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/**
* @file dot.h
* @brief SIMD-accelerated Dot Products for Real and Complex numbers.
* @author Ash Vardanian
* @date February 24, 2024
*
* Contains:
* - Dot Product for Real and Complex vectors
* - Conjugate Dot Product for Complex vectors
*
* For datatypes:
* - 64-bit IEEE floating point numbers
* - 32-bit IEEE floating point numbers
* - 16-bit IEEE floating point numbers
* - 16-bit brain floating point numbers
* - 8-bit unsigned integers
* - 8-bit signed integers
*
* For hardware architectures:
* - Arm: NEON, SVE
* - x86: Haswell, Ice Lake, Skylake, Genoa, Sapphire
*
* x86 intrinsics: https://www.intel.com/content/www/us/en/docs/intrinsics-guide/
* Arm intrinsics: https://developer.arm.com/architectures/instruction-sets/intrinsics/
*/
#ifndef SIMSIMD_DOT_H
#define SIMSIMD_DOT_H
#include "types.h"
#ifdef __cplusplus
extern "C" {
#endif
// clang-format off
/* Serial backends for all numeric types.
* By default they use 32-bit arithmetic, unless the arguments themselves contain 64-bit floats.
* For double-precision computation check out the "*_accurate" variants of those "*_serial" functions.
*/
SIMSIMD_PUBLIC void simsimd_dot_f64_serial(simsimd_f64_t const* a, simsimd_f64_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f64c_serial(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f64c_serial(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f32_serial(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_serial(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_serial(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_serial(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_serial(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_serial(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_bf16_serial(simsimd_bf16_t const* a, simsimd_bf16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16c_serial(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_serial(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_i8_serial(simsimd_i8_t const* a, simsimd_i8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_u8_serial(simsimd_u8_t const* a, simsimd_u8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
/* Double-precision serial backends for all numeric types.
* For single-precision computation check out the "*_serial" counterparts of those "*_accurate" functions.
*/
SIMSIMD_PUBLIC void simsimd_dot_f32_accurate(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_accurate(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_accurate(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_accurate(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_accurate(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_accurate(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_bf16_accurate(simsimd_bf16_t const* a, simsimd_bf16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16c_accurate(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_accurate(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
/* SIMD-powered backends for Arm NEON, mostly using 32-bit arithmetic over 128-bit words.
* By far the most portable backend, covering most Arm v8 devices, over a billion phones, and almost all
* server CPUs produced before 2023.
*/
SIMSIMD_PUBLIC void simsimd_dot_f32_neon(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_neon(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_neon(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_neon(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_neon(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_neon(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_i8_neon(simsimd_i8_t const* a, simsimd_i8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_u8_neon(simsimd_u8_t const* a, simsimd_u8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16_neon(simsimd_bf16_t const* a, simsimd_bf16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16c_neon(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_neon(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
/* SIMD-powered backends for Arm SVE, mostly using 32-bit arithmetic over variable-length platform-defined word sizes.
* Designed for Arm Graviton 3, Microsoft Cobalt, as well as Nvidia Grace and newer Ampere Altra CPUs.
*/
SIMSIMD_PUBLIC void simsimd_dot_f32_sve(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_sve(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_sve(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_sve(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_sve(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_sve(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f64_sve(simsimd_f64_t const* a, simsimd_f64_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f64c_sve(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f64c_sve(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
/* SIMD-powered backends for AVX2 CPUs of Haswell generation and newer, using 32-bit arithmetic over 256-bit words.
* First demonstrated in 2011, at least one Haswell-based processor was still being sold in 2022 — the Pentium G3420.
* Practically all modern x86 CPUs support AVX2, FMA, and F16C, making it a perfect baseline for SIMD algorithms.
* On other hand, there is no need to implement AVX2 versions of `f32` and `f64` functions, as those are
* properly vectorized by recent compilers.
*/
SIMSIMD_PUBLIC void simsimd_dot_f32_haswell(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_haswell(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_haswell(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_haswell(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_haswell(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_haswell(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_bf16_haswell(simsimd_bf16_t const* a, simsimd_bf16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_i8_haswell(simsimd_i8_t const* a, simsimd_i8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_u8_haswell(simsimd_u8_t const* a, simsimd_u8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
/* SIMD-powered backends for various generations of AVX512 CPUs.
* Skylake is handy, as it supports masked loads and other operations, avoiding the need for the tail loop.
* Ice Lake added VNNI, VPOPCNTDQ, IFMA, VBMI, VAES, GFNI, VBMI2, BITALG, VPCLMULQDQ, and other extensions for integral operations.
* Genoa added only BF16.
* Sapphire Rapids added tiled matrix operations, but we are most interested in the new mixed-precision FMA instructions.
*
* Sadly, we can't effectively interleave different kinds of arithmetic instructions to utilize more ports:
*
* > Like Intel server architectures since Skylake-X, SPR cores feature two 512-bit FMA units, and organize them in a similar fashion.
* > One 512-bit FMA unit is created by fusing two 256-bit ones on port 0 and port 1. The other is added to port 5, as a server-specific
* > core extension. The FMA units on port 0 and 1 are configured into 2×256-bit or 1×512-bit mode depending on whether 512-bit FMA
* > instructions are present in the scheduler. That means a mix of 256-bit and 512-bit FMA instructions will not achieve higher IPC
* > than executing 512-bit instructions alone.
*
* Source: https://chipsandcheese.com/p/a-peek-at-sapphire-rapids
*/
SIMSIMD_PUBLIC void simsimd_dot_f64_skylake(simsimd_f64_t const* a, simsimd_f64_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f64c_skylake(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f64c_skylake(simsimd_f64c_t const* a, simsimd_f64c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f32_skylake(simsimd_f32_t const* a, simsimd_f32_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f32c_skylake(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f32c_skylake(simsimd_f32c_t const* a, simsimd_f32c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_i8_ice(simsimd_i8_t const* a, simsimd_i8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_u8_ice(simsimd_u8_t const* a, simsimd_u8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16_genoa(simsimd_bf16_t const* a, simsimd_bf16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_bf16c_genoa(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_genoa(simsimd_bf16c_t const* a, simsimd_bf16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_f16_sapphire(simsimd_f16_t const* a, simsimd_f16_t const* b, simsimd_size_t n, simsimd_distance_t* result);
SIMSIMD_PUBLIC void simsimd_dot_f16c_sapphire(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_vdot_f16c_sapphire(simsimd_f16c_t const* a, simsimd_f16c_t const* b, simsimd_size_t n, simsimd_distance_t* results);
SIMSIMD_PUBLIC void simsimd_dot_i8_sierra(simsimd_i8_t const* a, simsimd_i8_t const* b, simsimd_size_t n, simsimd_distance_t* result);
// clang-format on
#define SIMSIMD_MAKE_DOT(name, input_type, accumulator_type, load_and_convert) \
SIMSIMD_PUBLIC void simsimd_dot_##input_type##_##name(simsimd_##input_type##_t const *a, \
simsimd_##input_type##_t const *b, simsimd_size_t n, \
simsimd_distance_t *result) { \
simsimd_##accumulator_type##_t ab = 0; \
for (simsimd_size_t i = 0; i != n; ++i) { \
simsimd_##accumulator_type##_t ai = load_and_convert(a + i); \
simsimd_##accumulator_type##_t bi = load_and_convert(b + i); \
ab += ai * bi; \
} \
*result = ab; \
}
#define SIMSIMD_MAKE_COMPLEX_DOT(name, input_type, accumulator_type, load_and_convert) \
SIMSIMD_PUBLIC void simsimd_dot_##input_type##_##name(simsimd_##input_type##_t const *a_pairs, \
simsimd_##input_type##_t const *b_pairs, \
simsimd_size_t count_pairs, simsimd_distance_t *results) { \
simsimd_##accumulator_type##_t ab_real = 0, ab_imag = 0; \
for (simsimd_size_t i = 0; i != count_pairs; ++i) { \
simsimd_##accumulator_type##_t ar = load_and_convert(&(a_pairs + i)->real); \
simsimd_##accumulator_type##_t br = load_and_convert(&(b_pairs + i)->real); \
simsimd_##accumulator_type##_t ai = load_and_convert(&(a_pairs + i)->imag); \
simsimd_##accumulator_type##_t bi = load_and_convert(&(b_pairs + i)->imag); \
ab_real += ar * br - ai * bi; \
ab_imag += ar * bi + ai * br; \
} \
results[0] = ab_real; \
results[1] = ab_imag; \
}
#define SIMSIMD_MAKE_COMPLEX_VDOT(name, input_type, accumulator_type, load_and_convert) \
