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Vectorize atan() for double.

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This commit is contained in:
Rasmus Munk Larsen
2022-10-01 01:49:30 +00:00
parent 1e1848fdb1
commit c475228b28
12 changed files with 104 additions and 4 deletions
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66
Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
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@@ -864,6 +864,68 @@ Packet patan_float(const Packet& x_in) {
return pselect(neg_mask, pnegate(p), p);
}
template<typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet patan_double(const Packet& x_in) {
typedef typename unpacket_traits<Packet>::type Scalar;
static_assert(std::is_same<Scalar, double>::value, "Scalar type must be double");
const Packet cst_one = pset1<Packet>(1.0);
constexpr double kPiOverTwo = static_cast<double>(M_PI_2);
const Packet cst_pi_over_two = pset1<Packet>(kPiOverTwo);
constexpr double kPiOverFour = static_cast<double>(M_PI_4);
const Packet cst_pi_over_four = pset1<Packet>(kPiOverFour);
const Packet cst_large = pset1<Packet>(2.4142135623730950488016887); // tan(3*pi/8);
const Packet cst_medium = pset1<Packet>(0.4142135623730950488016887); // tan(pi/8);
const Packet q0 = pset1<Packet>(-0.33333333333330028569463365784031338989734649658203);
const Packet q2 = pset1<Packet>(0.199999999990664090177006073645316064357757568359375);
const Packet q4 = pset1<Packet>(-0.142857141937123677255527809393242932856082916259766);
const Packet q6 = pset1<Packet>(0.111111065991039953404495577160560060292482376098633);
const Packet q8 = pset1<Packet>(-9.0907812986129224452902519715280504897236824035645e-2);
const Packet q10 = pset1<Packet>(7.6900542950704739442180368769186316058039665222168e-2);
const Packet q12 = pset1<Packet>(-6.6410112986494976294871150912513257935643196105957e-2);
const Packet q14 = pset1<Packet>(5.6920144995467943094258345126945641823112964630127e-2);
const Packet q16 = pset1<Packet>(-4.3577020814990513608577771265117917209863662719727e-2);
const Packet q18 = pset1<Packet>(2.1244050233624342527427586446719942614436149597168e-2);
const Packet neg_mask = pcmp_lt(x_in, pzero(x_in));
Packet x = pabs(x_in);
// Use the same range reduction strategy (to [0:tan(pi/8)]) as the
// Cephes library:
// "Large": For x >= tan(3*pi/8), use atan(1/x) = pi/2 - atan(x).
// "Medium": For x in [tan(pi/8) : tan(3*pi/8)),
// use atan(x) = pi/4 + atan((x-1)/(x+1)).
// "Small": For x < tan(pi/8), approximate atan(x) directly by a polynomial
// calculated using Sollya.
const Packet large_mask = pcmp_lt(cst_large, x);
x = pselect(large_mask, preciprocal(x), x);
const Packet medium_mask = pandnot(pcmp_lt(cst_medium, x), large_mask);
x = pselect(medium_mask, pdiv(psub(x, cst_one), padd(x, cst_one)), x);
// Approximate atan(x) on [0:tan(pi/8)] by a polynomial of the form
// P(x) = x + x^3 * Q(x^2),
// where Q(x^2) is a 9th order polynomial in x^2.
const Packet x2 = pmul(x, x);
const Packet x4 = pmul(x2, x2);
Packet q_odd = pmadd(q18, x4, q14);
Packet q_even = pmadd(q16, x4, q12);
q_odd = pmadd(q_odd, x4, q10);
q_even = pmadd(q_even, x4, q8);
q_odd = pmadd(q_odd, x4, q6);
q_even = pmadd(q_even, x4, q4);
q_odd = pmadd(q_odd, x4, q2);
q_even = pmadd(q_even, x4, q0);
const Packet q = pmadd(q_odd, x2, q_even);
Packet p = pmadd(q, pmul(x, x2), x);
// Apply transformations according to the range reduction masks.
p = pselect(large_mask, psub(cst_pi_over_two, p), p);
p = pselect(medium_mask, padd(cst_pi_over_four, p), p);
return pselect(neg_mask, pnegate(p), p);
}
template<typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pdiv_complex(const Packet& x, const Packet& y) {
@@ -958,8 +1020,8 @@ Packet psqrt_complex(const Packet& a) {
// Step 4. Compute solution for inputs with negative real part:
// [|eta0|, sign(y0)*rho0, |eta1|, sign(y1)*rho1]
const RealScalar neg_zero = RealScalar(numext::bit_cast<float>(0x80000000u));
const RealPacket cst_imag_sign_mask = pset1<Packet>(Scalar(RealScalar(0.0), neg_zero)).v;
const RealPacket cst_imag_sign_mask =
pset1<Packet>(Scalar(RealScalar(0.0), RealScalar(-0.0))).v;
RealPacket imag_signs = pand(a.v, cst_imag_sign_mask);
Packet negative_real_result;
// Notice that rho is positive, so taking it's absolute value is a noop.