| 1 | //===-- Abstract class for bit manipulation of float numbers. ---*- C++ -*-===// |
| 2 | // |
| 3 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| 4 | // See https://llvm.org/LICENSE.txt for license information. |
| 5 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| 6 | // |
| 7 | //===----------------------------------------------------------------------===// |
| 8 | |
| 9 | // ----------------------------------------------------------------------------- |
| 10 | // **** WARNING **** |
| 11 | // This file is shared with libc++. You should also be careful when adding |
| 12 | // dependencies to this file, since it needs to build for all libc++ targets. |
| 13 | // ----------------------------------------------------------------------------- |
| 14 | |
| 15 | #ifndef LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
| 16 | #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
| 17 | |
| 18 | #include "hdr/stdint_proxy.h" |
| 19 | #include "src/__support/CPP/bit.h" |
| 20 | #include "src/__support/CPP/type_traits.h" |
| 21 | #include "src/__support/common.h" |
| 22 | #include "src/__support/libc_assert.h" // LIBC_ASSERT |
| 23 | #include "src/__support/macros/attributes.h" // LIBC_INLINE, LIBC_INLINE_VAR |
| 24 | #include "src/__support/macros/config.h" |
| 25 | #include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_FLOAT128 |
| 26 | #include "src/__support/math_extras.h" // mask_trailing_ones |
| 27 | #include "src/__support/sign.h" // Sign |
| 28 | #include "src/__support/uint128.h" |
| 29 | |
| 30 | namespace LIBC_NAMESPACE_DECL { |
| 31 | namespace fputil { |
| 32 | |
| 33 | // The supported floating point types. |
| 34 | enum class FPType { |
| 35 | IEEE754_Binary16, |
| 36 | IEEE754_Binary32, |
| 37 | IEEE754_Binary64, |
| 38 | IEEE754_Binary128, |
| 39 | X86_Binary80, |
| 40 | BFloat16 |
| 41 | }; |
| 42 | |
| 43 | // The classes hierarchy is as follows: |
| 44 | // |
| 45 | // ┌───────────────────┐ |
| 46 | // │ FPLayout<FPType> │ |
| 47 | // └─────────▲─────────┘ |
| 48 | // │ |
| 49 | // ┌─────────┴─────────┐ |
| 50 | // │ FPStorage<FPType> │ |
| 51 | // └─────────▲─────────┘ |
| 52 | // │ |
| 53 | // ┌────────────┴─────────────┐ |
| 54 | // │ │ |
| 55 | // ┌────────┴─────────┐ ┌──────────────┴──────────────────┐ |
| 56 | // │ FPRepSem<FPType> │ │ FPRepSem<FPType::X86_Binary80 │ |
| 57 | // └────────▲─────────┘ └──────────────▲──────────────────┘ |
| 58 | // │ │ |
| 59 | // └────────────┬─────────────┘ |
| 60 | // │ |
| 61 | // ┌───────┴───────┐ |
| 62 | // │ FPRepImpl<T> │ |
| 63 | // └───────▲───────┘ |
| 64 | // │ |
| 65 | // ┌────────┴────────┐ |
| 66 | // ┌─────┴─────┐ ┌─────┴─────┐ |
| 67 | // │ FPRep<T> │ │ FPBits<T> │ |
| 68 | // └───────────┘ └───────────┘ |
| 69 | // |
| 70 | // - 'FPLayout' defines only a few constants, namely the 'StorageType' and |
| 71 | // length of the sign, the exponent, fraction and significand parts. |
| 72 | // - 'FPStorage' builds more constants on top of those from 'FPLayout' like |
| 73 | // exponent bias and masks. It also holds the bit representation of the |
| 74 | // floating point as a 'StorageType' type and defines tools to assemble or |
| 75 | // test these parts. |
| 76 | // - 'FPRepSem' defines functions to interact semantically with the floating |
| 77 | // point representation. The default implementation is the one for 'IEEE754', |
| 78 | // a specialization is provided for X86 Extended Precision. |
| 79 | // - 'FPRepImpl' derives from 'FPRepSem' and adds functions that are common to |
| 80 | // all implementations or build on the ones in 'FPRepSem'. |
| 81 | // - 'FPRep' exposes all functions from 'FPRepImpl' and returns 'FPRep' |
| 82 | // instances when using Builders (static functions to create values). |
| 83 | // - 'FPBits' exposes all the functions from 'FPRepImpl' but operates on the |
| 84 | // native C++ floating point type instead of 'FPType'. An additional 'get_val' |
| 85 | // function allows getting the C++ floating point type value back. Builders |
| 86 | // called from 'FPBits' return 'FPBits' instances. |
| 87 | |
| 88 | namespace internal { |
| 89 | |
| 90 | // Defines the layout (sign, exponent, significand) of a floating point type in |
| 91 | // memory. It also defines its associated StorageType, i.e., the unsigned |
| 92 | // integer type used to manipulate its representation. |
| 93 | // Additionally we provide the fractional part length, i.e., the number of bits |
| 94 | // after the decimal dot when the number is in normal form. |
| 95 | template <FPType> struct FPLayout {}; |
| 96 | |
| 97 | template <> struct FPLayout<FPType::IEEE754_Binary16> { |
| 98 | using StorageType = uint16_t; |