SIMSIMD_PUBLIC void simsimd_vdot_##input_type##_##name(simsimd_##input_type##_t const *a_pairs, \
simsimd_##input_type##_t const *b_pairs, \
simsimd_size_t count_pairs, simsimd_distance_t *results) { \
simsimd_##accumulator_type##_t ab_real = 0, ab_imag = 0; \
for (simsimd_size_t i = 0; i != count_pairs; ++i) { \
simsimd_##accumulator_type##_t ar = load_and_convert(&(a_pairs + i)->real); \
simsimd_##accumulator_type##_t br = load_and_convert(&(b_pairs + i)->real); \
simsimd_##accumulator_type##_t ai = load_and_convert(&(a_pairs + i)->imag); \
simsimd_##accumulator_type##_t bi = load_and_convert(&(b_pairs + i)->imag); \
ab_real += ar * br + ai * bi; \
ab_imag += ar * bi - ai * br; \
} \
results[0] = ab_real; \
results[1] = ab_imag; \
}
SIMSIMD_MAKE_DOT(serial, f64, f64, SIMSIMD_DEREFERENCE) // simsimd_dot_f64_serial
SIMSIMD_MAKE_COMPLEX_DOT(serial, f64c, f64, SIMSIMD_DEREFERENCE) // simsimd_dot_f64c_serial
SIMSIMD_MAKE_COMPLEX_VDOT(serial, f64c, f64, SIMSIMD_DEREFERENCE) // simsimd_vdot_f64c_serial
SIMSIMD_MAKE_DOT(serial, f32, f32, SIMSIMD_DEREFERENCE) // simsimd_dot_f32_serial
SIMSIMD_MAKE_COMPLEX_DOT(serial, f32c, f32, SIMSIMD_DEREFERENCE) // simsimd_dot_f32c_serial
SIMSIMD_MAKE_COMPLEX_VDOT(serial, f32c, f32, SIMSIMD_DEREFERENCE) // simsimd_vdot_f32c_serial
SIMSIMD_MAKE_DOT(serial, f16, f32, SIMSIMD_F16_TO_F32) // simsimd_dot_f16_serial
SIMSIMD_MAKE_COMPLEX_DOT(serial, f16c, f32, SIMSIMD_F16_TO_F32) // simsimd_dot_f16c_serial
SIMSIMD_MAKE_COMPLEX_VDOT(serial, f16c, f32, SIMSIMD_F16_TO_F32) // simsimd_vdot_f16c_serial
SIMSIMD_MAKE_DOT(serial, bf16, f32, SIMSIMD_BF16_TO_F32) // simsimd_dot_bf16_serial
SIMSIMD_MAKE_COMPLEX_DOT(serial, bf16c, f32, SIMSIMD_BF16_TO_F32) // simsimd_dot_bf16c_serial
SIMSIMD_MAKE_COMPLEX_VDOT(serial, bf16c, f32, SIMSIMD_BF16_TO_F32) // simsimd_vdot_bf16c_serial
SIMSIMD_MAKE_DOT(serial, i8, i64, SIMSIMD_DEREFERENCE) // simsimd_dot_i8_serial
SIMSIMD_MAKE_DOT(serial, u8, i64, SIMSIMD_DEREFERENCE) // simsimd_dot_u8_serial
SIMSIMD_MAKE_DOT(accurate, f32, f64, SIMSIMD_DEREFERENCE) // simsimd_dot_f32_accurate
SIMSIMD_MAKE_COMPLEX_DOT(accurate, f32c, f64, SIMSIMD_DEREFERENCE) // simsimd_dot_f32c_accurate
SIMSIMD_MAKE_COMPLEX_VDOT(accurate, f32c, f64, SIMSIMD_DEREFERENCE) // simsimd_vdot_f32c_accurate
SIMSIMD_MAKE_DOT(accurate, f16, f64, SIMSIMD_F16_TO_F32) // simsimd_dot_f16_accurate
SIMSIMD_MAKE_COMPLEX_DOT(accurate, f16c, f64, SIMSIMD_F16_TO_F32) // simsimd_dot_f16c_accurate
SIMSIMD_MAKE_COMPLEX_VDOT(accurate, f16c, f64, SIMSIMD_F16_TO_F32) // simsimd_vdot_f16c_accurate
SIMSIMD_MAKE_DOT(accurate, bf16, f64, SIMSIMD_BF16_TO_F32) // simsimd_dot_bf16_accurate
SIMSIMD_MAKE_COMPLEX_DOT(accurate, bf16c, f64, SIMSIMD_BF16_TO_F32) // simsimd_dot_bf16c_accurate
SIMSIMD_MAKE_COMPLEX_VDOT(accurate, bf16c, f64, SIMSIMD_BF16_TO_F32) // simsimd_vdot_bf16c_accurate
#if _SIMSIMD_TARGET_ARM
#if SIMSIMD_TARGET_NEON
#pragma GCC push_options
#pragma GCC target("arch=armv8-a+simd")
#pragma clang attribute push(__attribute__((target("arch=armv8-a+simd"))), apply_to = function)
SIMSIMD_INTERNAL float32x4_t _simsimd_partial_load_f32x4_neon(simsimd_f32_t const *x, simsimd_size_t n) {
union {
float32x4_t vec;
simsimd_f32_t scalars[4];
} result;
simsimd_size_t i = 0;
for (; i < n; ++i) result.scalars[i] = x[i];
for (; i < 4; ++i) result.scalars[i] = 0;
return result.vec;
}
SIMSIMD_PUBLIC void simsimd_dot_f32_neon(simsimd_f32_t const *a_scalars, simsimd_f32_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
float32x4_t ab_vec = vdupq_n_f32(0);
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 4 <= count_scalars; idx_scalars += 4) {
float32x4_t a_vec = vld1q_f32(a_scalars + idx_scalars);
float32x4_t b_vec = vld1q_f32(b_scalars + idx_scalars);
ab_vec = vfmaq_f32(ab_vec, a_vec, b_vec);
}
simsimd_f32_t ab = vaddvq_f32(ab_vec);
for (; idx_scalars < count_scalars; ++idx_scalars) ab += a_scalars[idx_scalars] * b_scalars[idx_scalars];
*result = ab;
}
SIMSIMD_PUBLIC void simsimd_dot_f32c_neon(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
simsimd_size_t idx_pairs = 0;
for (; idx_pairs + 4 <= count_pairs; idx_pairs += 4) {
// Unpack the input arrays into real and imaginary parts:
float32x4x2_t a_vec = vld2q_f32((simsimd_f32_t const *)(a_pairs + idx_pairs));
float32x4x2_t b_vec = vld2q_f32((simsimd_f32_t const *)(b_pairs + idx_pairs));
float32x4_t a_real_vec = a_vec.val[0];
float32x4_t a_imag_vec = a_vec.val[1];
float32x4_t b_real_vec = b_vec.val[0];
float32x4_t b_imag_vec = b_vec.val[1];
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmsq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
}
// Reduce horizontal sums:
simsimd_f32_t ab_real = vaddvq_f32(ab_real_vec);
simsimd_f32_t ab_imag = vaddvq_f32(ab_imag_vec);
// Handle the tail:
for (; idx_pairs != count_pairs; ++idx_pairs) {
simsimd_f32c_t a_pair = a_pairs[idx_pairs], b_pair = b_pairs[idx_pairs];
simsimd_f32_t ar = a_pair.real, ai = a_pair.imag, br = b_pair.real, bi = b_pair.imag;
ab_real += ar * br - ai * bi;
ab_imag += ar * bi + ai * br;
}
results[0] = ab_real;
results[1] = ab_imag;
}
SIMSIMD_PUBLIC void simsimd_vdot_f32c_neon(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
simsimd_size_t idx_pairs = 0;
for (; idx_pairs + 4 <= count_pairs; idx_pairs += 4) {
// Unpack the input arrays into real and imaginary parts:
float32x4x2_t a_vec = vld2q_f32((simsimd_f32_t const *)(a_pairs + idx_pairs));
float32x4x2_t b_vec = vld2q_f32((simsimd_f32_t const *)(b_pairs + idx_pairs));
float32x4_t a_real_vec = a_vec.val[0];
float32x4_t a_imag_vec = a_vec.val[1];
float32x4_t b_real_vec = b_vec.val[0];
float32x4_t b_imag_vec = b_vec.val[1];
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmaq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmsq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
}
// Reduce horizontal sums:
simsimd_f32_t ab_real = vaddvq_f32(ab_real_vec);
simsimd_f32_t ab_imag = vaddvq_f32(ab_imag_vec);
// Handle the tail:
for (; idx_pairs != count_pairs; ++idx_pairs) {
simsimd_f32c_t a_pair = a_pairs[idx_pairs], b_pair = b_pairs[idx_pairs];
simsimd_f32_t ar = a_pair.real, ai = a_pair.imag, br = b_pair.real, bi = b_pair.imag;
ab_real += ar * br + ai * bi;
ab_imag += ar * bi - ai * br;
}
results[0] = ab_real;
results[1] = ab_imag;
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_NEON
#if SIMSIMD_TARGET_NEON_I8
#pragma GCC push_options
#pragma GCC target("arch=armv8.2-a+dotprod")
#pragma clang attribute push(__attribute__((target("arch=armv8.2-a+dotprod"))), apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_i8_neon(simsimd_i8_t const *a_scalars, simsimd_i8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
int32x4_t ab_vec = vdupq_n_s32(0);
simsimd_size_t idx_scalars = 0;
// If the 128-bit `vdot_s32` intrinsic is unavailable, we can use the 64-bit `vdot_s32`.
// for (simsimd_size_t idx_scalars = 0; idx_scalars != n; idx_scalars += 8) {
// int16x8_t a_vec = vmovl_s8(vld1_s8(a_scalars + idx_scalars));
// int16x8_t b_vec = vmovl_s8(vld1_s8(b_scalars + idx_scalars));
// int16x8_t ab_part_vec = vmulq_s16(a_vec, b_vec);
// ab_vec = vaddq_s32(ab_vec, vaddq_s32(vmovl_s16(vget_high_s16(ab_part_vec)), //
// vmovl_s16(vget_low_s16(ab_part_vec))));
// }
for (; idx_scalars + 16 <= count_scalars; idx_scalars += 16) {
int8x16_t a_vec = vld1q_s8(a_scalars + idx_scalars);
int8x16_t b_vec = vld1q_s8(b_scalars + idx_scalars);
ab_vec = vdotq_s32(ab_vec, a_vec, b_vec);
}
// Take care of the tail:
simsimd_i32_t ab = vaddvq_s32(ab_vec);
for (; idx_scalars < count_scalars; ++idx_scalars) {
simsimd_i32_t ai = a_scalars[idx_scalars], bi = b_scalars[idx_scalars];
ab += ai * bi;
}
*result = ab;
}
SIMSIMD_PUBLIC void simsimd_dot_u8_neon(simsimd_u8_t const *a_scalars, simsimd_u8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
uint32x4_t ab_vec = vdupq_n_u32(0);
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 16 <= count_scalars; idx_scalars += 16) {
uint8x16_t a_vec = vld1q_u8(a_scalars + idx_scalars);
uint8x16_t b_vec = vld1q_u8(b_scalars + idx_scalars);
ab_vec = vdotq_u32(ab_vec, a_vec, b_vec);
}
// Take care of the tail:
simsimd_u32_t ab = vaddvq_u32(ab_vec);
for (; idx_scalars < count_scalars; ++idx_scalars) {
simsimd_u32_t ai = a_scalars[idx_scalars], bi = b_scalars[idx_scalars];
ab += ai * bi;
}
*result = ab;
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_NEON_I8
#if SIMSIMD_TARGET_NEON_F16
#pragma GCC push_options
#pragma GCC target("arch=armv8.2-a+simd+fp16")
#pragma clang attribute push(__attribute__((target("arch=armv8.2-a+simd+fp16"))), apply_to = function)
SIMSIMD_INTERNAL float16x4_t _simsimd_partial_load_f16x4_neon(simsimd_f16_t const *x, simsimd_size_t n) {
// In case the software emulation for `f16` scalars is enabled, the `simsimd_f16_to_f32`
// function will run. It is extremely slow, so even for the tail, let's combine serial
// loads and stores with vectorized math.
union {
float16x4_t vec;
simsimd_f16_t scalars[4];
} result;
simsimd_size_t i = 0;
for (; i < n; ++i) result.scalars[i] = x[i];
for (; i < 4; ++i) result.scalars[i] = 0;
return result.vec;
}
SIMSIMD_PUBLIC void simsimd_dot_f16_neon(simsimd_f16_t const *a_scalars, simsimd_f16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
float32x4_t a_vec, b_vec;
float32x4_t ab_vec = vdupq_n_f32(0);
simsimd_size_t i = 0;
simsimd_dot_f16_neon_cycle:
if (count_scalars < 4) {
a_vec = vcvt_f32_f16(_simsimd_partial_load_f16x4_neon(a_scalars, count_scalars));
b_vec = vcvt_f32_f16(_simsimd_partial_load_f16x4_neon(b_scalars, count_scalars));
count_scalars = 0;
}
else {
a_vec = vcvt_f32_f16(vld1_f16((simsimd_f16_for_arm_simd_t const *)a_scalars));
b_vec = vcvt_f32_f16(vld1_f16((simsimd_f16_for_arm_simd_t const *)b_scalars));
a_scalars += 4, b_scalars += 4, count_scalars -= 4;
}
ab_vec = vfmaq_f32(ab_vec, a_vec, b_vec);
if (count_scalars) goto simsimd_dot_f16_neon_cycle;
*result = vaddvq_f32(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f16c_neon(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// A nicer approach is to use `f16` arithmetic for the dot product, but that requires
// FMLA extensions available on Arm v8.3 and later. That we can also process 16 entries
// at once. That's how the original implementation worked, but compiling it was a nightmare :)
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
while (count_pairs >= 4) {
// Unpack the input arrays into real and imaginary parts.
