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Some fixes/cleanups for numeric_limits & fix for related bug in psqrt

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This commit is contained in:
Rasmus Munk Larsen 2022-01-07 01:10:17 +00:00
parent ed27d988c1
commit 96dc37a03b
6 changed files with 43 additions and 27 deletions
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19
Eigen/src/Core/arch/AVX/MathFunctions.h
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@ -101,17 +101,22 @@ pexp<Packet4d>(const Packet4d& _x) {
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet8f psqrt<Packet8f>(const Packet8f& _x) {
Packet8f minus_half_x = pmul(_x, pset1<Packet8f>(-0.5f));
Packet8f denormal_mask = pandnot(
pcmp_lt(_x, pset1<Packet8f>((std::numeric_limits<float>::min)())),
pcmp_lt(_x, pzero(_x)));
const Packet8f minus_half_x = pmul(_x, pset1<Packet8f>(-0.5f));
const Packet8f negative_mask = pcmp_lt(_x, pzero(_x));
const Packet8f denormal_mask =
pandnot(pcmp_lt(_x, pset1<Packet8f>((std::numeric_limits<float>::min)())),
negative_mask);
// Compute approximate reciprocal sqrt.
Packet8f x = _mm256_rsqrt_ps(_x);
Packet8f rs = _mm256_rsqrt_ps(_x);
// Flush negative arguments to zero. This is a workaround which ensures
// that sqrt of a negative denormal returns -NaN, despite _mm256_rsqrt_ps
// returning -Inf for such values.
const Packet8f x_flushed = pandnot(_x, negative_mask);
// Do a single step of Newton's iteration.
x = pmul(x, pmadd(minus_half_x, pmul(x,x), pset1<Packet8f>(1.5f)));
rs = pmul(rs, pmadd(minus_half_x, pmul(rs,rs), pset1<Packet8f>(1.5f)));
// Flush results for denormals to zero.
return pandnot(pmul(_x,x), denormal_mask);
return pandnot(pmul(x_flushed, rs), denormal_mask);
}
#else

12
Eigen/src/Core/arch/Default/BFloat16.h
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@ -137,21 +137,25 @@ struct numeric_limits<Eigen::bfloat16> {
static EIGEN_CONSTEXPR const bool has_infinity = true;
static EIGEN_CONSTEXPR const bool has_quiet_NaN = true;
static EIGEN_CONSTEXPR const bool has_signaling_NaN = true;
static EIGEN_CONSTEXPR const float_denorm_style has_denorm = std::denorm_absent;
static EIGEN_CONSTEXPR const float_denorm_style has_denorm = std::denorm_present;
static EIGEN_CONSTEXPR const bool has_denorm_loss = false;
static EIGEN_CONSTEXPR const std::float_round_style round_style = numeric_limits<float>::round_style;
static EIGEN_CONSTEXPR const bool is_iec559 = false;
static EIGEN_CONSTEXPR const bool is_iec559 = true;
// The C++ standard defines this as "true if the set of values representable
// by the type is finite." BFloat16 has finite precision.
static EIGEN_CONSTEXPR const bool is_bounded = true;
static EIGEN_CONSTEXPR const bool is_modulo = false;
static EIGEN_CONSTEXPR const int digits = 8;
static EIGEN_CONSTEXPR const int digits10 = 2;
static EIGEN_CONSTEXPR const int max_digits10 = 4;
static EIGEN_CONSTEXPR const int radix = 2;
static EIGEN_CONSTEXPR const int radix = numeric_limits<float>::radix;
static EIGEN_CONSTEXPR const int min_exponent = numeric_limits<float>::min_exponent;
static EIGEN_CONSTEXPR const int min_exponent10 = numeric_limits<float>::min_exponent10;
static EIGEN_CONSTEXPR const int max_exponent = numeric_limits<float>::max_exponent;
static EIGEN_CONSTEXPR const int max_exponent10 = numeric_limits<float>::max_exponent10;
static EIGEN_CONSTEXPR const bool traps = numeric_limits<float>::traps;
// IEEE754: "The implementer shall choose how tininess is detected, but shall
// detect tininess in the same way for all operations in radix two"
static EIGEN_CONSTEXPR const bool tinyness_before = numeric_limits<float>::tinyness_before;
static EIGEN_CONSTEXPR Eigen::bfloat16 (min)() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0080); }
@ -161,7 +165,7 @@ struct numeric_limits<Eigen::bfloat16> {
static EIGEN_CONSTEXPR Eigen::bfloat16 round_error() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x3f00); }
static EIGEN_CONSTEXPR Eigen::bfloat16 infinity() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f80); }
static EIGEN_CONSTEXPR Eigen::bfloat16 quiet_NaN() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fc0); }
static EIGEN_CONSTEXPR Eigen::bfloat16 signaling_NaN() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f81); }
static EIGEN_CONSTEXPR Eigen::bfloat16 signaling_NaN() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fa0); }
static EIGEN_CONSTEXPR Eigen::bfloat16 denorm_min() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0001); }
};

