 static const int radix = 2; 170 static const int min_exponent = -13; 171 static const int min_exponent10 = -4; 172 static const int max_exponent = 16; 173 static const int max_exponent10 = 4; 174 static const bool traps = true; 175 static const bool tinyness_before = false; 176 177 static Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x400); } 178 static Eigen::half lowest() { return Eigen::half_impl::raw_uint16_to_half(0xfbff); } 179 static Eigen::half (max)() { return Eigen::half_impl::raw_uint16_to_half(0x7bff); } 180 static Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x0800); } 181 static Eigen::half round_error() { return Eigen::half(0.5); } 182 static Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); } 183 static Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); } 184 static Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); } 185 static Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x1); } 186 }; 187 188 // If std::numeric_limits<T> is specialized, should also specialize 189 // std::numeric_limits<const T>, std::numeric_limits<volatile T>, and 190 // std::numeric_limits<const volatile T> 191 // https://stackoverflow.com/a/16519653/ 192 template<> 193 struct numeric_limits<const Eigen::half> : numeric_limits<Eigen::half> {}; 194 template<> 195 struct numeric_limits<volatile Eigen::half> : numeric_limits<Eigen::half> {}; 196 template<> 197 struct numeric_limits<const volatile Eigen::half> : numeric_limits<Eigen::half> {}; 198 } // end namespace std 199 200 namespace Eigen { 201 202 namespace half_impl { 203 204 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 205 206 // Intrinsics for native fp16 support. Note that on current hardware, 207 // these are no faster than float32_bits arithmetic (you need to use the half2 208 // versions to get the ALU speed increased), but you do save the 209 // conversion steps back and forth. 210 211 EIGEN_STRONG_INLINE __device__ half operator + (const half& a, const half& b) { 212 return __hadd(a, b); 213 } 214 EIGEN_STRONG_INLINE __device__ half operator * (const half& a, const half& b) { 215 return __hmul(a, b); 216 } 217 EIGEN_STRONG_INLINE __device__ half operator - (const half& a, const half& b) { 218 return __hsub(a, b); 219 } 220 EIGEN_STRONG_INLINE __device__ half operator / (const half& a, const half& b) { 221 float num = __half2float(a); 222 float denom = __half2float(b); 223 return __float2half(num / denom); 224 } 225 EIGEN_STRONG_INLINE __device__ half operator - (const half& a) { 226 return __hneg(a); 227 } 228 EIGEN_STRONG_INLINE __device__ half& operator += (half& a, const half& b) { 229 a = a + b; 230 return a; 231 } 232 EIGEN_STRONG_INLINE __device__ half& operator *= (half& a, const half& b) { 233 a = a * b; 234 return a; 235 } 236 EIGEN_STRONG_INLINE __device__ half& operator -= (half& a, const half& b) { 237 a = a - b; 238 return a; 239 } 240 EIGEN_STRONG_INLINE __device__ half& operator /= (half& a, const half& b) { 241 a = a / b; 242 return a; 243 } 244 EIGEN_STRONG_INLINE __device__ bool operator == (const half& a, const half& b) { 245 return __heq(a, b); 246 } 247 EIGEN_STRONG_INLINE __device__ bool operator != (const half& a, const half& b) { 248 return __hne(a, b); 249 } 250 EIGEN_STRONG_INLINE __device__ bool operator < (const half& a, const half& b) { 251 return __hlt(a, b); 252 } 253 EIGEN_STRONG_INLINE __device__ bool operator <= (const half& a, const half& b) { 254 return __hle(a, b); 255 } 256 EIGEN_STRONG_INLINE __device__ bool operator > (const half& a, const half& b) { 257 return __hgt(a, b); 258 } 259 EIGEN_STRONG_INLINE __device__ bool operator >= (const half& a, const half& b) { 260 return __hge(a, b); 261 } 262 263 #else // Emulate support for half floats 264 265 // Definitions for CPUs and older CUDA, mostly working through conversion 266 // to/from float32_bits. 267 268 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) { 269 return half(float(a) + float(b)); 270 } 271 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) { 272 return half(float(a) * float(b)); 273 } 274 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) { 275 return half(float(a) - float(b)); 276 } 277 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) { 278 return half(float(a) / float(b)); 279 } 280 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) { 281 half result; 282 result.x = a.x ^ 0x8000; 283 return result; 284 } 285 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) { 286 a = half(float(a) + float(b)); 287 return a; 288 } 289 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) { 290 a = half(float(a) * float(b)); 291 return a; 292 } 293 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) { 294 a = half(float(a) - float(b)); 295 return a; 296 } 297 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) { 298 a = half(float(a) / float(b)); 299 return a; 300 } 301 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) { 302 return numext::equal_strict(float(a),float(b)); 303 } 304 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) { 305 return numext::not_equal_strict(float(a), float(b)); 306 } 307 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) { 308 return float(a) < float(b); 309 } 310 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) { 311 return float(a) <= float(b); 312 } 313 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) { 314 return float(a) > float(b); 315 } 316 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) { 317 return float(a) >= float(b); 318 } 319 320 #endif // Emulate support for half floats 321 322 // Division by an index. Do it in full float precision to avoid accuracy 323 // issues in converting the denominator to half. 324 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) { 325 return half(static_cast<float>(a) / static_cast<float>(b)); 326 } 327 328 // Conversion routines, including fallbacks for the host or older CUDA. 329 // Note that newer Intel CPUs (Haswell or newer) have vectorized versions of 330 // these in hardware. If we need more performance on older/other CPUs, they are 331 // also possible to vectorize directly. 