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fast_float.h
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// Copyright 2022 Democritus University of Thrace
// Integrated Circuits Lab
//
// Fast-Float4HLS v1.0
// -------------------
// Floating Point Library of fast operators for High Level Synthesis
#ifndef __FASTFLOAT_H__
#define __FASTFLOAT_H__
#include <ac_fixed.h>
#include <ac_std_float.h>
template <int W>
bool lzc_reduce (ac_int<W,false> a) {
ac_int<W/2,false> odd, even;
// split odd even bits of a
#pragma unroll yes
SPLIT:for (int i=0; i < W/2; i++) {
even[i] = a[2*i];
odd[i] = a[2*i+1];
}
// prefix AND from MSB-to-LSB of inverted even bits
even = even.bit_complement();
ac_int<W/2,false> even_prefix;
ac_int<1,false> t=true;
#pragma unroll yes
PREFIXAND:for (int i=W/2-1; i >=0; i--) {
if (i == W/2-1) t = even[i];
else t = t & even[i];
even_prefix[i] = t;
}
// fix alignment of prefixed and terms
even_prefix = even_prefix >> 1;
even_prefix[W/2-1] = 1;
// prepare terms for each bit position
ac_int<W/2,false> tmp = even_prefix & odd;
// return the wide OR of those terms
return tmp.or_reduce();
}
// Version 1: try to do it
template<int N>
struct lzc_s {
template<typename T>
static void lzc(ac_int<N,false> a, T &out) {
ac_int<N/2, false> a0;
out[ac::log2_ceil<N>::val] = lzc_reduce<N>(a);
#pragma unroll yes
for (int i = 0; i < N / 2; i++) {
a0[i] = a[2*i] | a[2*i + 1];
}
lzc_s<N/2>::lzc(a0,out);
}
};
template<>
struct lzc_s<1> {
template<typename T>
static void lzc(ac_int<1,false> a, T &out) {
out[0] = a[0];
}
};
template<int N=8>
ac_int<ac::log2_ceil<N>::val+1,false> lzcount(ac_int<N,false> x) {
ac_int<ac::log2_ceil<N>::val+1,false> b,res;
lzc_s<N>::lzc(x,b);
// reverse bits
#pragma unroll yes
for (int i=0; i< ac::log2_ceil<N>::val+1; i++) {
res[i] = b[ac::log2_ceil<N>::val - i];
}
// complement them and send them out
return (res.or_reduce() == 0) ? (ac_int<ac::log2_ceil<N>::val+1,false>)0 : res.bit_complement();
}
template<int N>
struct max_s {
template<typename T>
static T max(T *a) {
T m0 = max_s<N/2>::max(a);
T m1 = max_s<N-N/2>::max(a+N/2);
return m0 > m1 ? m0 : m1;
}
};
template<>
struct max_s<1> {
template<typename T>
static T max(T *a) {
return a[0];
}
};
template<int N, typename T>
T max(T *a) {
return max_s<N>::max(a);
};
// Fast Float class
template<int M, int E>
class fast_float {
public:
typedef ac_int<M,false> man_t;
typedef ac_int<E,false> exp_t;
typedef ac_int<1,false> sgn_t;
man_t mantissa;
exp_t exponent;
sgn_t sign;
static const int width = M + E + 1;
static const int man_width = M;
static const int exp_width = E;
static const int e_bias = (1 << (E-1)) - 1;
static const int frac_bits = M + 1;
enum RND_ENUM {EVEN, ODD, INF};
// Constructors
fast_float() {};
fast_float(const ac_int<M+E+1,false> &in) {
this->operator=(in);
}
fast_float(const fast_float<M,E> &in) {
this->operator=(in);
}
~fast_float() {};
void set(sgn_t s, exp_t e, man_t m) {
sign = s;
exponent = e;
mantissa = m;
}
void setNan() { this->set(0, (1<<E)-1, 1); }
void setPosINF() { this->set(0, (1<<E)-1, 0); }
void setNegINF() { this->set(1, (1<<E)-1, 0); }
/*
* .to_float() is a non-synthesizable function that
* is used for converting the fast_float into a c++ float
*/
float to_float() {
ac_int<32,false> data;
for (int i=0; i<M; i++)
data[22-i] = mantissa[M-1-i];
for (int i=M; i<23; i++)
data[22-i] = 0;
ac_int<8,false> tmpExp = (exponent==0) ? ( ac_int<8,false>)0 : ( ac_int<8,false>)(exponent - e_bias + 127);
for (int i=0; i<8; i++)
data[23+i] = (exponent == (1<<E)+-1) ? 1 : tmpExp[i];
data[31] = sign;
ac_std_float<32,8> ieee_data;
ieee_data.set_data(data);
return ieee_data.to_float();
}
/** FLOATING POINT OPERATIONS **/
/* Floating Point Addition
* adds the value of 'a' to this fast_float and
* return the result to the 'output'.
