Improve accuracy of SIMD exp for small args

[gromacs.git] / src / gromacs / simd / impl_x86_mic / impl_x86_mic_simd_float.h

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 *
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#ifndef GMX_SIMD_IMPL_X86_MIC_SIMD_FLOAT_H
#define GMX_SIMD_IMPL_X86_MIC_SIMD_FLOAT_H

#include "config.h"

#include <cassert>
#include <cstdint>

#include <immintrin.h>

#include "gromacs/math/utilities.h"

namespace gmx
{

class SimdFloat
{
    public:
        SimdFloat() {}

        SimdFloat(float f) : simdInternal_(_mm512_set1_ps(f)) {}

        // Internal utility constructor to simplify return statements
        SimdFloat(__m512 simd) : simdInternal_(simd) {}

        __m512  simdInternal_;
};

class SimdFInt32
{
    public:
        SimdFInt32() {}

        SimdFInt32(std::int32_t i) : simdInternal_(_mm512_set1_epi32(i)) {}

        // Internal utility constructor to simplify return statements
        SimdFInt32(__m512i simd) : simdInternal_(simd) {}

        __m512i  simdInternal_;
};

class SimdFBool
{
    public:
        SimdFBool() {}

        SimdFBool(bool b) : simdInternal_(_mm512_int2mask( b ? 0xFFFF : 0)) {}

        // Internal utility constructor to simplify return statements
        SimdFBool(__mmask16 simd) : simdInternal_(simd) {}

        __mmask16  simdInternal_;
};

class SimdFIBool
{
    public:
        SimdFIBool() {}

        SimdFIBool(bool b) : simdInternal_(_mm512_int2mask( b ? 0xFFFF : 0)) {}

        // Internal utility constructor to simplify return statements
        SimdFIBool(__mmask16 simd) : simdInternal_(simd) {}

        __mmask16  simdInternal_;
};

static inline SimdFloat gmx_simdcall
simdLoad(const float *m)
{
    assert(std::size_t(m) % 64 == 0);
    return {
               _mm512_load_ps(m)
    };
}

static inline void gmx_simdcall
store(float *m, SimdFloat a)
{
    assert(std::size_t(m) % 64 == 0);
    _mm512_store_ps(m, a.simdInternal_);
}

static inline SimdFloat gmx_simdcall
simdLoadU(const float *m)
{
    return {
               _mm512_loadunpackhi_ps(_mm512_loadunpacklo_ps(_mm512_undefined_ps(), m), m+16)
    };
}

static inline void gmx_simdcall
storeU(float *m, SimdFloat a)
{
    _mm512_packstorelo_ps(m, a.simdInternal_);
    _mm512_packstorehi_ps(m+16, a.simdInternal_);
}

static inline SimdFloat gmx_simdcall
setZeroF()
{
    return {
               _mm512_setzero_ps()
    };
}

static inline SimdFInt32 gmx_simdcall
simdLoadFI(const std::int32_t * m)
{
    assert(std::size_t(m) % 64 == 0);
    return {
               _mm512_load_epi32(m)
    };
}

static inline void gmx_simdcall
store(std::int32_t * m, SimdFInt32 a)
{
    assert(std::size_t(m) % 64 == 0);
    _mm512_store_epi32(m, a.simdInternal_);
}

static inline SimdFInt32 gmx_simdcall
simdLoadUFI(const std::int32_t *m)
{
    return {
               _mm512_loadunpackhi_epi32(_mm512_loadunpacklo_epi32(_mm512_undefined_epi32(), m), m+16)
    };
}

static inline void gmx_simdcall
storeU(std::int32_t * m, SimdFInt32 a)
{
    _mm512_packstorelo_epi32(m, a.simdInternal_);
    _mm512_packstorehi_epi32(m+16, a.simdInternal_);
}

static inline SimdFInt32 gmx_simdcall
setZeroFI()
{
    return {
               _mm512_setzero_si512()
    };
}


template<int index>
static inline std::int32_t gmx_simdcall
extract(SimdFInt32 a)
{
    int r;
    _mm512_mask_packstorelo_epi32(&r, _mm512_mask2int(1<<index), a.simdInternal_);
    return r;
}

static inline SimdFloat gmx_simdcall
operator&(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_castsi512_ps(_mm512_and_epi32(_mm512_castps_si512(a.simdInternal_), _mm512_castps_si512(b.simdInternal_)))
    };
}

