| 1 | //===- llvm/Support/KnownFPClass.h - Stores known fplcass -------*- 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 | // This file contains a class for representing known fpclasses used by |
| 10 | // computeKnownFPClass. |
| 11 | // |
| 12 | //===----------------------------------------------------------------------===// |
| 13 | |
| 14 | #include "llvm/Support/KnownFPClass.h" |
| 15 | #include "llvm/ADT/APFloat.h" |
| 16 | #include "llvm/Support/ErrorHandling.h" |
| 17 | #include "llvm/Support/KnownBits.h" |
| 18 | |
| 19 | using namespace llvm; |
| 20 | |
| 21 | KnownFPClass::KnownFPClass(const APFloat &C) |
| 22 | : KnownFPClasses(C.classify()), SignBit(C.isNegative()) {} |
| 23 | |
| 24 | /// Return true if it's possible to assume IEEE treatment of input denormals in |
| 25 | /// \p F for \p Val. |
| 26 | static bool inputDenormalIsIEEE(DenormalMode Mode) { |
| 27 | return Mode.Input == DenormalMode::IEEE; |
| 28 | } |
| 29 | |
| 30 | static bool inputDenormalIsIEEEOrPosZero(DenormalMode Mode) { |
| 31 | return Mode.Input == DenormalMode::IEEE || |
| 32 | Mode.Input == DenormalMode::PositiveZero; |
| 33 | } |
| 34 | |
| 35 | bool KnownFPClass::isKnownNeverLogicalZero(DenormalMode Mode) const { |
| 36 | return isKnownNeverZero() && |
| 37 | (isKnownNeverSubnormal() || inputDenormalIsIEEE(Mode)); |
| 38 | } |
| 39 | |
| 40 | bool KnownFPClass::isKnownNeverLogicalNegZero(DenormalMode Mode) const { |
| 41 | return isKnownNeverNegZero() && |
| 42 | (isKnownNeverNegSubnormal() || inputDenormalIsIEEEOrPosZero(Mode)); |
| 43 | } |
| 44 | |
| 45 | bool KnownFPClass::isKnownNeverLogicalPosZero(DenormalMode Mode) const { |
| 46 | if (!isKnownNeverPosZero()) |
| 47 | return false; |
| 48 | |
| 49 | // If we know there are no denormals, nothing can be flushed to zero. |
| 50 | if (isKnownNeverSubnormal()) |
| 51 | return true; |
| 52 | |
| 53 | switch (Mode.Input) { |
| 54 | case DenormalMode::IEEE: |
| 55 | return true; |
| 56 | case DenormalMode::PreserveSign: |
| 57 | // Negative subnormal won't flush to +0 |
| 58 | return isKnownNeverPosSubnormal(); |
| 59 | case DenormalMode::PositiveZero: |
| 60 | default: |
| 61 | // Both positive and negative subnormal could flush to +0 |
| 62 | return false; |
| 63 | } |
| 64 | |
| 65 | llvm_unreachable("covered switch over denormal mode" ); |
| 66 | } |
| 67 | |
| 68 | void KnownFPClass::propagateDenormal(const KnownFPClass &Src, |
| 69 | DenormalMode Mode) { |
| 70 | KnownFPClasses = Src.KnownFPClasses; |
| 71 | // If we aren't assuming the source can't be a zero, we don't have to check if |
| 72 | // a denormal input could be flushed. |
| 73 | if (!Src.isKnownNeverPosZero() && !Src.isKnownNeverNegZero()) |
| 74 | return; |
| 75 | |
| 76 | // If we know the input can't be a denormal, it can't be flushed to 0. |
| 77 | if (Src.isKnownNeverSubnormal()) |
| 78 | return; |
| 79 | |
| 80 | if (!Src.isKnownNeverPosSubnormal() && Mode != DenormalMode::getIEEE()) |
| 81 | KnownFPClasses |= fcPosZero; |
| 82 | |
| 83 | if (!Src.isKnownNeverNegSubnormal() && Mode != DenormalMode::getIEEE()) { |
| 84 | if (Mode != DenormalMode::getPositiveZero()) |
| 85 | KnownFPClasses |= fcNegZero; |
| 86 | |
| 87 | if (Mode.Input == DenormalMode::PositiveZero || |
| 88 | Mode.Output == DenormalMode::PositiveZero || |
| 89 | Mode.Input == DenormalMode::Dynamic || |
| 90 | Mode.Output == DenormalMode::Dynamic) |
| 91 | KnownFPClasses |= fcPosZero; |
| 92 | } |
| 93 | } |
| 94 | |
| 95 | KnownFPClass KnownFPClass::minMaxLike(const KnownFPClass &LHS_, |
| 96 | const KnownFPClass &RHS_, MinMaxKind Kind, |
| 97 | DenormalMode Mode) { |
| 98 | KnownFPClass KnownLHS = LHS_; |
| 99 | KnownFPClass KnownRHS = RHS_; |
| 100 | |
| 101 | bool NeverNaN = KnownLHS.isKnownNeverNaN() || KnownRHS.isKnownNeverNaN(); |
| 102 | KnownFPClass Known = KnownLHS | KnownRHS; |
| 103 | |
| 104 | // If either operand is not NaN, the result is not NaN. |
| 105 | if (NeverNaN && |
| 106 | (Kind == MinMaxKind::minnum || Kind == MinMaxKind::maxnum || |
| 107 | Kind == MinMaxKind::minimumnum || Kind == MinMaxKind::maximumnum)) |
| 108 | Known.knownNot(RuleOut: fcNan); |
| 109 | |
| 110 | if (Kind == MinMaxKind::maxnum || Kind == MinMaxKind::maximumnum) { |
| 111 | if (KnownLHS.isKnownNeverNaN()) |
| 112 | Known.knownNot(RuleOut: orderedStrictlyLess(Mask: KnownLHS.KnownFPClasses)); |
| 113 | if (KnownRHS.isKnownNeverNaN()) |
| 114 | Known.knownNot(RuleOut: orderedStrictlyLess(Mask: KnownRHS.KnownFPClasses)); |
| 115 | } else if (Kind == MinMaxKind::maximum) { |
| 116 | Known.knownNot(RuleOut: orderedStrictlyLess(Mask: KnownLHS.KnownFPClasses) | |
