diff options
| -rw-r--r-- | include/llvm/ADT/APFloat.h | 33 | ||||
| -rw-r--r-- | lib/Support/APFloat.cpp | 248 | ||||
| -rw-r--r-- | unittests/ADT/APFloatTest.cpp | 420 |
3 files changed, 679 insertions, 22 deletions
diff --git a/include/llvm/ADT/APFloat.h b/include/llvm/ADT/APFloat.h index 872bad36bc..6ba3e8ff7c 100644 --- a/include/llvm/ADT/APFloat.h +++ b/include/llvm/ADT/APFloat.h @@ -81,6 +81,11 @@ although not really meaningful, and preserved in non-conversion operations. The exponent is implicitly all 1 bits. + APFloat does not provide any exception handling beyond default exception + handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause + by encoding Signaling NaNs with the first bit of its trailing significand as + 0. + TODO ==== @@ -273,6 +278,8 @@ public: opStatus mod(const APFloat &, roundingMode); opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode); opStatus roundToIntegral(roundingMode); + /// IEEE-754R 5.3.1: nextUp/nextDown. + opStatus next(bool nextDown); /* Sign operations. */ void changeSign(); @@ -325,6 +332,8 @@ public: bool isPosZero() const { return isZero() && !isNegative(); } bool isNegZero() const { return isZero() && isNegative(); } bool isDenormal() const; + /// IEEE-754R 5.7.2: isSignaling. Returns true if this is a signaling NaN. + bool isSignaling() const; APFloat &operator=(const APFloat &); @@ -386,6 +395,10 @@ private: unsigned int significandLSB() const; unsigned int significandMSB() const; void zeroSignificand(); + /// Return true if the significand excluding the integral bit is all ones. + bool isSignificandAllOnes() const; + /// Return true if the significand excluding the integral bit is all zeros. + bool isSignificandAllZeros() const; /* Arithmetic on special values. */ opStatus addOrSubtractSpecials(const APFloat &, bool subtract); @@ -393,10 +406,26 @@ private: opStatus multiplySpecials(const APFloat &); opStatus modSpecials(const APFloat &); - /* Miscellany. */ + /* Set to special values. */ + void makeLargest(bool Neg = false); + void makeSmallest(bool Neg = false); + void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0); static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, const APInt *fill); - void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0); + + /// \name Special value queries only useful internally to APFloat + /// @{ + + /// Returns true if and only if the number has the smallest possible non-zero + /// magnitude in the current semantics. + bool isSmallest() const; + /// Returns true if and only if the number has the largest possible finite + /// magnitude in the current semantics. + bool isLargest() const; + + /// @} + + /* Miscellany. */ opStatus normalize(roundingMode, lostFraction); opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); cmpResult compareAbsoluteValue(const APFloat &) const; diff --git a/lib/Support/APFloat.cpp b/lib/Support/APFloat.cpp index 57e60dac45..4efbaf7a90 100644 --- a/lib/Support/APFloat.cpp +++ b/lib/Support/APFloat.cpp @@ -685,6 +685,67 @@ APFloat::isDenormal() const { } bool +APFloat::isSmallest() const { + // The smallest number by magnitude in our format will be the smallest + // denormal, i.e. the floating point normal with exponent being minimum + // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0). + return isNormal() && exponent == semantics->minExponent && + significandMSB() == 0; +} + +bool APFloat::isSignificandAllOnes() const { + // Test if the significand excluding the integral bit is all ones. This allows + // us to test for binade boundaries. + const integerPart *Parts = significandParts(); + const unsigned PartCount = partCount(); + for (unsigned i = 0; i < PartCount - 1; i++) + if (~Parts[i]) + return false; + + // Set the unused high bits to all ones when we compare. + const unsigned NumHighBits = + PartCount*integerPartWidth - semantics->precision + 1; + assert(NumHighBits <= integerPartWidth && "Can not have more high bits to " + "fill than integerPartWidth"); + const integerPart HighBitFill = + ~integerPart(0) << (integerPartWidth - NumHighBits); + if (~(Parts[PartCount - 1] | HighBitFill)) + return false; + + return true; +} + +bool APFloat::isSignificandAllZeros() const { + // Test if the significand excluding the integral bit is all zeros. This + // allows us to test for binade boundaries. + const integerPart *Parts = significandParts(); + const unsigned