* The addition is implemented using dual path (Far-Near).
*/
template<RND_ENUM RND_MODE=EVEN, bool DENORMALS=false>
void fpa_dual(const fast_float<M,E> a, fast_float<M,E> &output) {
// Set create needed lengths.
const int signif_uniform_W = M + 4;
// Calculate effective sign.
const ac_int<1,false> sign_eff = sign ^ a.sign;
// Infinity check:
ac_int<1,false> inf_sign = sign;
bool Is_inf = false;
if (( exponent).and_reduce()) {
Is_inf = true;
} else if ((a.exponent).and_reduce()) {
inf_sign = a.sign;
Is_inf = true;
}
// End of infinity check.
// Create normalized significant with guard bits.
ac_int<signif_uniform_W,true> norm_significant_1;
ac_int<signif_uniform_W,true> norm_significant_2;
norm_significant_1 = mantissa;
norm_significant_1 <<= 2;
norm_significant_2 = a.mantissa;
norm_significant_2 <<= 2;
const ac_int<1,false> in_1_subnorm = ( exponent == 0);
const ac_int<1,false> in_2_subnorm = (a.exponent == 0);
const ac_int<1,false> both_ins_subnorm = in_1_subnorm & in_2_subnorm;
const ac_int<1,false> only_one_in_subnorm = in_1_subnorm ^ in_2_subnorm;
norm_significant_1[signif_uniform_W - 2] = (DENORMALS) ? ((in_1_subnorm) ? 0 : 1) : 1;
norm_significant_2[signif_uniform_W - 2] = (DENORMALS) ? ((in_2_subnorm) ? 0 : 1) : 1;
// Start of R-path:
// Compute exponent difference.
const ac_int<E + 1,true> R_exp_diff_1 = exponent - a.exponent;
const ac_int<E + 1,true> R_exp_diff_2 = a.exponent - exponent;
ac_int<E + 1,true> R_abs_exp_diff;
// Initialize swap variables.
ac_int<signif_uniform_W,true> R_nsignif_small;
ac_int<signif_uniform_W,true> R_nsignif_large;
ac_int<E,false> R_exp_large;
ac_int<1,false> R_sign_large = 0;
const int R_align_sft_extra_W = M + 3;
ac_int<signif_uniform_W + R_align_sft_extra_W,true> R_small_signif_aligner;
// Swap and allign.
if (!R_exp_diff_1[E]) {
R_nsignif_large = norm_significant_1;
R_exp_large = exponent;
R_sign_large = sign;
R_nsignif_small = norm_significant_2;
R_abs_exp_diff = R_exp_diff_1;
} else if (!R_exp_diff_2[E]) {
R_nsignif_large = norm_significant_2;
R_exp_large = a.exponent;
R_sign_large = a.sign;
R_nsignif_small = norm_significant_1;
R_abs_exp_diff = R_exp_diff_2;
}
R_small_signif_aligner = R_nsignif_small;
if (R_abs_exp_diff < R_align_sft_extra_W) {
R_small_signif_aligner <<= R_align_sft_extra_W;
if (DENORMALS) R_small_signif_aligner <<= only_one_in_subnorm;
R_small_signif_aligner >>= R_abs_exp_diff;
}
R_nsignif_small = R_small_signif_aligner.template slc<signif_uniform_W>(R_align_sft_extra_W);
const ac_int<1,false> R_sticky = (R_small_signif_aligner.template slc<R_align_sft_extra_W>(0)).or_reduce();
const ac_int<1,false> R_add_1 = !R_sticky;
// Significant Addition. Compute sum and both rounded sums.
ac_int<signif_uniform_W,false> R_sum;
ac_int<signif_uniform_W,false> R_rounded_sum; // rounded sum in case no normalization left shift is needed.
ac_int<signif_uniform_W,false> R_unnormal_rounded_sum; // rounded sum requires left shift normalition.