| 99 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 100 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 5; |
| 101 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 10; |
| 102 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
| 103 | }; |
| 104 | |
| 105 | template <> struct FPLayout<FPType::IEEE754_Binary32> { |
| 106 | using StorageType = uint32_t; |
| 107 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 108 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 8; |
| 109 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 23; |
| 110 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
| 111 | }; |
| 112 | |
| 113 | template <> struct FPLayout<FPType::IEEE754_Binary64> { |
| 114 | using StorageType = uint64_t; |
| 115 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 116 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 11; |
| 117 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 52; |
| 118 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
| 119 | }; |
| 120 | |
| 121 | template <> struct FPLayout<FPType::IEEE754_Binary128> { |
| 122 | using StorageType = UInt128; |
| 123 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 124 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 15; |
| 125 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 112; |
| 126 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
| 127 | }; |
| 128 | |
| 129 | template <> struct FPLayout<FPType::X86_Binary80> { |
| 130 | #if __SIZEOF_LONG_DOUBLE__ == 12 |
| 131 | using StorageType = UInt<__SIZEOF_LONG_DOUBLE__ * CHAR_BIT>; |
| 132 | #else |
| 133 | using StorageType = UInt128; |
| 134 | #endif |
| 135 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 136 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 15; |
| 137 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 64; |
| 138 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN - 1; |
| 139 | }; |
| 140 | |
| 141 | template <> struct FPLayout<FPType::BFloat16> { |
| 142 | using StorageType = uint16_t; |
| 143 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
| 144 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 8; |
| 145 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 7; |
| 146 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
| 147 | }; |
| 148 | |
| 149 | // FPStorage derives useful constants from the FPLayout above. |
| 150 | template <FPType fp_type> struct FPStorage : public FPLayout<fp_type> { |
| 151 | using UP = FPLayout<fp_type>; |
| 152 | |
| 153 | using UP::EXP_LEN; // The number of bits for the *exponent* part |
| 154 | using UP::SIG_LEN; // The number of bits for the *significand* part |
| 155 | using UP::SIGN_LEN; // The number of bits for the *sign* part |
| 156 | // For convenience, the sum of `SIG_LEN`, `EXP_LEN`, and `SIGN_LEN`. |
| 157 | LIBC_INLINE_VAR static constexpr int TOTAL_LEN = SIGN_LEN + EXP_LEN + SIG_LEN; |
| 158 | |
| 159 | // The number of bits after the decimal dot when the number is in normal form. |
| 160 | using UP::FRACTION_LEN; |
| 161 | |
| 162 | // An unsigned integer that is wide enough to contain all of the floating |
| 163 | // point bits. |
| 164 | using StorageType = typename UP::StorageType; |
| 165 | |
| 166 | // The number of bits in StorageType. |
| 167 | LIBC_INLINE_VAR static constexpr int STORAGE_LEN = |
| 168 | sizeof(StorageType) * CHAR_BIT; |
| 169 | static_assert(STORAGE_LEN >= TOTAL_LEN); |
| 170 | |
| 171 | // The exponent bias. Always positive. |
| 172 | LIBC_INLINE_VAR static constexpr int32_t EXP_BIAS = |
| 173 | (1U << (EXP_LEN - 1U)) - 1U; |
| 174 | static_assert(EXP_BIAS > 0); |
| 175 | |
| 176 | // The bit pattern that keeps only the *significand* part. |
| 177 | LIBC_INLINE_VAR static constexpr StorageType SIG_MASK = |
| 178 | mask_trailing_ones<StorageType, SIG_LEN>(); |
| 179 | // The bit pattern that keeps only the *exponent* part. |
| 180 | LIBC_INLINE_VAR static constexpr StorageType EXP_MASK = |
| 181 | mask_trailing_ones<StorageType, EXP_LEN>() << SIG_LEN; |
| 182 | // The bit pattern that keeps only the *sign* part. |
| 183 | LIBC_INLINE_VAR static constexpr StorageType SIGN_MASK = |
| 184 | mask_trailing_ones<StorageType, SIGN_LEN>() << (EXP_LEN + SIG_LEN); |
| 185 | // The bit pattern that keeps only the *exponent + significand* part. |
| 186 | LIBC_INLINE_VAR static constexpr StorageType EXP_SIG_MASK = |
| 187 | mask_trailing_ones<StorageType, EXP_LEN + SIG_LEN>(); |
| 188 | // The bit pattern that keeps only the *sign + exponent + significand* part. |
| 189 | LIBC_INLINE_VAR static constexpr StorageType FP_MASK = |
| 190 | mask_trailing_ones<StorageType, TOTAL_LEN>(); |
| 191 | // The bit pattern that keeps only the *fraction* part. |
| 192 | // i.e., the *significand* without the leading one. |