332 333 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw raw_uint16_to_half(unsigned short x) { 334 __half_raw h; 335 h.x = x; 336 return h; 337 } 338 339 union float32_bits { 340 unsigned int u; 341 float f; 342 }; 343 344 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff) { 345 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300 346 __half tmp_ff = __float2half(ff); 347 return *(__half_raw*)&tmp_ff; 348 349 #elif defined(EIGEN_HAS_FP16_C) 350 __half_raw h; 351 h.x = _cvtss_sh(ff, 0); 352 return h; 353 354 #else 355 float32_bits f; f.f = ff; 356 357 const float32_bits f32infty = { 255 << 23 }; 358 const float32_bits f16max = { (127 + 16) << 23 }; 359 const float32_bits denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 }; 360 unsigned int sign_mask = 0x80000000u; 361 __half_raw o; 362 o.x = static_cast<unsigned short>(0x0u); 363 364 unsigned int sign = f.u & sign_mask; 365 f.u ^= sign; 366 367 // NOTE all the integer compares in this function can be safely 368 // compiled into signed compares since all operands are below 369 // 0x80000000. Important if you want fast straight SSE2 code 370 // (since there's no unsigned PCMPGTD). 371 372 if (f.u >= f16max.u) { // result is Inf or NaN (all exponent bits set) 373 o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf 374 } else { // (De)normalized number or zero 375 if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero 376 // use a magic value to align our 10 mantissa bits at the bottom of 377 // the float. as long as FP addition is round-to-nearest-even this 378 // just works. 379 f.f += denorm_magic.f; 380 381 // and one integer subtract of the bias later, we have our final float! 382 o.x = static_cast<unsigned short>(f.u - denorm_magic.u); 383 } else { 384 unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd 385 386 // update exponent, rounding bias part 1 387 f.u += ((unsigned int)(15 - 127) << 23) + 0xfff; 388 // rounding bias part 2 389 f.u += mant_odd; 390 // take the bits! 391 o.x = static_cast<unsigned short>(f.u >> 13); 392 } 393 } 394 395 o.x |= static_cast<unsigned short>(sign >> 16); 396 return o; 397 #endif 398 } 399 400 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h) { 401 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300 402 return __half2float(h); 403 404 #elif defined(EIGEN_HAS_FP16_C) 405 return _cvtsh_ss(h.x); 406 407 #else 408 const float32_bits magic = { 113 << 23 }; 409 const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift 410 float32_bits o; 411 412 o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits 413 unsigned int exp = shifted_exp & o.u; // just the exponent 414 o.u += (127 - 15) << 23; // exponent adjust 415 416 // handle exponent special cases 417 if (exp == shifted_exp) { // Inf/NaN? 418 o.u += (128 - 16) << 23; // extra exp adjust 419 } else if (exp == 0) { // Zero/Denormal? 420 o.u += 1 << 23; // extra exp adjust 421 o.f -= magic.f; // renormalize 422 } 423 424 o.u |= (h.x & 0x8000) << 16; // sign bit 425 return o.f; 426 #endif 427 } 428 429 // --- standard functions --- 430 431 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const half& a) { 432 return (a.x & 0x7fff) == 0x7c00; 433 } 434 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const half& a) { 435 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 436 return __hisnan(a); 437 #else 438 return (a.x & 0x7fff) > 0x7c00; 439 #endif 440 } 441 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const half& a) { 442 return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a)); 443 } 444 445 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half abs(const half& a) { 446 half result; 447 result.x = a.x & 0x7FFF; 448 return result; 449 } 450 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) { 451 #if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530 452 return half(hexp(a)); 453 #else 454 return half(::expf(float(a))); 455 #endif 456 } 457 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) { 458 #if defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDACC_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 459 return half(::hlog(a)); 460 #else 461 return half(::logf(float(a))); 462 #endif 463 } 464 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log1p(const half& a) { 465 return half(numext::log1p(float(a))); 466 } 467 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) { 468 return half(::log10f(float(a))); 469 } 470 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) { 471 #if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530 472 return half(hsqrt(a)); 473 #else 474 return half(::sqrtf(float(a))); 475 #endif 476 } 477 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(const half& a, const half& b) { 478 return half(::powf(float(a), float(b))); 479 } 480 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sin(const half& a) { 481 return half(::sinf(float(a))); 482 } 483 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half cos(const half& a) { 484 return half(::cosf(float(a))); 485 } 486 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tan(const half& a) { 487 return half(::tanf(float(a))); 488 } 489 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tanh(const half& a) { 490 return half(::tanhf(float(a))); 491 } 492 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half floor(const