static inline SimdFloat gmx_simdcall
andNot(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_castsi512_ps(_mm512_andnot_epi32(_mm512_castps_si512(a.simdInternal_), _mm512_castps_si512(b.simdInternal_)))
    };
}

static inline SimdFloat gmx_simdcall
operator|(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_castsi512_ps(_mm512_or_epi32(_mm512_castps_si512(a.simdInternal_), _mm512_castps_si512(b.simdInternal_)))
    };
}

static inline SimdFloat gmx_simdcall
operator^(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_castsi512_ps(_mm512_xor_epi32(_mm512_castps_si512(a.simdInternal_), _mm512_castps_si512(b.simdInternal_)))
    };
}

static inline SimdFloat gmx_simdcall
operator+(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_add_ps(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
operator-(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_sub_ps(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
operator-(SimdFloat x)
{
    return {
               _mm512_addn_ps(x.simdInternal_, _mm512_setzero_ps())
    };
}

static inline SimdFloat gmx_simdcall
operator*(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_mul_ps(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
fma(SimdFloat a, SimdFloat b, SimdFloat c)
{
    return {
               _mm512_fmadd_ps(a.simdInternal_, b.simdInternal_, c.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
fms(SimdFloat a, SimdFloat b, SimdFloat c)
{
    return {
               _mm512_fmsub_ps(a.simdInternal_, b.simdInternal_, c.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
fnma(SimdFloat a, SimdFloat b, SimdFloat c)
{
    return {
               _mm512_fnmadd_ps(a.simdInternal_, b.simdInternal_, c.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
fnms(SimdFloat a, SimdFloat b, SimdFloat c)
{
    return {
               _mm512_fnmsub_ps(a.simdInternal_, b.simdInternal_, c.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
rsqrt(SimdFloat x)
{
    return {
               _mm512_rsqrt23_ps(x.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
rcp(SimdFloat x)
{
    return {
               _mm512_rcp23_ps(x.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
maskAdd(SimdFloat a, SimdFloat b, SimdFBool m)
{
    return {
               _mm512_mask_add_ps(a.simdInternal_, m.simdInternal_, a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
maskzMul(SimdFloat a, SimdFloat b, SimdFBool m)
{
    return {
               _mm512_mask_mul_ps(_mm512_setzero_ps(), m.simdInternal_, a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
maskzFma(SimdFloat a, SimdFloat b, SimdFloat c, SimdFBool m)
{
    return {
               _mm512_mask_mov_ps(_mm512_setzero_ps(), m.simdInternal_, _mm512_fmadd_ps(a.simdInternal_, b.simdInternal_, c.simdInternal_))
    };
}

static inline SimdFloat gmx_simdcall
maskzRsqrt(SimdFloat x, SimdFBool m)
{
    return {
               _mm512_mask_rsqrt23_ps(_mm512_setzero_ps(), m.simdInternal_, x.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
maskzRcp(SimdFloat x, SimdFBool m)
{
    return {
               _mm512_mask_rcp23_ps(_mm512_setzero_ps(), m.simdInternal_, x.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
abs(SimdFloat x)
{
    return {
               _mm512_castsi512_ps(_mm512_andnot_epi32(_mm512_castps_si512(_mm512_set1_ps(GMX_FLOAT_NEGZERO)), _mm512_castps_si512(x.simdInternal_)))
    };
}

static inline SimdFloat gmx_simdcall
max(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_gmax_ps(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
min(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_gmin_ps(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
round(SimdFloat x)
{
    return {
               _mm512_round_ps(x.simdInternal_, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE)
    };
}

static inline SimdFloat gmx_simdcall
trunc(SimdFloat x)
{
    return {
               _mm512_round_ps(x.simdInternal_, _MM_FROUND_TO_ZERO, _MM_EXPADJ_NONE)
    };
}

static inline SimdFloat gmx_simdcall
frexp(SimdFloat value, SimdFInt32 * exponent)
{
    __m512  rExponent = _mm512_getexp_ps(value.simdInternal_);
    __m512i iExponent =  _mm512_cvtfxpnt_round_adjustps_epi32(rExponent, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE);

    exponent->simdInternal_ = _mm512_add_epi32(iExponent, _mm512_set1_epi32(1));

    return {
               _mm512_getmant_ps(value.simdInternal_, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)
    };
}

template <MathOptimization opt = MathOptimization::Safe>
static inline SimdFloat gmx_simdcall
ldexp(SimdFloat value, SimdFInt32 exponent)
{
    const __m512i exponentBias = _mm512_set1_epi32(127);
    __m512i       iExponent    = _mm512_add_epi32(exponent.simdInternal_, exponentBias);

    if (opt == MathOptimization::Safe)
    {
        // Make sure biased argument is not negative
        iExponent = _mm512_max_epi32(iExponent, _mm512_setzero_epi32());
    }

    iExponent = _mm512_slli_epi32( iExponent, 23);

    return {
               _mm512_mul_ps(value.simdInternal_, _mm512_castsi512_ps(iExponent))
    };
}

static inline float gmx_simdcall
reduce(SimdFloat a)
{
    return _mm512_reduce_add_ps(a.simdInternal_);
}

