| 1 | //===-- Basic operations on floating point 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 | #ifndef LLVM_LIBC_SRC___SUPPORT_FPUTIL_BASICOPERATIONS_H |
| 10 | #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_BASICOPERATIONS_H |
| 11 | |
| 12 | #include "FEnvImpl.h" |
| 13 | #include "FPBits.h" |
| 14 | #include "dyadic_float.h" |
| 15 | |
| 16 | #include "src/__support/CPP/type_traits.h" |
| 17 | #include "src/__support/big_int.h" |
| 18 | #include "src/__support/common.h" |
| 19 | #include "src/__support/macros/config.h" |
| 20 | #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY |
| 21 | #include "src/__support/macros/properties/architectures.h" |
| 22 | #include "src/__support/macros/properties/types.h" |
| 23 | #include "src/__support/uint128.h" |
| 24 | |
| 25 | namespace LIBC_NAMESPACE_DECL { |
| 26 | namespace fputil { |
| 27 | |
| 28 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 29 | LIBC_INLINE constexpr T abs(T x) { |
| 30 | return FPBits<T>(x).abs().get_val(); |
| 31 | } |
| 32 | |
| 33 | namespace internal { |
| 34 | |
| 35 | template <typename T> |
| 36 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
| 37 | constexpr_max(T x, T y) { |
| 38 | FPBits<T> x_bits(x); |
| 39 | FPBits<T> y_bits(y); |
| 40 | |
| 41 | // To make sure that fmax(+0, -0) == +0 == fmax(-0, +0), whenever x and y |
| 42 | // have different signs and both are not NaNs, we return the number with |
| 43 | // positive sign. |
| 44 | if (x_bits.sign() != y_bits.sign()) |
| 45 | return x_bits.is_pos() ? x : y; |
| 46 | return x > y ? x : y; |
| 47 | } |
| 48 | |
| 49 | template <typename T> |
| 50 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
| 51 | max(T x, T y) { |
| 52 | return constexpr_max(x, y); |
| 53 | } |
| 54 | |
| 55 | #ifdef LIBC_TYPES_HAS_FLOAT16 |
| 56 | #if defined(__LIBC_USE_BUILTIN_FMAXF16_FMINF16) |
| 57 | template <> LIBC_INLINE constexpr float16 max(float16 x, float16 y) { |
| 58 | if (cpp::is_constant_evaluated()) |
| 59 | return constexpr_max(x, y); |
| 60 | return __builtin_fmaxf16(x, y); |
| 61 | } |
| 62 | #elif !defined(LIBC_TARGET_ARCH_IS_AARCH64) |
| 63 | template <> LIBC_INLINE constexpr float16 max(float16 x, float16 y) { |
| 64 | FPBits<float16> x_bits(x); |
| 65 | FPBits<float16> y_bits(y); |
| 66 | |
| 67 | int16_t xi = static_cast<int16_t>(x_bits.uintval()); |
| 68 | int16_t yi = static_cast<int16_t>(y_bits.uintval()); |
| 69 | return ((xi > yi) != (xi < 0 && yi < 0)) ? x : y; |
| 70 | } |
| 71 | #endif |
| 72 | #endif // LIBC_TYPES_HAS_FLOAT16 |
| 73 | |
| 74 | #if defined(__LIBC_USE_BUILTIN_FMAX_FMIN) && !defined(LIBC_TARGET_ARCH_IS_X86) |
| 75 | template <> LIBC_INLINE constexpr float max(float x, float y) { |
| 76 | if (cpp::is_constant_evaluated()) |
| 77 | return constexpr_max(x, y); |
| 78 | return __builtin_fmaxf(x, y); |
| 79 | } |
| 80 | |
| 81 | template <> LIBC_INLINE constexpr double max(double x, double y) { |
| 82 | if (cpp::is_constant_evaluated()) |
| 83 | return constexpr_max(x, y); |
