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Copy pathapyfixed_util.h
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1730 lines (1614 loc) · 62.5 KB
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/*
* APyFixed utility functions
*/
#ifndef _APYFIXED_UTIL_H
#define _APYFIXED_UTIL_H
#include "apytypes_common.h"
#include "apytypes_fwd.h"
#include "apytypes_intrinsics.h"
#include "apytypes_mp.h"
#include "apytypes_scratch_vector.h"
#include "apytypes_simd.h"
#include "apytypes_util.h"
#include "ieee754.h"
#include "python_util.h"
#include <algorithm>
#include <array>
#include <cassert>
#include <cstdint> // std::int64_t
#include <functional> // std::bind, std::function, std::placeholders
#include <iterator> // std::begin
#include <numeric>
#include <optional> // std::optional
#include <type_traits>
/* ********************************************************************************** *
* * Fixed-point iterator based in-place quantization with multi-limb support * *
* ********************************************************************************** */
template <typename RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_trn(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
limb_vector_asr(it_begin, it_end, -left_shift_amnt);
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_trn_inf(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (limb_vector_is_negative(it_begin, it_end)) {
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
} else { /* !limb_vector_is_negative(it_begin, it_end) */
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
apy_limb_t add_one = limb_vector_or_reduce(it_begin, it_end, bits);
std::fill(it_begin, it_end, 0);
*it_begin = add_one;
}
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_trn_zero(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (!limb_vector_is_negative(it_begin, it_end)) {
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else { /* limb_vector_is_negative(it_begin, it_end) */
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_trn_mag(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (!limb_vector_is_negative(it_begin, it_end)) {
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else { /* limb_vector_is_negative(it_begin, it_end) */
if (right_shift_amnt < unsigned(bits)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt);
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_trn_away(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (limb_vector_is_negative(it_begin, it_end)) {
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
apy_limb_t add_one = limb_vector_or_reduce(it_begin, it_end, bits);
std::fill(it_begin, it_end, 0);
*it_begin = add_one;
}
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd_zero(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_is_negative(it_begin, it_end)
|| limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd_inf(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (!limb_vector_is_negative(it_begin, it_end)
|| limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else if (right_shift_amnt == unsigned(bits)) {
if (limb_vector_is_negative(it_begin, it_end)
&& limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd_min_inf(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else if (right_shift_amnt == unsigned(bits)) {
if (limb_vector_is_negative(it_begin, it_end)
&& limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd_conv(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_test_bit(it_begin, it_end, right_shift_amnt)
|| limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_rnd_conv_odd(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (!limb_vector_test_bit(it_begin, it_end, right_shift_amnt)
|| limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1)) {
limb_vector_add_pow2(it_begin, it_end, right_shift_amnt - 1);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else if (right_shift_amnt == unsigned(bits)) {
bool fill_neg = limb_vector_is_negative(it_begin, it_end)
&& !limb_vector_or_reduce(it_begin, it_end, right_shift_amnt - 1);
std::fill(it_begin, it_end, fill_neg ? -1 : 0);
} else {
std::fill(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_jam(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
limb_vector_asr(it_begin, it_end, -left_shift_amnt);
}
limb_vector_set_bit(it_begin, it_end, 0, true);
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_jam_unbiased(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
unsigned right_shift_amnt = -left_shift_amnt;
if (right_shift_amnt < unsigned(bits)) {
if (limb_vector_or_reduce(it_begin, it_end, right_shift_amnt)) {
limb_vector_set_bit(it_begin, it_end, right_shift_amnt, true);
}
limb_vector_asr(it_begin, it_end, right_shift_amnt);
} else {
bool jam = limb_vector_or_reduce(it_begin, it_end, bits);
if (limb_vector_is_negative(it_begin, it_end)) {
std::fill(it_begin, it_end, -1);
} else {
std::fill(it_begin, it_end, 0);
}
limb_vector_set_bit(it_begin, it_end, 0, jam);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_stoch_equal(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits,
std::function<std::uint64_t()> get_random_uint64
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
auto left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
/*
* Proper 50/50 Bernoulli distribution if `GET_RANDOM_UINT64()` is uniformally
* distributed with high entropy.
