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Vectorize asinh and acosh for float and double

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libeigen/eigen!2376

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
This commit is contained in:
Rasmus Munk Larsen
2026-04-01 21:46:36 -07:00
parent 9513d3878e
commit d31a73437f
7 changed files with 77 additions and 67 deletions
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4
Eigen/src/Core/arch/AVX/PacketMath.h
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@@ -119,6 +119,8 @@ struct packet_traits<float> : default_packet_traits {
HasATanh = 1,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasLog = 1,
HasLog10 = 1,
HasExp = 1,
@@ -153,6 +155,8 @@ struct packet_traits<double> : default_packet_traits {
#endif
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasTanh = EIGEN_FAST_MATH,
HasErf = 1,
HasErfc = 1,

4
Eigen/src/Core/arch/AVX512/PacketMath.h
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@@ -174,6 +174,8 @@ struct packet_traits<float> : default_packet_traits {
HasATanh = 1,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasSqrt = 1,
HasRsqrt = 1,
HasCbrt = 1,
@@ -209,6 +211,8 @@ struct packet_traits<double> : default_packet_traits {
HasTan = EIGEN_FAST_MATH,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasLog = 1,
HasLog10 = 1,
HasExp = 1,

110
Eigen/src/Core/arch/Default/GenericPacketMathTrig.h
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@@ -977,9 +977,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcosh_double(const Pa
//----------------------------------------------------------------------
/** \internal \returns the inverse hyperbolic sine of \a x (coeff-wise).
For small |x|: asinh(x) = sign(x) * log1p(|x| + x^2/(1 + sqrt(1 + x^2)))
For large |x|: asinh(x) = sign(x) * (log(|x|) + ln(2))
Otherwise: asinh(x) = sign(x) * log(|x| + sqrt(x^2 + 1))
Uses a single log1p call by selecting the argument before the transcendental:
For moderate |x|: log1p(|x| + x^2 / (1 + sqrt(1 + x^2)))
For large |x|: log1p(|x| - 1) + ln2 (avoids x^2 overflow)
*/
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pasinh_float(const Packet& x) {
@@ -988,21 +988,21 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pasinh_float(const Pa
const Packet x_sign = pand(x, sign_mask);
const Packet one = pset1<Packet>(1.0f);
// For |x| < 0.5, use log1p formulation to avoid cancellation:
// asinh(x) = log1p(|x| + x^2 / (1 + sqrt(1 + x^2)))
const Packet x2 = pmul(abs_x, abs_x);
Packet p_small = generic_log1p(padd(abs_x, pdiv(x2, padd(one, psqrt(padd(one, x2))))));
// For 0.5 <= |x| < 1e10, use log(|x| + sqrt(x^2 + 1)).
Packet p_med = plog(padd(abs_x, psqrt(padd(x2, one))));
// For |x| >= 1e10, use log(2*|x|) = log(|x|) + ln(2) to avoid x^2 overflow.
const Packet ln2 = pset1<Packet>(0.6931471805599453f);
Packet p_large = padd(plog(abs_x), ln2);
const Packet small_mask = pcmp_lt(abs_x, pset1<Packet>(0.5f));
// For |x| >= 1e10, use log(2|x|) = log1p(|x| - 1) + ln2 to avoid x^2 overflow.
const Packet large_mask = pcmp_lt(pset1<Packet>(1e10f), abs_x);
Packet result = pselect(large_mask, p_large, pselect(small_mask, p_small, p_med));
// Guard x^2 against overflow in the large case.
const Packet x2 = pmul(abs_x, pselect(large_mask, pzero(abs_x), abs_x));
// For |x| < 1e10: log1p(|x| + x^2 / (1 + sqrt(1 + x^2))).
// Algebraically equivalent to log(|x| + sqrt(x^2 + 1))
// but avoids cancellation for small |x|.
Packet normal_arg = padd(abs_x, pdiv(x2, padd(one, psqrt(padd(one, x2)))));
// For |x| >= 1e10: log1p(|x| - 1), then add ln2 after.
Packet large_arg = psub(abs_x, one);
// Select argument, then call log1p once.
Packet result = generic_log1p(pselect(large_mask, large_arg, normal_arg));
// Add ln2 for the large path: log(2|x|) = log(|x|) + ln2 = log1p(|x|-1) + ln2.
const Packet ln2 = pset1<Packet>(0.6931471805599453f);
result = pselect(large_mask, padd(result, ln2), result);
return por(x_sign, result);
}
@@ -1013,49 +1013,37 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pasinh_double(const P
const Packet x_sign = pand(x, sign_mask);
const Packet one = pset1<Packet>(1.0);
const Packet x2 = pmul(abs_x, abs_x);
Packet p_small = generic_log1p(padd(abs_x, pdiv(x2, padd(one, psqrt(padd(one, x2))))));
