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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include <cm-cl/math.h>
#include <cm-cl/vector.h>
#include "f64consts.h"
using namespace cm;
/***********************************************************
* Important: Set rounding mode to RNE (RTE in CM);
* restore rounding mode before each return statement
* (Directed rounding modes could lead to infinite loops)
**********************************************************/
namespace {
template <int N>
CM_NODEBUG CM_INLINE vector<uint32_t, N> get_sign(vector<double, N> x) {
auto x_split = x.template format<uint32_t>();
vector<uint32_t, N> x_hi = x_split.template select<N, 2>(1);
return x_hi & sign_32bit;
}
template <int N>
CM_NODEBUG CM_INLINE vector<uint32_t, N> get_exp(vector<double, N> x) {
auto x_split = x.template format<uint32_t>();
vector<uint32_t, N> x_hi = x_split.template select<N, 2>(1);
return (x_hi >> exp_shift) & exp_mask;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N> and_mantissa_loss(vector<double, N> x) {
vector<uint32_t, 2 * N> x_split = x.template format<uint32_t>();
vector<uint32_t, N> x_lo = x_split.template select<N, 2>(0);
x_lo &= mantissa_32loss;
x_split.template select<N, 2>(0) = x_lo;
x = x_split.template format<double>();
return x;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N>
divide_by_mask(vector<double, N> a, vector<double, N> b, mask<N> filled_out) {
auto local_a = a;
local_a.merge(0, filled_out);
auto local_b = b;
local_b.merge(0, filled_out);
vector<double, N> q =
detail::__cm_cl_fdiv_ieee(local_a.cl_vector(), local_b.cl_vector());
return q;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N> round_to_int(vector<double, N> q) {
vector<double, N> one = 1.0;
vector<double, N> round = roundInt;
vector<double, N> S = math::mad(q, one, round);
q = math::mad(S, one, -round);
return q;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N> xor_sign(vector<double, N> a,
vector<uint32_t, N> sign) {
vector<uint32_t, 2 * N> a_split = a.template format<uint32_t>();
vector<uint32_t, N> a_hi = a_split.template select<N, 2>(1);
a_hi = a_hi ^ sign;
a_split.template select<N, 2>(1) = a_hi;
a = a_split.template format<double>();
return a;
}
template <int N>
CM_NODEBUG CM_INLINE mask<N> check_is_nan_or_inf(vector<double, N> q) {
auto q_split = q.template format<uint32_t>();
vector<uint32_t, N> q_hi = q_split.template select<N, 2>(1);
return (q_hi >= exp_32bitmask);
}
template <int N>
CM_NODEBUG CM_INLINE mask<N> check_is_nan(vector<double, N> q) {
auto q_split = q.template format<uint32_t>();
vector<uint32_t, N> q_lo = q_split.template select<N, 2>(0);
vector<uint32_t, N> q_hi = q_split.template select<N, 2>(1);
return (q_hi > exp_32bitmask) | (q_hi == exp_32bitmask & q_lo > 0);
}
template <int N>
CM_NODEBUG CM_INLINE void
__impl_rem_special_middle(vector<double, N> &a, vector<double, N> &b,
vector<double, N> &q, mask<N> filled_out) {
auto bs = b * twoPow1023;
auto bhalf2 = b * twoPow1022;
q = divide_by_mask(a, bs, filled_out);
mask<N> q_ge = check_is_nan_or_inf(q) & (filled_out == 0);
if (q_ge.any()) {
auto bs2 = bs * twoPow1023;
vector<double, N> q_local = divide_by_mask(a, bs2, q_ge == 0);
q_local = round_to_int(q_local);
auto a_local = math::mad(-bs2, q_local, a);
q_local = divide_by_mask(a_local, bs, q_ge == 0);
a.merge(a_local, q_ge);
q.merge(q_local, q_ge);
}
auto q_exp = get_exp(q);
mask<N> q_exp_ge = (q_exp >= exp_32threshold_shift) & (filled_out == 0);
do {
auto q_local = and_mantissa_loss(q);
// q is an integer
// a - b*q
auto a_local = math::mad(-bs, q_local, a);
q_local = divide_by_mask(a_local, bs, q_exp_ge == 0);
a.merge(a_local, q_exp_ge);
q.merge(q_local, q_exp_ge);
q_exp = get_exp(q_local);
q_exp_ge &= (q_exp >= exp_32threshold_shift);
} while (q_exp_ge.any());
q = round_to_int(q);
a = math::mad(-bs, q, a);
vector<double, N> a_mod = math::absolute(a.cl_vector());
mask<N> ge_bhalf = (a_mod > bhalf2) & (filled_out == 0);
do {
vector<double, N> q_local = divide_by_mask(a, bs, ge_bhalf == 0);
// round q.f to integer
q_local = round_to_int(q_local);
// a - b*q
auto a_local = math::mad(-bs, q_local, a);
q.merge(q_local, ge_bhalf);
a.merge(a_local, ge_bhalf);
a_mod = math::absolute(a.cl_vector());
ge_bhalf &= a_mod > bhalf2;
} while (ge_bhalf.any());
q = divide_by_mask(a, b, filled_out);
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N>
__impl_rem_body(vector<double, N> a, vector<double, N> b, vector<double, N> q,
vector<uint32_t, N> sgn_a, mask<N> filled_out) {
auto q_exp = get_exp(q);
auto local_a = a;
auto local_q = q;
mask<N> q_exp_ge = (q_exp >= exp_32threshold_shift) & (filled_out == 0);
do {
local_q = and_mantissa_loss(q);
local_a = math::mad(-b, local_q, a);
auto local_b = b;
local_q = divide_by_mask(local_a, local_b, q_exp_ge == 0);
q_exp = get_exp(local_q);
a.merge(local_a, q_exp_ge);
q.merge(local_q, q_exp_ge);
q_exp_ge &= (q_exp >= exp_32threshold_shift);
} while (q_exp_ge.any());
q = round_to_int(q);
a = math::mad(-b, q, a);
vector<double, N> local_abs_2a = math::absolute(a.cl_vector()) * 2;
mask<N> fabs2gb = (local_abs_2a > b) & (filled_out == 0);
local_a = a;
local_q = q;
do {
auto local_b = b;
local_q = divide_by_mask(local_a, local_b, fabs2gb == 0);
local_q = round_to_int(local_q);
local_a = math::mad(-b, local_q, local_a);
q.merge(local_q, fabs2gb);
a.merge(local_a, fabs2gb);
local_abs_2a = math::absolute(a.cl_vector()) * 2;
fabs2gb &= local_abs_2a > b;
} while (fabs2gb.any());
// apply sign
a = xor_sign(a, sgn_a);
return a;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N>
__impl_rem_special(vector<double, N> a, vector<double, N> b,
vector<double, N> q, vector<double, N> y,
vector<uint32_t, N> sgn_a, mask<N> filled_out) {
vector<double, N> result;
// y==0 or x==Inf?