*/
limb_vector_asr(it_begin, it_end, -left_shift_amnt);
if (get_random_uint64() % 2) {
limb_vector_add_pow2(it_begin, it_end, 0);
}
}
}
template <class RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void _quantize_stoch_weighted(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits,
std::function<std::uint64_t()> get_random_uint64
)
{
int frac_bits = bits - int_bits;
int new_frac_bits = new_bits - new_int_bits;
int left_shift_amnt = new_frac_bits - frac_bits;
if (left_shift_amnt >= 0) {
limb_vector_lsl(it_begin, it_end, left_shift_amnt);
} else {
std::size_t src_nlimbs = std::distance(it_begin, it_end);
unsigned bits_to_qntz = unsigned(-left_shift_amnt);
unsigned limbs_to_qntz = (bits_to_qntz - 1) / APY_LIMB_SIZE_BITS + 1;
unsigned qntz_bit_idx = bits_to_qntz % APY_LIMB_SIZE_BITS;
if (limbs_to_qntz == 1) {
// Fast path, only only limb to quantize
apy_limb_t rnd_word = get_random_uint64();
if (qntz_bit_idx) {
rnd_word &= (apy_limb_t(1) << qntz_bit_idx) - 1;
}
apy_inplace_addition_single_limb(&*it_begin, src_nlimbs, rnd_word);
limb_vector_asr(it_begin, it_end, bits_to_qntz);
} else {
// General path, can quantize infinitely many limbs
assert(limbs_to_qntz > 1);
ScratchVector<apy_limb_t> rnd_words(limbs_to_qntz);
for (auto&& rnd_word : rnd_words) {
rnd_word = get_random_uint64();
}
if (qntz_bit_idx) {
rnd_words.back() &= (apy_limb_t(1) << qntz_bit_idx) - 1;
}
apy_inplace_addition(&*it_begin, src_nlimbs, &rnd_words[0], limbs_to_qntz);
limb_vector_asr(it_begin, it_end, bits_to_qntz);
}
}
}
template <typename RANDOM_ACCESS_ITERATOR_INOUT>
static void quantize(
RANDOM_ACCESS_ITERATOR_INOUT it_begin,
RANDOM_ACCESS_ITERATOR_INOUT it_end,
int bits,
int int_bits,
int new_bits,
int new_int_bits,
QuantizationMode quantization,
std::optional<std::function<std::uint64_t()>> get_random_uint64 = std::nullopt
)
{
/*
* Note to authors trying to implement quantization modes: All the quantization
* methods (e.g., `_quantize_trn_zero()`) assumes that that the data being quantized
* has already been copied into the iterator region pointed to by `it_begin` and
* `it_end`. These set of functions simply shift the data in the iterator region
* into the correct place and performs any necessary quantization bit-fiddling.
*/
switch (quantization) {
case QuantizationMode::TRN:
_quantize_trn(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::TRN_INF:
_quantize_trn_inf(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::TRN_ZERO:
_quantize_trn_zero(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::TRN_MAG:
_quantize_trn_mag(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::TRN_AWAY:
_quantize_trn_away(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND:
_quantize_rnd(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND_ZERO:
_quantize_rnd_zero(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND_INF:
_quantize_rnd_inf(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND_MIN_INF:
_quantize_rnd_min_inf(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND_CONV:
_quantize_rnd_conv(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::RND_CONV_ODD:
_quantize_rnd_conv_odd(
it_begin, it_end, bits, int_bits, new_bits, new_int_bits
);
break;
case QuantizationMode::JAM:
_quantize_jam(it_begin, it_end, bits, int_bits, new_bits, new_int_bits);
break;
case QuantizationMode::JAM_UNBIASED:
_quantize_jam_unbiased(
it_begin, it_end, bits, int_bits, new_bits, new_int_bits
);
break;
case QuantizationMode::STOCH_EQUAL:
_quantize_stoch_equal(
it_begin, it_end, bits, int_bits, new_bits, new_int_bits, *get_random_uint64
);
break;
case QuantizationMode::STOCH_WEIGHTED:
