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Unify SSE and AVX pexp for double.
This commit is contained in:
Gael Guennebaud
parent
4a347a0054
commit
502f92fa10
@ -123,82 +123,8 @@ ptanh<Packet8f>(const Packet8f& x) {
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template <>
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EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d
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pexp<Packet4d>(const Packet4d& _x) {
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Packet4d x = _x;
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_EIGEN_DECLARE_CONST_Packet4d(1, 1.0);
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_EIGEN_DECLARE_CONST_Packet4d(2, 2.0);
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_EIGEN_DECLARE_CONST_Packet4d(half, 0.5);
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_EIGEN_DECLARE_CONST_Packet4d(exp_hi, 709.437);
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_EIGEN_DECLARE_CONST_Packet4d(exp_lo, -709.436139303);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_LOG2EF, 1.4426950408889634073599);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p0, 1.26177193074810590878e-4);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p1, 3.02994407707441961300e-2);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p2, 9.99999999999999999910e-1);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q0, 3.00198505138664455042e-6);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q1, 2.52448340349684104192e-3);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q2, 2.27265548208155028766e-1);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q3, 2.00000000000000000009e0);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C1, 0.693145751953125);
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_EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C2, 1.42860682030941723212e-6);
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_EIGEN_DECLARE_CONST_Packet4i(1023, 1023);
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Packet4d tmp, fx;
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// clamp x
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x = pmax(pmin(x, p4d_exp_hi), p4d_exp_lo);
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// Express exp(x) as exp(g + n*log(2)).
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fx = pmadd(p4d_cephes_LOG2EF, x, p4d_half);
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// Get the integer modulus of log(2), i.e. the "n" described above.
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fx = _mm256_floor_pd(fx);
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// Get the remainder modulo log(2), i.e. the "g" described above. Subtract
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// n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last
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// digits right.
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tmp = pmul(fx, p4d_cephes_exp_C1);
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Packet4d z = pmul(fx, p4d_cephes_exp_C2);
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x = psub(x, tmp);
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x = psub(x, z);
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Packet4d x2 = pmul(x, x);
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// Evaluate the numerator polynomial of the rational interpolant.
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Packet4d px = p4d_cephes_exp_p0;
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px = pmadd(px, x2, p4d_cephes_exp_p1);
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px = pmadd(px, x2, p4d_cephes_exp_p2);
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px = pmul(px, x);
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// Evaluate the denominator polynomial of the rational interpolant.
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Packet4d qx = p4d_cephes_exp_q0;
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qx = pmadd(qx, x2, p4d_cephes_exp_q1);
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qx = pmadd(qx, x2, p4d_cephes_exp_q2);
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qx = pmadd(qx, x2, p4d_cephes_exp_q3);
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// I don't really get this bit, copied from the SSE2 routines, so...
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// TODO(gonnet): Figure out what is going on here, perhaps find a better
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// rational interpolant?
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x = _mm256_div_pd(px, psub(qx, px));
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x = pmadd(p4d_2, x, p4d_1);
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// Build e=2^n by constructing the exponents in a 128-bit vector and
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// shifting them to where they belong in double-precision values.
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__m128i emm0 = _mm256_cvtpd_epi32(fx);
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emm0 = _mm_add_epi32(emm0, p4i_1023);
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emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0));
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__m128i lo = _mm_slli_epi64(emm0, 52);
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__m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52);
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__m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0);
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e = _mm256_insertf128_si256(e, hi, 1);
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// Construct the result 2^n * exp(g) = e * x. The max is used to catch
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// non-finite values in the input.
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return pmax(pmul(x, _mm256_castsi256_pd(e)), _x);
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pexp<Packet4d>(const Packet4d& x) {
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return pexp_double(x);
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}
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// Functions for sqrt.
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@ -405,6 +405,20 @@ template<> EIGEN_STRONG_INLINE Packet8f pldexp<Packet8f>(const Packet8f& a, cons
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return pldexp_float(a,exponent);
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}
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template<> EIGEN_STRONG_INLINE Packet4d pldexp<Packet4d>(const Packet4d& a, const Packet4d& exponent) {
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// Build e=2^n by constructing the exponents in a 128-bit vector and
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// shifting them to where they belong in double-precision values.