mask<N> b_isZero = b == 0.0;
result.merge(math::mad(-b, q, a), b_isZero);
filled_out |= b_isZero;
mask<N> a_isNan = check_is_nan_or_inf(a) & (filled_out == 0);
result.merge(math::mad(-b, q, a), a_isNan);
filled_out |= a_isNan;
// y is NaN?
auto b_exp = get_exp(b);
mask<N> b_isNan = check_is_nan(b) & (filled_out == 0);
result.merge(y + y, b_isNan);
filled_out |= b_isNan;
// q overflow
vector<double, N> bhalf = b * 0.5f;
// b * 0.5 underflows
mask<N> isBhalf_uderflows = (bhalf == 0.0) & (filled_out == 0);
if (isBhalf_uderflows.any()) {
auto result_lo = result.template select<N, 2>(0);
result_lo.merge(0, isBhalf_uderflows);
result.template select<N, 2>(0) = result_lo;
auto result_hi = result.template select<N, 2>(1);
result_hi.merge(sgn_a, isBhalf_uderflows);
result.template select<N, 2>(1) = result_hi;
}
filled_out |= isBhalf_uderflows;
if (filled_out.all())
return result;
a.merge(0, filled_out);
b.merge(0, filled_out);
q.merge(0, filled_out);
__impl_rem_special_middle(a, b, q, filled_out);
result.merge(__impl_rem_body(a, b, q, sgn_a, filled_out), filled_out == 0);
return result;
}
template <int N>
CM_NODEBUG CM_INLINE vector<double, N> __impl_rem_f64(vector<double, N> x,
vector<double, N> y) {
vector<double, N> a = x;
vector<double, N> b = y;
vector<uint32_t, N> sgn_a = get_sign(a);
a = math::absolute(a.cl_vector());
b = math::absolute(b.cl_vector());
// IEEE DIV, RN mode
vector<double, N> q = detail::__cm_cl_fdiv_ieee(a.cl_vector(), b.cl_vector());
// overflow, or special cases?
vector<double, N> result = 0.0f;
mask<N> filled_out;
mask<N> special_case = get_exp(q) == exp_mask;
if (special_case.any())
result.merge(__impl_rem_special(a, b, q, y, sgn_a, special_case == 0),
special_case);
filled_out = special_case;
// fast exit for a <= b
mask<N> fast_case = (a <= b) & (filled_out == 0);
if (fast_case.any()) {
// 2*a > b ?
mask<N> double_ge = a * 2.0 > b;
auto local_a = a;
local_a.merge(a - b, double_ge);
// using a*1.0 to flush denormal results to 0 in FTZ mode
const vector<double, N> allones = 1.0f;
const vector<double, N> zero = 0.0f;
local_a = math::mad(local_a, allones, zero);
result.merge(xor_sign(local_a, sgn_a), fast_case);
}
filled_out |= fast_case;
if (filled_out.all())
return result;
result.merge(__impl_rem_body(a, b, q, sgn_a, filled_out), (filled_out == 0));
return result;
}
} // namespace
CM_NODEBUG CM_NOINLINE extern "C" double __vc_builtin_frem_f64__rte_(double a,
double b) {
vector<double, 1> va = a;
vector<double, 1> vb = b;
return __impl_rem_f64(va, vb)[0];
}
#define FREM(WIDTH) \
CM_NODEBUG CM_NOINLINE extern "C" cl_vector<double, WIDTH> \
__vc_builtin_frem_v##WIDTH##f64__rte_(cl_vector<double, WIDTH> a, \
cl_vector<double, WIDTH> b) { \
vector<double, WIDTH> va{a}; \
vector<double, WIDTH> vb{b}; \
auto r = __impl_rem_f64(va, vb); \
return r.cl_vector(); \
}
FREM(1)
FREM(2)
FREM(4)
FREM(8)
FREM(16)
FREM(32)
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