// MSVC sadly doesn't recognize the `vld2_f16`, so we load the data as signed
// integers of the same size and reinterpret with `vreinterpret_f16_s16` afterwards.
int16x4x2_t a_vec = vld2_s16((short *)a_pairs);
int16x4x2_t b_vec = vld2_s16((short *)b_pairs);
float32x4_t a_real_vec = vcvt_f32_f16(vreinterpret_f16_s16(a_vec.val[0]));
float32x4_t a_imag_vec = vcvt_f32_f16(vreinterpret_f16_s16(a_vec.val[1]));
float32x4_t b_real_vec = vcvt_f32_f16(vreinterpret_f16_s16(b_vec.val[0]));
float32x4_t b_imag_vec = vcvt_f32_f16(vreinterpret_f16_s16(b_vec.val[1]));
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmsq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Reduce horizontal sums and aggregate with the tail:
simsimd_dot_f16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += vaddvq_f32(ab_real_vec);
results[1] += vaddvq_f32(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f16c_neon(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// A nicer approach is to use `f16` arithmetic for the dot product, but that requires
// FMLA extensions available on Arm v8.3 and later. That we can also process 16 entries
// at once. That's how the original implementation worked, but compiling it was a nightmare :)
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
while (count_pairs >= 4) {
// Unpack the input arrays into real and imaginary parts.
// MSVC sadly doesn't recognize the `vld2_f16`, so we load the data as signed
// integers of the same size and reinterpret with `vreinterpret_f16_s16` afterwards.
int16x4x2_t a_vec = vld2_s16((short *)a_pairs);
int16x4x2_t b_vec = vld2_s16((short *)b_pairs);
float32x4_t a_real_vec = vcvt_f32_f16(vreinterpret_f16_s16(a_vec.val[0]));
float32x4_t a_imag_vec = vcvt_f32_f16(vreinterpret_f16_s16(a_vec.val[1]));
float32x4_t b_real_vec = vcvt_f32_f16(vreinterpret_f16_s16(b_vec.val[0]));
float32x4_t b_imag_vec = vcvt_f32_f16(vreinterpret_f16_s16(b_vec.val[1]));
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmaq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmsq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Reduce horizontal sums and aggregate with the tail:
simsimd_vdot_f16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += vaddvq_f32(ab_real_vec);
results[1] += vaddvq_f32(ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_NEON_F16
#if SIMSIMD_TARGET_NEON_BF16
#pragma GCC push_options
#pragma GCC target("arch=armv8.6-a+simd+bf16")
#pragma clang attribute push(__attribute__((target("arch=armv8.6-a+simd+bf16"))), apply_to = function)
SIMSIMD_INTERNAL bfloat16x8_t _simsimd_partial_load_bf16x8_neon(simsimd_bf16_t const *x, simsimd_size_t n) {
union {
bfloat16x8_t vec;
simsimd_bf16_t scalars[8];
} result;
simsimd_size_t i = 0;
for (; i < n; ++i) result.scalars[i] = x[i];
for (; i < 8; ++i) result.scalars[i] = 0;
return result.vec;
}
SIMSIMD_PUBLIC void simsimd_dot_bf16_neon(simsimd_bf16_t const *a_scalars, simsimd_bf16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
bfloat16x8_t a_vec, b_vec;
float32x4_t ab_vec = vdupq_n_f32(0);
simsimd_dot_bf16_neon_cycle:
if (count_scalars < 8) {
a_vec = _simsimd_partial_load_bf16x8_neon(a_scalars, count_scalars);
b_vec = _simsimd_partial_load_bf16x8_neon(b_scalars, count_scalars);
count_scalars = 0;
}
else {
a_vec = vld1q_bf16((simsimd_bf16_for_arm_simd_t const *)a_scalars);
b_vec = vld1q_bf16((simsimd_bf16_for_arm_simd_t const *)b_scalars);
a_scalars += 8, b_scalars += 8, count_scalars -= 8;
}
ab_vec = vbfdotq_f32(ab_vec, a_vec, b_vec);
if (count_scalars) goto simsimd_dot_bf16_neon_cycle;
*result = vaddvq_f32(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_bf16c_neon(simsimd_bf16c_t const *a_pairs, simsimd_bf16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// A nicer approach is to use `bf16` arithmetic for the dot product, but that requires
// FMLA extensions available on Arm v8.3 and later. That we can also process 16 entries
// at once. That's how the original implementation worked, but compiling it was a nightmare :)
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
while (count_pairs >= 4) {
// Unpack the input arrays into real and imaginary parts.
// MSVC sadly doesn't recognize the `vld2_bf16`, so we load the data as signed
// integers of the same size and reinterpret with `vreinterpret_bf16_s16` afterwards.
int16x4x2_t a_vec = vld2_s16((short const *)a_pairs);
int16x4x2_t b_vec = vld2_s16((short const *)b_pairs);
float32x4_t a_real_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(a_vec.val[0]));
float32x4_t a_imag_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(a_vec.val[1]));
float32x4_t b_real_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(b_vec.val[0]));
float32x4_t b_imag_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(b_vec.val[1]));
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmsq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Reduce horizontal sums and aggregate with the tail:
simsimd_dot_bf16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += vaddvq_f32(ab_real_vec);
results[1] += vaddvq_f32(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_neon(simsimd_bf16c_t const *a_pairs, simsimd_bf16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// A nicer approach is to use `bf16` arithmetic for the dot product, but that requires
// FMLA extensions available on Arm v8.3 and later. That we can also process 16 entries
// at once. That's how the original implementation worked, but compiling it was a nightmare :)
float32x4_t ab_real_vec = vdupq_n_f32(0);
float32x4_t ab_imag_vec = vdupq_n_f32(0);
while (count_pairs >= 4) {
// Unpack the input arrays into real and imaginary parts.
// MSVC sadly doesn't recognize the `vld2_bf16`, so we load the data as signed
// integers of the same size and reinterpret with `vreinterpret_bf16_s16` afterwards.
int16x4x2_t a_vec = vld2_s16((short const *)a_pairs);
int16x4x2_t b_vec = vld2_s16((short const *)b_pairs);
float32x4_t a_real_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(a_vec.val[0]));
float32x4_t a_imag_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(a_vec.val[1]));
float32x4_t b_real_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(b_vec.val[0]));
float32x4_t b_imag_vec = vcvt_f32_bf16(vreinterpret_bf16_s16(b_vec.val[1]));
// Compute the dot product:
ab_real_vec = vfmaq_f32(ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = vfmaq_f32(ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = vfmaq_f32(ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = vfmsq_f32(ab_imag_vec, a_imag_vec, b_real_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Reduce horizontal sums and aggregate with the tail:
simsimd_vdot_bf16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += vaddvq_f32(ab_real_vec);
results[1] += vaddvq_f32(ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_NEON_BF16
#if SIMSIMD_TARGET_SVE
#pragma GCC push_options
#pragma GCC target("arch=armv8.2-a+sve")
#pragma clang attribute push(__attribute__((target("arch=armv8.2-a+sve"))), apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_f32_sve(simsimd_f32_t const *a_scalars, simsimd_f32_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
simsimd_size_t idx_scalars = 0;
svfloat32_t ab_vec = svdup_f32(0.f);
do {
svbool_t pg_vec = svwhilelt_b32((unsigned int)idx_scalars, (unsigned int)count_scalars);
svfloat32_t a_vec = svld1_f32(pg_vec, a_scalars + idx_scalars);
svfloat32_t b_vec = svld1_f32(pg_vec, b_scalars + idx_scalars);
ab_vec = svmla_f32_x(pg_vec, ab_vec, a_vec, b_vec);
idx_scalars += svcntw();
} while (idx_scalars < count_scalars);
*result = svaddv_f32(svptrue_b32(), ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f32c_sve(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat32_t ab_real_vec = svdup_f32(0.f);
svfloat32_t ab_imag_vec = svdup_f32(0.f);
do {
svbool_t pg_vec = svwhilelt_b32((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat32x2_t a_vec = svld2_f32(pg_vec, (simsimd_f32_t const *)(a_pairs + idx_pairs));
svfloat32x2_t b_vec = svld2_f32(pg_vec, (simsimd_f32_t const *)(b_pairs + idx_pairs));
svfloat32_t a_real_vec = svget2_f32(a_vec, 0);
svfloat32_t a_imag_vec = svget2_f32(a_vec, 1);
svfloat32_t b_real_vec = svget2_f32(b_vec, 0);
svfloat32_t b_imag_vec = svget2_f32(b_vec, 1);
ab_real_vec = svmla_f32_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmls_f32_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f32_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmla_f32_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcntw();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f32(svptrue_b32(), ab_real_vec);
results[1] = svaddv_f32(svptrue_b32(), ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f32c_sve(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat32_t ab_real_vec = svdup_f32(0.f);
svfloat32_t ab_imag_vec = svdup_f32(0.f);
do {
svbool_t pg_vec = svwhilelt_b32((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat32x2_t a_vec = svld2_f32(pg_vec, (simsimd_f32_t const *)(a_pairs + idx_pairs));
svfloat32x2_t b_vec = svld2_f32(pg_vec, (simsimd_f32_t const *)(b_pairs + idx_pairs));
svfloat32_t a_real_vec = svget2_f32(a_vec, 0);
svfloat32_t a_imag_vec = svget2_f32(a_vec, 1);
svfloat32_t b_real_vec = svget2_f32(b_vec, 0);
svfloat32_t b_imag_vec = svget2_f32(b_vec, 1);
ab_real_vec = svmla_f32_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmla_f32_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f32_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmls_f32_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcntw();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f32(svptrue_b32(), ab_real_vec);
results[1] = svaddv_f32(svptrue_b32(), ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f64_sve(simsimd_f64_t const *a_scalars, simsimd_f64_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