| 193 | LIBC_INLINE_VAR static constexpr StorageType FRACTION_MASK = |
| 194 | mask_trailing_ones<StorageType, FRACTION_LEN>(); |
| 195 | |
| 196 | static_assert((SIG_MASK & EXP_MASK & SIGN_MASK) == 0, "masks disjoint" ); |
| 197 | static_assert((SIG_MASK | EXP_MASK | SIGN_MASK) == FP_MASK, "masks cover" ); |
| 198 | |
| 199 | protected: |
| 200 | // Merge bits from 'a' and 'b' values according to 'mask'. |
| 201 | // Use 'a' bits when corresponding 'mask' bits are zeroes and 'b' bits when |
| 202 | // corresponding bits are ones. |
| 203 | LIBC_INLINE static constexpr StorageType merge(StorageType a, StorageType b, |
| 204 | StorageType mask) { |
| 205 | // https://graphics.stanford.edu/~seander/bithacks.html#MaskedMerge |
| 206 | return a ^ ((a ^ b) & mask); |
| 207 | } |
| 208 | |
| 209 | // A stongly typed integer that prevents mixing and matching integers with |
| 210 | // different semantics. |
| 211 | template <typename T> struct TypedInt { |
| 212 | using value_type = T; |
| 213 | LIBC_INLINE constexpr explicit TypedInt(T value) : value(value) {} |
| 214 | LIBC_INLINE constexpr TypedInt(const TypedInt &value) = default; |
| 215 | LIBC_INLINE constexpr TypedInt &operator=(const TypedInt &value) = default; |
| 216 | |
| 217 | LIBC_INLINE constexpr explicit operator T() const { return value; } |
| 218 | |
| 219 | LIBC_INLINE constexpr StorageType to_storage_type() const { |
| 220 | return StorageType(value); |
| 221 | } |
| 222 | |
| 223 | LIBC_INLINE friend constexpr bool operator==(TypedInt a, TypedInt b) { |
| 224 | return a.value == b.value; |
| 225 | } |
| 226 | LIBC_INLINE friend constexpr bool operator!=(TypedInt a, TypedInt b) { |
| 227 | return a.value != b.value; |
| 228 | } |
| 229 | |
| 230 | protected: |
| 231 | T value; |
| 232 | }; |
| 233 | |
| 234 | // An opaque type to store a floating point exponent. |
| 235 | // We define special values but it is valid to create arbitrary values as long |
| 236 | // as they are in the range [min, max]. |
| 237 | struct Exponent : public TypedInt<int32_t> { |
| 238 | using UP = TypedInt<int32_t>; |
| 239 | using UP::UP; |
| 240 | LIBC_INLINE static constexpr auto subnormal() { |
| 241 | return Exponent(-EXP_BIAS); |
| 242 | } |
| 243 | LIBC_INLINE static constexpr auto min() { return Exponent(1 - EXP_BIAS); } |
| 244 | LIBC_INLINE static constexpr auto zero() { return Exponent(0); } |
| 245 | LIBC_INLINE static constexpr auto max() { return Exponent(EXP_BIAS); } |
| 246 | LIBC_INLINE static constexpr auto inf() { return Exponent(EXP_BIAS + 1); } |
| 247 | }; |
| 248 | |
| 249 | // An opaque type to store a floating point biased exponent. |
| 250 | // We define special values but it is valid to create arbitrary values as long |
| 251 | // as they are in the range [zero, bits_all_ones]. |
| 252 | // Values greater than bits_all_ones are truncated. |
| 253 | struct BiasedExponent : public TypedInt<uint32_t> { |
| 254 | using UP = TypedInt<uint32_t>; |
| 255 | using UP::UP; |
| 256 | |
| 257 | LIBC_INLINE constexpr BiasedExponent(Exponent exp) |
| 258 | : UP(static_cast<uint32_t>(static_cast<int32_t>(exp) + EXP_BIAS)) {} |
| 259 | |
| 260 | // Cast operator to get convert from BiasedExponent to Exponent. |
| 261 | LIBC_INLINE constexpr operator Exponent() const { |
| 262 | return Exponent(static_cast<int32_t>(UP::value - EXP_BIAS)); |
| 263 | } |
| 264 | |
| 265 | LIBC_INLINE constexpr BiasedExponent &operator++() { |
| 266 | LIBC_ASSERT(*this != BiasedExponent(Exponent::inf())); |
| 267 | ++UP::value; |
| 268 | return *this; |
| 269 | } |
| 270 | |
| 271 | LIBC_INLINE constexpr BiasedExponent &operator--() { |
| 272 | LIBC_ASSERT(*this != BiasedExponent(Exponent::subnormal())); |
| 273 | --UP::value; |
| 274 | return *this; |
| 275 | } |
| 276 | }; |
| 277 | |
| 278 | // An opaque type to store a floating point significand. |
| 279 | // We define special values but it is valid to create arbitrary values as long |
| 280 | // as they are in the range [zero, bits_all_ones]. |
| 281 | // Note that the semantics of the Significand are implementation dependent. |
| 282 | // Values greater than bits_all_ones are truncated. |
| 283 | struct Significand : public TypedInt<StorageType> { |
| 284 | using UP = TypedInt<StorageType>; |
| 285 | using UP::UP; |
| 286 | |
| 287 | LIBC_INLINE friend constexpr Significand operator|(const Significand a, |
| 288 | const Significand b) { |
| 289 | return Significand( |
| 290 | StorageType(a.to_storage_type() | b.to_storage_type())); |
| 291 | } |
| 292 | LIBC_INLINE friend constexpr Significand operator^(const Significand a, |
| 293 | const Significand b) { |
| 294 | return Significand( |
| 295 | StorageType(a.to_storage_type() ^ b.to_storage_type())); |
| 296 | } |