| 117 | orderedStrictlyLess(Mask: KnownRHS.KnownFPClasses)); |
| 118 | } else if (Kind == MinMaxKind::minnum || Kind == MinMaxKind::minimumnum) { |
| 119 | if (KnownLHS.isKnownNeverNaN()) |
| 120 | Known.knownNot(RuleOut: orderedStrictlyGreater(Mask: KnownLHS.KnownFPClasses)); |
| 121 | if (KnownRHS.isKnownNeverNaN()) |
| 122 | Known.knownNot(RuleOut: orderedStrictlyGreater(Mask: KnownRHS.KnownFPClasses)); |
| 123 | } else if (Kind == MinMaxKind::minimum) { |
| 124 | Known.knownNot(RuleOut: orderedStrictlyGreater(Mask: KnownLHS.KnownFPClasses) | |
| 125 | orderedStrictlyGreater(Mask: KnownRHS.KnownFPClasses)); |
| 126 | } else |
| 127 | llvm_unreachable("unhandled intrinsic" ); |
| 128 | |
| 129 | // Fixup zero handling if denormals could be returned as a zero. |
| 130 | // |
| 131 | // As there's no spec for denormal flushing, be conservative with the |
| 132 | // treatment of denormals that could be flushed to zero. For older |
| 133 | // subtargets on AMDGPU the min/max instructions would not flush the |
| 134 | // output and return the original value. |
| 135 | // |
| 136 | if ((Known.KnownFPClasses & fcZero) != fcNone && |
| 137 | !Known.isKnownNeverSubnormal()) { |
| 138 | if (Mode != DenormalMode::getIEEE()) |
| 139 | Known.KnownFPClasses |= fcZero; |
| 140 | } |
| 141 | |
| 142 | if (Known.isKnownNeverNaN()) { |
| 143 | if (KnownLHS.SignBit && KnownRHS.SignBit && |
| 144 | *KnownLHS.SignBit == *KnownRHS.SignBit) { |
| 145 | if (*KnownLHS.SignBit) |
| 146 | Known.signBitMustBeOne(); |
| 147 | else |
| 148 | Known.signBitMustBeZero(); |
| 149 | } else if ((Kind == MinMaxKind::maximum || Kind == MinMaxKind::minimum || |
| 150 | Kind == MinMaxKind::maximumnum || |
| 151 | Kind == MinMaxKind::minimumnum) || |
| 152 | // FIXME: Should be using logical zero versions |
| 153 | ((KnownLHS.isKnownNeverNegZero() || |
| 154 | KnownRHS.isKnownNeverPosZero()) && |
| 155 | (KnownLHS.isKnownNeverPosZero() || |
| 156 | KnownRHS.isKnownNeverNegZero()))) { |
| 157 | // Don't take sign bit from NaN operands. |
| 158 | if (!KnownLHS.isKnownNeverNaN()) |
| 159 | KnownLHS.SignBit = std::nullopt; |
| 160 | if (!KnownRHS.isKnownNeverNaN()) |
| 161 | KnownRHS.SignBit = std::nullopt; |
| 162 | if ((Kind == MinMaxKind::maximum || Kind == MinMaxKind::maximumnum || |
| 163 | Kind == MinMaxKind::maxnum) && |
| 164 | (KnownLHS.SignBit == false || KnownRHS.SignBit == false)) |
| 165 | Known.signBitMustBeZero(); |
| 166 | else if ((Kind == MinMaxKind::minimum || Kind == MinMaxKind::minimumnum || |
| 167 | Kind == MinMaxKind::minnum) && |
| 168 | (KnownLHS.SignBit == true || KnownRHS.SignBit == true)) |
| 169 | Known.signBitMustBeOne(); |
| 170 | } |
| 171 | } |
| 172 | |
| 173 | return Known; |
| 174 | } |
| 175 | |
| 176 | KnownFPClass KnownFPClass::canonicalize(const KnownFPClass &KnownSrc, |
| 177 | DenormalMode DenormMode) { |
| 178 | KnownFPClass Known; |
| 179 | |
| 180 | // This is essentially a stronger form of |
| 181 | // propagateCanonicalizingSrc. Other "canonicalizing" operations don't |
| 182 | // actually have an IR canonicalization guarantee. |
| 183 | |
| 184 | // Canonicalize may flush denormals to zero, so we have to consider the |
| 185 | // denormal mode to preserve known-not-0 knowledge. |
| 186 | Known.KnownFPClasses = KnownSrc.KnownFPClasses | fcZero | fcQNan; |
| 187 | |
| 188 | // Stronger version of propagateNaN |
| 189 | // Canonicalize is guaranteed to quiet signaling nans. |
| 190 | if (KnownSrc.isKnownNeverNaN()) |
| 191 | Known.knownNot(RuleOut: fcNan); |
| 192 | else |
| 193 | Known.knownNot(RuleOut: fcSNan); |
| 194 | |
| 195 | // FIXME: Missing check of IEEE like types. |
| 196 | |
| 197 | // If the parent function flushes denormals, the canonical output cannot be a |
| 198 | // denormal. |
| 199 | if (DenormMode == DenormalMode::getIEEE()) { |
| 200 | if (KnownSrc.isKnownNever(Mask: fcPosZero)) |
| 201 | Known.knownNot(RuleOut: fcPosZero); |
| 202 | if (KnownSrc.isKnownNever(Mask: fcNegZero)) |
| 203 | Known.knownNot(RuleOut: fcNegZero); |
| 204 | return Known; |
| 205 | } |
| 206 | |
| 207 | if (DenormMode.inputsAreZero() || DenormMode.outputsAreZero()) |
| 208 | Known.knownNot(RuleOut: fcSubnormal); |
| 209 | |
| 210 | if (DenormMode == DenormalMode::getPreserveSign()) { |
| 211 | if (KnownSrc.isKnownNever(Mask: fcPosZero | fcPosSubnormal)) |
| 212 | Known.knownNot(RuleOut: fcPosZero); |
| 213 | if (KnownSrc.isKnownNever(Mask: fcNegZero | fcNegSubnormal)) |
| 214 | Known.knownNot(RuleOut: fcNegZero); |
| 215 | return Known; |
| 216 | } |
| 217 | |
| 218 | if (DenormMode.Input == DenormalMode::PositiveZero || |