_quantize_stoch_weighted(
it_begin, it_end, bits, int_bits, new_bits, new_int_bits, *get_random_uint64
);
break;
default:
APYTYPES_UNREACHABLE();
}
}
/* ********************************************************************************** *
* * Fixed-point iterator based in-place overflowing with multi-limb support * *
* ********************************************************************************** */
template <class RANDOM_ACCESS_ITERATOR>
static APY_INLINE void _overflow_twos_complement(
RANDOM_ACCESS_ITERATOR it_begin,
RANDOM_ACCESS_ITERATOR it_end,
int bits,
int int_bits
)
{
(void)int_bits;
(void)it_begin;
if (bits % APY_LIMB_SIZE_BITS) {
RANDOM_ACCESS_ITERATOR ms_limb_it = std::prev(it_end);
unsigned shift_amount = APY_LIMB_SIZE_BITS - (bits % APY_LIMB_SIZE_BITS);
*ms_limb_it = apy_limb_signed_t(*ms_limb_it << shift_amount) >> shift_amount;
}
}
template <class RANDOM_ACCESS_ITERATOR>
static APY_INLINE void _overflow_saturate(
RANDOM_ACCESS_ITERATOR it_begin,
RANDOM_ACCESS_ITERATOR it_end,
int bits,
int int_bits
)
{
(void)int_bits;
RANDOM_ACCESS_ITERATOR ms_limb_it = it_begin + bits_to_limbs(bits) - 1;
std::size_t utilized_bits_last_limb = (bits - 1) % APY_LIMB_SIZE_BITS + 1;
bool sign = apy_limb_signed_t(*std::prev(it_end)) < 0;
if (sign) {
if (!limb_vector_all_ones(ms_limb_it, it_end, utilized_bits_last_limb - 1)) {
std::fill(it_begin, ms_limb_it, 0);
*ms_limb_it = ~((apy_limb_t(1) << (utilized_bits_last_limb - 1)) - 1);
}
} else { /* !sign */
if (!limb_vector_all_zeros(ms_limb_it, it_end, utilized_bits_last_limb - 1)) {
std::fill(it_begin, ms_limb_it, apy_limb_t(-1));
*ms_limb_it = (apy_limb_t(1) << (utilized_bits_last_limb - 1)) - 1;
}
}
}
template <class RANDOM_ACCESS_ITERATOR>
static APY_INLINE void _overflow_numeric_std(
RANDOM_ACCESS_ITERATOR it_begin,
RANDOM_ACCESS_ITERATOR it_end,
int bits,
int int_bits
)
{
(void)int_bits;
RANDOM_ACCESS_ITERATOR ms_limb_it = it_begin + bits_to_limbs(bits) - 1;
std::size_t utilized_bits_last_limb = (bits - 1) % APY_LIMB_SIZE_BITS + 1;
bool sign = apy_limb_signed_t(*std::prev(it_end)) < 0;
if (sign) {
// Force a `1` into the sign position (and above)
*ms_limb_it |= ~((apy_limb_t(1) << (utilized_bits_last_limb - 1)) - 1);
} else { /* !sign */
// Force a `0` into the sign position (and above)
*ms_limb_it &= ((apy_limb_t(1) << (utilized_bits_last_limb - 1)) - 1);
}
}
template <class RANDOM_ACCESS_ITERATOR>
static void overflow(
RANDOM_ACCESS_ITERATOR it_begin,
RANDOM_ACCESS_ITERATOR it_end,
int new_bits,
int new_int_bits,
OverflowMode overflow
)
{
/*
* All overflow methods (e.g., `_overflow_saturate()`) assume that data being
* overflown has been copied to the iterator region [ `it_begin`, `it_end` ) and is
* shifted so that the binary point location is correct. The overflowing methods
* only manipulates bits in: [ `it_begin`, `it_begin + bits_to_limbs(new_bits)` ).
*/
switch (overflow) {
case OverflowMode::WRAP:
_overflow_twos_complement(it_begin, it_end, new_bits, new_int_bits);
break;
case OverflowMode::SAT:
_overflow_saturate(it_begin, it_end, new_bits, new_int_bits);
break;
case OverflowMode::NUMERIC_STD:
_overflow_numeric_std(it_begin, it_end, new_bits, new_int_bits);
break;
default:
throw NotImplementedException(
fmt::format(
"Not implemented: APyFixed::_overflow(): with mode: {}",
"unknown (did you pass `int` as `OverflowMode`?)"
)
);
}
}
/* ********************************************************************************** *
* * Fixed-point iterator based casting with quantization and overflowing * *
* ********************************************************************************** */
/*!