| 297 | LIBC_INLINE friend constexpr Significand operator>>(const Significand a, |
| 298 | int shift) { |
| 299 | return Significand(StorageType(a.to_storage_type() >> shift)); |
| 300 | } |
| 301 | |
| 302 | LIBC_INLINE static constexpr auto zero() { |
| 303 | return Significand(StorageType(0)); |
| 304 | } |
| 305 | LIBC_INLINE static constexpr auto lsb() { |
| 306 | return Significand(StorageType(1)); |
| 307 | } |
| 308 | LIBC_INLINE static constexpr auto msb() { |
| 309 | return Significand(StorageType(1) << (SIG_LEN - 1)); |
| 310 | } |
| 311 | LIBC_INLINE static constexpr auto bits_all_ones() { |
| 312 | return Significand(SIG_MASK); |
| 313 | } |
| 314 | }; |
| 315 | |
| 316 | LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp) { |
| 317 | return (exp.to_storage_type() << SIG_LEN) & EXP_MASK; |
| 318 | } |
| 319 | |
| 320 | LIBC_INLINE static constexpr StorageType encode(Significand value) { |
| 321 | return value.to_storage_type() & SIG_MASK; |
| 322 | } |
| 323 | |
| 324 | LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp, |
| 325 | Significand sig) { |
| 326 | return encode(exp) | encode(sig); |
| 327 | } |
| 328 | |
| 329 | LIBC_INLINE static constexpr StorageType encode(Sign sign, BiasedExponent exp, |
| 330 | Significand sig) { |
| 331 | if (sign.is_neg()) |
| 332 | return SIGN_MASK | encode(exp, sig); |
| 333 | return encode(exp, sig); |
| 334 | } |
| 335 | |
| 336 | // The floating point number representation as an unsigned integer. |
| 337 | StorageType bits{}; |
| 338 | |
| 339 | LIBC_INLINE constexpr FPStorage() : bits(0) {} |
| 340 | LIBC_INLINE constexpr FPStorage(StorageType value) : bits(value) {} |
| 341 | |
| 342 | // Observers |
| 343 | LIBC_INLINE constexpr StorageType exp_bits() const { return bits & EXP_MASK; } |
| 344 | LIBC_INLINE constexpr StorageType sig_bits() const { return bits & SIG_MASK; } |
| 345 | LIBC_INLINE constexpr StorageType exp_sig_bits() const { |
| 346 | return bits & EXP_SIG_MASK; |
| 347 | } |
| 348 | |
| 349 | // Parts |
| 350 | LIBC_INLINE constexpr BiasedExponent biased_exponent() const { |
| 351 | return BiasedExponent(static_cast<uint32_t>(exp_bits() >> SIG_LEN)); |
| 352 | } |
| 353 | LIBC_INLINE constexpr void set_biased_exponent(BiasedExponent biased) { |
| 354 | bits = merge(a: bits, b: encode(biased), mask: EXP_MASK); |
| 355 | } |
| 356 | |
| 357 | public: |
| 358 | LIBC_INLINE constexpr Sign sign() const { |
| 359 | return (bits & SIGN_MASK) ? Sign::NEG : Sign::POS; |
| 360 | } |
| 361 | LIBC_INLINE constexpr void set_sign(Sign signVal) { |
| 362 | if (sign() != signVal) |
| 363 | bits ^= SIGN_MASK; |
| 364 | } |
| 365 | }; |
| 366 | |
| 367 | // This layer defines all functions that are specific to how the the floating |
| 368 | // point type is encoded. It enables constructions, modification and observation |
| 369 | // of values manipulated as 'StorageType'. |
| 370 | template <FPType fp_type, typename RetT> |
| 371 | struct FPRepSem : public FPStorage<fp_type> { |
| 372 | using UP = FPStorage<fp_type>; |
| 373 | using typename UP::StorageType; |
| 374 | using UP::FRACTION_LEN; |
| 375 | using UP::FRACTION_MASK; |
| 376 | |
| 377 | protected: |
| 378 | using typename UP::Exponent; |
| 379 | using typename UP::Significand; |
| 380 | using UP::bits; |
| 381 | using UP::encode; |
| 382 | using UP::exp_bits; |
| 383 | using UP::exp_sig_bits; |
| 384 | using UP::sig_bits; |
| 385 | using UP::UP; |
| 386 | |
| 387 | public: |
| 388 | // Builders |
| 389 | LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) { |
| 390 | return RetT(encode(sign, Exponent::subnormal(), Significand::zero())); |
| 391 | } |
| 392 | LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) { |
| 393 | return RetT(encode(sign, Exponent::zero(), Significand::zero())); |
| 394 | } |
| 395 | LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) { |
| 396 | return RetT(encode(sign, Exponent::subnormal(), Significand::lsb())); |
| 397 | } |
| 398 | LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) { |
| 399 | return RetT( |
| 400 | encode(sign, Exponent::subnormal(), Significand::bits_all_ones())); |
| 401 | } |
| 402 | LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) { |
| 403 | return RetT(encode(sign, Exponent::min(), Significand::zero())); |
| 404 | } |
| 405 | LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) { |
| 406 | return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones())); |
| 407 | } |
| 408 | LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) { |
| 409 | return RetT(encode(sign, Exponent::inf(), Significand::zero())); |
| 410 | } |
| 411 | LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS, |
| 412 | StorageType v = 0) { |
| 413 | return RetT(encode(sign, Exponent::inf(), |