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Packet4i cst_1023 = pset1<Packet4i>(1023);
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__m128i emm0 = _mm256_cvtpd_epi32(exponent);
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emm0 = _mm_add_epi32(emm0, cst_1023);
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emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0));
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__m128i lo = _mm_slli_epi64(emm0, 52);
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__m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52);
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__m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0);
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e = _mm256_insertf128_si256(e, hi, 1);
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return pmul(a,_mm256_castsi256_pd(e));
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}
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// preduxp should be ok
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// FIXME: why is this ok? why isn't the simply implementation working as expected?
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template<> EIGEN_STRONG_INLINE Packet8f preduxp<Packet8f>(const Packet8f* vecs)
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@ -160,5 +160,74 @@ Packet pexp_float(const Packet _x)
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return pmax(pldexp(y,m), _x);
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}
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template <typename Packet>
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EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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EIGEN_UNUSED
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Packet pexp_double(const Packet _x)
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{
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Packet x = _x;
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const Packet cst_1 = pset1<Packet>(1.0);
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const Packet cst_2 = pset1<Packet>(2.0);
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const Packet cst_half = pset1<Packet>(0.5);
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const Packet cst_exp_hi = pset1<Packet>(709.437);
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const Packet cst_exp_lo = pset1<Packet>(-709.436139303);
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const Packet cst_cephes_LOG2EF = pset1<Packet>(1.4426950408889634073599);
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const Packet cst_cephes_exp_p0 = pset1<Packet>(1.26177193074810590878e-4);
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const Packet cst_cephes_exp_p1 = pset1<Packet>(3.02994407707441961300e-2);
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const Packet cst_cephes_exp_p2 = pset1<Packet>(9.99999999999999999910e-1);
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const Packet cst_cephes_exp_q0 = pset1<Packet>(3.00198505138664455042e-6);
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const Packet cst_cephes_exp_q1 = pset1<Packet>(2.52448340349684104192e-3);
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const Packet cst_cephes_exp_q2 = pset1<Packet>(2.27265548208155028766e-1);
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const Packet cst_cephes_exp_q3 = pset1<Packet>(2.00000000000000000009e0);
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const Packet cst_cephes_exp_C1 = pset1<Packet>(0.693145751953125);
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const Packet cst_cephes_exp_C2 = pset1<Packet>(1.42860682030941723212e-6);
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Packet tmp, fx;
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// clamp x
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x = pmax(pmin(x, cst_exp_hi), cst_exp_lo);
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// Express exp(x) as exp(g + n*log(2)).
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fx = pmadd(cst_cephes_LOG2EF, x, cst_half);
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// Get the integer modulus of log(2), i.e. the "n" described above.
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fx = pfloor(fx);
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// Get the remainder modulo log(2), i.e. the "g" described above. Subtract
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// n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last
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// digits right.
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tmp = pmul(fx, cst_cephes_exp_C1);
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Packet z = pmul(fx, cst_cephes_exp_C2);
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x = psub(x, tmp);
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x = psub(x, z);
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Packet x2 = pmul(x, x);
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// Evaluate the numerator polynomial of the rational interpolant.
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Packet px = cst_cephes_exp_p0;
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px = pmadd(px, x2, cst_cephes_exp_p1);
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px = pmadd(px, x2, cst_cephes_exp_p2);
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px = pmul(px, x);
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// Evaluate the denominator polynomial of the rational interpolant.
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Packet qx = cst_cephes_exp_q0;
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qx = pmadd(qx, x2, cst_cephes_exp_q1);
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qx = pmadd(qx, x2, cst_cephes_exp_q2);
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qx = pmadd(qx, x2, cst_cephes_exp_q3);
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// I don't really get this bit, copied from the SSE2 routines, so...
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// TODO(gonnet): Figure out what is going on here, perhaps find a better
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// rational interpolant?
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x = pdiv(px, psub(qx, px));
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x = pmadd(cst_2, x, cst_1);
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// Construct the result 2^n * exp(g) = e * x. The max is used to catch
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// non-finite values in the input.