| 219 | (DenormMode.Output == DenormalMode::PositiveZero && |
| 220 | DenormMode.Input == DenormalMode::IEEE)) { |
| 221 | // -0.0 is not a subnormal and should not be flushed. |
| 222 | if (KnownSrc.isKnownNever(Mask: fcNegZero)) |
| 223 | Known.knownNot(RuleOut: fcNegZero); |
| 224 | |
| 225 | if (KnownSrc.isKnownNever(Mask: fcPosZero | fcSubnormal)) |
| 226 | Known.knownNot(RuleOut: fcPosZero); |
| 227 | } |
| 228 | |
| 229 | return Known; |
| 230 | } |
| 231 | |
| 232 | KnownFPClass KnownFPClass::bitcast(const fltSemantics &FltSemantics, |
| 233 | const KnownBits &Bits) { |
| 234 | assert(FltSemantics.sizeInBits == Bits.getBitWidth() && |
| 235 | "Bitcast operand has incorrect bit width" ); |
| 236 | KnownFPClass Known; |
| 237 | |
| 238 | // Transfer information from the sign bit. |
| 239 | if (Bits.isNonNegative()) |
| 240 | Known.signBitMustBeZero(); |
| 241 | else if (Bits.isNegative()) |
| 242 | Known.signBitMustBeOne(); |
| 243 | |
| 244 | if (APFloat::isIEEELikeFP(FltSemantics)) { |
| 245 | // IEEE floats are NaN when all bits of the exponent plus at least one of |
| 246 | // the fraction bits are 1. This means: |
| 247 | // - If we assume unknown bits are 0 and the value is NaN, it will |
| 248 | // always be NaN |
| 249 | // - If we assume unknown bits are 1 and the value is not NaN, it can |
| 250 | // never be NaN |
| 251 | // Note: They do not hold for x86_fp80 format. |
| 252 | if (APFloat(FltSemantics, Bits.One).isNaN()) |
| 253 | Known.KnownFPClasses = fcNan; |
| 254 | else if (!APFloat(FltSemantics, ~Bits.Zero).isNaN()) |
| 255 | Known.knownNot(RuleOut: fcNan); |
| 256 | |
| 257 | // Build KnownBits representing Inf and check if it must be equal or |
| 258 | // unequal to this value. |
| 259 | auto InfKB = |
| 260 | KnownBits::makeConstant(C: APFloat::getInf(Sem: FltSemantics).bitcastToAPInt()); |
| 261 | InfKB.Zero.clearSignBit(); |
| 262 | if (const auto InfResult = KnownBits::eq(LHS: Bits, RHS: InfKB)) { |
| 263 | assert(!InfResult.value()); |
| 264 | Known.knownNot(RuleOut: fcInf); |
| 265 | } else if (Bits == InfKB) { |
| 266 | Known.KnownFPClasses = fcInf; |
| 267 | } |
| 268 | |
| 269 | // Build KnownBits representing Zero and check if it must be equal or |
| 270 | // unequal to this value. |
| 271 | auto ZeroKB = KnownBits::makeConstant( |
| 272 | C: APFloat::getZero(Sem: FltSemantics).bitcastToAPInt()); |
| 273 | ZeroKB.Zero.clearSignBit(); |
| 274 | if (const auto ZeroResult = KnownBits::eq(LHS: Bits, RHS: ZeroKB)) { |
| 275 | assert(!ZeroResult.value()); |
| 276 | Known.knownNot(RuleOut: fcZero); |
| 277 | } else if (Bits == ZeroKB) { |
| 278 | Known.KnownFPClasses = fcZero; |
| 279 | } |
| 280 | } |
| 281 | |
| 282 | return Known; |
| 283 | } |
| 284 | |
| 285 | // Handle known sign bit and nan cases for fadd. |
| 286 | static KnownFPClass fadd_impl(const KnownFPClass &KnownLHS, |
| 287 | const KnownFPClass &KnownRHS, DenormalMode Mode) { |
| 288 | KnownFPClass Known; |
| 289 | |
| 290 | // Adding positive and negative infinity produces NaN, but only if both |
| 291 | // opposite-sign infinity combinations are possible. |
| 292 | if (KnownLHS.isKnownNeverNaN() && KnownRHS.isKnownNeverNaN() && |
| 293 | (KnownLHS.isKnownNever(Mask: fcPosInf) || KnownRHS.isKnownNever(Mask: fcNegInf)) && |
| 294 | (KnownLHS.isKnownNever(Mask: fcNegInf) || KnownRHS.isKnownNever(Mask: fcPosInf))) |
| 295 | Known.knownNot(RuleOut: fcNan); |
| 296 | |
| 297 | if (KnownLHS.cannotBeOrderedLessThanZero() && |
| 298 | KnownRHS.cannotBeOrderedLessThanZero()) { |
| 299 | Known.knownNot(RuleOut: KnownFPClass::OrderedLessThanZeroMask); |
| 300 | |
| 301 | // This can't underflow if one of the operands is known normal. |
| 302 | if (KnownLHS.isKnownNever(Mask: fcZero | fcPosSubnormal) || |
| 303 | KnownRHS.isKnownNever(Mask: fcZero | fcPosSubnormal)) |
| 304 | Known.knownNot(RuleOut: fcZero | fcPosSubnormal); |
| 305 | } |
| 306 | |
| 307 | if (KnownLHS.cannotBeOrderedGreaterThanZero() && |
| 308 | KnownRHS.cannotBeOrderedGreaterThanZero()) { |
| 309 | Known.knownNot(RuleOut: KnownFPClass::OrderedGreaterThanZeroMask); |
| 310 | |
| 311 | // This can't underflow if one of the operands is known normal. |
| 312 | if (KnownLHS.isKnownNever(Mask: fcZero | fcNegSubnormal) || |
| 313 | KnownRHS.isKnownNever(Mask: fcZero | fcNegSubnormal)) |
| 314 | Known.knownNot(RuleOut: fcZero | fcNegSubnormal); |
| 315 | } |
| 316 | |
| 317 | return Known; |
| 318 | } |
| 319 | |
| 320 | KnownFPClass KnownFPClass::fadd(const KnownFPClass &KnownLHS, |
| 321 | const KnownFPClass &KnownRHS, |
| 322 | DenormalMode Mode) { |