| 414 | (v ? Significand(v) : (Significand::msb() >> 1)))); |
| 415 | } |
| 416 | LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS, |
| 417 | StorageType v = 0) { |
| 418 | return RetT( |
| 419 | encode(sign, Exponent::inf(), Significand::msb() | Significand(v))); |
| 420 | } |
| 421 | |
| 422 | // Observers |
| 423 | LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; } |
| 424 | LIBC_INLINE constexpr bool is_nan() const { |
| 425 | return exp_sig_bits() > encode(Exponent::inf(), Significand::zero()); |
| 426 | } |
| 427 | LIBC_INLINE constexpr bool is_quiet_nan() const { |
| 428 | return exp_sig_bits() >= encode(Exponent::inf(), Significand::msb()); |
| 429 | } |
| 430 | LIBC_INLINE constexpr bool is_signaling_nan() const { |
| 431 | return is_nan() && !is_quiet_nan(); |
| 432 | } |
| 433 | LIBC_INLINE constexpr bool is_inf() const { |
| 434 | return exp_sig_bits() == encode(Exponent::inf(), Significand::zero()); |
| 435 | } |
| 436 | LIBC_INLINE constexpr bool is_finite() const { |
| 437 | return exp_bits() != encode(Exponent::inf()); |
| 438 | } |
| 439 | LIBC_INLINE |
| 440 | constexpr bool is_subnormal() const { |
| 441 | return exp_bits() == encode(Exponent::subnormal()); |
| 442 | } |
| 443 | LIBC_INLINE constexpr bool is_normal() const { |
| 444 | return is_finite() && !is_subnormal(); |
| 445 | } |
| 446 | LIBC_INLINE constexpr RetT next_toward_inf() const { |
| 447 | if (is_finite()) |
| 448 | return RetT(bits + StorageType(1)); |
| 449 | return RetT(bits); |
| 450 | } |
| 451 | |
| 452 | // Returns the mantissa with the implicit bit set iff the current |
| 453 | // value is a valid normal number. |
| 454 | LIBC_INLINE constexpr StorageType get_explicit_mantissa() const { |
| 455 | if (is_subnormal()) |
| 456 | return sig_bits(); |
| 457 | return (StorageType(1) << UP::SIG_LEN) | sig_bits(); |
| 458 | } |
| 459 | }; |
| 460 | |
| 461 | // Specialization for the X86 Extended Precision type. |
| 462 | template <typename RetT> |
| 463 | struct FPRepSem<FPType::X86_Binary80, RetT> |
| 464 | : public FPStorage<FPType::X86_Binary80> { |
| 465 | using UP = FPStorage<FPType::X86_Binary80>; |
| 466 | using typename UP::StorageType; |
| 467 | using UP::FRACTION_LEN; |
| 468 | using UP::FRACTION_MASK; |
| 469 | |
| 470 | // The x86 80 bit float represents the leading digit of the mantissa |
| 471 | // explicitly. This is the mask for that bit. |
| 472 | static constexpr StorageType EXPLICIT_BIT_MASK = StorageType(1) |
| 473 | << FRACTION_LEN; |
| 474 | // The X80 significand is made of an explicit bit and the fractional part. |
| 475 | static_assert((EXPLICIT_BIT_MASK & FRACTION_MASK) == 0, |
| 476 | "the explicit bit and the fractional part should not overlap" ); |
| 477 | static_assert((EXPLICIT_BIT_MASK | FRACTION_MASK) == SIG_MASK, |
| 478 | "the explicit bit and the fractional part should cover the " |
| 479 | "whole significand" ); |
| 480 | |
| 481 | protected: |
| 482 | using typename UP::Exponent; |
| 483 | using typename UP::Significand; |
| 484 | using UP::encode; |
| 485 | using UP::UP; |
| 486 | |
| 487 | public: |
| 488 | // Builders |
| 489 | LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) { |
| 490 | return RetT(encode(sign, Exponent::subnormal(), Significand::zero())); |
| 491 | } |
| 492 | LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) { |
| 493 | return RetT(encode(sign, Exponent::zero(), Significand::msb())); |
| 494 | } |
| 495 | LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) { |
| 496 | return RetT(encode(sign, Exponent::subnormal(), Significand::lsb())); |
| 497 | } |
| 498 | LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) { |
| 499 | return RetT(encode(sign, Exponent::subnormal(), |
| 500 | Significand::bits_all_ones() ^ Significand::msb())); |
| 501 | } |
| 502 | LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) { |
| 503 | return RetT(encode(sign, Exponent::min(), Significand::msb())); |
| 504 | } |
| 505 | LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) { |
| 506 | return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones())); |
| 507 | } |
| 508 | LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) { |
| 509 | return RetT(encode(sign, Exponent::inf(), Significand::msb())); |
| 510 | } |
| 511 | LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS, |
| 512 | StorageType v = 0) { |
| 513 | return RetT(encode(sign, Exponent::inf(), |
| 514 | Significand::msb() | |
| 515 | (v ? Significand(v) : (Significand::msb() >> 2)))); |
| 516 | } |
| 517 | LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS, |
| 518 | StorageType v = 0) { |
| 519 | return RetT(encode(sign, Exponent::inf(), |
| 520 | Significand::msb() | (Significand::msb() >> 1) | |
| 521 | Significand(v))); |
| 522 | } |