20
Eigen/src/Core/arch/Default/Half.h
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@ -218,29 +218,33 @@ struct numeric_limits<Eigen::half> {
static EIGEN_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
static EIGEN_CONSTEXPR const bool has_denorm_loss = false;
static EIGEN_CONSTEXPR const std::float_round_style round_style = std::round_to_nearest;
static EIGEN_CONSTEXPR const bool is_iec559 = false;
static EIGEN_CONSTEXPR const bool is_bounded = false;
static EIGEN_CONSTEXPR const bool is_iec559 = true;
// The C++ standard defines this as "true if the set of values representable
// by the type is finite." Half has finite precision.
static EIGEN_CONSTEXPR const bool is_bounded = true;
static EIGEN_CONSTEXPR const bool is_modulo = false;
static EIGEN_CONSTEXPR const int digits = 11;
static EIGEN_CONSTEXPR const int digits10 = 3; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
static EIGEN_CONSTEXPR const int max_digits10 = 5; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
static EIGEN_CONSTEXPR const int radix = 2;
static EIGEN_CONSTEXPR const int radix = numeric_limits<float>::radix;
static EIGEN_CONSTEXPR const int min_exponent = -13;
static EIGEN_CONSTEXPR const int min_exponent10 = -4;
static EIGEN_CONSTEXPR const int max_exponent = 16;
static EIGEN_CONSTEXPR const int max_exponent10 = 4;
static EIGEN_CONSTEXPR const bool traps = true;
static EIGEN_CONSTEXPR const bool tinyness_before = false;
static EIGEN_CONSTEXPR const bool traps = numeric_limits<float>::traps;
// IEEE754: "The implementer shall choose how tininess is detected, but shall
// detect tininess in the same way for all operations in radix two"
static EIGEN_CONSTEXPR const bool tinyness_before = std::numeric_limits<float>::tinyness_before;
static EIGEN_CONSTEXPR Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x400); }
static EIGEN_CONSTEXPR Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x0400); }
static EIGEN_CONSTEXPR Eigen::half lowest() { return Eigen::half_impl::raw_uint16_to_half(0xfbff); }
static EIGEN_CONSTEXPR Eigen::half (max)() { return Eigen::half_impl::raw_uint16_to_half(0x7bff); }
static EIGEN_CONSTEXPR Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x0800); }
static EIGEN_CONSTEXPR Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x1400); }
static EIGEN_CONSTEXPR Eigen::half round_error() { return Eigen::half_impl::raw_uint16_to_half(0x3800); }
static EIGEN_CONSTEXPR Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); }
static EIGEN_CONSTEXPR Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
static EIGEN_CONSTEXPR Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7d00); }
static EIGEN_CONSTEXPR Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x1); }
static EIGEN_CONSTEXPR Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x0001); }
};
// If std::numeric_limits<T> is specialized, should also specialize

10
Eigen/src/Core/arch/SSE/MathFunctions.h
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@ -75,8 +75,6 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
return pcos_float(_x);
}
#if EIGEN_FAST_MATH
// Functions for sqrt.
// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step
// of Newton's method, at a cost of 1-2 bits of precision as opposed to the
@ -85,11 +83,13 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
// it can be inlined and pipelined with other computations, further reducing its
// effective latency. This is similar to Quake3's fast inverse square root.
// For detail see here: http://www.beyond3d.com/content/articles/8/
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
#if EIGEN_FAST_MATH
template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet4f psqrt<Packet4f>(const Packet4f& _x)
{
Packet4f minus_half_x = pmul(_x, pset1<Packet4f>(-0.5f));
Packet4f denormal_mask = pandnot(
const Packet4f minus_half_x = pmul(_x, pset1<Packet4f>(-0.5f));
const Packet4f denormal_mask = pandnot(
pcmp_lt(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())),
pcmp_lt(_x, pzero(_x)));

2
test/array_cwise.cpp
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@ -451,7 +451,7 @@ template<typename ArrayType> void array_real(const ArrayType& m)
const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
VERIFY_IS_CWISE_APPROX(s1/m1, s1 * m1.inverse());
// check inplace transpose
m3 = m1;

7
test/packetmath.cpp
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@ -890,7 +890,10 @@ void packetmath_real() {
data1[0] = std::numeric_limits<Scalar>::denorm_min();
data1[1] = -std::numeric_limits<Scalar>::denorm_min();
h.store(data2, internal::plog(h.load(data1)));
VERIFY_IS_APPROX(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
// TODO(rmlarsen): Re-enable for bfloat16.
if (!internal::is_same<Scalar, bfloat16>::value) {
VERIFY_IS_APPROX(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
}
VERIFY((numext::isnan)(data2[1]));
}
#endif
@ -917,7 +920,7 @@ void packetmath_real() {
if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
data1[1] = -std::numeric_limits<Scalar>::denorm_min();
} else {
data1[1] = -NumTraits<Scalar>::epsilon();
data1[1] = -((std::numeric_limits<Scalar>::min)());
}
h.store(data2, internal::psqrt(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));