if (sign_eff) {
R_sum = R_nsignif_large + (~R_nsignif_small) + R_add_1;
R_rounded_sum = R_nsignif_large + (~R_nsignif_small) + R_add_1 + 4;
R_unnormal_rounded_sum = R_nsignif_large + (~R_nsignif_small) + R_add_1 + 2;
} else {
R_sum = R_nsignif_large + R_nsignif_small;
R_rounded_sum = R_nsignif_large + R_nsignif_small + 4;
R_unnormal_rounded_sum = R_nsignif_large + R_nsignif_small + 2;
}
bool Ris_zero = !(R_sum.or_reduce());
// Normalize and overflow check R_sum, R_rounded_sum
// and R_unnormal_rounded_sum.
const ac_int<E,false> R_exp_large_plus_1 = R_exp_large + 1;
const ac_int<E,false> R_exp_large_min_1 = R_exp_large - 1;
bool R_sum_overf = false;
bool R_sum_is_unnormal = false;
bool R_rounded_sum_overf = false;
bool R_is_unnormal_rounded = false;
const ac_int<1,false> R_sum_sticky_hold = R_sum[0];
if (DENORMALS) {
if (R_sum[signif_uniform_W - 1]) {
R_sum >>= 1;
R_sum[0] = R_sum[0] | R_sum_sticky_hold;
R_sum_overf = true;
} else if (both_ins_subnorm && R_sum[signif_uniform_W - 2]) {
R_sum_overf = true;
} else if (!both_ins_subnorm && !R_sum[signif_uniform_W - 2]) {
R_sum <<= 1;
R_sum_is_unnormal = true;
}
} else {
if (R_sum[signif_uniform_W - 1]) {
R_sum >>= 1;
R_sum[0] = R_sum[0] | R_sum_sticky_hold;
R_sum_overf = true;
} else if (!R_sum[signif_uniform_W - 2]) {
R_sum <<= 1;
R_sum_is_unnormal = true;
}
}
if (DENORMALS) {
if (R_rounded_sum[signif_uniform_W - 1]) {
R_rounded_sum >>= 1;
R_rounded_sum_overf = true;
} else if (both_ins_subnorm && R_rounded_sum[signif_uniform_W - 2]) {
R_rounded_sum_overf = true;
}
} else {
if (R_rounded_sum[signif_uniform_W - 1]) {
R_rounded_sum >>= 1;
R_rounded_sum_overf = true;
}
}
if (DENORMALS) {
if (!both_ins_subnorm && !R_unnormal_rounded_sum.template slc<2>(signif_uniform_W - 2)) {
R_unnormal_rounded_sum <<= 1;
R_is_unnormal_rounded = true;
}
} else {
if (!R_unnormal_rounded_sum.template slc<2>(signif_uniform_W - 2)) {
R_unnormal_rounded_sum <<= 1;
R_is_unnormal_rounded = true;
}
}
// Rounding Decision.
bool rnd = false;
switch (RND_MODE) {
case EVEN:
// Round to nearest tie to even.
rnd = R_sum[1] & (R_sum[0] | R_sum[2] | R_sticky);
break;
case ODD:
// Round to nearest tie to odd.
rnd = R_sum[1] & (R_sum[0] | (!R_sum[2]) | R_sticky);
break;
case INF:
// Round infinity.
rnd = R_sum[1];
break;
}
ac_int<M,false> R_magn_result;
ac_int<E,false> R_exp_result;
if (rnd) {
if (R_is_unnormal_rounded) {
R_magn_result = R_unnormal_rounded_sum.template slc<M>(2);
R_exp_result = R_exp_large_min_1;
} else {
R_magn_result = R_rounded_sum.template slc<M>(2);
R_exp_result = (R_rounded_sum_overf) ? R_exp_large_plus_1 : R_exp_large;
}
} else {
R_magn_result = R_sum.template slc<M>(2);
if (R_sum_overf) {
R_exp_result = R_exp_large_plus_1;
} else if (R_sum_is_unnormal) {
R_exp_result = R_exp_large_min_1;
} else {
R_exp_result = R_exp_large;
}
}
// End of R-path.