PartCount = partCount(); + + for (unsigned i = 0; i < PartCount - 1; i++) + if (Parts[i]) + return false; + + const unsigned NumHighBits = + PartCount*integerPartWidth - semantics->precision + 1; + assert(NumHighBits <= integerPartWidth && "Can not have more high bits to " + "clear than integerPartWidth"); + const integerPart HighBitMask = ~integerPart(0) >> NumHighBits; + + if (Parts[PartCount - 1] & HighBitMask) + return false; + + return true; +} + +bool +APFloat::isLargest() const { + // The largest number by magnitude in our format will be the floating point + // number with maximum exponent and with significand that is all ones. + return isNormal() && exponent == semantics->maxExponent + && isSignificandAllOnes(); +} + +bool APFloat::bitwiseIsEqual(const APFloat &rhs) const { if (this == &rhs) return true; @@ -3236,42 +3297,60 @@ APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE) } } -APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) { - APFloat Val(Sem, fcNormal, Negative); - +/// Make this number the largest magnitude normal number in the given +/// semantics. +void APFloat::makeLargest(bool Negative) { // We want (in interchange format): // sign = {Negative} // exponent = 1..10 // significand = 1..1 + category = fcNormal; + sign = Negative; + exponent = semantics->maxExponent; - Val.exponent = Sem.maxExponent; // unbiased + // Use memset to set all but the highest integerPart to all ones. + integerPart *significand = significandParts(); + unsigned PartCount = partCount(); + memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1)); - // 1-initialize all bits.... - Val.zeroSignificand(); - integerPart *significand = Val.significandParts(); - unsigned N = partCountForBits(Sem.precision); - for (unsigned i = 0; i != N; ++i) - significand[i] = ~((integerPart) 0); + // Set the high integerPart especially setting all unused top bits for + // internal consistency. + const unsigned NumUnusedHighBits = + PartCount*integerPartWidth - semantics->precision; + significand[PartCount - 1] = ~integerPart(0) >> NumUnusedHighBits; +} + +/// Make this number the smallest magnitude denormal number in the given +/// semantics. +void APFloat::makeSmallest(bool Negative) { + // We want (in interchange format): + // sign = {Negative} + // exponent = 0..0 + // significand = 0..01 + category = fcNormal; + sign = Negative; + exponent = semantics->minExponent; + APInt::tcSet(significandParts(), 1, partCount()); +} - // ...and then clear the top bits for internal consistency. - if (Sem.precision % integerPartWidth != 0) - significand[N-1] &= - (((integerPart) 1) << (Sem.precision % integerPartWidth)) - 1; +APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) { + // We want (in interchange format): + // sign = {Negative} + // exponent = 1..10 + // significand = 1..1 + APFloat Val(Sem, uninitialized); + Val.makeLargest(Negative); return Val; } APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) { - APFloat Val(Sem, fcNormal, Negative); - // We want (in interchange format): // sign = {Negative} // exponent = 0..0 // significand = 0..01 - - Val.exponent = Sem.minExponent; // unbiased - Val.zeroSignificand(); - Val.significandParts()[0] = 1; + APFloat Val(Sem, uninitialized); + Val.makeSmallest(Negative); return Val; } @@ -3615,3 +3694,132 @@ bool APFloat::getExactInverse(APFloat *inv) const { return true; } + +bool APFloat::isSignaling() const { + if (!isNaN()) + return false; + + // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the + // first bit of the trailing significand being 0. + return !APInt::tcExtractBit(significandParts(), semantics->precision - 2); +} + +/// IEEE-754R 2008 5.3.1: nextUp/nextDown. +/// +/// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with +/// appropriate sign switching before/after the computation. +APFloat::opStatus APFloat::next(bool nextDown) { + // If we are performing nextDown, swap sign so we have -x. + if (nextDown) + changeSign(); + + // Compute nextUp(x) + opStatus result = opOK; + + // Handle each float category separately. + switch (category) { + case fcInfinity: + // nextUp(+inf) = +inf + if (!isNegative()) + break; + // nextUp(-inf) = -getLargest() + makeLargest(true); + break; + case fcNaN: + // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag. + // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not + // change the payload. + if (isSignaling()) { + result = opInvalidOp; + // For consistency, propogate the sign of the sNaN to the qNaN. + makeNaN(false, isNegative(), 0); + } + break; + case fcZero: + // nextUp(pm 0) = +getSmallest() + makeSmallest(false); + break; + case fcNormal: + // nextUp(-getSmallest()) = -0 + if (isSmallest() && isNegative()) { + APInt::tcSet(significandParts(), 0, partCount()); + category = fcZero; + exponent = 0; + break; + } + + // nextUp(getLargest()) == INFINITY + if (isLargest() && !isNegative()) { + APInt::tcSet(significandParts(), 0, partCount()); + category = fcInfinity; + exponent = semantics->maxExponent + 1; + break; + } + + // nextUp(normal) == normal + inc. + if (isNegative()) { + // If we are negative, we need to decrement the significand. + + // We only cross a binade boundary that requires adjusting the exponent + // if: + // 1. exponent != semantics->minExponent. This implies we are not in the + // smallest binade or are dealing with denormals. + // 2. Our significand excluding the integral bit is all zeros. + bool WillCrossBinadeBoundary = + exponent != semantics->minExponent && isSignificandAllZeros(); + + // Decrement the significand. + // + // We always do this since: + // 1. If we are dealing with a non binade decrement, by definition we + // just decrement the significand. + // 2. If we are dealing with a normal -> normal binade decrement, since + // we have an explicit integral bit the fact that all bits but the + // integral bit are zero implies that subtracting one will yield a + // significand with 0 integral bit and 1 in all other spots. Thus we + // must just adjust the exponent and set the integral bit to 1. + // 3. If we are dealing with a normal -> denormal binade decrement, + // since we set the integral bit to 0 when we represent denormals, we + // just decrement the significand. + integerPart *Parts = significandParts(); + APInt::tcDecrement(Parts, partCount()); + + if (WillCrossBinadeBoundary) { + // Our result is a normal number. Do the following: + // 1. Set the integral bit to 1. + // 2. Decrement the exponent. + APInt::tcSetBit(Parts, semantics->precision - 1); + exponent--; + } + } else { + // If we are positive, we need to increment the significand. + + // We only cross a binade boundary that requires adjusting the exponent if + // the input is not a denormal and all of said input's significand bits + // are set. If all of said conditions are true: clear the significand, set + // the integral bit to 1, and increment the exponent. If we have a + // denormal always increment since moving denormals and the numbers in the + // smallest normal binade have the same exponent in our representation. + bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes(); + + if (WillCrossBinadeBoundary) { + integerPart *Parts = significandParts(); + APInt::tcSet(Parts, 0, partCount()); + APInt::tcSetBit(Parts, semantics->precision - 1); + assert(exponent != semantics->maxExponent && + "We can not increment an exponent beyond the maxExponent allowed" + " by the given floating point semantics."); + exponent++; + } else { + incrementSignificand(); + } + } + break; + } + + // If we are performing nextDown, swap sign so we have -nextUp(-x) + if (nextDown) + changeSign(); + + return result; +} diff --git a/unittests/ADT/APFloatTest.cpp b/unittests/ADT/APFloatTest.cpp index 87744d547f..1d7ac99d68 100644 --- a/unittests/ADT/APFloatTest.cpp +++ b/unittests/ADT/APFloatTest.cpp @@ -33,6 +33,426 @@ static std::string convertToString(double d, unsigned Prec, unsigned Pad) { namespace { +TEST(APFloatTest, isSignaling) { + // We test qNaN, -qNaN, +sNaN, -sNaN with and without payloads. *NOTE* The + // positive/negative distinction is included only since the getQNaN/getSNaN + // API provides the option. + APInt payload = APInt::getOneBitSet(4, 2); + EXPECT_FALSE(APFloat::getQNaN(APFloat::IEEEsingle, false).isSignaling()); + EXPECT_FALSE(APFloat::getQNaN(APFloat::IEEEsingle, true).isSignaling()); + EXPECT_FALSE(APFloat::getQNaN(APFloat::IEEEsingle, false, &payload).isSignaling()); + EXPECT_FALSE(APFloat::getQNaN(APFloat::IEEEsingle, true, &payload).isSignaling()); + EXPECT_TRUE(APFloat::getSNaN(APFloat::IEEEsingle, false).isSignaling()); + EXPECT_TRUE(APFloat::getSNaN(APFloat::IEEEsingle, true).isSignaling()); + EXPECT_TRUE(APFloat::getSNaN(APFloat::IEEEsingle, false, &payload).isSignaling()); + EXPECT_TRUE(APFloat::getSNaN(APFloat::IEEEsingle, true, &payload).isSignaling()); +} + +TEST(APFloatTest, next) { + + APFloat