| 323 | KnownFPClass Known = fadd_impl(KnownLHS, KnownRHS, Mode); |
| 324 | |
| 325 | // (fadd x, 0.0) is guaranteed to return +0.0, not -0.0. |
| 326 | if ((KnownLHS.isKnownNeverLogicalNegZero(Mode) || |
| 327 | KnownRHS.isKnownNeverLogicalNegZero(Mode)) && |
| 328 | // Make sure output negative denormal can't flush to -0 |
| 329 | (Mode.Output == DenormalMode::IEEE || |
| 330 | Mode.Output == DenormalMode::PositiveZero)) |
| 331 | Known.knownNot(RuleOut: fcNegZero); |
| 332 | |
| 333 | return Known; |
| 334 | } |
| 335 | |
| 336 | KnownFPClass KnownFPClass::fadd_self(const KnownFPClass &KnownSrc, |
| 337 | DenormalMode Mode) { |
| 338 | KnownFPClass Known = fadd(KnownLHS: KnownSrc, KnownRHS: KnownSrc, Mode); |
| 339 | |
| 340 | // Doubling 0 will give the same 0. |
| 341 | if (KnownSrc.isKnownNeverLogicalPosZero(Mode) && |
| 342 | (Mode.Output == DenormalMode::IEEE || |
| 343 | (Mode.Output == DenormalMode::PreserveSign && |
| 344 | KnownSrc.isKnownNeverPosSubnormal()) || |
| 345 | (Mode.Output == DenormalMode::PositiveZero && |
| 346 | KnownSrc.isKnownNeverSubnormal()))) |
| 347 | Known.knownNot(RuleOut: fcPosZero); |
| 348 | |
| 349 | return Known; |
| 350 | } |
| 351 | |
| 352 | KnownFPClass KnownFPClass::fsub(const KnownFPClass &KnownLHS, |
| 353 | const KnownFPClass &KnownRHS, |
| 354 | DenormalMode Mode) { |
| 355 | return fadd(KnownLHS, KnownRHS: fneg(Src: KnownRHS), Mode); |
| 356 | } |
| 357 | |
| 358 | KnownFPClass KnownFPClass::fmul(const KnownFPClass &KnownLHS, |
| 359 | const KnownFPClass &KnownRHS, |
| 360 | DenormalMode Mode) { |
| 361 | KnownFPClass Known; |
| 362 | |
| 363 | // +X * +Y or -X * -Y => +Q |
| 364 | // +X * -Y or -X * +Y => -Q |
| 365 | Known.propagateXorSign(LHS: KnownLHS, RHS: KnownRHS); |
| 366 | |
| 367 | // Inf * Y => Inf or NaN |
| 368 | if (KnownLHS.isKnownAlways(Mask: fcInf | fcNan) || |
| 369 | KnownRHS.isKnownAlways(Mask: fcInf | fcNan)) |
| 370 | Known.knownNot(RuleOut: fcNormal | fcSubnormal | fcZero); |
| 371 | |
| 372 | // 0 * Y => 0 or NaN |
| 373 | if (KnownRHS.isKnownAlways(Mask: fcZero | fcNan) || |
| 374 | KnownLHS.isKnownAlways(Mask: fcZero | fcNan)) |
| 375 | Known.knownNot(RuleOut: fcNormal | fcSubnormal | fcInf); |
| 376 | |
| 377 | if (!KnownLHS.isKnownNeverNaN() || !KnownRHS.isKnownNeverNaN()) |
| 378 | return Known; |
| 379 | |
| 380 | // 0 * +/-inf => NaN |
| 381 | if ((KnownRHS.isKnownNeverInfinity() || |
| 382 | KnownLHS.isKnownNeverLogicalZero(Mode)) && |
| 383 | (KnownLHS.isKnownNeverInfinity() || |
| 384 | KnownRHS.isKnownNeverLogicalZero(Mode))) |
| 385 | Known.knownNot(RuleOut: fcNan); |
| 386 | |
| 387 | return Known; |
| 388 | } |
| 389 | |
| 390 | // TODO: This generalizes to known ranges |
| 391 | KnownFPClass KnownFPClass::fmul(const KnownFPClass &KnownLHS, |
| 392 | const APFloat &CRHS, DenormalMode Mode) { |
| 393 | // Match denormal scaling pattern, similar to the case in ldexp. If the |
| 394 | // constant's exponent is sufficiently large, the result cannot be subnormal. |
| 395 | |
| 396 | const fltSemantics &Flt = CRHS.getSemantics(); |
| 397 | unsigned Precision = APFloat::semanticsPrecision(Flt); |
| 398 | const int MantissaBits = Precision - 1; |
| 399 | |
| 400 | int MinKnownExponent = ilogb(Arg: CRHS); |
| 401 | bool CannotBeSubnormal = (MinKnownExponent >= MantissaBits); |
| 402 | |
| 403 | KnownFPClass Known = KnownFPClass::fmul(KnownLHS, KnownRHS: KnownFPClass(CRHS), Mode); |
| 404 | if (CannotBeSubnormal) |
| 405 | Known.knownNot(RuleOut: fcSubnormal); |
| 406 | |
| 407 | // Multiply of values <= 1 cannot introduce overflow. |
| 408 | if (KnownLHS.isKnownNever(Mask: fcInf)) { |
| 409 | if (MinKnownExponent < 0) |
| 410 | Known.knownNot(RuleOut: fcInf); |
| 411 | else if (MinKnownExponent == 0 && CRHS.compareAbsoluteValue(RHS: APFloat::getOne( |
| 412 | Sem: Flt)) == APFloat::cmpEqual) |
| 413 | Known.knownNot(RuleOut: fcInf); |
| 414 | } |
| 415 | |
| 416 | return Known; |
| 417 | } |
| 418 | |
| 419 | KnownFPClass KnownFPClass::fdiv(const KnownFPClass &KnownLHS, |
| 420 | const KnownFPClass &KnownRHS, |
| 421 | DenormalMode Mode) { |
| 422 | KnownFPClass Known; |
| 423 | |
| 424 | // Only 0/0, Inf/Inf produce NaN. |
| 425 | if (KnownLHS.isKnownNeverNaN() && KnownRHS.isKnownNeverNaN() && |
| 426 | (KnownLHS.isKnownNeverInfinity() || KnownRHS.isKnownNeverInfinity()) && |
| 427 | (KnownLHS.isKnownNeverLogicalZero(Mode) || |
| 428 | KnownRHS.isKnownNeverLogicalZero(Mode))) { |
| 429 | Known.knownNot(RuleOut: fcNan); |
| 430 | } |
| 431 | |
| 432 | // X / -0.0 => -Inf (or NaN) |
| 433 | // +X / +Y or -X / -Y => +Q |