// Start of N-path:
// 2-bit exponent difference.
const ac_int<3,true> N_exp_diff = exponent.template slc<2>(0) - a.exponent.template slc<2>(0);
// Swap and 1-bit allign.
ac_int<signif_uniform_W,true> N_nsignif_small;
ac_int<signif_uniform_W,true> N_nsignif_large;
ac_int<E,false> N_exp_large;
ac_int<1,false> N_sign_large = 0;
if (N_exp_diff[1]) {
N_nsignif_large = norm_significant_2;
N_exp_large = a.exponent;
N_sign_large = a.sign;
N_nsignif_small = norm_significant_1;
} else {
N_nsignif_large = norm_significant_1;
N_exp_large = exponent;
N_sign_large = sign;
N_nsignif_small = norm_significant_2;
}
if (DENORMALS) {
if (N_exp_diff.or_reduce() && (!only_one_in_subnorm)) {
N_nsignif_small >>= 1;
}
} else {
if (N_exp_diff.or_reduce()) {
N_nsignif_small >>= 1;
}
}
// Significant substraction.
const ac_int<signif_uniform_W,true> N_large_sub_small = N_nsignif_large - N_nsignif_small;
const ac_int<signif_uniform_W,true> N_small_sub_large = N_nsignif_small - N_nsignif_large;
ac_int<signif_uniform_W - 1,false> N_chosen_sub;
if (!N_small_sub_large[signif_uniform_W - 1]) {
N_sign_large = !N_sign_large;
N_chosen_sub = N_small_sub_large;
} else if (!N_large_sub_small[signif_uniform_W - 1]) {
N_chosen_sub = N_large_sub_small;
}
// Normalize chosen sub.
const bool N_no_normalize = N_chosen_sub[signif_uniform_W - 2];
bool N_zero = false;
// const ac_int<ac::nbits<signif_uniform_W-1>::val, false> N_lz_cnt = (N_chosen_sub).leading_sign(N_zero);
// M+3 = 23 + 3 = 26
// M+3 = 7 + 3 = 10
// M+3 = 3 + 3 = 6
const int ww = (M+3 <= 8) ? 8 :
(M+3 <= 16) ? 16 :
(M+3 <= 32) ? 32 : 64;
const int uu = ww - M - 3;
ac_int<ww,false> tcz = 0;
#pragma hls_unroll
for (int ii=0; ii<M+3; ii++)
tcz[ii+uu]=N_chosen_sub[ii];
const ac_int<ac::nbits<signif_uniform_W-1>::val, false> N_lz_cnt = lzcount<ww>(tcz);
// REMOVE LINE -3
// ADD LINES -2 AND -1
// CHANGES FOR LEADING ZERO COUNT
if (N_zero) {
N_exp_large = 0;
N_sign_large = 0;
} else {
N_chosen_sub <<= N_lz_cnt;
N_exp_large -= N_lz_cnt;
}
if (DENORMALS)
N_chosen_sub >>= ((N_exp_large == 0) && !both_ins_subnorm) ? 1 : 0;
// End of N-path.
// Result Decision.
const bool Is_R1 = (R_abs_exp_diff >= 2);
const bool Is_R2 = sign_eff & !Is_R1 & N_no_normalize;
const bool Is_R = !sign_eff | Is_R1 | Is_R2;
if (R_exp_result.and_reduce() & Is_R) {
Is_inf = true;
}
sgn_t tmp_s = (Is_inf) ? inf_sign : ((Is_R) ? R_sign_large : N_sign_large);
man_t tmp_m = (Is_inf) ? ac_int<M,false>(0) : ((Is_R) ? R_magn_result : N_chosen_sub.template slc<M>(2));
exp_t tmp_e = (Is_inf) ? ac_int<E,false>((1 << E) - 1) : ((Is_R) ? R_exp_result : N_exp_large);
bool zero_res = (Is_R) ? Ris_zero : !(N_chosen_sub.or_reduce());
sgn_t tmp_s_A = (in_1_subnorm) ? a.sign : (sgn_t)0;
man_t tmp_m_A = (in_1_subnorm) ? a.mantissa : (man_t)0;
exp_t tmp_e_A = (in_1_subnorm) ? a.exponent : (exp_t)0;
sgn_t tmp_s_B = (in_2_subnorm) ? sign : (sgn_t)0;
man_t tmp_m_B = (in_2_subnorm) ? mantissa : (man_t)0;
exp_t tmp_e_B = (in_2_subnorm) ? exponent : (exp_t)0;
output.sign = (DENORMALS) ? tmp_s : ((in_1_subnorm) ? tmp_s_A : ((in_2_subnorm) ? tmp_s_B : ((zero_res) ? (sgn_t)0 : tmp_s)));
output.exponent = (DENORMALS) ? tmp_e : ((in_1_subnorm) ? tmp_e_A : ((in_2_subnorm) ? tmp_e_B : ((zero_res) ? (exp_t)0 : tmp_e)));
output.mantissa = (DENORMALS) ? tmp_m : ((in_1_subnorm) ? tmp_m_A : ((in_2_subnorm) ? tmp_m_B : tmp_m));
}
template<RND_ENUM RND_MODE=EVEN, bool DENORMALS=false>
void fpma_dual(const fast_float<M,E> a, const fast_float<M,E> b, fast_float<M,E> &output) {
const bool t_in_a_is_inf = (exponent).and_reduce();
const bool t_in_c_is_inf = (a.exponent).and_reduce();
const bool t_in_b_is_inf = (b.exponent).and_reduce();
// Start by calculating the multiplication
//Infinite check
const bool mul_is_inf = t_in_a_is_inf | t_in_c_is_inf;
// Find mul sign.