| 84 | return __builtin_fmax(x, y); |
| 85 | } |
| 86 | #endif |
| 87 | |
| 88 | template <typename T> |
| 89 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
| 90 | constexpr_min(T x, T y) { |
| 91 | FPBits<T> x_bits(x); |
| 92 | FPBits<T> y_bits(y); |
| 93 | |
| 94 | // To make sure that fmin(+0, -0) == -0 == fmin(-0, +0), whenever x and y have |
| 95 | // different signs and both are not NaNs, we return the number with negative |
| 96 | // sign. |
| 97 | if (x_bits.sign() != y_bits.sign()) |
| 98 | return x_bits.is_neg() ? x : y; |
| 99 | return x < y ? x : y; |
| 100 | } |
| 101 | |
| 102 | template <typename T> |
| 103 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
| 104 | min(T x, T y) { |
| 105 | return constexpr_min(x, y); |
| 106 | } |
| 107 | |
| 108 | #ifdef LIBC_TYPES_HAS_FLOAT16 |
| 109 | #if defined(__LIBC_USE_BUILTIN_FMAXF16_FMINF16) |
| 110 | template <> LIBC_INLINE constexpr float16 min(float16 x, float16 y) { |
| 111 | if (cpp::is_constant_evaluated()) |
| 112 | return constexpr_min(x, y); |
| 113 | return __builtin_fminf16(x, y); |
| 114 | } |
| 115 | #elif !defined(LIBC_TARGET_ARCH_IS_AARCH64) |
| 116 | template <> LIBC_INLINE constexpr float16 min(float16 x, float16 y) { |
| 117 | FPBits<float16> x_bits(x); |
| 118 | FPBits<float16> y_bits(y); |
| 119 | |
| 120 | int16_t xi = static_cast<int16_t>(x_bits.uintval()); |
| 121 | int16_t yi = static_cast<int16_t>(y_bits.uintval()); |
| 122 | return ((xi < yi) != (xi < 0 && yi < 0)) ? x : y; |
| 123 | } |
| 124 | #endif |
| 125 | #endif // LIBC_TYPES_HAS_FLOAT16 |
| 126 | |
| 127 | #if defined(__LIBC_USE_BUILTIN_FMAX_FMIN) && !defined(LIBC_TARGET_ARCH_IS_X86) |
| 128 | template <> LIBC_INLINE constexpr float min(float x, float y) { |
| 129 | if (cpp::is_constant_evaluated()) |
| 130 | return constexpr_min(x, y); |
| 131 | return __builtin_fminf(x, y); |
| 132 | } |
| 133 | |
| 134 | template <> LIBC_INLINE constexpr double min(double x, double y) { |
| 135 | if (cpp::is_constant_evaluated()) |
| 136 | return constexpr_min(x, y); |
| 137 | return __builtin_fmin(x, y); |
| 138 | } |
| 139 | #endif |
| 140 | |
| 141 | } // namespace internal |
| 142 | |
| 143 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 144 | LIBC_INLINE constexpr T fmin(T x, T y) { |
| 145 | const FPBits<T> bitx(x), bity(y); |
| 146 | |
| 147 | if (bitx.is_nan()) |
| 148 | return y; |
| 149 | if (bity.is_nan()) |
| 150 | return x; |
| 151 | return internal::min(x, y); |
| 152 | } |
| 153 | |
| 154 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 155 | LIBC_INLINE constexpr T fmax(T x, T y) { |
| 156 | FPBits<T> bitx(x), bity(y); |
| 157 | |
| 158 | if (bitx.is_nan()) |
| 159 | return y; |
| 160 | if (bity.is_nan()) |
| 161 | return x; |
| 162 | return internal::max(x, y); |
| 163 | } |
| 164 | |
| 165 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 166 | LIBC_INLINE constexpr T fmaximum(T x, T y) { |
| 167 | FPBits<T> bitx(x), bity(y); |
| 168 | |
| 169 | if (bitx.is_nan()) |
| 170 | return x; |
| 171 | if (bity.is_nan()) |