simsimd_size_t idx_scalars = 0;
svfloat64_t ab_vec = svdup_f64(0.);
do {
svbool_t pg_vec = svwhilelt_b64((unsigned int)idx_scalars, (unsigned int)count_scalars);
svfloat64_t a_vec = svld1_f64(pg_vec, a_scalars + idx_scalars);
svfloat64_t b_vec = svld1_f64(pg_vec, b_scalars + idx_scalars);
ab_vec = svmla_f64_x(pg_vec, ab_vec, a_vec, b_vec);
idx_scalars += svcntd();
} while (idx_scalars < count_scalars);
*result = svaddv_f64(svptrue_b32(), ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f64c_sve(simsimd_f64c_t const *a_pairs, simsimd_f64c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat64_t ab_real_vec = svdup_f64(0.);
svfloat64_t ab_imag_vec = svdup_f64(0.);
do {
svbool_t pg_vec = svwhilelt_b64((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat64x2_t a_vec = svld2_f64(pg_vec, (simsimd_f64_t const *)(a_pairs + idx_pairs));
svfloat64x2_t b_vec = svld2_f64(pg_vec, (simsimd_f64_t const *)(b_pairs + idx_pairs));
svfloat64_t a_real_vec = svget2_f64(a_vec, 0);
svfloat64_t a_imag_vec = svget2_f64(a_vec, 1);
svfloat64_t b_real_vec = svget2_f64(b_vec, 0);
svfloat64_t b_imag_vec = svget2_f64(b_vec, 1);
ab_real_vec = svmla_f64_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmls_f64_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f64_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmla_f64_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcntd();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f64(svptrue_b64(), ab_real_vec);
results[1] = svaddv_f64(svptrue_b64(), ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f64c_sve(simsimd_f64c_t const *a_pairs, simsimd_f64c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat64_t ab_real_vec = svdup_f64(0.);
svfloat64_t ab_imag_vec = svdup_f64(0.);
do {
svbool_t pg_vec = svwhilelt_b64((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat64x2_t a_vec = svld2_f64(pg_vec, (simsimd_f64_t const *)(a_pairs + idx_pairs));
svfloat64x2_t b_vec = svld2_f64(pg_vec, (simsimd_f64_t const *)(b_pairs + idx_pairs));
svfloat64_t a_real_vec = svget2_f64(a_vec, 0);
svfloat64_t a_imag_vec = svget2_f64(a_vec, 1);
svfloat64_t b_real_vec = svget2_f64(b_vec, 0);
svfloat64_t b_imag_vec = svget2_f64(b_vec, 1);
ab_real_vec = svmla_f64_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmla_f64_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f64_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmls_f64_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcntd();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f64(svptrue_b64(), ab_real_vec);
results[1] = svaddv_f64(svptrue_b64(), ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#pragma GCC push_options
#pragma GCC target("arch=armv8.2-a+sve+fp16")
#pragma clang attribute push(__attribute__((target("arch=armv8.2-a+sve+fp16"))), apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_f16_sve(simsimd_f16_t const *a_scalars, simsimd_f16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
simsimd_size_t idx_scalars = 0;
svfloat16_t ab_vec = svdup_f16(0);
do {
svbool_t pg_vec = svwhilelt_b16((unsigned int)idx_scalars, (unsigned int)count_scalars);
svfloat16_t a_vec = svld1_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(a_scalars + idx_scalars));
svfloat16_t b_vec = svld1_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(b_scalars + idx_scalars));
ab_vec = svmla_f16_x(pg_vec, ab_vec, a_vec, b_vec);
idx_scalars += svcnth();
} while (idx_scalars < count_scalars);
simsimd_f16_for_arm_simd_t ab = svaddv_f16(svptrue_b16(), ab_vec);
*result = ab;
}
SIMSIMD_PUBLIC void simsimd_dot_f16c_sve(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat16_t ab_real_vec = svdup_f16(0);
svfloat16_t ab_imag_vec = svdup_f16(0);
do {
svbool_t pg_vec = svwhilelt_b32((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat16x2_t a_vec = svld2_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(a_pairs + idx_pairs));
svfloat16x2_t b_vec = svld2_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(b_pairs + idx_pairs));
svfloat16_t a_real_vec = svget2_f16(a_vec, 0);
svfloat16_t a_imag_vec = svget2_f16(a_vec, 1);
svfloat16_t b_real_vec = svget2_f16(b_vec, 0);
svfloat16_t b_imag_vec = svget2_f16(b_vec, 1);
ab_real_vec = svmla_f16_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmls_f16_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f16_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmla_f16_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcnth();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f16(svptrue_b16(), ab_real_vec);
results[1] = svaddv_f16(svptrue_b16(), ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f16c_sve(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
simsimd_size_t idx_pairs = 0;
svfloat16_t ab_real_vec = svdup_f16(0);
svfloat16_t ab_imag_vec = svdup_f16(0);
do {
svbool_t pg_vec = svwhilelt_b32((unsigned int)idx_pairs, (unsigned int)count_pairs);
svfloat16x2_t a_vec = svld2_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(a_pairs + idx_pairs));
svfloat16x2_t b_vec = svld2_f16(pg_vec, (simsimd_f16_for_arm_simd_t const *)(b_pairs + idx_pairs));
svfloat16_t a_real_vec = svget2_f16(a_vec, 0);
svfloat16_t a_imag_vec = svget2_f16(a_vec, 1);
svfloat16_t b_real_vec = svget2_f16(b_vec, 0);
svfloat16_t b_imag_vec = svget2_f16(b_vec, 1);
ab_real_vec = svmla_f16_x(pg_vec, ab_real_vec, a_real_vec, b_real_vec);
ab_real_vec = svmla_f16_x(pg_vec, ab_real_vec, a_imag_vec, b_imag_vec);
ab_imag_vec = svmla_f16_x(pg_vec, ab_imag_vec, a_real_vec, b_imag_vec);
ab_imag_vec = svmls_f16_x(pg_vec, ab_imag_vec, a_imag_vec, b_real_vec);
idx_pairs += svcnth();
} while (idx_pairs < count_pairs);
results[0] = svaddv_f16(svptrue_b16(), ab_real_vec);
results[1] = svaddv_f16(svptrue_b16(), ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_SVE
#endif // _SIMSIMD_TARGET_ARM
#if _SIMSIMD_TARGET_X86
#if SIMSIMD_TARGET_HASWELL
#pragma GCC push_options
#pragma GCC target("avx2", "f16c", "fma")
#pragma clang attribute push(__attribute__((target("avx2,f16c,fma"))), apply_to = function)
SIMSIMD_INTERNAL simsimd_f64_t _simsimd_reduce_f64x4_haswell(__m256d vec) {
// Reduce the double-precision vector to a scalar
// Horizontal add the first and second double-precision values, and third and fourth
__m128d vec_low = _mm256_castpd256_pd128(vec);
__m128d vec_high = _mm256_extractf128_pd(vec, 1);
__m128d vec128 = _mm_add_pd(vec_low, vec_high);
// Horizontal add again to accumulate all four values into one
vec128 = _mm_hadd_pd(vec128, vec128);
// Convert the final sum to a scalar double-precision value and return
return _mm_cvtsd_f64(vec128);
}
SIMSIMD_INTERNAL simsimd_f64_t _simsimd_reduce_f32x8_haswell(__m256 vec) {
// Convert the lower and higher 128-bit lanes of the input vector to double precision
__m128 low_f32 = _mm256_castps256_ps128(vec);
__m128 high_f32 = _mm256_extractf128_ps(vec, 1);
// Convert single-precision (float) vectors to double-precision (double) vectors
__m256d low_f64 = _mm256_cvtps_pd(low_f32);
__m256d high_f64 = _mm256_cvtps_pd(high_f32);
// Perform the addition in double-precision
__m256d sum = _mm256_add_pd(low_f64, high_f64);
return _simsimd_reduce_f64x4_haswell(sum);
}
SIMSIMD_INTERNAL simsimd_i32_t _simsimd_reduce_i32x8_haswell(__m256i vec) {
__m128i low = _mm256_castsi256_si128(vec);
__m128i high = _mm256_extracti128_si256(vec, 1);
__m128i sum = _mm_add_epi32(low, high);
sum = _mm_hadd_epi32(sum, sum);
sum = _mm_hadd_epi32(sum, sum);
return _mm_cvtsi128_si32(sum);
}
SIMSIMD_PUBLIC void simsimd_dot_f32_haswell(simsimd_f32_t const *a_scalars, simsimd_f32_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *results) {
__m256 ab_vec = _mm256_setzero_ps();
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 8 <= count_scalars; idx_scalars += 8) {
__m256 a_vec = _mm256_loadu_ps(a_scalars + idx_scalars);
__m256 b_vec = _mm256_loadu_ps(b_scalars + idx_scalars);
ab_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_vec);
}
simsimd_f64_t ab = _simsimd_reduce_f32x8_haswell(ab_vec);
for (; idx_scalars < count_scalars; ++idx_scalars) ab += a_scalars[idx_scalars] * b_scalars[idx_scalars];
*results = ab;
}
SIMSIMD_PUBLIC void simsimd_dot_f32c_haswell(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// The naive approach would be to use FMA and FMS instructions on different parts of the vectors.
// Prior to that we would need to shuffle the input vectors to separate real and imaginary parts.
// Both operations are quite expensive, and the resulting kernel would run at 2.5 GB/s.
// __m128 ab_real_vec = _mm_setzero_ps();
// __m128 ab_imag_vec = _mm_setzero_ps();
// __m256i permute_vec = _mm256_set_epi32(7, 5, 3, 1, 6, 4, 2, 0);
// simsimd_size_t idx_pairs = 0;
// for (; idx_pairs + 4 <= count_pairs; idx_pairs += 4) {
// __m256 a_vec = _mm256_loadu_ps((simsimd_f32_t const *)(a_pairs + idx_pairs));
// __m256 b_vec = _mm256_loadu_ps((simsimd_f32_t const *)(b_pairs + idx_pairs));
// __m256 a_shuffled = _mm256_permutevar8x32_ps(a_vec, permute_vec);
// __m256 b_shuffled = _mm256_permutevar8x32_ps(b_vec, permute_vec);
// __m128 a_real_vec = _mm256_extractf128_ps(a_shuffled, 0);
// __m128 a_imag_vec = _mm256_extractf128_ps(a_shuffled, 1);
// __m128 b_real_vec = _mm256_extractf128_ps(b_shuffled, 0);
// __m128 b_imag_vec = _mm256_extractf128_ps(b_shuffled, 1);
// ab_real_vec = _mm_fmadd_ps(a_real_vec, b_real_vec, ab_real_vec);
// ab_real_vec = _mm_fnmadd_ps(a_imag_vec, b_imag_vec, ab_real_vec);
// ab_imag_vec = _mm_fmadd_ps(a_real_vec, b_imag_vec, ab_imag_vec);
// ab_imag_vec = _mm_fmadd_ps(a_imag_vec, b_real_vec, ab_imag_vec);
// }
//
// Instead, we take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors. Moreover, `XOR` can be placed after the primary loop.
// Both operations are quite cheap, and the throughput doubles from 2.5 GB/s to 5 GB/s.
