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https://gitlab.com/libeigen/eigen.git
synced 2026-04-10 11:34:33 +08:00
Updated pfrexp implementation.
The original implementation fails for 0, denormals, inf, and NaN. See #2150
This commit is contained in:
Antonio Sanchez
committed by
Rasmus Munk Larsen
Rasmus Munk Larsen
parent
9ad4096ccb
commit
7ff0b7a980
@@ -25,80 +25,114 @@ pset(const typename unpacket_traits<Packet>::type (&a)[N] /* a */) {
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return pload<Packet>(a);
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}
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template<typename Packet> EIGEN_STRONG_INLINE Packet
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pfrexp_float(const Packet& a, Packet& exponent) {
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// Creates a Scalar integer type with same bit-width.
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template<typename T> struct make_integer;
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template<> struct make_integer<float> { typedef numext::int32_t type; };
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template<> struct make_integer<double> { typedef numext::int64_t type; };
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template<> struct make_integer<half> { typedef numext::int16_t type; };
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template<> struct make_integer<bfloat16> { typedef numext::int16_t type; };
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template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
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Packet pfrexp_generic_get_biased_exponent(const Packet& a) {
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typedef typename unpacket_traits<Packet>::type Scalar;
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typedef typename unpacket_traits<Packet>::integer_packet PacketI;
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const Packet cst_126f = pset1<Packet>(126.0f);
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const Packet cst_half = pset1<Packet>(0.5f);
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const Packet cst_inv_mant_mask = pset1frombits<Packet>(~0x7f800000u);
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exponent = psub(pcast<PacketI,Packet>(plogical_shift_right<23>(preinterpret<PacketI>(pabs<Packet>(a)))), cst_126f);
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return por(pand(a, cst_inv_mant_mask), cst_half);
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EIGEN_CONSTEXPR int mantissa_bits = numext::numeric_limits<Scalar>::digits - 1;
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return pcast<PacketI, Packet>(plogical_shift_right<mantissa_bits>(preinterpret<PacketI>(pabs(a))));
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}
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template<typename Packet> EIGEN_STRONG_INLINE Packet
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pfrexp_double(const Packet& a, Packet& exponent) {
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typedef typename unpacket_traits<Packet>::integer_packet PacketI;
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const Packet cst_1022d = pset1<Packet>(1022.0);
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const Packet cst_half = pset1<Packet>(0.5);
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const Packet cst_inv_mant_mask = pset1frombits<Packet, uint64_t>(static_cast<uint64_t>(~0x7ff0000000000000ull));
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exponent = psub(pcast<PacketI,Packet>(plogical_shift_right<52>(preinterpret<PacketI>(pabs<Packet>(a)))), cst_1022d);
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return por(pand(a, cst_inv_mant_mask), cst_half);
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// Safely applies frexp, correctly handles denormals.
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// Assumes IEEE floating point format.
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template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
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Packet pfrexp_generic(const Packet& a, Packet& exponent) {
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typedef typename unpacket_traits<Packet>::type Scalar;
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typedef typename make_unsigned<typename make_integer<Scalar>::type>::type ScalarUI;
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EIGEN_CONSTEXPR int total_bits = sizeof(Scalar) * CHAR_BIT;
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EIGEN_CONSTEXPR int mantissa_bits = numext::numeric_limits<Scalar>::digits - 1;
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EIGEN_CONSTEXPR int exponent_bits = total_bits - mantissa_bits - 1;
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EIGEN_CONSTEXPR ScalarUI scalar_sign_mantissa_mask =
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~(((ScalarUI(1) << exponent_bits) - ScalarUI(1)) << mantissa_bits); // ~0x7f800000
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const Packet sign_mantissa_mask = pset1frombits<Packet>(static_cast<ScalarUI>(scalar_sign_mantissa_mask));
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const Packet half = pset1<Packet>(Scalar(0.5));
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const Packet zero = pzero(a);
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const Packet normal_min = pset1<Packet>((numext::numeric_limits<Scalar>::min)()); // Minimum normal value, 2^-126
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// To handle denormals, normalize by multiplying by 2^(mantissa_bits+1).