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//return pmax(pmul(x, _mm256_castsi256_pd(e)), _x);
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return pmax(pldexp(x,fx), _x);
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}
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} // end namespace internal
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} // end namespace Eigen
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@ -32,78 +32,11 @@ Packet4f pexp<Packet4f>(const Packet4f& _x)
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{
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return pexp_float(_x);
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}
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet2d pexp<Packet2d>(const Packet2d& _x)
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Packet2d pexp<Packet2d>(const Packet2d& x)
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{
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Packet2d x = _x;
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_EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
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_EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
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_EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
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_EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
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_EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
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static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
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Packet2d tmp, fx;
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Packet4i emm0;
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// clamp x
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x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
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/* express exp(x) as exp(g + n*log(2)) */
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fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
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#ifdef EIGEN_VECTORIZE_SSE4_1
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fx = _mm_floor_pd(fx);
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#else
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emm0 = _mm_cvttpd_epi32(fx);
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tmp = _mm_cvtepi32_pd(emm0);
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/* if greater, substract 1 */
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Packet2d mask = _mm_cmpgt_pd(tmp, fx);
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mask = _mm_and_pd(mask, p2d_1);
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fx = psub(tmp, mask);
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#endif
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tmp = pmul(fx, p2d_cephes_exp_C1);
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Packet2d z = pmul(fx, p2d_cephes_exp_C2);
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x = psub(x, tmp);
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x = psub(x, z);
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Packet2d x2 = pmul(x,x);
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Packet2d px = p2d_cephes_exp_p0;
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px = pmadd(px, x2, p2d_cephes_exp_p1);
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px = pmadd(px, x2, p2d_cephes_exp_p2);
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px = pmul (px, x);
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Packet2d qx = p2d_cephes_exp_q0;
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qx = pmadd(qx, x2, p2d_cephes_exp_q1);
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qx = pmadd(qx, x2, p2d_cephes_exp_q2);
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qx = pmadd(qx, x2, p2d_cephes_exp_q3);
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x = pdiv(px,psub(qx,px));
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x = pmadd(p2d_2,x,p2d_1);
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// build 2^n
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emm0 = _mm_cvttpd_epi32(fx);
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emm0 = _mm_add_epi32(emm0, p4i_1023_0);
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emm0 = _mm_slli_epi32(emm0, 20);
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emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
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return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);
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return pexp_double(x);
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}
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/* evaluation of 4 sines at once, using SSE2 intrinsics.
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@ -338,6 +338,21 @@ template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4
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template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return _mm_cmpeq_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) { return _mm_cmpnge_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(b,a); }
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template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b,a); }
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template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(b,a); }
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#ifdef EIGEN_VECTORIZE_SSE4_1
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template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, 0); }
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@ -356,27 +371,24 @@ template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
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Packet4f tmp = _mm_cvtepi32_ps(emm0);
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/* if greater, substract 1 */
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Packet4f mask = _mm_cmpgt_ps(tmp, a);
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mask = _mm_and_ps(mask, cst_1);
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mask = pand(mask, cst_1);
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return psub(tmp, mask);
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}
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// WARNING: this pfloor implementation makes sense for small inputs only,
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// It is currently only used by pexp and not exposed through HasFloor.
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template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
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{
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const Packet2d cst_1 = pset1<Packet2d>(1.0);
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Packet4i emm0 = _mm_cvttpd_epi32(a);
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Packet2d tmp = _mm_cvtepi32_pd(emm0);
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/* if greater, substract 1 */
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Packet2d mask = _mm_cmpgt_pd(tmp, a);
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mask = pand(mask, cst_1);
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return psub(tmp, mask);
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}
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#endif
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template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
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template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
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template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
|
||||
|
||||
template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(b,a); }
|
||||
template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b,a); }
|
||||
template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(b,a); }
|
||||
|
||||
template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
|
||||
template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
|
||||
template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
|
||||
@ -557,6 +569,15 @@ template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, cons
|
||||
return pldexp_float(a,exponent);
|
||||
}
|
||||
|
||||
template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
|
||||
const __m128i cst_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
|
||||
Packet4i emm0 = _mm_cvttpd_epi32(exponent);
|
||||
emm0 = padd(emm0, cst_1023_0);
|
||||
emm0 = _mm_slli_epi32(emm0, 20);
|
||||
emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
|
||||
return pmul(a, Packet2d(_mm_castsi128_pd(emm0)));
|
||||
}
|
||||
|
||||
// with AVX, the default implementations based on pload1 are faster
|
||||
#ifndef __AVX__
|
||||
template<> EIGEN_STRONG_INLINE void
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user