__m256 ab_real_vec = _mm256_setzero_ps();
__m256 ab_imag_vec = _mm256_setzero_ps();
__m256i sign_flip_vec = _mm256_set1_epi64x(0x8000000000000000);
__m256i swap_adjacent_vec = _mm256_set_epi8( //
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4, // Points to the second f32 in 128-bit lane
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4 // Points to the second f32 in 128-bit lane
);
simsimd_size_t idx_pairs = 0;
for (; idx_pairs + 4 <= count_pairs; idx_pairs += 4) {
__m256 a_vec = _mm256_loadu_ps((simsimd_f32_t const *)(a_pairs + idx_pairs));
__m256 b_vec = _mm256_loadu_ps((simsimd_f32_t const *)(b_pairs + idx_pairs));
__m256 b_swapped_vec = _mm256_castsi256_ps(_mm256_shuffle_epi8(_mm256_castps_si256(b_vec), swap_adjacent_vec));
ab_real_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_real_vec);
ab_imag_vec = _mm256_fmadd_ps(a_vec, b_swapped_vec, ab_imag_vec);
}
// Flip the sign bit in every second scalar before accumulation:
ab_real_vec = _mm256_castsi256_ps(_mm256_xor_si256(_mm256_castps_si256(ab_real_vec), sign_flip_vec));
// Reduce horizontal sums:
simsimd_distance_t ab_real = _simsimd_reduce_f32x8_haswell(ab_real_vec);
simsimd_distance_t ab_imag = _simsimd_reduce_f32x8_haswell(ab_imag_vec);
// Handle the tail:
for (; idx_pairs != count_pairs; ++idx_pairs) {
simsimd_f32c_t a_pair = a_pairs[idx_pairs], b_pair = b_pairs[idx_pairs];
simsimd_f32_t ar = a_pair.real, ai = a_pair.imag, br = b_pair.real, bi = b_pair.imag;
ab_real += ar * br - ai * bi;
ab_imag += ar * bi + ai * br;
}
results[0] = ab_real;
results[1] = ab_imag;
}
SIMSIMD_PUBLIC void simsimd_vdot_f32c_haswell(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m256 ab_real_vec = _mm256_setzero_ps();
__m256 ab_imag_vec = _mm256_setzero_ps();
__m256i sign_flip_vec = _mm256_set1_epi64x(0x8000000000000000);
__m256i swap_adjacent_vec = _mm256_set_epi8( //
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4, // Points to the second f32 in 128-bit lane
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4 // Points to the second f32 in 128-bit lane
);
simsimd_size_t idx_pairs = 0;
for (; idx_pairs + 4 <= count_pairs; idx_pairs += 4) {
__m256 a_vec = _mm256_loadu_ps((simsimd_f32_t const *)(a_pairs + idx_pairs));
__m256 b_vec = _mm256_loadu_ps((simsimd_f32_t const *)(b_pairs + idx_pairs));
ab_real_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_real_vec);
b_vec = _mm256_castsi256_ps(_mm256_shuffle_epi8(_mm256_castps_si256(b_vec), swap_adjacent_vec));
ab_imag_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_imag_vec);
}
// Flip the sign bit in every second scalar before accumulation:
ab_imag_vec = _mm256_castsi256_ps(_mm256_xor_si256(_mm256_castps_si256(ab_imag_vec), sign_flip_vec));
// Reduce horizontal sums:
simsimd_distance_t ab_real = _simsimd_reduce_f32x8_haswell(ab_real_vec);
simsimd_distance_t ab_imag = _simsimd_reduce_f32x8_haswell(ab_imag_vec);
// Handle the tail:
for (; idx_pairs != count_pairs; ++idx_pairs) {
simsimd_f32c_t a_pair = a_pairs[idx_pairs], b_pair = b_pairs[idx_pairs];
simsimd_f32_t ar = a_pair.real, ai = a_pair.imag, br = b_pair.real, bi = b_pair.imag;
ab_real += ar * br + ai * bi;
ab_imag += ar * bi - ai * br;
}
results[0] = ab_real;
results[1] = ab_imag;
}
SIMSIMD_INTERNAL __m256 _simsimd_partial_load_f16x8_haswell(simsimd_f16_t const *a, simsimd_size_t n) {
// In case the software emulation for `f16` scalars is enabled, the `simsimd_f16_to_f32`
// function will run. It is extremely slow, so even for the tail, let's combine serial
// loads and stores with vectorized math.
union {
__m128i vec;
simsimd_f16_t scalars[8];
} result;
simsimd_size_t i = 0;
for (; i < n; ++i) result.scalars[i] = a[i];
for (; i < 8; ++i) result.scalars[i] = 0;
return _mm256_cvtph_ps(result.vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f16_haswell(simsimd_f16_t const *a_scalars, simsimd_f16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m256 a_vec, b_vec;
__m256 ab_vec = _mm256_setzero_ps();
simsimd_dot_f16_haswell_cycle:
if (count_scalars < 8) {
a_vec = _simsimd_partial_load_f16x8_haswell(a_scalars, count_scalars);
b_vec = _simsimd_partial_load_f16x8_haswell(b_scalars, count_scalars);
count_scalars = 0;
}
else {
a_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)a_scalars));
b_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)b_scalars));
count_scalars -= 8, a_scalars += 8, b_scalars += 8;
}
// We can silence the NaNs using blends:
//
// __m256 a_is_nan = _mm256_cmp_ps(a_vec, a_vec, _CMP_UNORD_Q);
// __m256 b_is_nan = _mm256_cmp_ps(b_vec, b_vec, _CMP_UNORD_Q);
// ab_vec = _mm256_blendv_ps(_mm256_fmadd_ps(a_vec, b_vec, ab_vec), ab_vec, _mm256_or_ps(a_is_nan, b_is_nan));
//
ab_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_vec);
if (count_scalars) goto simsimd_dot_f16_haswell_cycle;
*result = _simsimd_reduce_f32x8_haswell(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f16c_haswell(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// Ideally the implementation would load 256 bits worth of vector data at a time,
// shuffle those within a register, split in halfs, and only then upcast.
// That way, we are stepping through 32x 16-bit vector components at a time, or 16 dimensions.
// Sadly, shuffling 16-bit entries in a YMM register is hard to implement efficiently.
//
// Simpler approach is to load 128 bits at a time, upcast, and then shuffle.
// This mostly replicates the `simsimd_dot_f32c_haswell`.
__m256 ab_real_vec = _mm256_setzero_ps();
__m256 ab_imag_vec = _mm256_setzero_ps();
__m256i sign_flip_vec = _mm256_set1_epi64x(0x8000000000000000);
__m256i swap_adjacent_vec = _mm256_set_epi8( //
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4, // Points to the second f32 in 128-bit lane
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4 // Points to the second f32 in 128-bit lane
);
while (count_pairs >= 4) {
__m256 a_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)a_pairs));
__m256 b_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)b_pairs));
__m256 b_swapped_vec = _mm256_castsi256_ps(_mm256_shuffle_epi8(_mm256_castps_si256(b_vec), swap_adjacent_vec));
ab_real_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_real_vec);
ab_imag_vec = _mm256_fmadd_ps(a_vec, b_swapped_vec, ab_imag_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Flip the sign bit in every second scalar before accumulation:
ab_real_vec = _mm256_castsi256_ps(_mm256_xor_si256(_mm256_castps_si256(ab_real_vec), sign_flip_vec));
// Reduce horizontal sums and aggregate with the tail:
simsimd_dot_f16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += _simsimd_reduce_f32x8_haswell(ab_real_vec);
results[1] += _simsimd_reduce_f32x8_haswell(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f16c_haswell(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
// Ideally the implementation would load 256 bits worth of vector data at a time,
// shuffle those within a register, split in halfs, and only then upcast.
// That way, we are stepping through 32x 16-bit vector components at a time, or 16 dimensions.
// Sadly, shuffling 16-bit entries in a YMM register is hard to implement efficiently.
//
// Simpler approach is to load 128 bits at a time, upcast, and then shuffle.
// This mostly replicates the `simsimd_vdot_f32c_haswell`.
__m256 ab_real_vec = _mm256_setzero_ps();
__m256 ab_imag_vec = _mm256_setzero_ps();
__m256i sign_flip_vec = _mm256_set1_epi64x(0x8000000000000000);
__m256i swap_adjacent_vec = _mm256_set_epi8( //
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4, // Points to the second f32 in 128-bit lane
11, 10, 9, 8, // Points to the third f32 in 128-bit lane
15, 14, 13, 12, // Points to the fourth f32 in 128-bit lane
3, 2, 1, 0, // Points to the first f32 in 128-bit lane
7, 6, 5, 4 // Points to the second f32 in 128-bit lane
);
while (count_pairs >= 4) {
__m256 a_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)a_pairs));
__m256 b_vec = _mm256_cvtph_ps(_mm_lddqu_si128((__m128i const *)b_pairs));
ab_real_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_real_vec);
b_vec = _mm256_castsi256_ps(_mm256_shuffle_epi8(_mm256_castps_si256(b_vec), swap_adjacent_vec));
ab_imag_vec = _mm256_fmadd_ps(a_vec, b_vec, ab_imag_vec);
count_pairs -= 4, a_pairs += 4, b_pairs += 4;
}
// Flip the sign bit in every second scalar before accumulation:
ab_imag_vec = _mm256_castsi256_ps(_mm256_xor_si256(_mm256_castps_si256(ab_imag_vec), sign_flip_vec));
// Reduce horizontal sums and aggregate with the tail:
simsimd_dot_f16c_serial(a_pairs, b_pairs, count_pairs, results);
results[0] += _simsimd_reduce_f32x8_haswell(ab_real_vec);
results[1] += _simsimd_reduce_f32x8_haswell(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_i8_haswell(simsimd_i8_t const *a_scalars, simsimd_i8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m256i ab_i32_low_vec = _mm256_setzero_si256();
__m256i ab_i32_high_vec = _mm256_setzero_si256();
// AVX2 has no instructions for 8-bit signed integer dot-products,
// but it has a weird instruction for mixed signed-unsigned 8-bit dot-product.
// So we need to normalize the first vector to its absolute value,
// and shift the product sign into the second vector.
//
// __m256i a_i8_abs_vec = _mm256_abs_epi8(a_i8_vec);
// __m256i b_i8_flipped_vec = _mm256_sign_epi8(b_i8_vec, a_i8_vec);
// __m256i ab_i16_vec = _mm256_maddubs_epi16(a_i8_abs_vec, b_i8_flipped_vec);
//
// The problem with this approach, however, is the `-128` value in the second vector.
// Flipping its sign will do nothing, and the result will be incorrect.
// This can easily lead to noticeable numerical errors in the final result.
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 32 <= count_scalars; idx_scalars += 32) {
__m256i a_i8_vec = _mm256_lddqu_si256((__m256i const *)(a_scalars + idx_scalars));
__m256i b_i8_vec = _mm256_lddqu_si256((__m256i const *)(b_scalars + idx_scalars));
// Upcast `int8` to `int16`
__m256i a_i16_low_vec = _mm256_cvtepi8_epi16(_mm256_extracti128_si256(a_i8_vec, 0));
__m256i a_i16_high_vec = _mm256_cvtepi8_epi16(_mm256_extracti128_si256(a_i8_vec, 1));
__m256i b_i16_low_vec = _mm256_cvtepi8_epi16(_mm256_extracti128_si256(b_i8_vec, 0));
__m256i b_i16_high_vec = _mm256_cvtepi8_epi16(_mm256_extracti128_si256(b_i8_vec, 1));
// Multiply and accumulate at `int16` level, accumulate at `int32` level
ab_i32_low_vec = _mm256_add_epi32(ab_i32_low_vec, _mm256_madd_epi16(a_i16_low_vec, b_i16_low_vec));
ab_i32_high_vec = _mm256_add_epi32(ab_i32_high_vec, _mm256_madd_epi16(a_i16_high_vec, b_i16_high_vec));
}
// Horizontal sum across the 256-bit register
int ab = _simsimd_reduce_i32x8_haswell(_mm256_add_epi32(ab_i32_low_vec, ab_i32_high_vec));
// Take care of the tail:
for (; idx_scalars < count_scalars; ++idx_scalars) ab += (int)(a_scalars[idx_scalars]) * b_scalars[idx_scalars];
*result = ab;
}
SIMSIMD_PUBLIC void simsimd_dot_u8_haswell(simsimd_u8_t const *a_scalars, simsimd_u8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m256i ab_i32_low_vec = _mm256_setzero_si256();
__m256i ab_i32_high_vec = _mm256_setzero_si256();
__m256i const zeros_vec = _mm256_setzero_si256();
// AVX2 has no instructions for unsigned 8-bit integer dot-products,
// but it has a weird instruction for mixed signed-unsigned 8-bit dot-product.