Packet p_med = plog(padd(abs_x, psqrt(padd(x2, one))));
const Packet ln2 = pset1<Packet>(0.6931471805599453);
Packet p_large = padd(plog(abs_x), ln2);
const Packet small_mask = pcmp_lt(abs_x, pset1<Packet>(0.5));
const Packet large_mask = pcmp_lt(pset1<Packet>(1e150), abs_x);
Packet result = pselect(large_mask, p_large, pselect(small_mask, p_small, p_med));
const Packet x2 = pmul(abs_x, pselect(large_mask, pzero(abs_x), abs_x));
Packet normal_arg = padd(abs_x, pdiv(x2, padd(one, psqrt(padd(one, x2)))));
Packet large_arg = psub(abs_x, one);
Packet result = generic_log1p(pselect(large_mask, large_arg, normal_arg));
const Packet ln2 = pset1<Packet>(0.6931471805599453);
result = pselect(large_mask, padd(result, ln2), result);
return por(x_sign, result);
}
/** \internal \returns the inverse hyperbolic cosine of \a x (coeff-wise).
Uses acosh(x) = log(x + sqrt(x^2 - 1)) for x >= 1.
Uses a single log1p call by selecting the argument before the transcendental:
For moderate x: log1p(t + sqrt(t*(t+2))) where t = x - 1
For huge x: log1p(t) + ln2 (avoids t*(t+2) overflow)
Returns NaN for x < 1.
*/
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pacosh_float(const Packet& x) {
const Packet one = pset1<Packet>(1.0f);
// For x near 1, use log1p to avoid cancellation:
// acosh(x) = log(x + sqrt(x^2-1)) = log(x + sqrt((x-1)(x+1)))
// For x close to 1, let t = x-1, then:
// acosh(x) = log1p(t + sqrt(t*(t+2)))
const Packet t = psub(x, one);
const Packet small_mask = pcmp_lt(t, pset1<Packet>(0.5f));
// Small path: acosh(x) = log1p(t + sqrt(t*(t+2)))
const Packet two = pset1<Packet>(2.0f);
Packet p_small = generic_log1p(padd(t, psqrt(pmul(t, padd(t, two)))));
// Large path: acosh(x) = log(x + sqrt(x^2-1))
// For very large x, use log(2*x) to avoid overflow in x^2.
const Packet large_threshold = pset1<Packet>(1e10f);
const Packet huge_mask = pcmp_lt(large_threshold, x);
const Packet x2_safe = pselect(huge_mask, one, pmul(x, x));
Packet p_large = plog(padd(x, psqrt(psub(x2_safe, one))));
const Packet log2 = pset1<Packet>(0.6931471805599453f);
p_large = pselect(huge_mask, padd(plog(x), log2), p_large);
Packet result = pselect(small_mask, p_small, p_large);
const Packet t = psub(x, one);
const Packet huge_mask = pcmp_lt(pset1<Packet>(1e10f), x);
// Guard t*(t+2) against overflow in the huge case.
const Packet t_tp2 = pmul(pselect(huge_mask, pzero(t), t), padd(t, two));
Packet normal_arg = padd(t, psqrt(t_tp2));
// For huge x: acosh(x) = log(2x) = log1p(x - 1) + ln2.
Packet huge_arg = t;
// Select argument, then call log1p once.
Packet result = generic_log1p(pselect(huge_mask, huge_arg, normal_arg));
const Packet ln2 = pset1<Packet>(0.6931471805599453f);
result = pselect(huge_mask, padd(result, ln2), result);
// Return NaN for x < 1.
const Packet invalid_mask = pcmp_lt(x, one);
return por(invalid_mask, result);
@@ -1064,23 +1052,15 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pacosh_float(const Pa
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pacosh_double(const Packet& x) {
const Packet one = pset1<Packet>(1.0);
const Packet t = psub(x, one);
const Packet small_mask = pcmp_lt(t, pset1<Packet>(0.5));
// Small path: acosh(x) = log1p(t + sqrt(t*(t+2)))
const Packet two = pset1<Packet>(2.0);
Packet p_small = generic_log1p(padd(t, psqrt(pmul(t, padd(t, two)))));
// Large path: acosh(x) = log(x + sqrt(x^2-1))
const Packet large_threshold = pset1<Packet>(1e150);
const Packet huge_mask = pcmp_lt(large_threshold, x);
const Packet x2_safe = pselect(huge_mask, one, pmul(x, x));
Packet p_large = plog(padd(x, psqrt(psub(x2_safe, one))));
const Packet log2 = pset1<Packet>(0.6931471805599453);
p_large = pselect(huge_mask, padd(plog(x), log2), p_large);
Packet result = pselect(small_mask, p_small, p_large);
const Packet t = psub(x, one);
const Packet huge_mask = pcmp_lt(pset1<Packet>(1e150), x);
const Packet t_tp2 = pmul(pselect(huge_mask, pzero(t), t), padd(t, two));
Packet normal_arg = padd(t, psqrt(t_tp2));
Packet huge_arg = t;
Packet result = generic_log1p(pselect(huge_mask, huge_arg, normal_arg));
const Packet ln2 = pset1<Packet>(0.6931471805599453);
result = pselect(huge_mask, padd(result, ln2), result);
const Packet invalid_mask = pcmp_lt(x, one);
return por(invalid_mask, result);
}