| 172 | return y; |
| 173 | return internal::max(x, y); |
| 174 | } |
| 175 | |
| 176 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 177 | LIBC_INLINE constexpr T fminimum(T x, T y) { |
| 178 | const FPBits<T> bitx(x), bity(y); |
| 179 | |
| 180 | if (bitx.is_nan()) |
| 181 | return x; |
| 182 | if (bity.is_nan()) |
| 183 | return y; |
| 184 | return internal::min(x, y); |
| 185 | } |
| 186 | |
| 187 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 188 | LIBC_INLINE constexpr T fmaximum_num(T x, T y) { |
| 189 | FPBits<T> bitx(x), bity(y); |
| 190 | if (bitx.is_signaling_nan() || bity.is_signaling_nan()) { |
| 191 | fputil::raise_except_if_required(FE_INVALID); |
| 192 | if (bitx.is_nan() && bity.is_nan()) |
| 193 | return FPBits<T>::quiet_nan().get_val(); |
| 194 | } |
| 195 | if (bitx.is_nan()) |
| 196 | return y; |
| 197 | if (bity.is_nan()) |
| 198 | return x; |
| 199 | return internal::max(x, y); |
| 200 | } |
| 201 | |
| 202 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 203 | LIBC_INLINE constexpr T fminimum_num(T x, T y) { |
| 204 | FPBits<T> bitx(x), bity(y); |
| 205 | if (bitx.is_signaling_nan() || bity.is_signaling_nan()) { |
| 206 | fputil::raise_except_if_required(FE_INVALID); |
| 207 | if (bitx.is_nan() && bity.is_nan()) |
| 208 | return FPBits<T>::quiet_nan().get_val(); |
| 209 | } |
| 210 | if (bitx.is_nan()) |
| 211 | return y; |
| 212 | if (bity.is_nan()) |
| 213 | return x; |
| 214 | return internal::min(x, y); |
| 215 | } |
| 216 | |
| 217 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 218 | LIBC_INLINE constexpr T fmaximum_mag(T x, T y) { |
| 219 | FPBits<T> bitx(x), bity(y); |
| 220 | |
| 221 | if (abs(x) > abs(y)) |
| 222 | return x; |
| 223 | if (abs(y) > abs(x)) |
| 224 | return y; |
| 225 | return fmaximum(x, y); |
| 226 | } |
| 227 | |
| 228 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 229 | LIBC_INLINE constexpr T fminimum_mag(T x, T y) { |
| 230 | FPBits<T> bitx(x), bity(y); |
| 231 | |
| 232 | if (abs(x) < abs(y)) |
| 233 | return x; |
| 234 | if (abs(y) < abs(x)) |
| 235 | return y; |
| 236 | return fminimum(x, y); |
| 237 | } |
| 238 | |
| 239 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 240 | LIBC_INLINE constexpr T fmaximum_mag_num(T x, T y) { |
| 241 | FPBits<T> bitx(x), bity(y); |
| 242 | |
| 243 | if (abs(x) > abs(y)) |
| 244 | return x; |
| 245 | if (abs(y) > abs(x)) |
| 246 | return y; |
| 247 | return fmaximum_num(x, y); |
| 248 | } |
| 249 | |
| 250 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 251 | LIBC_INLINE constexpr T fminimum_mag_num(T x, T y) { |
| 252 | FPBits<T> bitx(x), bity(y); |
| 253 | |
| 254 | if (abs(x) < abs(y)) |
| 255 | return x; |
| 256 | if (abs(y) < abs(x)) |
| 257 | return y; |
| 258 | return fminimum_num(x, y); |
| 259 | } |
| 260 | |
| 261 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 262 | LIBC_INLINE T constexpr fdim(T x, T y) { |
| 263 | FPBits<T> bitx(x), bity(y); |
| 264 | |
| 265 | if (bitx.is_nan()) { |
| 266 | return x; |