| 523 | |
| 524 | // Observers |
| 525 | LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; } |
| 526 | LIBC_INLINE constexpr bool is_nan() const { |
| 527 | // Most encoding forms from the table found in |
| 528 | // https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format |
| 529 | // are interpreted as NaN. |
| 530 | // More precisely : |
| 531 | // - Pseudo-Infinity |
| 532 | // - Pseudo Not a Number |
| 533 | // - Signalling Not a Number |
| 534 | // - Floating-point Indefinite |
| 535 | // - Quiet Not a Number |
| 536 | // - Unnormal |
| 537 | // This can be reduced to the following logic: |
| 538 | if (exp_bits() == encode(Exponent::inf())) |
| 539 | return !is_inf(); |
| 540 | if (exp_bits() != encode(Exponent::subnormal())) |
| 541 | return (sig_bits() & encode(Significand::msb())) == 0; |
| 542 | return false; |
| 543 | } |
| 544 | LIBC_INLINE constexpr bool is_quiet_nan() const { |
| 545 | return exp_sig_bits() >= |
| 546 | encode(Exponent::inf(), |
| 547 | Significand::msb() | (Significand::msb() >> 1)); |
| 548 | } |
| 549 | LIBC_INLINE constexpr bool is_signaling_nan() const { |
| 550 | return is_nan() && !is_quiet_nan(); |
| 551 | } |
| 552 | LIBC_INLINE constexpr bool is_inf() const { |
| 553 | return exp_sig_bits() == encode(Exponent::inf(), Significand::msb()); |
| 554 | } |
| 555 | LIBC_INLINE constexpr bool is_finite() const { |
| 556 | return !is_inf() && !is_nan(); |
| 557 | } |
| 558 | LIBC_INLINE |
| 559 | constexpr bool is_subnormal() const { |
| 560 | return exp_bits() == encode(Exponent::subnormal()); |
| 561 | } |
| 562 | LIBC_INLINE constexpr bool is_normal() const { |
| 563 | const auto exp = exp_bits(); |
| 564 | if (exp == encode(Exponent::subnormal()) || exp == encode(Exponent::inf())) |
| 565 | return false; |
| 566 | return get_implicit_bit(); |
| 567 | } |
| 568 | LIBC_INLINE constexpr RetT next_toward_inf() const { |
| 569 | if (is_finite()) { |
| 570 | if (exp_sig_bits() == max_normal().uintval()) { |
| 571 | return inf(sign: sign()); |
| 572 | } else if (exp_sig_bits() == max_subnormal().uintval()) { |
| 573 | return min_normal(sign: sign()); |
| 574 | } else if (sig_bits() == SIG_MASK) { |
| 575 | return RetT(encode(sign(), ++biased_exponent(), Significand::zero())); |
| 576 | } else { |
| 577 | return RetT(bits + StorageType(1)); |
| 578 | } |
| 579 | } |
| 580 | return RetT(bits); |
| 581 | } |
| 582 | |
| 583 | LIBC_INLINE constexpr StorageType get_explicit_mantissa() const { |
| 584 | return sig_bits(); |
| 585 | } |
| 586 | |
| 587 | // This functions is specific to FPRepSem<FPType::X86_Binary80>. |
| 588 | // TODO: Remove if possible. |
| 589 | LIBC_INLINE constexpr bool get_implicit_bit() const { |
| 590 | return static_cast<bool>(bits & EXPLICIT_BIT_MASK); |
| 591 | } |
| 592 | |
| 593 | // This functions is specific to FPRepSem<FPType::X86_Binary80>. |
| 594 | // TODO: Remove if possible. |
| 595 | LIBC_INLINE constexpr void set_implicit_bit(bool implicitVal) { |
| 596 | if (get_implicit_bit() != implicitVal) |
| 597 | bits ^= EXPLICIT_BIT_MASK; |
| 598 | } |
| 599 | }; |
| 600 | |
| 601 | // 'FPRepImpl' is the bottom of the class hierarchy that only deals with |
| 602 | // 'FPType'. The operations dealing with specific float semantics are |
| 603 | // implemented by 'FPRepSem' above and specialized when needed. |
| 604 | // |
| 605 | // The 'RetT' type is being propagated up to 'FPRepSem' so that the functions |
| 606 | // creating new values (Builders) can return the appropriate type. That is, when |
| 607 | // creating a value through 'FPBits' below the builder will return an 'FPBits' |
| 608 | // value. |
| 609 | // FPBits<float>::zero(); // returns an FPBits<> |
| 610 | // |
| 611 | // When we don't care about specific C++ floating point type we can use |
| 612 | // 'FPRep' and specify the 'FPType' directly. |
| 613 | // FPRep<FPType::IEEE754_Binary32:>::zero() // returns an FPRep<> |
| 614 | template <FPType fp_type, typename RetT> |
| 615 | struct FPRepImpl : public FPRepSem<fp_type, RetT> { |
| 616 | using UP = FPRepSem<fp_type, RetT>; |
| 617 | using StorageType = typename UP::StorageType; |
| 618 | |
| 619 | protected: |
| 620 | using UP::bits; |
| 621 | using UP::encode; |
| 622 | using UP::exp_bits; |
| 623 | using UP::exp_sig_bits; |
| 624 | |
| 625 | using typename UP::BiasedExponent; |
| 626 | using typename UP::Exponent; |
| 627 | using typename UP::Significand; |
| 628 | |
| 629 | using UP::FP_MASK; |
| 630 | |
| 631 | public: |
| 632 | // Constants. |
| 633 | using UP::EXP_BIAS; |
| 634 | using UP::EXP_MASK; |
| 635 | using UP::FRACTION_MASK; |
| 636 | using UP::SIG_LEN; |
| 637 | using UP::SIG_MASK; |
| 638 | using UP::SIGN_MASK; |
| 639 | LIBC_INLINE_VAR static constexpr int MAX_BIASED_EXPONENT = |
