//////////////////////////////////////////////////////////////// // // this code was taken from http://shibatch.sourceforge.net/ // Many thanks to the author: Naoki Shibata // // Copyright Naoki Shibata and contributors 2010 - 2021. // Distributed under the Boost Software License, Version 1.0. // (See accompanying file sleef_LICENSE.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // //////////////////////////////////////////////////////////////// #ifndef __AVX__ #error Please specify -mavx. #endif #ifdef __GNUC__ #define INLINE __attribute__((always_inline)) #else #define INLINE inline #endif #include #include typedef __m256d vdouble; typedef __m128i vint; typedef __m256i vmask; typedef __m256 vfloat; typedef struct { vint x, y; } vint2; // static INLINE vint vrint_vi_vd(vdouble vd) { return _mm256_cvtpd_epi32(vd); } static INLINE vint vtruncate_vi_vd(vdouble vd) { return _mm256_cvttpd_epi32(vd); } static INLINE vdouble vcast_vd_vi(vint vi) { return _mm256_cvtepi32_pd(vi); } static INLINE vdouble vcast_vd_d(double d) { return _mm256_set_pd(d, d, d, d); } static INLINE vint vcast_vi_i(int i) { return _mm_set_epi32(i, i, i, i); } static INLINE vmask vreinterpret_vm_vd(vdouble vd) { return (__m256i)vd; } static INLINE vdouble vreinterpret_vd_vm(vmask vm) { return (__m256d)vm; } static INLINE vmask vreinterpret_vm_vf(vfloat vf) { return (__m256i)vf; } static INLINE vfloat vreinterpret_vf_vm(vmask vm) { return (__m256)vm; } // static INLINE vfloat vcast_vf_f(float f) { return _mm256_set_ps(f, f, f, f, f, f, f, f); } static INLINE vfloat vaddf(vfloat x, vfloat y) { return _mm256_add_ps(x, y); } static INLINE vfloat vsubf(vfloat x, vfloat y) { return _mm256_sub_ps(x, y); } static INLINE vfloat vmulf(vfloat x, vfloat y) { return _mm256_mul_ps(x, y); } static INLINE vfloat vdivf(vfloat x, vfloat y) { return _mm256_div_ps(x, y); } static INLINE vfloat vrecf(vfloat x) { return vdivf(vcast_vf_f(1.0f), x); } static INLINE vfloat vsqrtf(vfloat x) { return _mm256_sqrt_ps(x); } static INLINE vfloat vmaxf(vfloat x, vfloat y) { return _mm256_max_ps(x, y); } static INLINE vfloat vminf(vfloat x, vfloat y) { return _mm256_min_ps(x, y); } // static INLINE vdouble vadd(vdouble x, vdouble y) { return _mm256_add_pd(x, y); } static INLINE vdouble vsub(vdouble x, vdouble y) { return _mm256_sub_pd(x, y); } static INLINE vdouble vmul(vdouble x, vdouble y) { return _mm256_mul_pd(x, y); } static INLINE vdouble vdiv(vdouble x, vdouble y) { return _mm256_div_pd(x, y); } static INLINE vdouble vrec(vdouble x) { return _mm256_div_pd(_mm256_set_pd(1, 1, 1, 1), x); } static INLINE vdouble vsqrt(vdouble x) { return _mm256_sqrt_pd(x); } static INLINE vdouble vmla(vdouble x, vdouble y, vdouble z) { return vadd(vmul(x, y), z); } static INLINE vdouble vmax(vdouble x, vdouble y) { return _mm256_max_pd(x, y); } static INLINE vdouble vmin(vdouble x, vdouble y) { return _mm256_min_pd(x, y); } static INLINE vdouble vabs(vdouble d) { return (__m256d)_mm256_andnot_pd(_mm256_set_pd(-0.0, -0.0, -0.0, -0.0), d); } static INLINE vdouble vneg(vdouble d) { return (__m256d)_mm256_xor_pd(_mm256_set_pd(-0.0, -0.0, -0.0, -0.0), d); } // static INLINE vint vaddi(vint x, vint y) { return _mm_add_epi32(x, y); } static INLINE vint vsubi(vint x, vint y) { return _mm_sub_epi32(x, y); } static INLINE vint vandi(vint x, vint y) { return _mm_and_si128(x, y); } static INLINE vint vandnoti(vint x, vint y) { return _mm_andnot_si128(x, y); } static INLINE vint vori(vint x, vint y) { return _mm_or_si128(x, y); } static INLINE vint vxori(vint x, vint y) { return _mm_xor_si128(x, y); } static INLINE vint vslli(vint x, int c) { return _mm_slli_epi32 (x, c); } static INLINE vint vsrli(vint x, int c) { return _mm_srli_epi32 (x, c); } static INLINE vint vsrai(vint x, int c) { return _mm_srai_epi32 (x, c); } // static INLINE vmask vandm(vmask x, vmask y) { return (vmask)_mm256_and_pd((__m256d)x, (__m256d)y); } static INLINE vmask vandnotm(vmask x, vmask y) { return (vmask)_mm256_andnot_pd((__m256d)x, (__m256d)y); } static INLINE vmask vorm(vmask x, vmask y) { return (vmask)_mm256_or_pd((__m256d)x, (__m256d)y); } static INLINE vmask vxorm(vmask x, vmask y) { return (vmask)_mm256_xor_pd((__m256d)x, (__m256d)y); } static INLINE vmask vmask_eq(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_EQ_OQ); } static INLINE vmask vmask_neq(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_NEQ_OQ); } static INLINE vmask vmask_lt(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_LT_OQ); } static INLINE vmask vmask_le(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_LE_OQ); } static INLINE vmask vmask_gt(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_GT_OQ); } static INLINE vmask vmask_ge(vdouble x, vdouble y) { return (__m256i)_mm256_cmp_pd(x, y, _CMP_GE_OQ); } static INLINE vmask vmaskf_eq(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_EQ_OQ); } static INLINE vmask vmaskf_neq(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_NEQ_OQ); } static INLINE vmask vmaskf_lt(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_LT_OQ); } static INLINE vmask vmaskf_le(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_LE_OQ); } static INLINE vmask vmaskf_gt(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_GT_OQ); } static INLINE vmask vmaskf_ge(vfloat x, vfloat y) { return (__m256i)_mm256_cmp_ps(x, y, _CMP_GE_OQ); } static INLINE vmask vmaski_eq(vint x, vint y) { __m256d r = _mm256_cvtepi32_pd(_mm_and_si128(_mm_cmpeq_epi32(x, y), _mm_set_epi32(1, 1, 1, 1))); return vmask_eq(r, _mm256_set_pd(1, 1, 1, 1)); } static INLINE vdouble vsel(vmask mask, vdouble x, vdouble y) { return (__m256d)vorm(vandm(mask, (__m256i)x), vandnotm(mask, (__m256i)y)); } static INLINE vint vseli_lt(vdouble d0, vdouble d1, vint x, vint y) { __m128i