const ac_int<1,false> mul_sign = sign ^ a.sign;
// Create significants of mul.
ac_int<M+1,false> mul_signif_a = mantissa;
ac_int<M+1,false> mul_signif_b = a.mantissa;
const ac_int<1,false> a_denorm = (exponent == 0);
const ac_int<1,false> b_denorm = (a.exponent == 0);
const ac_int<1,false> c_denorm = (b.exponent == 0);
const ac_int<1,false> a_and_b_denorm = a_denorm & b_denorm;
const ac_int<1,false> a_or_b_denorm = a_denorm ^ b_denorm;
mul_signif_a[M] = (DENORMALS) ? ((a_denorm) ? 0 : 1) : 1;
mul_signif_b[M] = (DENORMALS) ? ((b_denorm) ? 0 : 1) : 1;
if (DENORMALS) {
mul_signif_a <<= a_denorm;
mul_signif_b <<= b_denorm;
}
// Calculate exponent result
/*static*/ const ac_int<E,false> mul_exp_base = (1 << (E-1)) - 1;
/*static*/ const ac_int<E,false> mul_exp_base_min_1 = (1 << (E-1)) - 2;
const ac_int<E+2,true> mul_exp_overf = exponent + a.exponent - mul_exp_base_min_1;
const ac_int<E+2,true> mul_exp = exponent + a.exponent - mul_exp_base;
// Do the multiplication.
/*static*/ const int mul_input_W = M + 1;
/*static*/ const int mul_W = (mul_input_W) << 1;
ac_int<mul_W,false> mul_prod1, mul_prod;
mul_prod1 = mul_signif_a*mul_signif_b;
mul_prod = (DENORMALS) ? mul_prod1 : ((a_denorm || b_denorm) ? (ac_int<mul_W,false>)0 : mul_prod1);
ac_int<1,false> mul_overf = mul_prod[mul_W-1];
mul_prod <<= !mul_overf;
ac_int<E+3,true> mul_exp_result1 = (mul_overf) ? mul_exp_overf : mul_exp;
ac_int<E+3,true> mul_exp_result = (DENORMALS) ? mul_exp_result1 : ((a_denorm || b_denorm) ? (ac_int<E+3,true>)0 : mul_exp_result1);
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
bool mul_zero = (DENORMALS) ? false : (a_denorm || b_denorm);
int mul_prod_lz_cnt = 0;
if (DENORMALS) {
// int mul_prod_lz_cnt = (mul_prod).leading_sign(mul_zero);
// 2*M+2 = 2*(23 + 1) = 48
// 2*M+2 = 2*(7 + 1) = 16
// 2*M+2 = 2*(3 + 1) = 8
const int ww = (2*M+2 <= 8) ? 8 :
(2*M+2 <= 16) ? 16 :
(2*M+2 <= 32) ? 32 : 64;
const int uu = ww - mul_W;
ac_int<ww,false> tcz = 0;
#pragma hls_unroll
for (int ii=0; ii<mul_W; ii++)
tcz[ii+uu]=mul_prod[ii];
int mul_prod_lz_cnt = lzcount<ww>(tcz);//.leading_sign(mul_zero);
if (mul_zero) {
mul_exp_result = 0;
} else {
mul_prod <<= mul_prod_lz_cnt;
mul_exp_result -= mul_prod_lz_cnt;
}
}
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// ONLY CHANGE FIX IT
// Perform the addition
//Infinite check
bool add_is_inf = mul_is_inf | t_in_b_is_inf;
// Calculate add effective operation.
const ac_int<1,false> add_eff_sign = mul_sign ^ b.sign;
// Create add significant.