| 434 | // +X / -Y or -X / +Y => -Q |
| 435 | Known.propagateXorSign(LHS: KnownLHS, RHS: KnownRHS); |
| 436 | |
| 437 | // 0 / X => 0 or NaN |
| 438 | if (KnownLHS.isKnownAlways(Mask: fcZero)) |
| 439 | Known.knownNot(RuleOut: fcSubnormal | fcNormal | fcInf); |
| 440 | |
| 441 | // X / 0 => NaN or Inf |
| 442 | if (KnownRHS.isKnownAlways(Mask: fcZero)) |
| 443 | Known.knownNot(RuleOut: fcFinite); |
| 444 | |
| 445 | return Known; |
| 446 | } |
| 447 | |
| 448 | KnownFPClass KnownFPClass::fdiv_self(const KnownFPClass &KnownSrc, |
| 449 | DenormalMode Mode) { |
| 450 | // X / X is always exactly 1.0 or a NaN. |
| 451 | KnownFPClass Known(fcNan | fcPosNormal); |
| 452 | |
| 453 | if (KnownSrc.isKnownNeverInfOrNaN() && KnownSrc.isKnownNeverLogicalZero(Mode)) |
| 454 | Known.knownNot(RuleOut: fcNan); |
| 455 | else if (KnownSrc.isKnownNever(Mask: fcSNan)) |
| 456 | Known.knownNot(RuleOut: fcSNan); |
| 457 | |
| 458 | return Known; |
| 459 | } |
| 460 | KnownFPClass KnownFPClass::frem_self(const KnownFPClass &KnownSrc, |
| 461 | DenormalMode Mode) { |
| 462 | // X % X is always exactly [+-]0.0 or a NaN. |
| 463 | KnownFPClass Known(fcNan | fcZero); |
| 464 | |
| 465 | if (KnownSrc.isKnownNeverInfOrNaN() && KnownSrc.isKnownNeverLogicalZero(Mode)) |
| 466 | Known.knownNot(RuleOut: fcNan); |
| 467 | else if (KnownSrc.isKnownNever(Mask: fcSNan)) |
| 468 | Known.knownNot(RuleOut: fcSNan); |
| 469 | |
| 470 | return Known; |
| 471 | } |
| 472 | |
| 473 | KnownFPClass KnownFPClass::fma(const KnownFPClass &KnownLHS, |
| 474 | const KnownFPClass &KnownRHS, |
| 475 | const KnownFPClass &KnownAddend, |
| 476 | DenormalMode Mode) { |
| 477 | KnownFPClass Mul = fmul(KnownLHS, KnownRHS, Mode); |
| 478 | |
| 479 | // FMA differs from the base fmul + fadd handling only in the treatment of -0 |
| 480 | // results. |
| 481 | // |
| 482 | // If the multiply is a -0 due to rounding, the final -0 + 0 will be -0, |
| 483 | // unlike for a separate fadd. |
| 484 | return fadd_impl(KnownLHS: Mul, KnownRHS: KnownAddend, Mode); |
| 485 | } |
| 486 | |
| 487 | KnownFPClass KnownFPClass::fma_square(const KnownFPClass &KnownSquared, |
| 488 | const KnownFPClass &KnownAddend, |
| 489 | DenormalMode Mode) { |
| 490 | KnownFPClass Squared = square(Src: KnownSquared, Mode); |
| 491 | KnownFPClass Known = fadd_impl(KnownLHS: Squared, KnownRHS: KnownAddend, Mode); |
| 492 | |
| 493 | // Since we know the squared input must be positive, the add of opposite sign |
| 494 | // infinities nan hazard only applies for negative inf. |
| 495 | // |
| 496 | // TODO: Alternatively to proving addend is not -inf, we could know Squared is |
| 497 | // not pinf. Other than the degenerate always-subnormal input case, we can't |
| 498 | // prove that without a known range. |
| 499 | if (KnownAddend.isKnownNever(Mask: fcNegInf | fcNan) && Squared.isKnownNever(Mask: fcNan)) |
| 500 | Known.knownNot(RuleOut: fcNan); |
| 501 | |
| 502 | return Known; |
| 503 | } |
| 504 | |
| 505 | KnownFPClass KnownFPClass::exp(const KnownFPClass &KnownSrc) { |
| 506 | KnownFPClass Known; |
| 507 | Known.knownNot(RuleOut: fcNegative); |
| 508 | |
| 509 | Known.propagateNaN(Src: KnownSrc); |
| 510 | |
| 511 | if (KnownSrc.cannotBeOrderedLessThanZero()) { |
| 512 | // If the source is positive this cannot underflow. |
| 513 | Known.knownNot(RuleOut: fcPosZero); |
| 514 | |
| 515 | // Cannot introduce denormal values. |
| 516 | Known.knownNot(RuleOut: fcPosSubnormal); |
| 517 | } |
| 518 | |
| 519 | // If the source is negative, this cannot overflow to infinity. |
| 520 | if (KnownSrc.cannotBeOrderedGreaterThanZero()) |
| 521 | Known.knownNot(RuleOut: fcPosInf); |
| 522 | |
| 523 | return Known; |
| 524 | } |
| 525 | |
| 526 | void KnownFPClass::propagateCanonicalizingSrc(const KnownFPClass &Src, |
| 527 | DenormalMode Mode) { |
| 528 | propagateDenormal(Src, Mode); |
| 529 | propagateNaN(Src, /*PreserveSign=*/true); |
| 530 | } |
| 531 | |
| 532 | KnownFPClass KnownFPClass::log(const KnownFPClass &KnownSrc, |
| 533 | DenormalMode Mode) { |
| 534 | KnownFPClass Known; |
| 535 | Known.knownNot(RuleOut: fcNegZero | fcSubnormal); |
| 536 | |
| 537 | if (KnownSrc.isKnownNeverPosInfinity()) |
| 538 | Known.knownNot(RuleOut: fcPosInf); |
| 539 | |
| 540 | if (KnownSrc.isKnownNeverNaN() && KnownSrc.cannotBeOrderedLessThanZero()) |
| 541 | Known.knownNot(RuleOut: fcNan); |
| 542 | |
| 543 | if (KnownSrc.isKnownNeverLogicalZero(Mode)) |
| 544 | Known.knownNot(RuleOut: fcNegInf); |
| 545 | |
| 546 | return Known; |
| 547 | } |
| 548 | |
| 549 | KnownFPClass KnownFPClass::sqrt(const KnownFPClass &KnownSrc, |