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 32 <= count_scalars; idx_scalars += 32) {
__m256i a_u8_vec = _mm256_lddqu_si256((__m256i const *)(a_scalars + idx_scalars));
__m256i b_u8_vec = _mm256_lddqu_si256((__m256i const *)(b_scalars + idx_scalars));
// Upcast `uint8` to `int16`. Unlike the signed version, we can use the unpacking
// instructions instead of extracts, as they are much faster and more efficient.
__m256i a_i16_low_vec = _mm256_unpacklo_epi8(a_u8_vec, zeros_vec);
__m256i a_i16_high_vec = _mm256_unpackhi_epi8(a_u8_vec, zeros_vec);
__m256i b_i16_low_vec = _mm256_unpacklo_epi8(b_u8_vec, zeros_vec);
__m256i b_i16_high_vec = _mm256_unpackhi_epi8(b_u8_vec, zeros_vec);
// Multiply and accumulate at `int16` level, accumulate at `int32` level
ab_i32_low_vec = _mm256_add_epi32(ab_i32_low_vec, _mm256_madd_epi16(a_i16_low_vec, b_i16_low_vec));
ab_i32_high_vec = _mm256_add_epi32(ab_i32_high_vec, _mm256_madd_epi16(a_i16_high_vec, b_i16_high_vec));
}
// Horizontal sum across the 256-bit register
int ab = _simsimd_reduce_i32x8_haswell(_mm256_add_epi32(ab_i32_low_vec, ab_i32_high_vec));
// Take care of the tail:
for (; idx_scalars < count_scalars; ++idx_scalars) ab += (int)(a_scalars[idx_scalars]) * b_scalars[idx_scalars];
*result = ab;
}
SIMSIMD_INTERNAL __m256 _simsimd_bf16x8_to_f32x8_haswell(__m128i x) {
// Upcasting from `bf16` to `f32` is done by shifting the `bf16` values by 16 bits to the left, like:
return _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_cvtepu16_epi32(x), 16));
}
SIMSIMD_INTERNAL __m128i _simsimd_f32x8_to_bf16x8_haswell(__m256 x) {
// Pack the 32-bit integers into 16-bit integers.
// This is less trivial than unpacking: https://stackoverflow.com/a/77781241/2766161
// The best approach is to shuffle within lanes first: https://stackoverflow.com/a/49723746/2766161
// Our shuffling mask will drop the low 2-bytes from every 4-byte word.
__m256i trunc_elements = _mm256_shuffle_epi8( //
_mm256_castps_si256(x), //
_mm256_set_epi8( //
-1, -1, -1, -1, -1, -1, -1, -1, 15, 14, 11, 10, 7, 6, 3, 2, //
-1, -1, -1, -1, -1, -1, -1, -1, 15, 14, 11, 10, 7, 6, 3, 2 //
));
__m256i ordered = _mm256_permute4x64_epi64(trunc_elements, 0x58);
__m128i result = _mm256_castsi256_si128(ordered);
return result;
}
SIMSIMD_INTERNAL __m128i _simsimd_partial_load_bf16x8_haswell(simsimd_bf16_t const *a, simsimd_size_t n) {
// In case the software emulation for `bf16` scalars is enabled, the `simsimd_bf16_to_f32`
// function will run. It is extremely slow, so even for the tail, let's combine serial
// loads and stores with vectorized math.
union {
__m128i vec;
simsimd_bf16_t scalars[8];
} result;
simsimd_size_t i = 0;
for (; i < n; ++i) result.scalars[i] = a[i];
for (; i < 8; ++i) result.scalars[i] = 0;
return result.vec;
}
SIMSIMD_PUBLIC void simsimd_dot_bf16_haswell(simsimd_bf16_t const *a_scalars, simsimd_bf16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m128i a_vec, b_vec;
__m256 ab_vec = _mm256_setzero_ps();
simsimd_dot_bf16_haswell_cycle:
if (count_scalars < 8) {
a_vec = _simsimd_partial_load_bf16x8_haswell(a_scalars, count_scalars);
b_vec = _simsimd_partial_load_bf16x8_haswell(b_scalars, count_scalars);
count_scalars = 0;
}
else {
a_vec = _mm_lddqu_si128((__m128i const *)a_scalars);
b_vec = _mm_lddqu_si128((__m128i const *)b_scalars);
a_scalars += 8, b_scalars += 8, count_scalars -= 8;
}
ab_vec = _mm256_fmadd_ps(_simsimd_bf16x8_to_f32x8_haswell(a_vec), _simsimd_bf16x8_to_f32x8_haswell(b_vec), ab_vec);
if (count_scalars) goto simsimd_dot_bf16_haswell_cycle;
*result = _simsimd_reduce_f32x8_haswell(ab_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_HASWELL
#if SIMSIMD_TARGET_SKYLAKE
#pragma GCC push_options
#pragma GCC target("avx2", "avx512f", "avx512vl", "avx512bw", "bmi2")
#pragma clang attribute push(__attribute__((target("avx2,avx512f,avx512vl,avx512bw,bmi2"))), apply_to = function)
SIMSIMD_INTERNAL simsimd_f64_t _simsimd_reduce_f32x16_skylake(__m512 a) {
__m512 x = _mm512_add_ps(a, _mm512_shuffle_f32x4(a, a, _MM_SHUFFLE(0, 0, 3, 2)));
__m128 r = _mm512_castps512_ps128(_mm512_add_ps(x, _mm512_shuffle_f32x4(x, x, _MM_SHUFFLE(0, 0, 0, 1))));
r = _mm_hadd_ps(r, r);
return _mm_cvtss_f32(_mm_hadd_ps(r, r));
}
SIMSIMD_INTERNAL __m512 _simsimd_bf16x16_to_f32x16_skylake(__m256i a) {
// Upcasting from `bf16` to `f32` is done by shifting the `bf16` values by 16 bits to the left, like:
return _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_cvtepu16_epi32(a), 16));
}
SIMSIMD_INTERNAL __m256i _simsimd_f32x16_to_bf16x16_skylake(__m512 a) {
// Add 2^15 and right shift 16 to do round-nearest
__m512i x = _mm512_srli_epi32(_mm512_add_epi32(_mm512_castps_si512(a), _mm512_set1_epi32(1 << 15)), 16);
return _mm512_cvtepi32_epi16(x);
}
SIMSIMD_PUBLIC void simsimd_dot_f32_skylake(simsimd_f32_t const *a_scalars, simsimd_f32_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512 a_vec, b_vec;
__m512 ab_vec = _mm512_setzero();
simsimd_dot_f32_skylake_cycle:
if (count_scalars < 16) {
__mmask16 mask = (__mmask16)_bzhi_u32(0xFFFFFFFF, count_scalars);
a_vec = _mm512_maskz_loadu_ps(mask, a_scalars);
b_vec = _mm512_maskz_loadu_ps(mask, b_scalars);
count_scalars = 0;
}
else {
a_vec = _mm512_loadu_ps(a_scalars);
b_vec = _mm512_loadu_ps(b_scalars);
a_scalars += 16, b_scalars += 16, count_scalars -= 16;
}
ab_vec = _mm512_fmadd_ps(a_vec, b_vec, ab_vec);
if (count_scalars) goto simsimd_dot_f32_skylake_cycle;
*result = _simsimd_reduce_f32x16_skylake(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f64_skylake(simsimd_f64_t const *a_scalars, simsimd_f64_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512d a_vec, b_vec;
__m512d ab_vec = _mm512_setzero_pd();
simsimd_dot_f64_skylake_cycle:
if (count_scalars < 8) {
__mmask8 mask = (__mmask8)_bzhi_u32(0xFFFFFFFF, count_scalars);
a_vec = _mm512_maskz_loadu_pd(mask, a_scalars);
b_vec = _mm512_maskz_loadu_pd(mask, b_scalars);
count_scalars = 0;
}
else {
a_vec = _mm512_loadu_pd(a_scalars);
b_vec = _mm512_loadu_pd(b_scalars);
a_scalars += 8, b_scalars += 8, count_scalars -= 8;
}
ab_vec = _mm512_fmadd_pd(a_vec, b_vec, ab_vec);
if (count_scalars) goto simsimd_dot_f64_skylake_cycle;
*result = _mm512_reduce_add_pd(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f32c_skylake(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512 a_vec, b_vec;
__m512 ab_real_vec = _mm512_setzero();
__m512 ab_imag_vec = _mm512_setzero();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi64(0x8000000000000000);
simsimd_dot_f32c_skylake_cycle:
if (count_pairs < 8) {
__mmask16 mask = (__mmask16)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_ps(mask, a_pairs);
b_vec = _mm512_maskz_loadu_ps(mask, b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_ps(a_pairs);
b_vec = _mm512_loadu_ps(b_pairs);
a_pairs += 8, b_pairs += 8, count_pairs -= 8;
}
ab_real_vec = _mm512_fmadd_ps(b_vec, a_vec, ab_real_vec);
b_vec = _mm512_permute_ps(b_vec, 0xB1); //? Swap adjacent entries within each pair
ab_imag_vec = _mm512_fmadd_ps(b_vec, a_vec, ab_imag_vec);
if (count_pairs) goto simsimd_dot_f32c_skylake_cycle;
// Flip the sign bit in every second scalar before accumulation:
ab_real_vec = _mm512_castsi512_ps(_mm512_xor_si512(_mm512_castps_si512(ab_real_vec), sign_flip_vec));
// Reduce horizontal sums:
results[0] = _simsimd_reduce_f32x16_skylake(ab_real_vec);
results[1] = _simsimd_reduce_f32x16_skylake(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f32c_skylake(simsimd_f32c_t const *a_pairs, simsimd_f32c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512 a_vec, b_vec;
__m512 ab_real_vec = _mm512_setzero();
__m512 ab_imag_vec = _mm512_setzero();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi64(0x8000000000000000);
__m512i const swap_adjacent_vec = _mm512_set_epi8( //
59, 58, 57, 56, 63, 62, 61, 60, 51, 50, 49, 48, 55, 54, 53, 52, // 4th 128-bit lane
43, 42, 41, 40, 47, 46, 45, 44, 35, 34, 33, 32, 39, 38, 37, 36, // 3rd 128-bit lane
27, 26, 25, 24, 31, 30, 29, 28, 19, 18, 17, 16, 23, 22, 21, 20, // 2nd 128-bit lane
11, 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4 // 1st 128-bit lane
);
simsimd_vdot_f32c_skylake_cycle:
if (count_pairs < 8) {
__mmask16 mask = (__mmask16)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_ps(mask, (simsimd_f32_t const *)a_pairs);
b_vec = _mm512_maskz_loadu_ps(mask, (simsimd_f32_t const *)b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_ps((simsimd_f32_t const *)a_pairs);
b_vec = _mm512_loadu_ps((simsimd_f32_t const *)b_pairs);
a_pairs += 8, b_pairs += 8, count_pairs -= 8;
}
ab_real_vec = _mm512_fmadd_ps(a_vec, b_vec, ab_real_vec);
b_vec = _mm512_permute_ps(b_vec, 0xB1); //? Swap adjacent entries within each pair
ab_imag_vec = _mm512_fmadd_ps(a_vec, b_vec, ab_imag_vec);
if (count_pairs) goto simsimd_vdot_f32c_skylake_cycle;
// Flip the sign bit in every second scalar before accumulation:
ab_imag_vec = _mm512_castsi512_ps(_mm512_xor_si512(_mm512_castps_si512(ab_imag_vec), sign_flip_vec));
// Reduce horizontal sums:
results[0] = _simsimd_reduce_f32x16_skylake(ab_real_vec);
results[1] = _simsimd_reduce_f32x16_skylake(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f64c_skylake(simsimd_f64c_t const *a_pairs, simsimd_f64c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512d a_vec, b_vec;
__m512d ab_real_vec = _mm512_setzero_pd();
__m512d ab_imag_vec = _mm512_setzero_pd();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set_epi64( //
0x8000000000000000, 0x0000000000000000, 0x8000000000000000, 0x0000000000000000, //
0x8000000000000000, 0x0000000000000000, 0x8000000000000000, 0x0000000000000000 //
);
simsimd_dot_f64c_skylake_cycle:
if (count_pairs < 4) {
__mmask8 mask = (__mmask8)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_pd(mask, a_pairs);
b_vec = _mm512_maskz_loadu_pd(mask, b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_pd(a_pairs);
b_vec = _mm512_loadu_pd(b_pairs);
a_pairs += 4, b_pairs += 4, count_pairs -= 4;
}
ab_real_vec = _mm512_fmadd_pd(b_vec, a_vec, ab_real_vec);
b_vec = _mm512_permute_pd(b_vec, 0x55); //? Same as 0b01010101.