ac_int<mul_W,false> add_signif_c = (DENORMALS) ? b.mantissa : ((c_denorm) ? (man_t)0 : b.mantissa);
add_signif_c[M] = (DENORMALS) ? ((c_denorm) ? 0 : 1) : 1;
if (DENORMALS) add_signif_c <<= c_denorm;
add_signif_c <<= M + 1;
// Start of Far Path:
// Compute exponent difference.
const ac_int<E + 3,true> Far_exp_diff_1 = mul_exp_result - b.exponent;
const ac_int<E + 3,true> Far_exp_diff_2 = b.exponent - mul_exp_result;
ac_int<E+2,false> Far_abs_exp_diff;
// Initialize swap variables.
ac_int<mul_W+1,true> Far_nsignif_small;
ac_int<mul_W,false> Far_nsignif_large;
ac_int<E+1,false> Far_exp_large;
ac_int<1,false> Far_sign_large;
ac_int<1,false> Far_large_is_mul;
const int Far_align_extra_W = M + 3;
ac_int<mul_W + Far_align_extra_W,false> Far_small_signif_aligner;
// Swap and allign.
if (!Far_exp_diff_1[E+2]) {
Far_nsignif_large = mul_prod;
Far_exp_large = mul_exp_result;
Far_sign_large = mul_sign;
Far_nsignif_small = add_signif_c;
Far_abs_exp_diff = Far_exp_diff_1.template slc<E+1>(0);
Far_large_is_mul = 1;
} else if (!Far_exp_diff_2[E+2]) {
Far_nsignif_large = add_signif_c;
Far_exp_large = b.exponent;
Far_sign_large = b.sign;
Far_nsignif_small = mul_prod;
Far_abs_exp_diff = Far_exp_diff_2.template slc<E+1>(0);
Far_large_is_mul = 0;
}
Far_small_signif_aligner = Far_nsignif_small;
const int Far_align_max_sft = (Far_large_is_mul) ? mul_W : Far_align_extra_W;
Far_small_signif_aligner <<= Far_align_extra_W;
if (Far_abs_exp_diff < Far_align_max_sft) {
Far_small_signif_aligner >>= Far_abs_exp_diff;
} else {
Far_small_signif_aligner >>= Far_align_max_sft;
}
Far_nsignif_small = Far_small_signif_aligner.template slc<mul_W>(Far_align_extra_W);
const ac_int<1,false> Far_sticky = (Far_small_signif_aligner.template slc<Far_align_extra_W>(0)).or_reduce();
const ac_int<1,false> Far_add_1 = (add_eff_sign) ? (!Far_sticky) : 0;
const ac_int<E+1,false> Far_exp_large_overf = Far_exp_large + 1;
const ac_int<E+1,false> Far_exp_large_underf = Far_exp_large - 1;
ac_int<E+1,false> Far_exp_result;
const ac_int<mul_W+1,true> Far_nsignif_small_compl2 = (add_eff_sign) ? (~Far_nsignif_small) : Far_nsignif_small;
const ac_int<mul_W+2,true> Far_sum_1 = Far_nsignif_large + Far_nsignif_small_compl2 + Far_add_1;
const ac_int<mul_W+2,true> Far_sum_2 = Far_nsignif_small - Far_nsignif_large;
ac_int<1,false> Far_sign_result;
ac_int<mul_W+1,false> Far_sum;
if (!Far_sum_2[mul_W+1]) {
Far_sign_result = !Far_sign_large;
Far_sum = Far_sum_2;
}
if (!Far_sum_1[mul_W+1]) {
Far_sign_result = Far_sign_large;
Far_sum = Far_sum_1;
}
const ac_int<1,false> Far_sticky_hold = Far_sum[0];
if (Far_sum[mul_W]) {
Far_sum >>= 1;
Far_sum[0] = Far_sum[0] | Far_sticky_hold;
Far_exp_result = Far_exp_large_overf;
} else if (!Far_sum[mul_W-1]) {
Far_sum <<= 1;
Far_exp_result = Far_exp_large_underf;
} else {
Far_exp_result = Far_exp_large;
}
// Start of Near Path:
// 2-bit exponent difference.
const ac_int<2,false> mul_exp_result_slc = mul_exp_result.template slc<2>(0);
const ac_int<3,true> Near_exp_diff = mul_exp_result_slc - b.exponent.template slc<2>(0);
// Swap and 1-bit allign.