half& a) { 493 #if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300 494 return half(hfloor(a)); 495 #else 496 return half(::floorf(float(a))); 497 #endif 498 } 499 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half ceil(const half& a) { 500 #if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300 501 return half(hceil(a)); 502 #else 503 return half(::ceilf(float(a))); 504 #endif 505 } 506 507 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(const half& a, const half& b) { 508 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 509 return __hlt(b, a) ? b : a; 510 #else 511 const float f1 = static_cast<float>(a); 512 const float f2 = static_cast<float>(b); 513 return f2 < f1 ? b : a; 514 #endif 515 } 516 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(const half& a, const half& b) { 517 #if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 518 return __hlt(a, b) ? b : a; 519 #else 520 const float f1 = static_cast<float>(a); 521 const float f2 = static_cast<float>(b); 522 return f1 < f2 ? b : a; 523 #endif 524 } 525 526 EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const half& v) { 527 os << static_cast<float>(v); 528 return os; 529 } 530 531 } // end namespace half_impl 532 533 // import Eigen::half_impl::half into Eigen namespace 534 // using half_impl::half; 535 536 namespace internal { 537 538 template<> 539 struct random_default_impl<half, false, false> 540 { 541 static inline half run(const half& x, const half& y) 542 { 543 return x + (y-x) * half(float(std::rand()) / float(RAND_MAX)); 544 } 545 static inline half run() 546 { 547 return run(half(-1.f), half(1.f)); 548 } 549 }; 550 551 template<> struct is_arithmetic<half> { enum { value = true }; }; 552 553 } // end namespace internal 554 555 template<> struct NumTraits<Eigen::half> 556 : GenericNumTraits<Eigen::half> 557 { 558 enum { 559 IsSigned = true, 560 IsInteger = false, 561 IsComplex = false, 562 RequireInitialization = false 563 }; 564 565 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half epsilon() { 566 return half_impl::raw_uint16_to_half(0x0800); 567 } 568 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half dummy_precision() { return Eigen::half(1e-2f); } 569 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half highest() { 570 return half_impl::raw_uint16_to_half(0x7bff); 571 } 572 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half lowest() { 573 return half_impl::raw_uint16_to_half(0xfbff); 574 } 575 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half infinity() { 576 return half_impl::raw_uint16_to_half(0x7c00); 577 } 578 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() { 579 return half_impl::raw_uint16_to_half(0x7c01); 580 } 581 }; 582 583 } // end namespace Eigen 584 585 // C-like standard mathematical functions and trancendentals. 586 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half fabsh(const Eigen::half& a) { 587 Eigen::half result; 588 result.x = a.x & 0x7FFF; 589 return result; 590 } 591 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exph(const Eigen::half& a) { 592 return Eigen::half(::expf(float(a))); 593 } 594 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half logh(const Eigen::half& a) { 595 #if EIGEN_CUDACC_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530 596 return Eigen::half(::hlog(a)); 597 #else 598 return Eigen::half(::logf(float(a))); 599 #endif 600 } 601 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrth(const Eigen::half& a) { 602 return Eigen::half(::sqrtf(float(a))); 603 } 604 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half powh(const Eigen::half& a, const Eigen::half& b) { 605 return Eigen::half(::powf(float(a), float(b))); 606 } 607 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floorh(const Eigen::half& a) { 608 return Eigen::half(::floorf(float(a))); 609 } 610 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceilh(const Eigen::half& a) { 611 return Eigen::half(::ceilf(float(a))); 612 } 613 614 namespace std { 615 616 #if __cplusplus > 199711L 617 template <> 618 struct hash<Eigen::half> { 619 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::half& a) const { 620 return static_cast<std::size_t>(a.x); 621 } 622 }; 623 #endif 624 625 } // end namespace std 626 627 628 // Add the missing shfl_xor intrinsic 629 #if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300 630 __device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) { 631 #if EIGEN_CUDACC_VER < 90000 632 return static_cast<Eigen::half>(__shfl_xor(static_cast<float>(var), laneMask, width)); 633 #else 634 return static_cast<Eigen::half>(__shfl_xor_sync(0xFFFFFFFF, static_cast<float>(var), laneMask, width)); 635 #endif 636 } 637 #endif 638 639 // ldg() has an overload for __half_raw, but we also need one for Eigen::half. 640 #if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350 641 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) { 642 return Eigen::half_impl::raw_uint16_to_half( 643 __ldg(reinterpret_cast<const unsigned short*>(ptr))); 644 } 645 #endif 646 647 648 #if defined(EIGEN_CUDA_ARCH) 649 namespace Eigen { 650 namespace numext { 651 652 template<> 653 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE 654 bool (isnan)(const Eigen::half& h) { 655 return (half_impl::isnan)(h); 656 } 657 658 template<> 659 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE 660 bool (isinf)(const Eigen::half& h) { 661 return (half_impl::isinf)(h); 662 } 663 664 template<> 665 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE 666 bool (isfinite)(const Eigen::half& h) { 667 return (half_impl::isfinite)(h); 668 } 669 670 } // namespace Eigen 671 } // namespace numext 672 #endif 673 674 #endif // EIGEN_HALF_CUDA_H 675