// Picky, picky, picky:
// icc-16 complains about "Illegal value of immediate argument to intrinsic"
// unless we use
// 1) Ordered-quiet for ==
// 2) Unordered-quiet for !=
// 3) Ordered-signaling for < and <=

static inline SimdFBool gmx_simdcall
operator==(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_cmp_ps_mask(a.simdInternal_, b.simdInternal_, _CMP_EQ_OQ)
    };
}

static inline SimdFBool gmx_simdcall
operator!=(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_cmp_ps_mask(a.simdInternal_, b.simdInternal_, _CMP_NEQ_UQ)
    };
}

static inline SimdFBool gmx_simdcall
operator<(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_cmp_ps_mask(a.simdInternal_, b.simdInternal_, _CMP_LT_OS)
    };
}

static inline SimdFBool gmx_simdcall
operator<=(SimdFloat a, SimdFloat b)
{
    return {
               _mm512_cmp_ps_mask(a.simdInternal_, b.simdInternal_, _CMP_LE_OS)
    };
}

static inline SimdFBool gmx_simdcall
testBits(SimdFloat a)
{
    return {
               _mm512_test_epi32_mask( _mm512_castps_si512(a.simdInternal_), _mm512_castps_si512(a.simdInternal_) )
    };
}

static inline SimdFBool gmx_simdcall
operator&&(SimdFBool a, SimdFBool b)
{
    return {
               _mm512_kand(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFBool gmx_simdcall
operator||(SimdFBool a, SimdFBool b)
{
    return {
               _mm512_kor(a.simdInternal_, b.simdInternal_)
    };
}

static inline bool gmx_simdcall
anyTrue(SimdFBool a)
{
    return _mm512_mask2int(a.simdInternal_) != 0;
}

static inline SimdFloat gmx_simdcall
selectByMask(SimdFloat a, SimdFBool m)
{
    return {
               _mm512_mask_mov_ps(_mm512_setzero_ps(), m.simdInternal_, a.simdInternal_)
    };
}

static inline SimdFloat gmx_simdcall
selectByNotMask(SimdFloat a, SimdFBool m)
{
    return {
               _mm512_mask_mov_ps(a.simdInternal_, m.simdInternal_, _mm512_setzero_ps())
    };
}

static inline SimdFloat gmx_simdcall
blend(SimdFloat a, SimdFloat b, SimdFBool sel)
{
    return {
               _mm512_mask_blend_ps(sel.simdInternal_, a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator<<(SimdFInt32 a, int n)
{
    return {
               _mm512_slli_epi32(a.simdInternal_, n)
    };
}

static inline SimdFInt32 gmx_simdcall
operator>>(SimdFInt32 a, int n)
{
    return {
               _mm512_srli_epi32(a.simdInternal_, n)
    };
}

static inline SimdFInt32 gmx_simdcall
operator&(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_and_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
andNot(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_andnot_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator|(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_or_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator^(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_xor_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator+(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_add_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator-(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_sub_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
operator*(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_mullo_epi32(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFIBool gmx_simdcall
operator==(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_cmp_epi32_mask(a.simdInternal_, b.simdInternal_, _MM_CMPINT_EQ)
    };
}

static inline SimdFIBool gmx_simdcall
testBits(SimdFInt32 a)
{
    return {
               _mm512_test_epi32_mask( a.simdInternal_, a.simdInternal_ )
    };
}

static inline SimdFIBool gmx_simdcall
operator<(SimdFInt32 a, SimdFInt32 b)
{
    return {
               _mm512_cmp_epi32_mask(a.simdInternal_, b.simdInternal_, _MM_CMPINT_LT)
    };
}

static inline SimdFIBool gmx_simdcall
operator&&(SimdFIBool a, SimdFIBool b)
{
    return {
               _mm512_kand(a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFIBool gmx_simdcall
operator||(SimdFIBool a, SimdFIBool b)
{
    return {
               _mm512_kor(a.simdInternal_, b.simdInternal_)
    };
}

