Simd sincos double
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index bb246ea..5dd5ce2 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -142,6 +142,8 @@
HasCmp = 1,
HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
HasLog = 1,
HasExp = 1,
HasSqrt = 1,
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index 5327d7e..aa338d1 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -156,6 +156,8 @@
HasBlend = 1,
HasSqrt = 1,
HasRsqrt = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
HasLog = 1,
HasExp = 1,
HasATan = 1,
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index c973efd..1a700a2 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -696,6 +696,173 @@
return psincos_float<false>(x);
}
+// Trigonometric argument reduction for double for inputs smaller than 15.
+// Reduces trigonometric arguments for double inputs where x < 15. Given an argument x and its corresponding quadrant
+// count n, the function computes and returns the reduced argument t such that x = n * pi/2 + t.
+template <typename Packet>
+Packet trig_reduce_small_double(const Packet& x, const Packet& q) {
+ // Pi/2 split into 2 values
+ const Packet cst_pio2_a = pset1<Packet>(-1.570796325802803);
+ const Packet cst_pio2_b = pset1<Packet>(-9.920935184482005e-10);
+
+ Packet t;
+ t = pmadd(cst_pio2_a, q, x);
+ t = pmadd(cst_pio2_b, q, t);
+ return t;
+}
+
+// Trigonometric argument reduction for double for inputs smaller than 1e14.
+// Reduces trigonometric arguments for double inputs where x < 1e14. Given an argument x and its corresponding quadrant
+// count n, the function computes and returns the reduced argument t such that x = n * pi/2 + t.
+template <typename Packet>
+Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Packet& q_low) {
+ // Pi/2 split into 4 values
+ const Packet cst_pio2_a = pset1<Packet>(-1.570796325802803);
+ const Packet cst_pio2_b = pset1<Packet>(-9.920935184482005e-10);
+ const Packet cst_pio2_c = pset1<Packet>(-6.123234014771656e-17);
+ const Packet cst_pio2_d = pset1<Packet>(1.903488962019325e-25);
+
+ Packet t;
+ t = pmadd(cst_pio2_a, q_high, x);
+ t = pmadd(cst_pio2_a, q_low, t);
+ t = pmadd(cst_pio2_b, q_high, t);
+ t = pmadd(cst_pio2_b, q_low, t);
+ t = pmadd(cst_pio2_c, q_high, t);
+ t = pmadd(cst_pio2_c, q_low, t);
+ t = pmadd(cst_pio2_d, padd(q_low, q_high), t);
+ return t;
+}
+
+template <bool ComputeSine, typename Packet, bool ComputeBoth = false>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+#if EIGEN_COMP_GNUC_STRICT
+ __attribute__((optimize("-fno-unsafe-math-optimizations")))
+#endif
+ Packet
+ psincos_double(const Packet& x) {
+ typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+
+ // If the argument is smaller than this value, use a simpler argument reduction
+ const double small_th = 15;
+ // If the argument is bigger than this value, use the non-vectorized std version
+ const double huge_th = 1e14;
+
+ const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ // Integer Packet constants
+ const PacketI cst_one = pset1<PacketI>(1);
+ // Constant for splitting
+ const Packet cst_split = pset1<Packet>(1 << 24);
+
+ Packet x_abs = pabs(x);
+
+ // Scale x by 2/Pi
+ PacketI q_int;
+ Packet s;
+
+ // TODO Implement huge angle argument reduction
+ if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
+ Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
+ q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
+ Packet q_low = pcast<PacketI, Packet>(q_int);
+ s = trig_reduce_medium_double(x_abs, q_high, q_low);
+ } else {
+ Packet qval_noround = pmul(x_abs, cst_2oPI);
+ q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
+ Packet q = pcast<PacketI, Packet>(q_int);
+ s = trig_reduce_small_double(x_abs, q);
+ }
+
+ // All the upcoming approximating polynomials have even exponents
+ Packet ss = pmul(s, s);
+
+ // Padé approximant of cos(x)
+ // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ // MATLAB code to compute those coefficients:
+ // syms x;
+ // cosf = @(x) cos(x);
+ // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ Packet scos = pdiv(sc4_num, sc4_denum);
+
+ // Padé approximant of sin(x)
+ // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ // MATLAB code to compute those coefficients:
+ // syms x;
+ // sinf = @(x) sin(x);
+ // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ Packet sign_bit, sFinalRes;
+ if (ComputeBoth) {
+ Packet peven = peven_mask(x);
+ sign_bit = pselect((s), sign_sin, sign_cos);
+ sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
+ } else {
+ sign_bit = ComputeSine ? sign_sin : sign_cos;
+ sFinalRes = ComputeSine ? pselect(poly_mask, ssin, scos) : pselect(poly_mask, scos, ssin);
+ }
+ sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ sFinalRes = pxor(sFinalRes, sign_bit);
+
+ // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ // using std::sin and std::cos
+ // TODO Remove it when huge angle argument reduction is implemented
+ if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ const int PacketSize = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
+ pstoreu(x_cpy, x);
+ pstoreu(sincos_vals, sFinalRes);
+ for (int k = 0; k < PacketSize; ++k) {
+ double val = x_cpy[k];
+ if (std::abs(val) > huge_th && (numext::isfinite)(val)) {
+ if (ComputeBoth)
+ sincos_vals[k] = k % 2 == 0 ? std::sin(val) : std::cos(val);
+ else
+ sincos_vals[k] = ComputeSine ? std::sin(val) : std::cos(val);
+ }
+ }
+ sFinalRes = ploadu<Packet>(sincos_vals);
+ }
+ return sFinalRes;
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
+ return psincos_double<true>(x);
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcos_double(const Packet& x) {
+ return psincos_double<false>(x);
+}
+
// Generic implementation of acos(x).
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pacos_float(const Packet& x_in) {
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
index 9560de2..05cac5c 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
@@ -82,6 +82,14 @@
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcos_float(const Packet& x);
+/** \internal \returns sin(x) for double precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x);
+
+/** \internal \returns cos(x) for double precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcos_double(const Packet& x);
+
/** \internal \returns asin(x) for single precision float */
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pasin_float(const Packet& x);
@@ -158,6 +166,8 @@
#define EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_DOUBLE(PACKET) \
EIGEN_DOUBLE_PACKET_FUNCTION(atan, PACKET) \
EIGEN_DOUBLE_PACKET_FUNCTION(log, PACKET) \
+ EIGEN_DOUBLE_PACKET_FUNCTION(sin, PACKET) \
+ EIGEN_DOUBLE_PACKET_FUNCTION(cos, PACKET) \
EIGEN_DOUBLE_PACKET_FUNCTION(log2, PACKET) \
EIGEN_DOUBLE_PACKET_FUNCTION(exp, PACKET)
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index 71e5f5f..2c18b5d 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -5177,8 +5177,8 @@
HasLog = 1,
HasATan = 1,
#endif
- HasSin = 0,
- HasCos = 0,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
HasSqrt = 1,
HasRsqrt = 1,
HasTanh = 0,
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index 008d6dd..7e6a1b9 100644
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -218,6 +218,8 @@
HasCmp = 1,
HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
HasLog = 1,
HasExp = 1,
HasSqrt = 1,