| 267 | } |
| 268 | |
| 269 | if (bity.is_nan()) { |
| 270 | return y; |
| 271 | } |
| 272 | |
| 273 | return (x > y ? x - y : T(0)); |
| 274 | } |
| 275 | |
| 276 | // Avoid reusing `issignaling` macro. |
| 277 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 278 | LIBC_INLINE constexpr int issignaling_impl(const T &x) { |
| 279 | FPBits<T> sx(x); |
| 280 | return sx.is_signaling_nan(); |
| 281 | } |
| 282 | |
| 283 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
| 284 | LIBC_INLINE constexpr int canonicalize(T &cx, const T &x) { |
| 285 | FPBits<T> sx(x); |
| 286 | if constexpr (get_fp_type<T>() == FPType::X86_Binary80) { |
| 287 | // All the pseudo and unnormal numbers are not canonical. |
| 288 | // More precisely : |
| 289 | // Exponent | Significand | Meaning |
| 290 | // | Bits 63-62 | Bits 61-0 | |
| 291 | // All Ones | 00 | Zero | Pseudo Infinity, Value = SNaN |
| 292 | // All Ones | 00 | Non-Zero | Pseudo NaN, Value = SNaN |
| 293 | // All Ones | 01 | Anything | Pseudo NaN, Value = SNaN |
| 294 | // | Bit 63 | Bits 62-0 | |
| 295 | // All zeroes | One | Anything | Pseudo Denormal, Value = |
| 296 | // | | | (−1)**s × m × 2**−16382 |
| 297 | // All Other | Zero | Anything | Unnormal, Value = SNaN |
| 298 | // Values | | | |
| 299 | bool bit63 = sx.get_implicit_bit(); |
| 300 | UInt128 mantissa = sx.get_explicit_mantissa(); |
| 301 | bool bit62 = static_cast<bool>((mantissa & (1ULL << 62)) >> 62); |
| 302 | int exponent = sx.get_biased_exponent(); |
| 303 | if (exponent == 0x7FFF) { |
| 304 | if (!bit63 && !bit62) { |
| 305 | if (mantissa == 0) { |
| 306 | cx = FPBits<T>::quiet_nan(sx.sign(), mantissa).get_val(); |
| 307 | raise_except_if_required(FE_INVALID); |
| 308 | return 1; |
| 309 | } |
| 310 | cx = FPBits<T>::quiet_nan(sx.sign(), mantissa).get_val(); |
| 311 | raise_except_if_required(FE_INVALID); |
| 312 | return 1; |
| 313 | } else if (!bit63 && bit62) { |
| 314 | cx = FPBits<T>::quiet_nan(sx.sign(), mantissa).get_val(); |
| 315 | raise_except_if_required(FE_INVALID); |
| 316 | return 1; |
| 317 | } else if (LIBC_UNLIKELY(sx.is_signaling_nan())) { |
| 318 | cx = FPBits<T>::quiet_nan(sx.sign(), sx.get_explicit_mantissa()) |
| 319 | .get_val(); |
| 320 | raise_except_if_required(FE_INVALID); |
| 321 | return 1; |
| 322 | } else |
| 323 | cx = x; |
| 324 | } else if (exponent == 0 && bit63) |
| 325 | cx = FPBits<T>::make_value(mantissa, 0).get_val(); |
| 326 | else if (exponent != 0 && !bit63) { |
| 327 | cx = FPBits<T>::quiet_nan(sx.sign(), mantissa).get_val(); |
| 328 | raise_except_if_required(FE_INVALID); |
| 329 | return 1; |
| 330 | } else if (LIBC_UNLIKELY(sx.is_signaling_nan())) { |
| 331 | cx = |
| 332 | FPBits<T>::quiet_nan(sx.sign(), sx.get_explicit_mantissa()).get_val(); |
| 333 | raise_except_if_required(FE_INVALID); |
| 334 | return 1; |
| 335 | } else |
| 336 | cx = x; |
| 337 | } else if (LIBC_UNLIKELY(sx.is_signaling_nan())) { |
| 338 | cx = FPBits<T>::quiet_nan(sx.sign(), sx.get_explicit_mantissa()).get_val(); |
