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Use the Cephes double subtraction trick in pexp<float> even when FMA is available. Otherwise the accuracy drops from 1 ulp to 3 ulp.

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Rasmus Munk Larsen 2021-02-18 20:49:18 +00:00
parent 12fd3dd655
commit 7f09d3487d
1 changed files with 4 additions and 11 deletions
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15
Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
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@ -1,4 +1,3 @@
// This file is part of Eigen, a lightweight C++ template library // This file is part of Eigen, a lightweight C++ template library
// for linear algebra. // for linear algebra.
// //
@ -468,16 +467,10 @@ Packet pexp_float(const Packet _x)
// Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is // Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is
// subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating // subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating
// truncation errors. // truncation errors.
Packet r; const Packet cst_cephes_exp_C1 = pset1<Packet>(-0.693359375f);
#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD const Packet cst_cephes_exp_C2 = pset1<Packet>(2.12194440e-4f);
const Packet cst_nln2 = pset1<Packet>(-0.6931471805599453f); Packet r = pmadd(m, cst_cephes_exp_C1, x);
r = pmadd(m, cst_nln2, x); r = pmadd(m, cst_cephes_exp_C2, r);
#else
const Packet cst_cephes_exp_C1 = pset1<Packet>(0.693359375f);
const Packet cst_cephes_exp_C2 = pset1<Packet>(-2.12194440e-4f);
r = psub(x, pmul(m, cst_cephes_exp_C1));
r = psub(r, pmul(m, cst_cephes_exp_C2));
#endif
Packet r2 = pmul(r, r); Packet r2 = pmul(r, r);
Packet r3 = pmul(r2, r); Packet r3 = pmul(r2, r);