| 550 | DenormalMode Mode) { |
| 551 | KnownFPClass Known; |
| 552 | Known.knownNot(RuleOut: fcPosSubnormal); |
| 553 | |
| 554 | if (KnownSrc.isKnownNeverPosInfinity()) |
| 555 | Known.knownNot(RuleOut: fcPosInf); |
| 556 | if (KnownSrc.isKnownNever(Mask: fcSNan)) |
| 557 | Known.knownNot(RuleOut: fcSNan); |
| 558 | |
| 559 | // Any negative value besides -0 returns a nan. |
| 560 | if (KnownSrc.isKnownNeverNaN() && KnownSrc.cannotBeOrderedLessThanZero()) |
| 561 | Known.knownNot(RuleOut: fcNan); |
| 562 | |
| 563 | // The only negative value that can be returned is -0 for -0 inputs. |
| 564 | Known.knownNot(RuleOut: fcNegInf | fcNegSubnormal | fcNegNormal); |
| 565 | |
| 566 | // If the input denormal mode could be PreserveSign, a negative |
| 567 | // subnormal input could produce a negative zero output. |
| 568 | if (KnownSrc.isKnownNeverLogicalNegZero(Mode)) |
| 569 | Known.knownNot(RuleOut: fcNegZero); |
| 570 | |
| 571 | return Known; |
| 572 | } |
| 573 | |
| 574 | KnownFPClass KnownFPClass::sin(const KnownFPClass &KnownSrc) { |
| 575 | KnownFPClass Known; |
| 576 | |
| 577 | // Return NaN on infinite inputs. |
| 578 | Known.knownNot(RuleOut: fcInf); |
| 579 | if (KnownSrc.isKnownNeverNaN() && KnownSrc.isKnownNeverInfinity()) |
| 580 | Known.knownNot(RuleOut: fcNan); |
| 581 | |
| 582 | return Known; |
| 583 | } |
| 584 | |
| 585 | KnownFPClass KnownFPClass::cos(const KnownFPClass &KnownSrc) { |
| 586 | return sin(KnownSrc); |
| 587 | } |
| 588 | |
| 589 | KnownFPClass KnownFPClass::tan(const KnownFPClass &KnownSrc) { |
| 590 | KnownFPClass Known; |
| 591 | |
| 592 | // tan never returns Inf (tan(+-Inf) = NaN; tan(finite) = finite). |
| 593 | Known.knownNot(RuleOut: fcInf); |
| 594 | |
| 595 | // NaN propagates. tan(+-Inf) is NaN. |
| 596 | if (KnownSrc.isKnownNeverNaN() && KnownSrc.isKnownNeverInfinity()) |
| 597 | Known.knownNot(RuleOut: fcNan); |
| 598 | |
| 599 | return Known; |
| 600 | } |
| 601 | |
| 602 | KnownFPClass KnownFPClass::sinh(const KnownFPClass &KnownSrc) { |
| 603 | KnownFPClass Known; |
| 604 | |
| 605 | // sinh is sign-preserving: sinh(x) < 0 iff x < 0. |
| 606 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 607 | Known.knownNot(RuleOut: fcNegative); |
| 608 | |
| 609 | Known.propagateNaN(Src: KnownSrc); |
| 610 | |
| 611 | return Known; |
| 612 | } |
| 613 | |
| 614 | KnownFPClass KnownFPClass::cosh(const KnownFPClass &KnownSrc) { |
| 615 | KnownFPClass Known; |
| 616 | |
| 617 | // cosh(x) >= 1 for all real x; cosh(+-Inf) = +Inf. Never negative. |
| 618 | Known.knownNot(RuleOut: fcNegative); |
| 619 | |
| 620 | Known.propagateNaN(Src: KnownSrc); |
| 621 | |
| 622 | return Known; |
| 623 | } |
| 624 | |
| 625 | KnownFPClass KnownFPClass::tanh(const KnownFPClass &KnownSrc) { |
| 626 | KnownFPClass Known; |
| 627 | |
| 628 | // tanh is bounded to (-1, 1), never Inf. |
| 629 | Known.knownNot(RuleOut: fcInf); |
| 630 | |
| 631 | // tanh is sign-preserving: tanh(x) < 0 iff x < 0. |
| 632 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 633 | Known.knownNot(RuleOut: fcNegative); |
| 634 | |
| 635 | Known.propagateNaN(Src: KnownSrc); |
| 636 | |
| 637 | return Known; |
| 638 | } |
| 639 | |
| 640 | KnownFPClass KnownFPClass::asin(const KnownFPClass &KnownSrc) { |
| 641 | KnownFPClass Known; |
| 642 | |
| 643 | // asin is bounded to [-pi/2, pi/2], never Inf. |
| 644 | Known.knownNot(RuleOut: fcInf); |
| 645 | |
| 646 | // asin is sign-preserving. |
| 647 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 648 | Known.knownNot(RuleOut: fcNegative); |
| 649 | |
| 650 | // NaN propagates. asin(x) is also NaN for |x| > 1, so we cannot rule |
| 651 | // out NaN without knowing the source is in [-1, 1]. |
| 652 | Known.propagateNaN(Src: KnownSrc); |
| 653 | |
| 654 | return Known; |
| 655 | } |
| 656 | |
| 657 | KnownFPClass KnownFPClass::acos(const KnownFPClass &KnownSrc) { |
| 658 | KnownFPClass Known; |
| 659 | |
| 660 | // acos is bounded to [0, pi], never Inf or negative. |
| 661 | Known.knownNot(RuleOut: fcInf); |
| 662 | Known.knownNot(RuleOut: fcNegative); |
| 663 | |
| 664 | // NaN propagates. acos(x) is also NaN for |x| > 1, so we cannot rule |
| 665 | // out NaN without knowing the source is in [-1, 1]. |
| 666 | Known.propagateNaN(Src: KnownSrc); |
| 667 | |
| 668 | return Known; |
| 669 | } |
| 670 | |
| 671 | KnownFPClass KnownFPClass::atan(const KnownFPClass &KnownSrc) { |
| 672 | KnownFPClass Known; |
| 673 | |
| 674 | // atan is bounded to (-pi/2, pi/2), never Inf. atan(+-Inf) = +-pi/2 (finite). |
| 675 | Known.knownNot(RuleOut: fcInf); |
| 676 | |
| 677 | // atan is sign-preserving: atan(x) < 0 iff x < 0. |