| 339 | raise_except_if_required(FE_INVALID); |
| 340 | return 1; |
| 341 | } else |
| 342 | cx = x; |
| 343 | return 0; |
| 344 | } |
| 345 | |
| 346 | template <typename T> |
| 347 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, bool> |
| 348 | totalorder(T x, T y) { |
| 349 | using FPBits = FPBits<T>; |
| 350 | FPBits x_bits(x); |
| 351 | FPBits y_bits(y); |
| 352 | |
| 353 | using StorageType = typename FPBits::StorageType; |
| 354 | StorageType x_u = x_bits.uintval(); |
| 355 | StorageType y_u = y_bits.uintval(); |
| 356 | |
| 357 | bool has_neg = ((x_u | y_u) & FPBits::SIGN_MASK) != 0; |
| 358 | return x_u == y_u || ((x_u < y_u) != has_neg); |
| 359 | } |
| 360 | |
| 361 | template <typename T> |
| 362 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, bool> |
| 363 | totalordermag(T x, T y) { |
| 364 | return FPBits<T>(x).abs().uintval() <= FPBits<T>(y).abs().uintval(); |
| 365 | } |
| 366 | |
| 367 | template <typename T> |
| 368 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
| 369 | getpayload(T x) { |
| 370 | using FPBits = FPBits<T>; |
| 371 | using StorageType = typename FPBits::StorageType; |
| 372 | FPBits x_bits(x); |
| 373 | |
| 374 | if (!x_bits.is_nan()) |
| 375 | return T(-1.0); |
| 376 | |
| 377 | StorageType payload = x_bits.uintval() & (FPBits::FRACTION_MASK >> 1); |
| 378 | |
| 379 | if constexpr (is_big_int_v<StorageType>) { |
| 380 | DyadicFloat<FPBits::STORAGE_LEN> payload_dfloat(Sign::POS, 0, payload); |
| 381 | |
| 382 | return static_cast<T>(payload_dfloat); |
| 383 | } else { |
| 384 | return static_cast<T>(payload); |
| 385 | } |
| 386 | } |
| 387 | |
| 388 | template <bool IsSignaling, typename T> |
| 389 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, bool> |
| 390 | setpayload(T &res, T pl) { |
| 391 | using FPBits = FPBits<T>; |
| 392 | FPBits pl_bits(pl); |
| 393 | |
| 394 | // Signaling NaNs don't have the mantissa's MSB set to 1, so they need a |
| 395 | // non-zero payload to distinguish them from infinities. |
| 396 | if (!IsSignaling && pl_bits.is_zero()) { |
| 397 | res = FPBits::quiet_nan(Sign::POS).get_val(); |
| 398 | return false; |
| 399 | } |
| 400 | |
| 401 | int pl_exp = pl_bits.get_exponent(); |
| 402 | |
| 403 | if (pl_bits.is_neg() || pl_exp < 0 || pl_exp >= FPBits::FRACTION_LEN - 1 || |
| 404 | ((pl_bits.get_mantissa() << pl_exp) & FPBits::FRACTION_MASK) != 0) { |
| 405 | res = T(0.0); |
| 406 | return true; |
| 407 | } |
| 408 | |
| 409 | using StorageType = typename FPBits::StorageType; |
| 410 | StorageType v(pl_bits.get_explicit_mantissa() >> |
| 411 | (FPBits::FRACTION_LEN - pl_exp)); |
| 412 | |
| 413 | if constexpr (IsSignaling) |
| 414 | res = FPBits::signaling_nan(Sign::POS, v).get_val(); |
| 415 | else |
| 416 | res = FPBits::quiet_nan(Sign::POS, v).get_val(); |
| 417 | return false; |
| 418 | } |
| 419 | |
| 420 | } // namespace fputil |
| 421 | } // namespace LIBC_NAMESPACE_DECL |
| 422 | |
| 423 | #endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_BASICOPERATIONS_H |
| 424 | |