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const Packet is_denormal = pcmp_lt(pabs(a), normal_min);
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EIGEN_CONSTEXPR ScalarUI scalar_normalization_offset = ScalarUI(mantissa_bits + 1); // 24
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// The following cannot be constexpr because bfloat16(uint16_t) is not constexpr.
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const Scalar scalar_normalization_factor = Scalar(ScalarUI(1) << int(scalar_normalization_offset)); // 2^24
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const Packet normalization_factor = pset1<Packet>(scalar_normalization_factor);
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const Packet normalized_a = pselect(is_denormal, pmul(a, normalization_factor), a);
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// Determine exponent offset: -126 if normal, -126-24 if denormal
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const Scalar scalar_exponent_offset = -Scalar((ScalarUI(1)<<(exponent_bits-1)) - ScalarUI(2)); // -126
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Packet exponent_offset = pset1<Packet>(scalar_exponent_offset);
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const Packet normalization_offset = pset1<Packet>(-Scalar(scalar_normalization_offset)); // -24
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exponent_offset = pselect(is_denormal, padd(exponent_offset, normalization_offset), exponent_offset);
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// Determine exponent and mantissa from normalized_a.
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exponent = pfrexp_generic_get_biased_exponent(normalized_a);
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// Zero, Inf and NaN return 'a' unmodified, exponent is zero
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// (technically the exponent is unspecified for inf/NaN, but GCC/Clang set it to zero)
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const Scalar scalar_non_finite_exponent = Scalar((ScalarUI(1) << exponent_bits) - ScalarUI(1)); // 255
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const Packet non_finite_exponent = pset1<Packet>(scalar_non_finite_exponent);
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const Packet is_zero_or_not_finite = por(pcmp_eq(a, zero), pcmp_eq(exponent, non_finite_exponent));
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const Packet m = pselect(is_zero_or_not_finite, a, por(pand(normalized_a, sign_mantissa_mask), half));
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exponent = pselect(is_zero_or_not_finite, zero, padd(exponent, exponent_offset));
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return m;
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}
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// Safely applies ldexp, correctly handles overflows, underflows and denormals.
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// Assumes IEEE floating point format.
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template<typename Packet>
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struct pldexp_impl {
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template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
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Packet pldexp_generic(const Packet& a, const Packet& exponent) {
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// We want to return a * 2^exponent, allowing for all possible integer
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// exponents without overflowing or underflowing in intermediate
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// computations.
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//
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// Since 'a' and the output can be denormal, the maximum range of 'exponent'
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// to consider for a float is:
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// -255-23 -> 255+23
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// Below -278 any finite float 'a' will become zero, and above +278 any
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// finite float will become inf, including when 'a' is the smallest possible
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// denormal.
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//
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// Unfortunately, 2^(278) cannot be represented using either one or two
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// finite normal floats, so we must split the scale factor into at least
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// three parts. It turns out to be faster to split 'exponent' into four
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// factors, since [exponent>>2] is much faster to compute that [exponent/3].
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//
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// Set e = min(max(exponent, -278), 278);
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// b = floor(e/4);
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// out = ((((a * 2^(b)) * 2^(b)) * 2^(b)) * 2^(e-3*b))
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//
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// This will avoid any intermediate overflows and correctly handle 0, inf,
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// NaN cases.
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typedef typename unpacket_traits<Packet>::integer_packet PacketI;
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typedef typename unpacket_traits<Packet>::type Scalar;
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typedef typename unpacket_traits<PacketI>::type ScalarI;
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enum {
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TotalBits = sizeof(Scalar) * CHAR_BIT,
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MantissaBits = std::numeric_limits<Scalar>::digits - 1,
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ExponentBits = int(TotalBits) - int(MantissaBits) - 1
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};
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static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
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Packet run(const Packet& a, const Packet& exponent) {
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// We want to return a * 2^exponent, allowing for all possible integer
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// exponents without overflowing or underflowing in intermediate
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// computations.
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//
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// Since 'a' and the output can be denormal, the maximum range of 'exponent'
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// to consider for a float is:
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// -255-23 -> 255+23
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// Below -278 any finite float 'a' will become zero, and above +278 any
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// finite float will become inf, including when 'a' is the smallest possible
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// denormal.