ac_int<mul_W+1,true> Near_nsignif_large = (Near_exp_diff[1]) ? add_signif_c : mul_prod;
ac_int<E+1,false> Near_exp_large = (Near_exp_diff[1]) ? (ac_int<E+1,false>)b.exponent : (ac_int<E+1,false>)mul_exp_result;
ac_int<1,false> Near_sign_large = (Near_exp_diff[1]) ? b.sign : mul_sign;
ac_int<mul_W+1,true> Near_nsignif_small = (Near_exp_diff[1]) ? mul_prod : add_signif_c;
ac_int<1,false> Near_sticky_hold = 0;
if (Near_exp_diff.or_reduce()) {
Near_sticky_hold = Near_nsignif_small[0];
Near_nsignif_small >>= 1;
}
const ac_int<1,false> Near_add_1 = !Near_sticky_hold;
// Significant substraction.
const ac_int<mul_W+1,true> Near_large_sub_small = Near_nsignif_large + (~Near_nsignif_small) + Near_add_1;
const ac_int<mul_W+1,true> Near_small_sub_large = Near_nsignif_small - Near_nsignif_large;
ac_int<E+1,false> Near_exp_result;
ac_int<mul_W,false> Near_chosen_sub;
ac_int<1,false> Near_sign_result;
if (!Near_large_sub_small[mul_W]) {
Near_sign_result = Near_sign_large;
Near_chosen_sub = Near_large_sub_small;
} else if (!Near_small_sub_large[mul_W]) {
Near_sign_result = !Near_sign_large;
Near_chosen_sub = Near_small_sub_large;
}
bool Near_zero = false;
//const int Near_lz_cnt = (Near_chosen_sub).leading_sign(Near_zero);
// 2*M+2 = 2*(23 + 1) = 48
// 2*M+2 = 2*(7 + 1) = 16
// 2*M+2 = 2*(3 + 1) = 8
const int ww = (2*M+2 <= 8) ? 8 :
(2*M+2 <= 16) ? 16 :
(2*M+2 <= 32) ? 32 : 64;
const int uu = ww - mul_W;
ac_int<ww,false> tcz = 0;
#pragma hls_unroll
for (int ii=0; ii<mul_W; ii++)
tcz[ii+uu]=Near_chosen_sub[ii];
const int Near_lz_cnt = lzcount<ww>(tcz);
if (Near_zero) {
Near_exp_result = 0;
} else {
Near_chosen_sub <<= Near_lz_cnt;
Near_exp_result = Near_exp_large - Near_lz_cnt;
}
const bool Is_Near = (Far_abs_exp_diff < 2) & add_eff_sign;
ac_int<mul_W,false> Chosen_signif_result = (Is_Near) ? (ac_int<mul_W+1, false>)Near_chosen_sub : Far_sum;
ac_int<E+1,false> Chosen_exp_result = (Is_Near) ? Near_exp_result : Far_exp_result;
ac_int<1,false> Chosen_sign_result = (Is_Near) ? Near_sign_result : Far_sign_result;
ac_int<1,false> Chosen_sticky = (Is_Near) ? Near_sticky_hold : Far_sticky;
// Round.
/*static*/ const int inj_point = M + 1;
ac_int<1,false> round;
switch (RND_MODE) {
case EVEN:
// Round to nearest tie to even.
round = Chosen_signif_result[inj_point-1] & (Chosen_signif_result[inj_point] | Chosen_signif_result[inj_point-2] | Chosen_sticky);
break;
case ODD:
// Round to nearest tie to odd.
round = Chosen_signif_result[inj_point-1] & (Chosen_signif_result[inj_point] | (!Chosen_signif_result[inj_point-2]) | Chosen_sticky);
break;
case INF:
// Round infinity.