ab_imag_vec = _mm512_fmadd_pd(b_vec, a_vec, ab_imag_vec);
if (count_pairs) goto simsimd_dot_f64c_skylake_cycle;
// Flip the sign bit in every second scalar before accumulation:
ab_real_vec = _mm512_castsi512_pd(_mm512_xor_si512(_mm512_castpd_si512(ab_real_vec), sign_flip_vec));
// Reduce horizontal sums:
results[0] = _mm512_reduce_add_pd(ab_real_vec);
results[1] = _mm512_reduce_add_pd(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f64c_skylake(simsimd_f64c_t const *a_pairs, simsimd_f64c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512d a_vec, b_vec;
__m512d ab_real_vec = _mm512_setzero_pd();
__m512d ab_imag_vec = _mm512_setzero_pd();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set_epi64( //
0x8000000000000000, 0x0000000000000000, 0x8000000000000000, 0x0000000000000000, //
0x8000000000000000, 0x0000000000000000, 0x8000000000000000, 0x0000000000000000 //
);
simsimd_vdot_f64c_skylake_cycle:
if (count_pairs < 4) {
__mmask8 mask = (__mmask8)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_pd(mask, (simsimd_f32_t const *)a_pairs);
b_vec = _mm512_maskz_loadu_pd(mask, (simsimd_f32_t const *)b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_pd((simsimd_f32_t const *)a_pairs);
b_vec = _mm512_loadu_pd((simsimd_f32_t const *)b_pairs);
a_pairs += 4, b_pairs += 4, count_pairs -= 4;
}
ab_real_vec = _mm512_fmadd_pd(a_vec, b_vec, ab_real_vec);
b_vec = _mm512_permute_pd(b_vec, 0x55); //? Same as 0b01010101.
ab_imag_vec = _mm512_fmadd_pd(a_vec, b_vec, ab_imag_vec);
if (count_pairs) goto simsimd_vdot_f64c_skylake_cycle;
// Flip the sign bit in every second scalar before accumulation:
ab_imag_vec = _mm512_castsi512_pd(_mm512_xor_si512(_mm512_castpd_si512(ab_imag_vec), sign_flip_vec));
// Reduce horizontal sums:
results[0] = _mm512_reduce_add_pd(ab_real_vec);
results[1] = _mm512_reduce_add_pd(ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_SKYLAKE
#if SIMSIMD_TARGET_GENOA
#pragma GCC push_options
#pragma GCC target("avx2", "avx512f", "avx512vl", "bmi2", "avx512bw", "avx512bf16")
#pragma clang attribute push(__attribute__((target("avx2,avx512f,avx512vl,bmi2,avx512bw,avx512bf16"))), \
apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_bf16_genoa(simsimd_bf16_t const *a_scalars, simsimd_bf16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512i a_i16_vec, b_i16_vec;
__m512 ab_vec = _mm512_setzero_ps();
simsimd_dot_bf16_genoa_cycle:
if (count_scalars < 32) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_scalars);
a_i16_vec = _mm512_maskz_loadu_epi16(mask, a_scalars);
b_i16_vec = _mm512_maskz_loadu_epi16(mask, b_scalars);
count_scalars = 0;
}
else {
a_i16_vec = _mm512_loadu_epi16(a_scalars);
b_i16_vec = _mm512_loadu_epi16(b_scalars);
a_scalars += 32, b_scalars += 32, count_scalars -= 32;
}
ab_vec = _mm512_dpbf16_ps(ab_vec, (__m512bh)(a_i16_vec), (__m512bh)(b_i16_vec));
if (count_scalars) goto simsimd_dot_bf16_genoa_cycle;
*result = _simsimd_reduce_f32x16_skylake(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_bf16c_genoa(simsimd_bf16c_t const *a_pairs, simsimd_bf16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512i a_vec, b_vec;
__m512 ab_real_vec = _mm512_setzero_ps();
__m512 ab_imag_vec = _mm512_setzero_ps();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi32(0x80000000);
__m512i const swap_adjacent_vec = _mm512_set_epi8( //
61, 60, 63, 62, 57, 56, 59, 58, 53, 52, 55, 54, 49, 48, 51, 50, // 4th 128-bit lane
45, 44, 47, 46, 41, 40, 43, 42, 37, 36, 39, 38, 33, 32, 35, 34, // 3rd 128-bit lane
29, 28, 31, 30, 25, 24, 27, 26, 21, 20, 23, 22, 17, 16, 19, 18, // 2nd 128-bit lane
13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2 // 1st 128-bit lane
);
simsimd_dot_bf16c_genoa_cycle:
if (count_pairs < 16) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_epi16(mask, (simsimd_i16_t const *)a_pairs);
b_vec = _mm512_maskz_loadu_epi16(mask, (simsimd_i16_t const *)b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_epi16((simsimd_i16_t const *)a_pairs);
b_vec = _mm512_loadu_epi16((simsimd_i16_t const *)b_pairs);
a_pairs += 16, b_pairs += 16, count_pairs -= 16;
}
ab_real_vec = _mm512_dpbf16_ps(ab_real_vec, (__m512bh)(_mm512_xor_si512(b_vec, sign_flip_vec)), (__m512bh)(a_vec));
ab_imag_vec =
_mm512_dpbf16_ps(ab_imag_vec, (__m512bh)(_mm512_shuffle_epi8(b_vec, swap_adjacent_vec)), (__m512bh)(a_vec));
if (count_pairs) goto simsimd_dot_bf16c_genoa_cycle;
// Reduce horizontal sums:
results[0] = _simsimd_reduce_f32x16_skylake(ab_real_vec);
results[1] = _simsimd_reduce_f32x16_skylake(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_bf16c_genoa(simsimd_bf16c_t const *a_pairs, simsimd_bf16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512i a_vec, b_vec;
__m512 ab_real_vec = _mm512_setzero_ps();
__m512 ab_imag_vec = _mm512_setzero_ps();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi32(0x80000000);
__m512i const swap_adjacent_vec = _mm512_set_epi8( //
61, 60, 63, 62, 57, 56, 59, 58, 53, 52, 55, 54, 49, 48, 51, 50, // 4th 128-bit lane
45, 44, 47, 46, 41, 40, 43, 42, 37, 36, 39, 38, 33, 32, 35, 34, // 3rd 128-bit lane
29, 28, 31, 30, 25, 24, 27, 26, 21, 20, 23, 22, 17, 16, 19, 18, // 2nd 128-bit lane
13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2 // 1st 128-bit lane
);
simsimd_dot_bf16c_genoa_cycle:
if (count_pairs < 16) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_epi16(mask, (simsimd_i16_t const *)a_pairs);
b_vec = _mm512_maskz_loadu_epi16(mask, (simsimd_i16_t const *)b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_epi16((simsimd_i16_t const *)a_pairs);
b_vec = _mm512_loadu_epi16((simsimd_i16_t const *)b_pairs);
a_pairs += 16, b_pairs += 16, count_pairs -= 16;
}
ab_real_vec = _mm512_dpbf16_ps(ab_real_vec, (__m512bh)(a_vec), (__m512bh)(b_vec));
a_vec = _mm512_xor_si512(a_vec, sign_flip_vec);
b_vec = _mm512_shuffle_epi8(b_vec, swap_adjacent_vec);
ab_imag_vec = _mm512_dpbf16_ps(ab_imag_vec, (__m512bh)(a_vec), (__m512bh)(b_vec));
if (count_pairs) goto simsimd_dot_bf16c_genoa_cycle;
// Reduce horizontal sums:
results[0] = _simsimd_reduce_f32x16_skylake(ab_real_vec);
results[1] = _simsimd_reduce_f32x16_skylake(ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_GENOA
#if SIMSIMD_TARGET_SAPPHIRE
#pragma GCC push_options
#pragma GCC target("avx2", "avx512f", "avx512vl", "bmi2", "avx512bw", "avx512fp16")
#pragma clang attribute push(__attribute__((target("avx2,avx512f,avx512vl,bmi2,avx512bw,avx512fp16"))), \
apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_f16_sapphire(simsimd_f16_t const *a_scalars, simsimd_f16_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512i a_i16_vec, b_i16_vec;
__m512h ab_vec = _mm512_setzero_ph();
simsimd_dot_f16_sapphire_cycle:
if (count_scalars < 32) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_scalars);
a_i16_vec = _mm512_maskz_loadu_epi16(mask, a_scalars);
b_i16_vec = _mm512_maskz_loadu_epi16(mask, b_scalars);
count_scalars = 0;
}
else {
a_i16_vec = _mm512_loadu_epi16(a_scalars);
b_i16_vec = _mm512_loadu_epi16(b_scalars);
a_scalars += 32, b_scalars += 32, count_scalars -= 32;
}
ab_vec = _mm512_fmadd_ph(_mm512_castsi512_ph(a_i16_vec), _mm512_castsi512_ph(b_i16_vec), ab_vec);
if (count_scalars) goto simsimd_dot_f16_sapphire_cycle;
*result = _mm512_reduce_add_ph(ab_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_f16c_sapphire(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512i a_vec, b_vec;
__m512h ab_real_vec = _mm512_setzero_ph();
__m512h ab_imag_vec = _mm512_setzero_ph();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi32(0x80000000);
__m512i const swap_adjacent_vec = _mm512_set_epi8( //
61, 60, 63, 62, 57, 56, 59, 58, 53, 52, 55, 54, 49, 48, 51, 50, // 4th 128-bit lane
45, 44, 47, 46, 41, 40, 43, 42, 37, 36, 39, 38, 33, 32, 35, 34, // 3rd 128-bit lane
29, 28, 31, 30, 25, 24, 27, 26, 21, 20, 23, 22, 17, 16, 19, 18, // 2nd 128-bit lane
13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2 // 1st 128-bit lane
);
simsimd_dot_f16c_sapphire_cycle:
if (count_pairs < 16) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_epi16(mask, a_pairs);
b_vec = _mm512_maskz_loadu_epi16(mask, b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_epi16(a_pairs);
b_vec = _mm512_loadu_epi16(b_pairs);
a_pairs += 16, b_pairs += 16, count_pairs -= 16;
}
// TODO: Consider using `_mm512_fmaddsub` and `_mm512_fcmadd_pch`
ab_real_vec = _mm512_fmadd_ph(_mm512_castsi512_ph(_mm512_xor_si512(b_vec, sign_flip_vec)),
_mm512_castsi512_ph(a_vec), ab_real_vec);
ab_imag_vec = _mm512_fmadd_ph(_mm512_castsi512_ph(_mm512_shuffle_epi8(b_vec, swap_adjacent_vec)),
_mm512_castsi512_ph(a_vec), ab_imag_vec);
if (count_pairs) goto simsimd_dot_f16c_sapphire_cycle;
// Reduce horizontal sums:
// TODO: Optimize this with tree-like reductions
results[0] = _mm512_reduce_add_ph(ab_real_vec);
results[1] = _mm512_reduce_add_ph(ab_imag_vec);
}
SIMSIMD_PUBLIC void simsimd_vdot_f16c_sapphire(simsimd_f16c_t const *a_pairs, simsimd_f16c_t const *b_pairs,
simsimd_size_t count_pairs, simsimd_distance_t *results) {
__m512i a_vec, b_vec;
__m512h ab_real_vec = _mm512_setzero_ph();
__m512h ab_imag_vec = _mm512_setzero_ph();
// We take into account, that FMS is the same as FMA with a negative multiplier.