static inline bool gmx_simdcall
anyTrue(SimdFIBool a)
{
    return _mm512_mask2int(a.simdInternal_) != 0;
}

static inline SimdFInt32 gmx_simdcall
selectByMask(SimdFInt32 a, SimdFIBool m)
{
    return {
               _mm512_mask_mov_epi32(_mm512_setzero_epi32(), m.simdInternal_, a.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
selectByNotMask(SimdFInt32 a, SimdFIBool m)
{
    return {
               _mm512_mask_mov_epi32(a.simdInternal_, m.simdInternal_, _mm512_setzero_epi32())
    };
}

static inline SimdFInt32 gmx_simdcall
blend(SimdFInt32 a, SimdFInt32 b, SimdFIBool sel)
{
    return {
               _mm512_mask_blend_epi32(sel.simdInternal_, a.simdInternal_, b.simdInternal_)
    };
}

static inline SimdFInt32 gmx_simdcall
cvtR2I(SimdFloat a)
{
    return {
               _mm512_cvtfxpnt_round_adjustps_epi32(a.simdInternal_, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE)
    };
}

static inline SimdFInt32 gmx_simdcall
cvttR2I(SimdFloat a)
{
    return {
               _mm512_cvtfxpnt_round_adjustps_epi32(a.simdInternal_, _MM_FROUND_TO_ZERO, _MM_EXPADJ_NONE)
    };
}

static inline SimdFloat gmx_simdcall
cvtI2R(SimdFInt32 a)
{
    return {
               _mm512_cvtfxpnt_round_adjustepi32_ps(a.simdInternal_, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE)
    };
}

static inline SimdFIBool gmx_simdcall
cvtB2IB(SimdFBool a)
{
    return {
               a.simdInternal_
    };
}

static inline SimdFBool gmx_simdcall
cvtIB2B(SimdFIBool a)
{
    return {
               a.simdInternal_
    };
}


template <MathOptimization opt = MathOptimization::Safe>
static inline SimdFloat gmx_simdcall
exp2(SimdFloat x)
{
    return {
               _mm512_exp223_ps(_mm512_cvtfxpnt_round_adjustps_epi32(x.simdInternal_, _MM_ROUND_MODE_NEAREST, _MM_EXPADJ_24))
    };
}

template <MathOptimization opt = MathOptimization::Safe>
static inline SimdFloat gmx_simdcall
exp(SimdFloat x)
{
    const __m512     argscale    = _mm512_set1_ps(1.44269504088896341f);
    const __m512     invargscale = _mm512_set1_ps(-0.69314718055994528623f);

    if (opt == MathOptimization::Safe)
    {
        // Set the limit to gurantee flush to zero
        const SimdFloat smallArgLimit(-88.f);
        // Since we multiply the argument by 1.44, for the safe version we need to make
        // sure this doesn't result in overflow
        x = max(x, smallArgLimit);
    }

    __m512  xscaled = _mm512_mul_ps(x.simdInternal_, argscale);
    __m512  r       = _mm512_exp223_ps(_mm512_cvtfxpnt_round_adjustps_epi32(xscaled, _MM_ROUND_MODE_NEAREST, _MM_EXPADJ_24));

    // exp2a23_ps provides 23 bits of accuracy, but we ruin some of that with our argument
    // scaling. To correct this, we find the difference between the scaled argument and
    // the true one (extended precision arithmetics does not appear to be necessary to
    // fulfill our accuracy requirements) and then multiply by the exponent of this
    // correction since exp(a+b)=exp(a)*exp(b).
    // Note that this only adds two instructions (and maybe some constant loads).

    // find the difference
    x         = _mm512_fmadd_ps(invargscale, xscaled, x.simdInternal_);
    // x will now be a _very_ small number, so approximate exp(x)=1+x.
    // We should thus apply the correction as r'=r*(1+x)=r+r*x
    r         = _mm512_fmadd_ps(r, x.simdInternal_, r);
    return {
               r
    };
}

static inline SimdFloat gmx_simdcall
log(SimdFloat x)
{
    return {
               _mm512_mul_ps(_mm512_set1_ps(0.693147180559945286226764f), _mm512_log2ae23_ps(x.simdInternal_))
    };
}

}      // namespace gmx

#endif // GMX_SIMD_IMPL_X86_MIC_SIMD_FLOAT_H