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/*========================== begin_copyright_notice ============================
Copyright (C) 2018-2021 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include "PacketBuilder.h"
// need to disable this to use INFINITY and NAN values
#pragma warning(disable : 4756 4056)
//#include <math.h>
namespace pktz
{
//////////////////////////////////////////////////////////////////////////
/// @brief Computes log2(a) using either scalar log2 function from the runtime
/// or vector approximation
/// @param a - src float vector
Value* PacketBuilder::VLOG2PS(Value* a)
{
Value* result;
// fast log2 approximation
// log2(x) = (x.ExpPart - 127) + log(1.xFracPart)
Value* asInt = BITCAST(a, mSimdInt32Ty);
Value* b = SUB(AND(ASHR(asInt, 23), 255), VIMMED1(127));
Value* intermResult = SI_TO_FP(b, mSimdFP32Ty);
Value* fa = OR(AND(asInt, VIMMED1(0x007FFFFF)), VIMMED1(127 << 23));
fa = BITCAST(fa, mSimdFP32Ty);
fa = FSUB(fa, VIMMED1(1.0f));
// log(x) = (1.4386183024320163f + (-0.640238532500937f +
// 0.20444600983623412f*fx)*fx)*fx;
result = FMUL(fa, VIMMED1(0.20444600983623412f));
result = FADD(result, VIMMED1(-0.640238532500937f));
result = FMUL(fa, result);
result = FADD(result, VIMMED1(1.4386183024320163f));
result = FMUL(result, fa);
result = FADD(result, intermResult);
// handle bad input
// 0 -> -inf
Value* zeroInput = FCMP_OEQ(a, VIMMED1(0.0f));
result = SELECT(zeroInput, VIMMED1(-INFINITY), result);
// -F -> NAN
Value* negInput = FCMP_OLT(a, VIMMED1(0.0f));
result = SELECT(negInput, VIMMED1(NAN), result);
// inf -> inf
Value* infInput = FCMP_OEQ(a, VIMMED1(INFINITY));
result = SELECT(infInput, VIMMED1(INFINITY), result);
// NAN -> NAN
Value* nanInput = FCMP_UNO(a, a);
result = SELECT(nanInput, VIMMED1(NAN), result);
result->setName("log2.");
return result;
}
//////////////////////////////////////////////////////////////////////////
/// @brief Computes a^2.4 using either scalar pow function from the runtime
/// or vector approximation
/// @param a - src float vector
Value* PacketBuilder::VPOW24PS(Value* a)
{
Value* result;
// approximation algorithm from
// http://stackoverflow.com/questions/6475373/optimizations-for-pow-with-const-non-integer-exponent
// computes a^2.4 with approximately 5% overestimate.
// can reduce the error further with a few more terms
const float expnum = 24;
const float expden = 10;
const float coeffnum = 1.0f;
const float coeffden = 1.0f;
Value* correctionFactor =
VIMMED1(exp2f(127.f * expden / expnum - 127.f) *
powf(1.f * coeffnum / coeffden, 1.0f * expden / expnum));
result = FMUL(a, correctionFactor);
result = SI_TO_FP(BITCAST(result, mSimdInt32Ty), mSimdFP32Ty);
result = FMUL(result, VIMMED1(1.f * expnum / expden));
result = BITCAST(FP_TO_SI(result, mSimdInt32Ty), mSimdFP32Ty);
result->setName("pow24.");
return result;
}
#define EXP_POLY_DEGREE 3
#define POLY0(x, c0) VIMMED1(c0)
#define POLY1(x, c0, c1) FADD(FMUL(POLY0(x, c1), x), VIMMED1(c0))
#define POLY2(x, c0, c1, c2) FADD(FMUL(POLY1(x, c1, c2), x), VIMMED1(c0))
#define POLY3(x, c0, c1, c2, c3) FADD(FMUL(POLY2(x, c1, c2, c3), x), VIMMED1(c0))
#define POLY4(x, c0, c1, c2, c3, c4) FADD(FMUL(POLY3(x, c1, c2, c3, c4), x), VIMMED1(c0))
#define POLY5(x, c0, c1, c2, c3, c4, c5) FADD(FMUL(POLY4(x, c1, c2, c3, c4, c5), x), VIMMED1(c0))
//////////////////////////////////////////////////////////////////////////
/// @brief Computes 2^x using either scalar pow function from the runtime
/// or vector approximation
/// @param a - src float vector
Value* PacketBuilder::VEXP2PS(Value* a)
{
Value* result;
// fast exp2 taken from here:
// http://jrfonseca.blogspot.com/2008/09/fast-sse2-pow-tables-or-polynomials.html
a = VMINPS(a, VIMMED1(129.0f));
a = VMAXPS(a, VIMMED1(-126.99999f));
Value* ipart = FP_TO_SI(FSUB(a, VIMMED1(0.5f)), mSimdInt32Ty);
Value* fpart = FSUB(a, SI_TO_FP(ipart, mSimdFP32Ty));
Value* expipart = BITCAST(SHL(ADD(ipart, VIMMED1(127)), 23), mSimdFP32Ty);
#if EXP_POLY_DEGREE == 5
Value* expfpart = POLY5(fpart,
9.9999994e-1f,
6.9315308e-1f,
2.4015361e-1f,
5.5826318e-2f,
8.9893397e-3f,
1.8775767e-3f);
#endif
#if EXP_POLY_DEGREE == 4
Value* expfpart = POLY4(
fpart, 1.0000026f, 6.9300383e-1f, 2.4144275e-1f, 5.2011464e-2f, 1.3534167e-2f);
#endif
#if EXP_POLY_DEGREE == 3
Value* expfpart =
POLY3(fpart, 9.9992520e-1f, 6.9583356e-1f, 2.2606716e-1f, 7.8024521e-2f);
#endif
#if EXP_POLY_DEGREE == 2
Value* expfpart = POLY2(fpart, 1.0017247f, 6.5763628e-1f, 3.3718944e-1f);
#endif
result = FMUL(expipart, expfpart, "exp2.");
return result;
}
}
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