round = Chosen_signif_result[inj_point-1];
break;
}
ac_int<M+1,false> Final_signif = Chosen_signif_result.template slc<M+1>(inj_point);
bool zero_res = !(Final_signif.or_reduce() | round);
Chosen_sign_result = (zero_res) ? mul_sign : Chosen_sign_result;
ac_int<M+2,false> Final_signif_result = Final_signif + round;
ac_int<E+1,false> Chosen_exp_result_overf = Chosen_exp_result + 1;
ac_int<E+1,false> Final_exp_result;
if (Final_signif_result[M+1]) {
Final_signif_result >>= 1;
Final_exp_result = Chosen_exp_result_overf;
} else {
Final_exp_result = Chosen_exp_result;
}
add_is_inf = (Final_exp_result >= ((1 << E) - 1)) ? true : add_is_inf;
const ac_int<1,false> inf_sign = (t_in_b_is_inf) ? b.sign : mul_sign;
output.sign = (add_is_inf) ? inf_sign :((zero_res) ? (sgn_t)0 : Chosen_sign_result);
output.exponent = (add_is_inf) ? (exp_t)((1 << E) - 1) : ((zero_res) ? (exp_t)0 : Final_exp_result.template slc<E>(0));
output.mantissa = (add_is_inf) ? (man_t)0 : Final_signif_result.template slc<M>(0);
}
template<RND_ENUM RND_MODE=EVEN, bool DENORMALS=false>
void fpmul(const fast_float<M,E> a, fast_float<M,E> &output) {
static const ac_int<E,false> mul_exp_base = (1 << (E-1)) - 1;
static const int signif_W = M + 1;
static const int mul_W = (signif_W) << 1;
ac_int<1,false> a_is_zero, c_is_zero;
// Sign Calculation
const ac_int<1,false> sign_res = sign ^ a.sign;
// Create significants of mul.
ac_int<M+1,false> mul_signif_a = mantissa;
ac_int<M+1,false> mul_signif_c = a.mantissa;
ac_int<1,false> is_a_subnormal = (exponent == 0);
ac_int<1,false> is_c_subnormal = (a.exponent == 0);
mul_signif_a[M] = (DENORMALS) ? ((is_a_subnormal) ? 0 : 1) : 1;
mul_signif_c[M] = (DENORMALS) ? ((is_c_subnormal) ? 0 : 1) : 1;
if (DENORMALS) {
mul_signif_a <<= is_a_subnormal;
mul_signif_c <<= is_c_subnormal;
a_is_zero = ~(mul_signif_a.or_reduce());
c_is_zero = ~(mul_signif_c.or_reduce());
}
// Infinity Check.
bool Is_inf = ((exponent).and_reduce() | (a.exponent).and_reduce());
// Calculate exponent result and overf exponent result.
ac_int<E+2,true> mul_exp = (DENORMALS) ?
((a_is_zero | c_is_zero) ? (ac_int<E+2,true>)0 : (ac_int<E+2,true>)(exponent + a.exponent - mul_exp_base)) :
((is_a_subnormal | is_c_subnormal)) ? (ac_int<E+2,true>)0 : (ac_int<E+2,true>)(exponent + a.exponent - mul_exp_base);
if (mul_exp < 0)
mul_exp = 0;
else if (mul_exp >= ((1<<E)-1))
mul_exp = ((1<<E)-1);
// Overflow Exponent Calculation
ac_int<E+2,true> mul_exp_overf = (DENORMALS) ?
((a_is_zero | c_is_zero) ? (ac_int<E+2,true>)0 : (ac_int<E+2,true>)(exponent + a.exponent - mul_exp_base + 1)) :
((is_a_subnormal | is_c_subnormal)) ? (ac_int<E+2,true>)0 : (ac_int<E+2,true>)(exponent + a.exponent - mul_exp_base + 1);
if (mul_exp_overf < 0)
mul_exp_overf = 0;
else if (mul_exp_overf >= ((1<<E)-1))
mul_exp_overf = ((1<<E)-1);
ac_int<E+2,true> right_shift;
if (DENORMALS) {
right_shift = (a_is_zero | c_is_zero) ? (ac_int<E+2,true>)0 : (ac_int<E+2,true>)(mul_exp_base - exponent - a.exponent);
if (right_shift < 0)
right_shift = 0;
else if (right_shift > M+2)
right_shift = M+2;
}
ac_int<1,false> mul_zero = (DENORMALS) ? (a_is_zero | c_is_zero) : (is_a_subnormal | is_c_subnormal);
// Do the multiplication.
ac_int<mul_W,false> mul_res = mul_signif_a*mul_signif_c;
ac_int<mul_W,false> mul_prod = (DENORMALS) ? ((a_is_zero | c_is_zero) ? (ac_int<mul_W,false>)0 : mul_res) : ((is_a_subnormal | is_c_subnormal) ? (ac_int<mul_W,false>)0 : mul_res);
// Overflow Check.
ac_int<1,false> mul_overflow = mul_prod[mul_W-1];
ac_int<E+2,true> exp_res = (mul_overflow) ? mul_exp_overf : mul_exp;
// Normalization.
if (DENORMALS) {