* General casting method for fixed-point numbers. General casting can perform both
* quantization and overflowing. The size of the output region
* (`std::distance(dst_begin, dst_end)`) must be greater than or equal to the size of
* the input region (`std::distance(src_begin, src_end)`), even when the output
* bit-specifiers are smaller then the input bit-specifiers (hence the name unsafe).
*/
template <typename RANDOM_ACCESS_ITERATOR_IN, typename RANDOM_ACCESS_ITERATOR_OUT>
static APY_INLINE void fixed_point_cast_unsafe(
RANDOM_ACCESS_ITERATOR_IN src_begin,
RANDOM_ACCESS_ITERATOR_IN src_end,
RANDOM_ACCESS_ITERATOR_OUT dst_begin,
RANDOM_ACCESS_ITERATOR_OUT dst_end,
int src_bits,
int src_int_bits,
int dst_bits,
int dst_int_bits,
QuantizationMode q_mode,
OverflowMode v_mode
)
{
assert(std::distance(src_begin, src_end) <= std::distance(dst_begin, dst_end));
// Copy data into the result region and sign extend
limb_vector_copy_sign_extend(src_begin, src_end, dst_begin, dst_end);
// First perform quantization
quantize(
dst_begin,
dst_end,
src_bits,
src_int_bits,
dst_bits,
dst_int_bits,
q_mode,
rnd64_fx
);
// Then perform overflowing
overflow(dst_begin, dst_end, dst_bits, dst_int_bits, v_mode);
}
template <typename RANDOM_ACCESS_ITERATOR_IN, typename RANDOM_ACCESS_ITERATOR_OUT>
static APY_INLINE void fixed_point_cast(
RANDOM_ACCESS_ITERATOR_IN src_begin,
RANDOM_ACCESS_ITERATOR_IN src_end,
RANDOM_ACCESS_ITERATOR_OUT dst_begin,
RANDOM_ACCESS_ITERATOR_OUT dst_end,
int src_bits,
int src_int_bits,
int dst_bits,
int dst_int_bits,
QuantizationMode q_mode,
OverflowMode v_mode
)
{
const auto FX_CAST_UNSAFE = [&](auto begin, auto end, auto d_begin, auto d_end) {
fixed_point_cast_unsafe(
begin,
end,
d_begin,
d_end,
src_bits,
src_int_bits,
dst_bits,
dst_int_bits,
q_mode,
v_mode
);
};
if (std::distance(src_begin, src_end) <= std::distance(dst_begin, dst_end)) {
FX_CAST_UNSAFE(src_begin, src_end, dst_begin, dst_end);
} else {
ScratchVector<apy_limb_t, 8> res(std::distance(src_begin, src_end));
FX_CAST_UNSAFE(src_begin, src_end, std::begin(res), std::end(res));
std::copy_n(std::begin(res), bits_to_limbs(dst_bits), dst_begin);
}
}
/*!
* Casting when there is known before hand that no quantization or overflowing will
* occur. Takes `left_shift_amount` which is the destination fractional bits minus the
* source fractional bits.
*/
template <typename RANDOM_ACCESS_ITERATOR_IN, typename RANDOM_ACCESS_ITERATOR_OUT>
static APY_INLINE void _cast_no_quantize_no_overflow(
RANDOM_ACCESS_ITERATOR_IN src_begin,
RANDOM_ACCESS_ITERATOR_IN src_end,
RANDOM_ACCESS_ITERATOR_OUT dst_begin,
RANDOM_ACCESS_ITERATOR_OUT dst_end,
unsigned int left_shift_amount
)
{
// Copy data into the result region and sign extend
limb_vector_copy_sign_extend(src_begin, src_end, dst_begin, dst_end);
// Shift data into position
limb_vector_lsl(dst_begin, dst_end, left_shift_amount);
}
/*!
* Casting when there is known before hand that no quantization or overflowing will
* occur. Takes `left_shift_amount` which is the destination fractional bits minus the
* source fractional bits.