| 678 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 679 | Known.knownNot(RuleOut: fcNegative); |
| 680 | |
| 681 | Known.propagateNaN(Src: KnownSrc); |
| 682 | |
| 683 | return Known; |
| 684 | } |
| 685 | |
| 686 | KnownFPClass KnownFPClass::atan2(const KnownFPClass &KnownLHS, |
| 687 | const KnownFPClass &KnownRHS) { |
| 688 | KnownFPClass Known; |
| 689 | |
| 690 | // atan2 result is in (-pi, pi], never Inf. |
| 691 | Known.knownNot(RuleOut: fcInf); |
| 692 | |
| 693 | // NaN if either operand is NaN. |
| 694 | if (KnownLHS.isKnownNeverNaN() && KnownRHS.isKnownNeverNaN()) |
| 695 | Known.knownNot(RuleOut: fcNan); |
| 696 | |
| 697 | return Known; |
| 698 | } |
| 699 | |
| 700 | KnownFPClass KnownFPClass::fpext(const KnownFPClass &KnownSrc, |
| 701 | const fltSemantics &DstTy, |
| 702 | const fltSemantics &SrcTy) { |
| 703 | // Infinity, nan and zero propagate from source. |
| 704 | KnownFPClass Known = KnownSrc; |
| 705 | |
| 706 | // All subnormal inputs should be in the normal range in the result type. |
| 707 | if (APFloat::isRepresentableAsNormalIn(Src: SrcTy, Dst: DstTy)) { |
| 708 | if (Known.KnownFPClasses & fcPosSubnormal) |
| 709 | Known.KnownFPClasses |= fcPosNormal; |
| 710 | if (Known.KnownFPClasses & fcNegSubnormal) |
| 711 | Known.KnownFPClasses |= fcNegNormal; |
| 712 | Known.knownNot(RuleOut: fcSubnormal); |
| 713 | } |
| 714 | |
| 715 | // Sign bit of a nan isn't guaranteed. |
| 716 | if (!Known.isKnownNeverNaN()) |
| 717 | Known.SignBit = std::nullopt; |
| 718 | |
| 719 | return Known; |
| 720 | } |
| 721 | |
| 722 | KnownFPClass KnownFPClass::fptrunc(const KnownFPClass &KnownSrc) { |
| 723 | KnownFPClass Known; |
| 724 | |
| 725 | // Sign should be preserved |
| 726 | // TODO: Handle cannot be ordered greater than zero |
| 727 | if (KnownSrc.cannotBeOrderedLessThanZero()) |
| 728 | Known.knownNot(RuleOut: KnownFPClass::OrderedLessThanZeroMask); |
| 729 | |
| 730 | Known.propagateNaN(Src: KnownSrc, PreserveSign: true); |
| 731 | |
| 732 | // Infinity needs a range check. |
| 733 | return Known; |
| 734 | } |
| 735 | |
| 736 | KnownFPClass KnownFPClass::roundToIntegral(const KnownFPClass &KnownSrc, |
| 737 | bool IsTrunc, |
| 738 | bool IsMultiUnitFPType) { |
| 739 | KnownFPClass Known; |
| 740 | |
| 741 | // Integer results cannot be subnormal. |
| 742 | Known.knownNot(RuleOut: fcSubnormal); |
| 743 | |
| 744 | Known.propagateNaN(Src: KnownSrc, PreserveSign: true); |
| 745 | |
| 746 | // Pass through infinities, except PPC_FP128 is a special case for |
| 747 | // intrinsics other than trunc. |
| 748 | if (IsTrunc || !IsMultiUnitFPType) { |
| 749 | if (KnownSrc.isKnownNeverPosInfinity()) |
| 750 | Known.knownNot(RuleOut: fcPosInf); |
| 751 | if (KnownSrc.isKnownNeverNegInfinity()) |
| 752 | Known.knownNot(RuleOut: fcNegInf); |
| 753 | } |
| 754 | |
| 755 | // Negative round ups to 0 produce -0 |
| 756 | if (KnownSrc.isKnownNever(Mask: fcPosFinite)) |
| 757 | Known.knownNot(RuleOut: fcPosFinite); |
| 758 | if (KnownSrc.isKnownNever(Mask: fcNegFinite)) |
| 759 | Known.knownNot(RuleOut: fcNegFinite); |
| 760 | |
| 761 | return Known; |
| 762 | } |
| 763 | |
| 764 | KnownFPClass KnownFPClass::frexp_mant(const KnownFPClass &KnownSrc, |
| 765 | DenormalMode Mode) { |
| 766 | KnownFPClass Known; |
| 767 | Known.knownNot(RuleOut: fcSubnormal); |
| 768 | |
| 769 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 770 | Known.knownNot(RuleOut: fcNegative); |
| 771 | else { |
| 772 | if (KnownSrc.isKnownNeverLogicalNegZero(Mode)) |
| 773 | Known.knownNot(RuleOut: fcNegZero); |
| 774 | if (KnownSrc.isKnownNever(Mask: fcNegInf)) |
| 775 | Known.knownNot(RuleOut: fcNegInf); |
| 776 | } |
| 777 | |
| 778 | if (KnownSrc.isKnownNever(Mask: fcPositive)) |
| 779 | Known.knownNot(RuleOut: fcPositive); |
| 780 | else { |
| 781 | if (KnownSrc.isKnownNeverLogicalPosZero(Mode)) |
| 782 | Known.knownNot(RuleOut: fcPosZero); |
| 783 | if (KnownSrc.isKnownNever(Mask: fcPosInf)) |
| 784 | Known.knownNot(RuleOut: fcPosInf); |
| 785 | } |
| 786 | |
| 787 | Known.propagateNaN(Src: KnownSrc); |
| 788 | return Known; |
| 789 | } |
| 790 | |
| 791 | KnownFPClass KnownFPClass::ldexp(const KnownFPClass &KnownSrc, |
| 792 | const KnownBits &ExpBits, |
| 793 | const fltSemantics &Flt, DenormalMode Mode) { |
| 794 | KnownFPClass Known; |
| 795 | Known.propagateNaN(Src: KnownSrc, /*PropagateSign=*/PreserveSign: true); |
| 796 | |
| 797 | // Sign is preserved, but underflows may produce zeroes. |
| 798 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 799 | Known.knownNot(RuleOut: fcNegative); |