| 640 | (1 << UP::EXP_LEN) - 1; |
| 641 | |
| 642 | // CTors |
| 643 | LIBC_INLINE constexpr FPRepImpl() = default; |
| 644 | LIBC_INLINE constexpr explicit FPRepImpl(StorageType x) : UP(x) {} |
| 645 | |
| 646 | // Comparison |
| 647 | LIBC_INLINE constexpr friend bool operator==(FPRepImpl a, FPRepImpl b) { |
| 648 | return a.uintval() == b.uintval(); |
| 649 | } |
| 650 | LIBC_INLINE constexpr friend bool operator!=(FPRepImpl a, FPRepImpl b) { |
| 651 | return a.uintval() != b.uintval(); |
| 652 | } |
| 653 | |
| 654 | // Representation |
| 655 | LIBC_INLINE constexpr StorageType uintval() const { return bits & FP_MASK; } |
| 656 | LIBC_INLINE constexpr void set_uintval(StorageType value) { |
| 657 | bits = (value & FP_MASK); |
| 658 | } |
| 659 | |
| 660 | // Builders |
| 661 | using UP::inf; |
| 662 | using UP::max_normal; |
| 663 | using UP::max_subnormal; |
| 664 | using UP::min_normal; |
| 665 | using UP::min_subnormal; |
| 666 | using UP::one; |
| 667 | using UP::quiet_nan; |
| 668 | using UP::signaling_nan; |
| 669 | using UP::zero; |
| 670 | |
| 671 | // Modifiers |
| 672 | LIBC_INLINE constexpr RetT abs() const { |
| 673 | return RetT(static_cast<StorageType>(bits & UP::EXP_SIG_MASK)); |
| 674 | } |
| 675 | |
| 676 | // Observers |
| 677 | using UP::get_explicit_mantissa; |
| 678 | using UP::is_finite; |
| 679 | using UP::is_inf; |
| 680 | using UP::is_nan; |
| 681 | using UP::is_normal; |
| 682 | using UP::is_quiet_nan; |
| 683 | using UP::is_signaling_nan; |
| 684 | using UP::is_subnormal; |
| 685 | using UP::is_zero; |
| 686 | using UP::next_toward_inf; |
| 687 | using UP::sign; |
| 688 | LIBC_INLINE constexpr bool is_inf_or_nan() const { return !is_finite(); } |
| 689 | LIBC_INLINE constexpr bool is_neg() const { return sign().is_neg(); } |
| 690 | LIBC_INLINE constexpr bool is_pos() const { return sign().is_pos(); } |
| 691 | |
| 692 | LIBC_INLINE constexpr uint16_t get_biased_exponent() const { |
| 693 | return static_cast<uint16_t>(static_cast<uint32_t>(UP::biased_exponent())); |
| 694 | } |
| 695 | |
| 696 | LIBC_INLINE constexpr void set_biased_exponent(StorageType biased) { |
| 697 | UP::set_biased_exponent(BiasedExponent(static_cast<uint32_t>(biased))); |
| 698 | } |
| 699 | |
| 700 | LIBC_INLINE constexpr int get_exponent() const { |
| 701 | return static_cast<int32_t>(Exponent(UP::biased_exponent())); |
| 702 | } |
| 703 | |
| 704 | // If the number is subnormal, the exponent is treated as if it were the |
| 705 | // minimum exponent for a normal number. This is to keep continuity between |
| 706 | // the normal and subnormal ranges, but it causes problems for functions where |
| 707 | // values are calculated from the exponent, since just subtracting the bias |
| 708 | // will give a slightly incorrect result. Additionally, zero has an exponent |
| 709 | // of zero, and that should actually be treated as zero. |
| 710 | LIBC_INLINE constexpr int get_explicit_exponent() const { |
| 711 | Exponent exponent(UP::biased_exponent()); |
| 712 | if (is_zero()) |
| 713 | exponent = Exponent::zero(); |
| 714 | if (exponent == Exponent::subnormal()) |
| 715 | exponent = Exponent::min(); |
| 716 | return static_cast<int32_t>(exponent); |
| 717 | } |
| 718 | |
| 719 | LIBC_INLINE constexpr StorageType get_mantissa() const { |
| 720 | return bits & FRACTION_MASK; |
| 721 | } |
| 722 | |
| 723 | LIBC_INLINE constexpr void set_mantissa(StorageType mantVal) { |
| 724 | bits = UP::merge(bits, mantVal, FRACTION_MASK); |
| 725 | } |
| 726 | |
| 727 | LIBC_INLINE constexpr void set_significand(StorageType sigVal) { |
| 728 | bits = UP::merge(bits, sigVal, SIG_MASK); |
| 729 | } |
| 730 | // Unsafe function to create a floating point representation. |
| 731 | // It simply packs the sign, biased exponent and mantissa values without |
| 732 | // checking bound nor normalization. |
| 733 | // |
| 734 | // WARNING: For X86 Extended Precision, implicit bit needs to be set correctly |
| 735 | // in the 'mantissa' by the caller. This function will not check for its |
| 736 | // validity. |
| 737 | // |
| 738 | // FIXME: Use an uint32_t for 'biased_exp'. |
| 739 | LIBC_INLINE static constexpr RetT |
| 740 | create_value(Sign sign, StorageType biased_exp, StorageType mantissa) { |
| 741 | return RetT(encode(sign, BiasedExponent(static_cast<uint32_t>(biased_exp)), |
| 742 | Significand(mantissa))); |
| 743 | } |
| 744 | |
| 745 | // The function converts integer number and unbiased exponent to proper |
| 746 | // float T type: |
| 747 | // Result = number * 2^(ep+1 - exponent_bias) |
| 748 | // Be careful! |
| 749 | // 1) "ep" is the raw exponent value. |
| 750 | // 2) The function adds +1 to ep for seamless normalized to denormalized |