*/
template <typename RANDOM_ACCESS_ITERATOR_IN, typename RANDOM_ACCESS_ITERATOR_OUT>
static APY_INLINE void _cast_no_quantize_no_overflow(
RANDOM_ACCESS_ITERATOR_IN src,
RANDOM_ACCESS_ITERATOR_OUT dst,
std::size_t src_limbs,
std::size_t dst_limbs,
std::size_t n_items,
unsigned int left_shift_amount
)
{
/*
* Specialization #1: `src` and `dst` have equally many limbs
*/
if (src_limbs == dst_limbs) {
// Copy data into the result
std::copy_n(src, src_limbs * n_items, dst);
if (left_shift_amount > 0) {
if (src_limbs == 1) { /* src_limbs == dst_limbs == 1 */
for (std::size_t i = 0; i < n_items; i++) {
dst[i] = src[i] << left_shift_amount;
}
} else { /* src_limbs == dst_limbs > 1 */
unsigned limb_skip = left_shift_amount / APY_LIMB_SIZE_BITS;
unsigned limb_shift = left_shift_amount % APY_LIMB_SIZE_BITS;
for (std::size_t i = 0; i < n_items; i++) {
limb_vector_lsl_inner(
dst + (i + 0) * dst_limbs,
dst + (i + 1) * dst_limbs,
limb_skip,
limb_shift,
dst_limbs
);
}
}
}
return; // early return specialization #1
}
/*
* General case: `dst_limbs > src_limbs`
*/
if (left_shift_amount > 0) {
for (std::size_t i = 0; i < n_items; i++) {
_cast_no_quantize_no_overflow(
src + (i + 0) * src_limbs, // src_begin
src + (i + 1) * src_limbs, // src_end
dst + (i + 0) * dst_limbs, // dst_begin,
dst + (i + 1) * dst_limbs, // dst_end
left_shift_amount // left_shift_amount
);
}
} else {
for (std::size_t i = 0; i < n_items; i++) {
limb_vector_copy_sign_extend(
src + (i + 0) * src_limbs, // src_begin
src + (i + 1) * src_limbs, // src_end
dst + (i + 0) * dst_limbs, // dst_begin,
dst + (i + 1) * dst_limbs // dst_end
);
}
}
}
/* ********************************************************************************** *
* * Fixed-point iterator based arithmetic functions with multi-limb support * *
* ********************************************************************************** */
//! Iterator-based multi-limb two's complement fixed-point product. The scratch
//! vector `prod_abs` must have space for at least `src1_limbs + src2_limbs` limbs. The
//! scratch vectors `op1_abs` and `op2_abs` must have space for at least `src1_limbs`
//! and `src2_limbs` limbs, respectively. No overlap between `prod_abs` and `op[12]_abs`
//! allowed. Overlap between `prod_abs` and `dst` is allowed
//! if `dst_limbs >= src1_limbs + src2_limbs`.
template <
typename RANDOM_ACCESS_ITERATOR_IN1,
typename RANDOM_ACCESS_ITERATOR_IN2,
typename RANDOM_ACCESS_ITERATOR_OUT,
typename RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void fixed_point_product(
RANDOM_ACCESS_ITERATOR_IN1 src1,
RANDOM_ACCESS_ITERATOR_IN2 src2,
RANDOM_ACCESS_ITERATOR_OUT dst,
std::size_t src1_limbs,
std::size_t src2_limbs,
std::size_t dst_limbs,
RANDOM_ACCESS_ITERATOR_INOUT op1_abs,
RANDOM_ACCESS_ITERATOR_INOUT op2_abs,
RANDOM_ACCESS_ITERATOR_INOUT prod_abs
)
{
// Retrieve the absolute value of both operands
bool sign1 = limb_vector_abs(src1, src1 + src1_limbs, op1_abs);
bool sign2 = limb_vector_abs(src2, src2 + src2_limbs, op2_abs);
// Resulting sign
bool result_sign = sign1 ^ sign2;
// Perform the multiplication of absolute values
if (src1_limbs < src2_limbs) {
apy_unsigned_multiplication(
&prod_abs[0], &op2_abs[0], src2_limbs, &op1_abs[0], src1_limbs
);
} else {
apy_unsigned_multiplication(
&prod_abs[0], &op1_abs[0], src1_limbs, &op2_abs[0], src2_limbs
);
}
// Possibly negate and copy the result back
std::size_t prod_limbs = src1_limbs + src2_limbs;
if (result_sign) {
if (dst_limbs <= prod_limbs) {
limb_vector_negate(prod_abs, prod_abs + dst_limbs, dst);
} else {
bool is_zero = limb_vector_negate(prod_abs, prod_abs + prod_limbs, dst);
apy_limb_t fill_val = is_zero ? apy_limb_t(0) : apy_limb_t(-1);
std::fill_n(prod_abs + prod_limbs, dst_limbs - prod_limbs, fill_val);
}
} else {
if (dst_limbs <= prod_limbs) {
std::copy(prod_abs, prod_abs + dst_limbs, dst);
} else {
std::copy(prod_abs, prod_abs + prod_limbs, dst);
std::fill_n(prod_abs + prod_limbs, dst_limbs - prod_limbs, apy_limb_t(0));
}
}
}
//! Iterator-based multi-limb two's complement fixed-point squaring. The scratch
//! vector `prod_abs` must have space for at least `2 * src_limbs` limbs. The scratch
//! vector `op_abs` must have space for at least `src_limbs` limbs. No overlap
//! between `prod_abs` and `op_abs` allowed. Overlap between `prod_abs` and `dst` is
//! allowed if `dst_limbs >= 2 * src_limbs`.