| 800 | else if (KnownSrc.cannotBeOrderedLessThanZero()) |
| 801 | Known.knownNot(RuleOut: OrderedLessThanZeroMask); |
| 802 | |
| 803 | if (KnownSrc.isKnownNever(Mask: fcPositive)) |
| 804 | Known.knownNot(RuleOut: fcPositive); |
| 805 | else if (KnownSrc.cannotBeOrderedGreaterThanZero()) |
| 806 | Known.knownNot(RuleOut: OrderedGreaterThanZeroMask); |
| 807 | |
| 808 | unsigned Precision = APFloat::semanticsPrecision(Flt); |
| 809 | const int MantissaBits = Precision - 1; |
| 810 | |
| 811 | if (ExpBits.getSignedMinValue().sge(RHS: static_cast<int64_t>(MantissaBits))) |
| 812 | Known.knownNot(RuleOut: fcSubnormal); |
| 813 | |
| 814 | if (ExpBits.isConstant() && ExpBits.getConstant().isZero()) { |
| 815 | // ldexp(x, 0) -> x, so propagate everything. |
| 816 | Known.propagateCanonicalizingSrc(Src: KnownSrc, Mode); |
| 817 | } else if (ExpBits.isNegative()) { |
| 818 | // If we know the power is <= 0, can't introduce inf |
| 819 | if (KnownSrc.isKnownNeverPosInfinity()) |
| 820 | Known.knownNot(RuleOut: fcPosInf); |
| 821 | if (KnownSrc.isKnownNeverNegInfinity()) |
| 822 | Known.knownNot(RuleOut: fcNegInf); |
| 823 | } else if (ExpBits.isNonNegative()) { |
| 824 | // If we know the power is >= 0, can't introduce subnormal or zero |
| 825 | if (KnownSrc.isKnownNeverPosSubnormal()) |
| 826 | Known.knownNot(RuleOut: fcPosSubnormal); |
| 827 | if (KnownSrc.isKnownNeverNegSubnormal()) |
| 828 | Known.knownNot(RuleOut: fcNegSubnormal); |
| 829 | if (KnownSrc.isKnownNeverLogicalPosZero(Mode)) |
| 830 | Known.knownNot(RuleOut: fcPosZero); |
| 831 | if (KnownSrc.isKnownNeverLogicalNegZero(Mode)) |
| 832 | Known.knownNot(RuleOut: fcNegZero); |
| 833 | } |
| 834 | |
| 835 | return Known; |
| 836 | } |
| 837 | |
| 838 | KnownFPClass KnownFPClass::powi(const KnownFPClass &KnownSrc, |
| 839 | const KnownBits &ExponentKnownBits) { |
| 840 | KnownFPClass Known; |
| 841 | Known.propagateNaN(Src: KnownSrc); |
| 842 | |
| 843 | if (ExponentKnownBits.isZero()) { |
| 844 | // powi(QNaN, 0) returns 1.0, and powi(SNaN, 0) may non-deterministically |
| 845 | // return 1.0 or a NaN. |
| 846 | if (KnownSrc.isKnownNever(Mask: fcSNan)) { |
| 847 | Known.knownNot(RuleOut: ~fcPosNormal); |
| 848 | return Known; |
| 849 | } |
| 850 | |
| 851 | Known.knownNot(RuleOut: ~(fcPosNormal | fcNan)); |
| 852 | return Known; |
| 853 | } |
| 854 | |
| 855 | // powi(x, exp) --> inf |
| 856 | // when: |
| 857 | // * powi(inf, exp), exp > 0 |
| 858 | // * powi(+/-0, exp), exp < 0 |
| 859 | // * powi(finite, exp), |exp| > 1 |
| 860 | // * powi(subnormal, -1) |
| 861 | // TODO: |
| 862 | // 1. This simple all or nothing approach. We can do better |
| 863 | // and cover sign/parity and exp > 1 vs exp < -1 separately. |
| 864 | // 2. powi(0/nan, exp), exp > 0 can be refinable |
| 865 | // to fcNan | fcZero | fcPosNormal. |
| 866 | { |
| 867 | APInt MinExp = ExponentKnownBits.getSignedMinValue(); |
| 868 | APInt MaxExp = ExponentKnownBits.getSignedMaxValue(); |
| 869 | |
| 870 | // powi(inf, exp), exp > 0 |
| 871 | bool MayInfSrc = |
| 872 | !KnownSrc.isKnownNever(Mask: fcInf) && MaxExp.isStrictlyPositive(); |
| 873 | |
| 874 | // powi(+/-0, exp), exp < 0 |
| 875 | bool MayDivByZero = !KnownSrc.isKnownNever(Mask: fcZero) && MinExp.isNegative(); |
| 876 | |
| 877 | // powi(finite, exp), |exp| > 1 |
| 878 | bool MayFinite = !KnownSrc.isKnownNever(Mask: fcNormal | fcSubnormal); |
| 879 | bool MayAbsExpGT1 = MinExp.slt(RHS: -1) || MaxExp.sgt(RHS: 1); |
| 880 | bool MayFiniteOverflow = MayFinite && MayAbsExpGT1; |
| 881 | |
| 882 | // powi(subnormal, -1) |
| 883 | bool MayBeNegOne = ExponentKnownBits.Zero.isZero(); |
| 884 | bool MaySubnormInv = !KnownSrc.isKnownNever(Mask: fcSubnormal) && MayBeNegOne; |
| 885 | |
| 886 | if (!MayInfSrc && !MayDivByZero && !MayFiniteOverflow && !MaySubnormInv) |
| 887 | Known.knownNot(RuleOut: fcInf); |
| 888 | } |
| 889 | |
| 890 | if (ExponentKnownBits.isEven()) { |
| 891 | Known.knownNot(RuleOut: fcNegative); |
| 892 | return Known; |
| 893 | } |
| 894 | |
| 895 | // Given that exp is an integer, here are the |
| 896 | // ways that pow can return a negative value: |
| 897 | // |
| 898 | // pow(-x, exp) --> negative if exp is odd and x is negative. |
| 899 | // pow(-0, exp) --> -inf if exp is negative odd. |
| 900 | // pow(-0, exp) --> -0 if exp is positive odd. |
| 901 | // pow(-inf, exp) --> -0 if exp is negative odd. |
| 902 | // pow(-inf, exp) --> -inf if exp is positive odd. |
| 903 | if (KnownSrc.isKnownNever(Mask: fcNegative)) |
| 904 | Known.knownNot(RuleOut: fcNegative); |
| 905 | |
| 906 | return Known; |
| 907 | } |
| 908 | |