4
Eigen/src/Core/arch/NEON/PacketMath.h
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@@ -204,6 +204,8 @@ struct packet_traits<float> : default_packet_traits {
HasATanh = 1,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasLog = 1,
HasLog10 = 1,
HasExp = 1,
@@ -5051,6 +5053,8 @@ struct packet_traits<double> : default_packet_traits {
HasATanh = 1,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
#endif
HasSin = EIGEN_FAST_MATH,
HasCos = EIGEN_FAST_MATH,

4
Eigen/src/Core/arch/SSE/PacketMath.h
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@@ -192,6 +192,8 @@ struct packet_traits<float> : default_packet_traits {
HasATanh = 1,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasLog = 1,
HasLog1p = 1,
HasLog10 = 1,
@@ -225,6 +227,8 @@ struct packet_traits<double> : default_packet_traits {
HasTan = EIGEN_FAST_MATH,
HasSinh = 1,
HasCosh = 1,
HasASinh = 1,
HasACosh = 1,
HasTanh = EIGEN_FAST_MATH,
HasErf = EIGEN_FAST_MATH,
HasErfc = EIGEN_FAST_MATH,

12
Eigen/src/Core/functors/UnaryFunctors.h
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@@ -765,11 +765,15 @@ struct functor_traits<scalar_sinh_op<Scalar>> {
template <typename Scalar>
struct scalar_asinh_op {
EIGEN_DEVICE_FUNC constexpr inline Scalar operator()(const Scalar& a) const { return numext::asinh(a); }
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
return internal::pasinh(a);
}
};
template <typename Scalar>
struct functor_traits<scalar_asinh_op<Scalar>> {
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasASinh };
};
/** \internal
@@ -796,11 +800,15 @@ struct functor_traits<scalar_cosh_op<Scalar>> {
template <typename Scalar>
struct scalar_acosh_op {
EIGEN_DEVICE_FUNC constexpr inline Scalar operator()(const Scalar& a) const { return numext::acosh(a); }
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
return internal::pacosh(a);
}
};
template <typename Scalar>
struct functor_traits<scalar_acosh_op<Scalar>> {
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasACosh };
};
/** \internal

6
benchmarks/Core/bench_cwise_math.cpp
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@@ -52,6 +52,8 @@ BENCH_CWISE_UNARY(Atan, a.atan(), -10, 10)
BENCH_CWISE_UNARY(Sinh, a.sinh(), -5, 5)
BENCH_CWISE_UNARY(Cosh, a.cosh(), -5, 5)
BENCH_CWISE_UNARY(Tanh, a.tanh(), -5, 5)
BENCH_CWISE_UNARY(Asinh, a.asinh(), -5, 5)
BENCH_CWISE_UNARY(Acosh, a.acosh(), 1.01, 10)
BENCH_CWISE_UNARY(Atanh, a.atanh(), -0.99, 0.99)
BENCH_CWISE_UNARY(Log10, a.log10(), 0.01, 100)
BENCH_CWISE_UNARY(Erf, Eigen::erf(a), -4, 4)
@@ -155,6 +157,8 @@ BENCHMARK(BM_Atan<float>) CWISE_SIZES ->Name("Atan_float");
BENCHMARK(BM_Sinh<float>) CWISE_SIZES ->Name("Sinh_float");
BENCHMARK(BM_Cosh<float>) CWISE_SIZES ->Name("Cosh_float");
BENCHMARK(BM_Tanh<float>) CWISE_SIZES ->Name("Tanh_float");
BENCHMARK(BM_Asinh<float>) CWISE_SIZES ->Name("Asinh_float");
BENCHMARK(BM_Acosh<float>) CWISE_SIZES ->Name("Acosh_float");
BENCHMARK(BM_Atanh<float>) CWISE_SIZES ->Name("Atanh_float");
BENCHMARK(BM_Log10<float>) CWISE_SIZES ->Name("Log10_float");
BENCHMARK(BM_Erf<float>) CWISE_SIZES ->Name("Erf_float");
@@ -188,6 +192,8 @@ BENCHMARK(BM_Atan<double>) CWISE_SIZES ->Name("Atan_double");
BENCHMARK(BM_Sinh<double>) CWISE_SIZES ->Name("Sinh_double");
BENCHMARK(BM_Cosh<double>) CWISE_SIZES ->Name("Cosh_double");
BENCHMARK(BM_Tanh<double>) CWISE_SIZES ->Name("Tanh_double");
BENCHMARK(BM_Asinh<double>) CWISE_SIZES ->Name("Asinh_double");
BENCHMARK(BM_Acosh<double>) CWISE_SIZES ->Name("Acosh_double");
BENCHMARK(BM_Atanh<double>) CWISE_SIZES ->Name("Atanh_double");
BENCHMARK(BM_Log10<double>) CWISE_SIZES ->Name("Log10_double");
BENCHMARK(BM_Erf<double>) CWISE_SIZES ->Name("Erf_double");