template <
typename RANDOM_ACCESS_ITERATOR_IN,
typename RANDOM_ACCESS_ITERATOR_OUT,
typename RANDOM_ACCESS_ITERATOR_INOUT>
static APY_INLINE void fixed_point_square(
RANDOM_ACCESS_ITERATOR_IN src,
RANDOM_ACCESS_ITERATOR_OUT dst,
std::size_t src_limbs,
std::size_t dst_limbs,
RANDOM_ACCESS_ITERATOR_INOUT op_abs,
RANDOM_ACCESS_ITERATOR_INOUT prod_abs
)
{
limb_vector_abs(src, src + src_limbs, op_abs);
apy_unsigned_square(&*prod_abs, &*op_abs, src_limbs);
if (dst_limbs <= 2 * src_limbs) {
std::copy_n(prod_abs, dst_limbs, dst);
} else {
std::copy_n(prod_abs, 2 * src_limbs, dst);
std::fill_n(prod_abs + 2 * src_limbs, dst_limbs - 2 * src_limbs, apy_limb_t(0));
}
}
//! Iterator-based multi-limb fixed-point hadamard product
template <typename RANDOM_ACCESS_ITERATOR_IN, typename RANDOM_ACCESS_ITERATOR_OUT>
static void fixed_point_hadamard_product(
RANDOM_ACCESS_ITERATOR_IN src1,
RANDOM_ACCESS_ITERATOR_IN src2,
RANDOM_ACCESS_ITERATOR_OUT dst,
std::size_t src1_limbs, // Number of limbs in one fixed-point of `src1`
std::size_t src2_limbs, // Number of limbs in one fixed-point of `src2`
std::size_t dst_limbs, // `dst_limbs` <= `src1_limbs` + `src2_limbs`
std::size_t n_items // Number of elements to use in inner product
)
{
ScratchVector<apy_limb_t, 8> op1_abs(src1_limbs);
ScratchVector<apy_limb_t, 8> op2_abs(src2_limbs);
ScratchVector<apy_limb_t, 16> prod_abs(src1_limbs + src2_limbs);
for (std::size_t i = 0; i < n_items; i++) {
fixed_point_product(
src1 + i * src1_limbs,
src2 + i * src2_limbs,
dst + i * dst_limbs,
src1_limbs,
src2_limbs,
dst_limbs,
std::begin(op1_abs),
std::begin(op2_abs),
std::begin(prod_abs)
);
}
}
struct FixedPointInnerProduct {
explicit FixedPointInnerProduct(
const APyFixedSpec& src1_spec,
const APyFixedSpec& src2_spec,
const APyFixedSpec& dst_spec,
const std::optional<APyFixedAccumulatorOption> acc_mode
)
: src1_limbs { bits_to_limbs(src1_spec.bits) }
, src2_limbs { bits_to_limbs(src2_spec.bits) }
, dst_limbs { bits_to_limbs(dst_spec.bits) }
, acc_mode { acc_mode }
{
if (!acc_mode.has_value()) {
if (dst_limbs == 1) {
// Specialization #1: the resulting number of limbs is exactly one and
// no accumulator mode has been set. Use the SIMD inner product.