| 751 | // transition. |
| 752 | // 3) The function does not check exponent high limit. |
| 753 | // 4) "number" zero value is not processed correctly. |
| 754 | // 5) Number is unsigned, so the result can be only positive. |
| 755 | LIBC_INLINE static constexpr RetT make_value(StorageType number, int ep) { |
| 756 | FPRepImpl result(0); |
| 757 | int lz = |
| 758 | UP::FRACTION_LEN + 1 - (UP::STORAGE_LEN - cpp::countl_zero(number)); |
| 759 | |
| 760 | number <<= lz; |
| 761 | ep -= lz; |
| 762 | |
| 763 | if (LIBC_LIKELY(ep >= 0)) { |
| 764 | // Implicit number bit will be removed by mask |
| 765 | result.set_significand(number); |
| 766 | result.set_biased_exponent(static_cast<StorageType>(ep + 1)); |
| 767 | } else { |
| 768 | result.set_significand(number >> static_cast<unsigned>(-ep)); |
| 769 | } |
| 770 | return RetT(result.uintval()); |
| 771 | } |
| 772 | }; |
| 773 | |
| 774 | // A generic class to manipulate floating point formats. |
| 775 | // It derives its functionality to FPRepImpl above. |
| 776 | template <FPType fp_type> |
| 777 | struct FPRep : public FPRepImpl<fp_type, FPRep<fp_type>> { |
| 778 | using UP = FPRepImpl<fp_type, FPRep<fp_type>>; |
| 779 | using StorageType = typename UP::StorageType; |
| 780 | using UP::UP; |
| 781 | |
| 782 | LIBC_INLINE constexpr explicit operator StorageType() const { |
| 783 | return UP::uintval(); |
| 784 | } |
| 785 | }; |
| 786 | |
| 787 | } // namespace internal |
| 788 | |
| 789 | // Returns the FPType corresponding to C++ type T on the host. |
| 790 | template <typename T> LIBC_INLINE static constexpr FPType get_fp_type() { |
| 791 | using UnqualT = cpp::remove_cv_t<T>; |
| 792 | if constexpr (cpp::is_same_v<UnqualT, float> && FLT_MANT_DIG == 24) |
| 793 | return FPType::IEEE754_Binary32; |
| 794 | else if constexpr (cpp::is_same_v<UnqualT, double> && DBL_MANT_DIG == 53) |
| 795 | return FPType::IEEE754_Binary64; |
| 796 | else if constexpr (cpp::is_same_v<UnqualT, long double>) { |
| 797 | if constexpr (LDBL_MANT_DIG == 53) |
| 798 | return FPType::IEEE754_Binary64; |
| 799 | else if constexpr (LDBL_MANT_DIG == 64) |
| 800 | return FPType::X86_Binary80; |
| 801 | else if constexpr (LDBL_MANT_DIG == 113) |
| 802 | return FPType::IEEE754_Binary128; |
| 803 | } |
| 804 | #if defined(LIBC_TYPES_HAS_FLOAT16) |
| 805 | else if constexpr (cpp::is_same_v<UnqualT, float16>) |
| 806 | return FPType::IEEE754_Binary16; |
| 807 | #endif |
| 808 | #if defined(LIBC_TYPES_HAS_FLOAT128) |
| 809 | else if constexpr (cpp::is_same_v<UnqualT, float128>) |
| 810 | return FPType::IEEE754_Binary128; |
| 811 | #endif |
| 812 | else if constexpr (cpp::is_same_v<UnqualT, bfloat16>) |
| 813 | return FPType::BFloat16; |
| 814 | else |
| 815 | static_assert(cpp::always_false<UnqualT>, "Unsupported type" ); |
| 816 | } |
| 817 | |
| 818 | // ----------------------------------------------------------------------------- |
| 819 | // **** WARNING **** |
| 820 | // This interface is shared with libc++, if you change this interface you need |
| 821 | // to update it in both libc and libc++. You should also be careful when adding |
| 822 | // dependencies to this file, since it needs to build for all libc++ targets. |
| 823 | // ----------------------------------------------------------------------------- |
| 824 | // A generic class to manipulate C++ floating point formats. |
| 825 | // It derives its functionality to FPRepImpl above. |
| 826 | template <typename T> |
| 827 | struct FPBits final : public internal::FPRepImpl<get_fp_type<T>(), FPBits<T>> { |
| 828 | static_assert(cpp::is_floating_point_v<T>, |
| 829 | "FPBits instantiated with invalid type." ); |
| 830 | using UP = internal::FPRepImpl<get_fp_type<T>(), FPBits<T>>; |
| 831 | using StorageType = typename UP::StorageType; |
| 832 | |
| 833 | // Constructors. |
| 834 | LIBC_INLINE constexpr FPBits() = default; |
| 835 | |
| 836 | template <typename XType> LIBC_INLINE constexpr explicit FPBits(XType x) { |
| 837 | using Unqual = typename cpp::remove_cv_t<XType>; |
| 838 | if constexpr (cpp::is_same_v<Unqual, T>) { |
| 839 | UP::bits = cpp::bit_cast<StorageType>(x); |
| 840 | } else if constexpr (cpp::is_same_v<Unqual, StorageType>) { |
| 841 | UP::bits = x; |
| 842 | } else { |
| 843 | // We don't want accidental type promotions/conversions, so we require |
| 844 | // exact type match. |
| 845 | static_assert(cpp::always_false<XType>); |
| 846 | } |
| 847 | } |
| 848 | |
| 849 | // Floating-point conversions. |
| 850 | LIBC_INLINE constexpr T get_val() const { return cpp::bit_cast<T>(UP::bits); } |
| 851 | }; |
| 852 | |
| 853 | } // namespace fputil |
| 854 | } // namespace LIBC_NAMESPACE_DECL |
| 855 | |
| 856 | #endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
| 857 | |