test(APFloat::IEEEquad, APFloat::uninitialized); + APFloat expected(APFloat::IEEEquad, APFloat::uninitialized); + + // 1. Test Special Cases Values. + // + // Test all special values for nextUp and nextDown perscribed by IEEE-754R + // 2008. These are: + // 1. +inf + // 2. -inf + // 3. getLargest() + // 4. -getLargest() + // 5. getSmallest() + // 6. -getSmallest() + // 7. qNaN + // 8. sNaN + // 9. +0 + // 10. -0 + + // nextUp(+inf) = +inf. + test = APFloat::getInf(APFloat::IEEEquad, false); + expected = APFloat::getInf(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isInfinity()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+inf) = -nextUp(-inf) = -(-getLargest()) = getLargest() + test = APFloat::getInf(APFloat::IEEEquad, false); + expected = APFloat::getLargest(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-inf) = -getLargest() + test = APFloat::getInf(APFloat::IEEEquad, true); + expected = APFloat::getLargest(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-inf) = -nextUp(+inf) = -(+inf) = -inf. + test = APFloat::getInf(APFloat::IEEEquad, true); + expected = APFloat::getInf(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isInfinity() && test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(getLargest()) = +inf + test = APFloat::getLargest(APFloat::IEEEquad, false); + expected = APFloat::getInf(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isInfinity() && !test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(getLargest()) = -nextUp(-getLargest()) + // = -(-getLargest() + inc) + // = getLargest() - inc. + test = APFloat::getLargest(APFloat::IEEEquad, false); + expected = APFloat(APFloat::IEEEquad, + "0x1.fffffffffffffffffffffffffffep+16383"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(!test.isInfinity() && !test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-getLargest()) = -getLargest() + inc. + test = APFloat::getLargest(APFloat::IEEEquad, true); + expected = APFloat(APFloat::IEEEquad, + "-0x1.fffffffffffffffffffffffffffep+16383"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-getLargest()) = -nextUp(getLargest()) = -(inf) = -inf. + test = APFloat::getLargest(APFloat::IEEEquad, true); + expected = APFloat::getInf(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isInfinity() && test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(getSmallest()) = getSmallest() + inc. + test = APFloat(APFloat::IEEEquad, "0x0.0000000000000000000000000001p-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x0.0000000000000000000000000002p-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(getSmallest()) = -nextUp(-getSmallest()) = -(-0) = +0. + test = APFloat(APFloat::IEEEquad, "0x0.0000000000000000000000000001p-16382"); + expected = APFloat::getZero(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isZero() && !test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-getSmallest()) = -0. + test = APFloat(APFloat::IEEEquad, "-0x0.0000000000000000000000000001p-16382"); + expected = APFloat::getZero(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isZero() && test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-getSmallest()) = -nextUp(getSmallest()) = -getSmallest() - inc. + test = APFloat(APFloat::IEEEquad, "-0x0.0000000000000000000000000001p-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x0.0000000000000000000000000002p-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(qNaN) = qNaN + test = APFloat::getQNaN(APFloat::IEEEquad, false); + expected = APFloat::getQNaN(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(qNaN) = qNaN + test = APFloat::getQNaN(APFloat::IEEEquad, false); + expected = APFloat::getQNaN(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(sNaN) = qNaN + test = APFloat::getSNaN(APFloat::IEEEquad, false); + expected = APFloat::getQNaN(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opInvalidOp); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(sNaN) = qNaN + test = APFloat::getSNaN(APFloat::IEEEquad, false); + expected = APFloat::getQNaN(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(true), APFloat::opInvalidOp); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(+0) = +getSmallest() + test = APFloat::getZero(APFloat::IEEEquad, false); + expected = APFloat::getSmallest(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+0) = -nextUp(-0) = -getSmallest() + test = APFloat::getZero(APFloat::IEEEquad, false); + expected = APFloat::getSmallest(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-0) = +getSmallest() + test = APFloat::getZero(APFloat::IEEEquad, true); + expected = APFloat::getSmallest(APFloat::IEEEquad, false); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-0) = -nextUp(0) = -getSmallest() + test = APFloat::getZero(APFloat::IEEEquad, true); + expected = APFloat::getSmallest(APFloat::IEEEquad, true); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // 2. Binade Boundary Tests. + + // 2a. Test denormal <-> normal binade boundaries. + // * nextUp(+Largest Denormal) -> +Smallest Normal. + // * nextDown(-Largest Denormal) -> -Smallest Normal. + // * nextUp(-Smallest Normal) -> -Largest Denormal. + // * nextDown(+Smallest Normal) -> +Largest Denormal. + + // nextUp(+Largest Denormal) -> +Smallest Normal. + test = APFloat(APFloat::IEEEquad, "0x0.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x1.0000000000000000000000000000p-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_FALSE(test.isDenormal()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-Largest Denormal) -> -Smallest Normal. + test = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.0000000000000000000000000000p-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_FALSE(test.isDenormal()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-Smallest Normal) -> -LargestDenormal. + test = APFloat(APFloat::IEEEquad, + "-0x1.0000000000000000000000000000p-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffffffffp-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+Smallest Normal) -> +Largest Denormal. + test = APFloat(APFloat::IEEEquad, + "+0x1.0000000000000000000000000000p-16382"); + expected = APFloat(APFloat::IEEEquad, + "+0x0.ffffffffffffffffffffffffffffp-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // 2b. Test normal <-> normal binade boundaries. + // * nextUp(-Normal Binade Boundary) -> -Normal Binade Boundary + 1. + // * nextDown(+Normal Binade Boundary) -> +Normal Binade Boundary - 1. + // * nextUp(+Normal Binade Boundary - 1) -> +Normal Binade Boundary. + // * nextDown(-Normal Binade Boundary + 1) -> -Normal Binade Boundary. + + // nextUp(-Normal Binade Boundary) -> -Normal Binade Boundary + 1. + test = APFloat(APFloat::IEEEquad, "-0x1p+1"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffffffffp+0"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+Normal Binade Boundary) -> +Normal Binade Boundary - 1. + test = APFloat(APFloat::IEEEquad, "0x1p+1"); + expected = APFloat(APFloat::IEEEquad, "0x1.ffffffffffffffffffffffffffffp+0"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(+Normal Binade Boundary - 1) -> +Normal Binade Boundary. + test = APFloat(APFloat::IEEEquad, "0x1.ffffffffffffffffffffffffffffp+0"); + expected = APFloat(APFloat::IEEEquad, "0x1p+1"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-Normal Binade Boundary + 1) -> -Normal Binade Boundary. + test = APFloat(APFloat::IEEEquad, "-0x1.ffffffffffffffffffffffffffffp+0"); + expected = APFloat(APFloat::IEEEquad, "-0x1p+1"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // 2c. Test using next at binade boundaries with a direction away from the + // binade boundary. Away from denormal <-> normal boundaries. + // + // This is to make sure that even though we are at a binade boundary, since + // we are rounding away, we do not trigger the binade boundary code. Thus we + // test: + // * nextUp(-Largest Denormal) -> -Largest Denormal + inc. + // * nextDown(+Largest Denormal) -> +Largest Denormal - inc. + // * nextUp(+Smallest Normal) -> +Smallest Normal + inc. + // * nextDown(-Smallest Normal) -> -Smallest Normal - inc. + + // nextUp(-Largest Denormal) -> -Largest Denormal + inc. + test = APFloat(APFloat::IEEEquad, "-0x0.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x0.fffffffffffffffffffffffffffep-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+Largest Denormal) -> +Largest Denormal - inc. + test = APFloat(APFloat::IEEEquad, "0x0.