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//
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// Unfortunately, 2^(278) cannot be represented using either one or two
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// finite normal floats, so we must split the scale factor into at least
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// three parts. It turns out to be faster to split 'exponent' into four
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// factors, since [exponent>>2] is much faster to compute that [exponent/3].
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//
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// Set e = min(max(exponent, -278), 278);
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// b = floor(e/4);
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// out = ((((a * 2^(b)) * 2^(b)) * 2^(b)) * 2^(e-3*b))
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//
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// This will avoid any intermediate overflows and correctly handle 0, inf,
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// NaN cases.
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const Packet max_exponent = pset1<Packet>(Scalar( (ScalarI(1)<<int(ExponentBits)) + ScalarI(MantissaBits) - ScalarI(1))); // 278
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const PacketI bias = pset1<PacketI>((ScalarI(1)<<(int(ExponentBits)-1)) - ScalarI(1)); // 127
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const PacketI e = pcast<Packet, PacketI>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
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PacketI b = parithmetic_shift_right<2>(e); // floor(e/4);
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Packet c = preinterpret<Packet>(plogical_shift_left<int(MantissaBits)>(padd(b, bias))); // 2^b
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Packet out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
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b = psub(psub(psub(e, b), b), b); // e - 3b
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c = preinterpret<Packet>(plogical_shift_left<int(MantissaBits)>(padd(b, bias))); // 2^(e-3*b)
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out = pmul(out, c);
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return out;
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}
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};
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EIGEN_CONSTEXPR int total_bits = sizeof(Scalar) * CHAR_BIT;
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EIGEN_CONSTEXPR int mantissa_bits = numext::numeric_limits<Scalar>::digits - 1;
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EIGEN_CONSTEXPR int exponent_bits = total_bits - mantissa_bits - 1;
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const Packet max_exponent = pset1<Packet>(Scalar((ScalarI(1)<<exponent_bits) + ScalarI(mantissa_bits - 1))); // 278
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const PacketI bias = pset1<PacketI>((ScalarI(1)<<(exponent_bits-1)) - ScalarI(1)); // 127
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const PacketI e = pcast<Packet, PacketI>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
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PacketI b = parithmetic_shift_right<2>(e); // floor(e/4);
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Packet c = preinterpret<Packet>(plogical_shift_left<mantissa_bits>(padd(b, bias))); // 2^b
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Packet out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
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b = psub(psub(psub(e, b), b), b); // e - 3b
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c = preinterpret<Packet>(plogical_shift_left<mantissa_bits>(padd(b, bias))); // 2^(e-3*b)
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out = pmul(out, c);
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return out;
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}
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// Explicitly multiplies
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// a * (2^e)
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// clamping e to the range
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// [std::numeric_limits<Scalar>::min_exponent-2, std::numeric_limits<Scalar>::max_exponent]
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// [numeric_limits<Scalar>::min_exponent-2, numeric_limits<Scalar>::max_exponent]
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//
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// This is approx 7x faster than pldexp_impl, but will prematurely over/underflow
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// if 2^e doesn't fit into a normal floating-point Scalar.
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@@ -111,7 +145,7 @@ struct pldexp_fast_impl {
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typedef typename unpacket_traits<PacketI>::type ScalarI;
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enum {
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TotalBits = sizeof(Scalar) * CHAR_BIT,
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MantissaBits = std::numeric_limits<Scalar>::digits - 1,
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MantissaBits = numext::numeric_limits<Scalar>::digits - 1,
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ExponentBits = int(TotalBits) - int(MantissaBits) - 1
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};
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@@ -126,14 +160,6 @@ struct pldexp_fast_impl {
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}
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};
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template<typename Packet> EIGEN_STRONG_INLINE Packet
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pldexp_float(const Packet& a, const Packet& exponent)
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{ return pldexp_impl<Packet>::run(a, exponent); }
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template<typename Packet> EIGEN_STRONG_INLINE Packet
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pldexp_double(const Packet& a, const Packet& exponent)
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{ return pldexp_impl<Packet>::run(a, exponent); }
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// Natural or base 2 logarithm.
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// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
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// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
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