mask = _mm256_cvtpd_epi32(_mm256_and_pd(_mm256_cmp_pd(d0, d1, _CMP_LT_OQ), _mm256_set_pd(1.0, 1.0, 1.0, 1.0))); mask = _mm_cmpeq_epi32(mask, _mm_set_epi32(1, 1, 1, 1)); return vori(vandi(mask, x), vandnoti(mask, y)); } // static INLINE vint2 vcast_vi2_vm(vmask vm) { vint2 r; r.x = _mm256_castsi256_si128(vm); r.y = _mm256_extractf128_si256(vm, 1); return r; } static INLINE vmask vcast_vm_vi2(vint2 vi) { vmask m = _mm256_castsi128_si256(vi.x); m = _mm256_insertf128_si256(m, vi.y, 1); return m; } static INLINE vint2 vrint_vi2_vf(vfloat vf) { return vcast_vi2_vm((vmask)_mm256_cvtps_epi32(vf)); } static INLINE vint2 vtruncate_vi2_vf(vfloat vf) { return vcast_vi2_vm((vmask)_mm256_cvttps_epi32(vf)); } static INLINE vfloat vcast_vf_vi2(vint2 vi) { return _mm256_cvtepi32_ps((vmask)vcast_vm_vi2(vi)); } static INLINE vint2 vcast_vi2_i(int i) { vint2 r; r.x = r.y = vcast_vi_i(i); return r; } static INLINE vint2 vaddi2(vint2 x, vint2 y) { vint2 r; r.x = vaddi(x.x, y.x); r.y = vaddi(x.y, y.y); return r; } static INLINE vint2 vsubi2(vint2 x, vint2 y) { vint2 r; r.x = vsubi(x.x, y.x); r.y = vsubi(x.y, y.y); return r; } static INLINE vint2 vandi2(vint2 x, vint2 y) { vint2 r; r.x = vandi(x.x, y.x); r.y = vandi(x.y, y.y); return r; } static INLINE vint2 vandnoti2(vint2 x, vint2 y) { vint2 r; r.x = vandnoti(x.x, y.x); r.y = vandnoti(x.y, y.y); return r; } static INLINE vint2 vori2(vint2 x, vint2 y) { vint2 r; r.x = vori(x.x, y.x); r.y = vori(x.y, y.y); return r; } static INLINE vint2 vxori2(vint2 x, vint2 y) { vint2 r; r.x = vxori(x.x, y.x); r.y = vxori(x.y, y.y); return r; } static INLINE vint2 vslli2(vint2 x, int c) { vint2 r; r.x = vslli(x.x, c); r.y = vslli(x.y, c); return r; } static INLINE vint2 vsrli2(vint2 x, int c) { vint2 r; r.x = vsrli(x.x, c); r.y = vsrli(x.y, c); return r; } static INLINE vint2 vsrai2(vint2 x, int c) { vint2 r; r.x = vsrai(x.x, c); r.y = vsrai(x.y, c); return r; } static INLINE vmask vmaski2_eq(vint2 x, vint2 y) { vint2 r; r.x = _mm_cmpeq_epi32(x.x, y.x); r.y = _mm_cmpeq_epi32(x.y, y.y); return vcast_vm_vi2(r); } static INLINE vint2 vseli2(vmask m, vint2 x, vint2 y) { vint2 r, m2 = vcast_vi2_vm(m); r.x = vori(vandi(m2.x, x.x), vandnoti(m2.x, y.x)); r.y = vori(vandi(m2.y, x.y), vandnoti(m2.y, y.y)); return r; } // static INLINE double vcast_d_vd(vdouble v) { double s[4]; _mm256_storeu_pd(s, v); return s[0]; } static INLINE float vcast_f_vf(vfloat v) { float s[8]; _mm256_storeu_ps(s, v); return s[0]; } static INLINE vmask vsignbit(vdouble d) { return (vmask)_mm256_and_pd(d, _mm256_set_pd(-0.0, -0.0, -0.0, -0.0)); } static INLINE vdouble vsign(vdouble d) { return _mm256_or_pd(_mm256_set_pd(1.0, 1.0, 1.0, 1.0), (vdouble)vsignbit(d)); } static INLINE vdouble vmulsign(vdouble x, vdouble y) { return (__m256d)vxorm((__m256i)x, vsignbit(y)); } static INLINE vmask vmask_isinf(vdouble d) { return (vmask)_mm256_cmp_pd(vabs(d), _mm256_set_pd(INFINITY, INFINITY, INFINITY, INFINITY), _CMP_EQ_OQ); } static INLINE vmask vmask_ispinf(vdouble d) { return (vmask)_mm256_cmp_pd(d, _mm256_set_pd(INFINITY, INFINITY, INFINITY, INFINITY), _CMP_EQ_OQ); } static INLINE vmask vmask_isminf(vdouble d) { return (vmask)_mm256_cmp_pd(d, _mm256_set_pd(-INFINITY, -INFINITY, -INFINITY, -INFINITY), _CMP_EQ_OQ); } static INLINE vmask vmask_isnan(vdouble d) { return (vmask)_mm256_cmp_pd(d, d, _CMP_NEQ_UQ); } static INLINE vdouble visinf(vdouble d) { return _mm256_and_pd((vdouble)vmask_isinf(d), vsign(d)); } static INLINE vdouble visinf2(vdouble d, vdouble m) { return _mm256_and_pd((vdouble)vmask_isinf(d), _mm256_or_pd((vdouble)vsignbit(d), m)); } static INLINE vdouble vpow2i(vint q) { vint r; vdouble y; q = _mm_add_epi32(_mm_set_epi32(0x3ff, 0x3ff, 0x3ff, 0x3ff), q); q = _mm_slli_epi32(q, 20); r = (__m128i)_mm_shuffle_ps((__m128)q, (__m128)q, _MM_SHUFFLE(1, 0, 0, 0)); y = _mm256_castpd128_pd256((__m128d)r); r = (__m128i)_mm_shuffle_ps((__m128)q, (__m128)q, _MM_SHUFFLE(3, 2, 2, 2)); y = _mm256_insertf128_pd(y, (__m128d)r, 1); y = _mm256_and_pd(y, (__m256d)_mm256_set_epi32(0xfff00000, 0, 0xfff00000, 0, 0xfff00000, 0, 0xfff00000, 0)); return y; } static INLINE vdouble vldexp(vdouble x, vint q) { vint m = _mm_srai_epi32(q, 31); m = _mm_slli_epi32(_mm_sub_epi32(_mm_srai_epi32(_mm_add_epi32(m, q), 9), m), 7); q = _mm_sub_epi32(q, _mm_slli_epi32(m, 2)); vdouble y = vpow2i(m); return vmul(vmul(vmul(vmul(vmul(x, y), y), y), y), vpow2i(q)); } static INLINE vint vilogbp1(vdouble d) { vint q, r, c; vmask m = vmask_lt(d, vcast_vd_d(4.9090934652977266E-91)); d = vsel(m, vmul(vcast_vd_d(2.037035976334486E90), d), d); c = _mm256_cvtpd_epi32(vsel(m, vcast_vd_d(300 + 0x3fe), vcast_vd_d(0x3fe))); q = (__m128i)_mm256_castpd256_pd128(d); q = (__m128i)_mm_shuffle_ps((__m128)q, _mm_set_ps(0, 0, 0, 0), _MM_SHUFFLE(0, 0, 3, 1)); r = (__m128i)_mm256_extractf128_pd(d, 1); r = (__m128i)_mm_shuffle_ps(_mm_set_ps(0, 0, 0, 0), (__m128)r, _MM_SHUFFLE(3, 1, 0, 0)); q = _mm_or_si128(q, r); q = _mm_srli_epi32(q, 20); q = _mm_sub_epi32(q, c); return q; } static INLINE vdouble vupper(vdouble d) { return (__m256d)_mm256_and_pd(d, (vdouble)_mm256_set_epi32(0xffffffff, 0xf8000000, 0xffffffff, 0xf8000000, 0xffffffff, 0xf8000000, 0xffffffff, 0xf8000000)); } // typedef struct { vdouble x, y; } vdouble2; static INLINE vdouble2 dd(vdouble h, vdouble l) { vdouble2 ret = {h, l}; return ret; } static INLINE vdouble2 vsel2(vmask mask, vdouble2 x, vdouble2 y) { return dd((__m256d)vorm(vandm(mask, (__m256i)x.x), vandnotm(mask, (__m256i)y.x)), (__m256d)vorm(vandm(mask, (__m256i)x.y), vandnotm(mask, (__m256i)y.y))); } static INLINE vdouble2 abs_d(vdouble2 x) { return dd((__m256d)_mm256_xor_pd(_mm256_and_pd(_mm256_set_pd(-0.0, -0.0, -0.0, -0.0), x.x), x.x), (__m256d)_mm256_xor_pd(_mm256_and_pd(_mm256_set_pd(-0.0, -0.0, -0.0, -0.0), x.x), x.y)); }