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x0.fffffffffffffffffffffffffffep-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(+Smallest Normal) -> +Smallest Normal + inc. + test = APFloat(APFloat::IEEEquad, "0x1.0000000000000000000000000000p-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x1.0000000000000000000000000001p-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-Smallest Normal) -> -Smallest Normal - inc. + test = APFloat(APFloat::IEEEquad, "-0x1.0000000000000000000000000000p-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.0000000000000000000000000001p-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // 2d. Test values which cause our exponent to go to min exponent. This + // is to ensure that guards in the code to check for min exponent + // trigger properly. + // * nextUp(-0x1p-16381) -> -0x1.ffffffffffffffffffffffffffffp-16382 + // * nextDown(-0x1.ffffffffffffffffffffffffffffp-16382) -> + // -0x1p-16381 + // * nextUp(0x1.ffffffffffffffffffffffffffffp-16382) -> 0x1p-16382 + // * nextDown(0x1p-16382) -> 0x1.ffffffffffffffffffffffffffffp-16382 + + // nextUp(-0x1p-16381) -> -0x1.ffffffffffffffffffffffffffffp-16382 + test = APFloat(APFloat::IEEEquad, "-0x1p-16381"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffffffffp-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-0x1.ffffffffffffffffffffffffffffp-16382) -> + // -0x1p-16381 + test = APFloat(APFloat::IEEEquad, "-0x1.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, "-0x1p-16381"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(0x1.ffffffffffffffffffffffffffffp-16382) -> 0x1p-16381 + test = APFloat(APFloat::IEEEquad, "0x1.ffffffffffffffffffffffffffffp-16382"); + expected = APFloat(APFloat::IEEEquad, "0x1p-16381"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(0x1p-16381) -> 0x1.ffffffffffffffffffffffffffffp-16382 + test = APFloat(APFloat::IEEEquad, "0x1p-16381"); + expected = APFloat(APFloat::IEEEquad, + "0x1.ffffffffffffffffffffffffffffp-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // 3. Now we test both denormal/normal computation which will not cause us + // to go across binade boundaries. Specifically we test: + // * nextUp(+Denormal) -> +Denormal. + // * nextDown(+Denormal) -> +Denormal. + // * nextUp(-Denormal) -> -Denormal. + // * nextDown(-Denormal) -> -Denormal. + // * nextUp(+Normal) -> +Normal. + // * nextDown(+Normal) -> +Normal. + // * nextUp(-Normal) -> -Normal. + // * nextDown(-Normal) -> -Normal. + + // nextUp(+Denormal) -> +Denormal. + test = APFloat(APFloat::IEEEquad, + "0x0.ffffffffffffffffffffffff000cp-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x0.ffffffffffffffffffffffff000dp-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+Denormal) -> +Denormal. + test = APFloat(APFloat::IEEEquad, + "0x0.ffffffffffffffffffffffff000cp-16382"); + expected = APFloat(APFloat::IEEEquad, + "0x0.ffffffffffffffffffffffff000bp-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-Denormal) -> -Denormal. + test = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffff000cp-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffff000bp-16382"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-Denormal) -> -Denormal + test = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffff000cp-16382"); + expected = APFloat(APFloat::IEEEquad, + "-0x0.ffffffffffffffffffffffff000dp-16382"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(+Normal) -> +Normal. + test = APFloat(APFloat::IEEEquad, + "0x1.ffffffffffffffffffffffff000cp-16000"); + expected = APFloat(APFloat::IEEEquad, + "0x1.ffffffffffffffffffffffff000dp-16000"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(+Normal) -> +Normal. + test = APFloat(APFloat::IEEEquad, + "0x1.ffffffffffffffffffffffff000cp-16000"); + expected = APFloat(APFloat::IEEEquad, + "0x1.ffffffffffffffffffffffff000bp-16000"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(!test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextUp(-Normal) -> -Normal. + test = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffff000cp-16000"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffff000bp-16000"); + EXPECT_EQ(test.next(false), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); + + // nextDown(-Normal) -> -Normal. + test = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffff000cp-16000"); + expected = APFloat(APFloat::IEEEquad, + "-0x1.ffffffffffffffffffffffff000dp-16000"); + EXPECT_EQ(test.next(true), APFloat::opOK); + EXPECT_TRUE(!test.isDenormal()); + EXPECT_TRUE(test.isNegative()); + EXPECT_TRUE(test.bitwiseIsEqual(expected)); +} + TEST(APFloatTest, FMA) { APFloat::roundingMode rdmd = APFloat::rmNearestTiesToEven; |