// To multiply a floating-point value by -1, we can use the `XOR` instruction to flip the sign bit.
// This way we can avoid the shuffling and the need for separate real and imaginary parts.
// For the imaginary part of the product, we would need to swap the real and imaginary parts of
// one of the vectors.
__m512i const sign_flip_vec = _mm512_set1_epi32(0x80000000);
__m512i const swap_adjacent_vec = _mm512_set_epi8( //
61, 60, 63, 62, 57, 56, 59, 58, 53, 52, 55, 54, 49, 48, 51, 50, // 4th 128-bit lane
45, 44, 47, 46, 41, 40, 43, 42, 37, 36, 39, 38, 33, 32, 35, 34, // 3rd 128-bit lane
29, 28, 31, 30, 25, 24, 27, 26, 21, 20, 23, 22, 17, 16, 19, 18, // 2nd 128-bit lane
13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2 // 1st 128-bit lane
);
simsimd_dot_f16c_sapphire_cycle:
if (count_pairs < 16) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_pairs * 2);
a_vec = _mm512_maskz_loadu_epi16(mask, a_pairs);
b_vec = _mm512_maskz_loadu_epi16(mask, b_pairs);
count_pairs = 0;
}
else {
a_vec = _mm512_loadu_epi16(a_pairs);
b_vec = _mm512_loadu_epi16(b_pairs);
a_pairs += 16, b_pairs += 16, count_pairs -= 16;
}
// TODO: Consider using `_mm512_fmaddsub` and `_mm512_fcmadd_pch`
ab_real_vec = _mm512_fmadd_ph(_mm512_castsi512_ph(a_vec), _mm512_castsi512_ph(b_vec), ab_real_vec);
a_vec = _mm512_xor_si512(a_vec, sign_flip_vec);
b_vec = _mm512_shuffle_epi8(b_vec, swap_adjacent_vec);
ab_imag_vec = _mm512_fmadd_ph(_mm512_castsi512_ph(a_vec), _mm512_castsi512_ph(b_vec), ab_imag_vec);
if (count_pairs) goto simsimd_dot_f16c_sapphire_cycle;
// Reduce horizontal sums:
results[0] = _mm512_reduce_add_ph(ab_real_vec);
results[1] = _mm512_reduce_add_ph(ab_imag_vec);
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_SAPPHIRE
#if SIMSIMD_TARGET_ICE
#pragma GCC push_options
#pragma GCC target("avx2", "avx512f", "avx512vl", "bmi2", "avx512bw", "avx512vnni")
#pragma clang attribute push(__attribute__((target("avx2,avx512f,avx512vl,bmi2,avx512bw,avx512vnni"))), \
apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_i8_ice(simsimd_i8_t const *a_scalars, simsimd_i8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512i a_i16_vec, b_i16_vec;
__m512i ab_i32_vec = _mm512_setzero_si512();
simsimd_dot_i8_ice_cycle:
if (count_scalars < 32) {
__mmask32 mask = (__mmask32)_bzhi_u32(0xFFFFFFFF, count_scalars);
a_i16_vec = _mm512_cvtepi8_epi16(_mm256_maskz_loadu_epi8(mask, a_scalars));
b_i16_vec = _mm512_cvtepi8_epi16(_mm256_maskz_loadu_epi8(mask, b_scalars));
count_scalars = 0;
}
else {
a_i16_vec = _mm512_cvtepi8_epi16(_mm256_lddqu_si256((__m256i const *)a_scalars));
b_i16_vec = _mm512_cvtepi8_epi16(_mm256_lddqu_si256((__m256i const *)b_scalars));
a_scalars += 32, b_scalars += 32, count_scalars -= 32;
}
// Unfortunately we can't use the `_mm512_dpbusd_epi32` intrinsics here either,
// as it's asymmetric with respect to the sign of the input arguments:
// Signed(ZeroExtend16(a_scalars.byte[4*j]) * SignExtend16(b_scalars.byte[4*j]))
// So we have to use the `_mm512_dpwssd_epi32` intrinsics instead, upcasting
// to 16-bit beforehand.
ab_i32_vec = _mm512_dpwssd_epi32(ab_i32_vec, a_i16_vec, b_i16_vec);
if (count_scalars) goto simsimd_dot_i8_ice_cycle;
*result = _mm512_reduce_add_epi32(ab_i32_vec);
}
SIMSIMD_PUBLIC void simsimd_dot_u8_ice(simsimd_u8_t const *a_scalars, simsimd_u8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m512i a_u8_vec, b_u8_vec;
__m512i a_i16_low_vec, a_i16_high_vec, b_i16_low_vec, b_i16_high_vec;
__m512i ab_i32_low_vec = _mm512_setzero_si512();
__m512i ab_i32_high_vec = _mm512_setzero_si512();
__m512i const zeros_vec = _mm512_setzero_si512();
simsimd_dot_u8_ice_cycle:
if (count_scalars < 64) {
__mmask64 mask = (__mmask64)_bzhi_u64(0xFFFFFFFFFFFFFFFF, count_scalars);
a_u8_vec = _mm512_maskz_loadu_epi8(mask, a_scalars);
b_u8_vec = _mm512_maskz_loadu_epi8(mask, b_scalars);
count_scalars = 0;
}
else {
a_u8_vec = _mm512_loadu_si512(a_scalars);
b_u8_vec = _mm512_loadu_si512(b_scalars);
a_scalars += 64, b_scalars += 64, count_scalars -= 64;
}
// Upcast `uint8` to `int16`. Unlike the signed version, we can use the unpacking
// instructions instead of extracts, as they are much faster and more efficient.
a_i16_low_vec = _mm512_unpacklo_epi8(a_u8_vec, zeros_vec);
a_i16_high_vec = _mm512_unpackhi_epi8(a_u8_vec, zeros_vec);
b_i16_low_vec = _mm512_unpacklo_epi8(b_u8_vec, zeros_vec);
b_i16_high_vec = _mm512_unpackhi_epi8(b_u8_vec, zeros_vec);
// Unfortunately we can't use the `_mm512_dpbusd_epi32` intrinsics here either,
// as it's asymmetric with respect to the sign of the input arguments:
// Signed(ZeroExtend16(a.byte[4*j]) * SignExtend16(b.byte[4*j]))
// So we have to use the `_mm512_dpwssd_epi32` intrinsics instead, upcasting
// to 16-bit beforehand.
ab_i32_low_vec = _mm512_dpwssd_epi32(ab_i32_low_vec, a_i16_low_vec, b_i16_low_vec);
ab_i32_high_vec = _mm512_dpwssd_epi32(ab_i32_high_vec, a_i16_high_vec, b_i16_high_vec);
if (count_scalars) goto simsimd_dot_u8_ice_cycle;
*result = _mm512_reduce_add_epi32(_mm512_add_epi32(ab_i32_low_vec, ab_i32_high_vec));
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_ICE
#if SIMSIMD_TARGET_SIERRA
#pragma GCC push_options
#pragma GCC target("avx2", "bmi2", "avx2vnni")
#pragma clang attribute push(__attribute__((target("avx2,bmi2,avx2vnni"))), apply_to = function)
SIMSIMD_PUBLIC void simsimd_dot_i8_sierra(simsimd_i8_t const *a_scalars, simsimd_i8_t const *b_scalars,
simsimd_size_t count_scalars, simsimd_distance_t *result) {
__m256i ab_i32_vec = _mm256_setzero_si256();
simsimd_size_t idx_scalars = 0;
for (; idx_scalars + 32 <= count_scalars; idx_scalars += 32) {
__m256i a_i8_vec = _mm256_lddqu_si256((__m256i const *)(a_scalars + idx_scalars));
__m256i b_i8_vec = _mm256_lddqu_si256((__m256i const *)(b_scalars + idx_scalars));
ab_i32_vec = _mm256_dpbssds_epi32(ab_i32_vec, a_i8_vec, b_i8_vec);
}
// Further reduce to a single sum for each vector
int ab = _simsimd_reduce_i32x8_haswell(ab_i32_vec);
// Take care of the tail:
for (; idx_scalars < count_scalars; ++idx_scalars) ab += (int)(a_scalars[idx_scalars]) * b_scalars[idx_scalars];
*result = ab;
}
#pragma clang attribute pop
#pragma GCC pop_options
#endif // SIMSIMD_TARGET_SIERRA
#endif // _SIMSIMD_TARGET_X86
#ifdef __cplusplus
}
#endif
#endif
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