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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include "f32consts.h"
#include <cm-cl/math.h>
#include <cm-cl/vector.h>
using namespace cm;
namespace {
/***********************************************************
* Important: Set rounding mode to RNE;
* restore rounding mode before each return statement
* (Directed rounding modes could lead to infinite loops)
**********************************************************/
template <int N>
CM_NODEBUG CM_INLINE vector<uint32_t, N> get_sign(vector<float, N> x) {
vector<uint32_t, N> x_int = x.template format<uint32_t>();
return x_int & sign_bit;
}
template <int N>
CM_NODEBUG CM_INLINE vector<uint32_t, N> get_exp(vector<float, N> x) {
vector<uint32_t, N> x_int = x.template format<uint32_t>();
return (x_int >> exp_shift) & exp_mask;
}
template <int N>
CM_NODEBUG CM_INLINE vector<float, N> xor_sign(vector<float, N> a,
vector<uint32_t, N> sign) {
vector<uint32_t, N> a_int = a.template format<uint32_t>();
a_int = a_int ^ sign;
return a_int.template format<float>();
}
template <int N>
CM_NODEBUG CM_INLINE mask<N> check_is_nan_or_inf(vector<float, N> q) {
vector<uint32_t, N> q_int = q.template format<uint32_t>();
return (q_int >= exp_bitmask);
}
template <int N> CM_NODEBUG CM_INLINE mask<N> check_is_nan(vector<float, N> q) {
vector<uint32_t, N> q_int = q.template format<uint32_t>();
return (q_int > exp_bitmask);
}
template <int N>
CM_NODEBUG CM_INLINE vector<float, N>
divide_by_mask(vector<float, N> a, vector<float, N> b, mask<N> filled_out) {
auto local_a = a;
local_a.merge(exp_bias << exp_shift, filled_out);
if (filled_out.all())
return local_a;
auto local_b = b;
local_b.merge(exp_bias << exp_shift, filled_out);
vector<float, 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<float, N>
__impl_rem_body(vector<float, N> a, vector<float, N> b, vector<float, N> q,
vector<uint32_t, N> sgn_a, mask<N> filled_out) {
// round q.f to integer (use rnde instruction)
q = math::roundne(q);
// a - b*q
a = math::mad(-b, q, a);
vector<float, N> local_abs_2a = math::absolute(a.cl_vector()) * 2.0f;
mask<N> fabs2gb = (local_abs_2a > b) & (filled_out == 0);
// 2*fabs(a) > b
while (1) {
auto local_q = divide_by_mask(a, b, fabs2gb == 0);
// round q.f to integer, using rnde instruction (RNE mode)
local_q = math::roundne(local_q);
// a - b*q
auto local_a = math::mad(-b, local_q, a);
q.merge(local_q, fabs2gb);
a.merge(local_a, fabs2gb);
local_abs_2a = math::absolute(a.cl_vector()) * 2.0f;
fabs2gb &= local_abs_2a > b;
if ((fabs2gb == 0).all())
break;
}
// apply sign
a = xor_sign(a, sgn_a);
return a;
}
template <int N>
CM_NODEBUG CM_INLINE vector<float, N>
__impl_rem_special(vector<float, N> a, vector<float, N> b, vector<float, N> q,
vector<float, N> y, vector<uint32_t, N> sgn_a,
mask<N> in_mask) {
vector<float, N> result;
mask<N> filled_out = in_mask == 0;
// y==0 or x==Inf?
mask<N> b_isZero = (b == 0.0) & (filled_out == 0);
result.merge(math::mad(-b, q, a), b_isZero);
filled_out |= b_isZero;
auto 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?
mask<N> b_isNan = check_is_nan(b) & (filled_out == 0);
result.merge(y + y, b_isNan);
filled_out |= b_isNan;
if (filled_out.all())
return result;
// q.f overflow
// b* 2*1023
auto bs = b * twoPow127;
auto bhalf2 = b * twoPow126;
q = divide_by_mask(a, bs, filled_out);
auto q_isNan = check_is_nan_or_inf(q) & (filled_out == 0);
if (q_isNan.any()) {
vector<float, N> bs2 = 1.0;
// b* 2*127 * 2^127
bs2.merge(bs * twoPow127, q_isNan);
vector<float, N> local_a = 0;
local_a.merge(a, q_isNan);
auto local_q = divide_by_mask(local_a, bs2, q_isNan == 0);
// round to integral
local_q = math::roundne(local_q);
local_a = math::mad(-bs2, local_q, local_a);
vector<float, N> local_bs = 1.0;
local_bs.merge(bs, q_isNan);
local_q = divide_by_mask(local_a, local_bs, q_isNan == 0);
a.merge(local_a, q_isNan);
q.merge(local_q, q_isNan);
}
// round q.f to integer (use rnde instruction)
q = math::roundne(q);
// a - b*q
a = math::mad(-bs, q, a);
vector<float, N> a_mod = math::absolute(a.cl_vector());
mask<N> ge_bhalf = (a_mod > bhalf2) & (filled_out == 0);
vector<float, N> local_a = 0.0;
vector<float, N> local_bs = 1.0;
while (1) {
local_a.merge(a, ge_bhalf);
local_bs.merge(bs, ge_bhalf);
vector<float, N> local_q = divide_by_mask(local_a, local_bs, ge_bhalf == 0);
// round q.f to integer
local_q = math::roundne(local_q);
// a - b*q
local_a = math::mad(-local_bs, local_q, local_a);
a.merge(local_a, ge_bhalf);
q.merge(local_q, ge_bhalf);
vector<float, N> a_mod = math::absolute(a.cl_vector());
ge_bhalf &= (a_mod > bhalf2) & ge_bhalf;
if ((ge_bhalf == 0).all())
break;
}
vector<float, N> local_q = divide_by_mask(a, b, filled_out);
q.merge(local_q, filled_out == 0);
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<float, N> __impl_rem_f32(vector<float, N> x,
vector<float, N> y) {
vector<float, N> a = x;
vector<float, N> b = y;
vector<float, N> result = 123.0f;
mask<N> filled_out = false;
// sign of x
auto sgn_a = get_sign(a);
// |x|, |y|
a = math::absolute(a.cl_vector());
b = math::absolute(b.cl_vector());
// IEEE DIV, RN mode
vector<float, N> q = detail::__cm_cl_fdiv_ieee(a.cl_vector(), b.cl_vector());
// overflow, or special cases
auto q_exp = get_exp(q);
mask<N> special_case = q_exp == exp_mask;
if (special_case.any()) {
// here we must copy a, b.. e.t.c to do not spoil values for future
auto res_special = __impl_rem_special(a, b, q, y, sgn_a, special_case);
result.merge(res_special, special_case);
if (special_case.all())
return result;
}
filled_out |= special_case;
mask<N> fast_case = (a <= b) & (filled_out == 0);
// fast exit for a <= b
if (fast_case.any()) {
mask<N> float_ge = a * 2.0f > b;
auto local_a = a;
if (float_ge.any())
local_a.merge(a - b, float_ge & fast_case);
const vector<float, N> one = 1.0f;
const vector<float, N> zero = 0.0f;
// using a*1.0f to flush denormal results to 0 in FTZ mode
local_a.merge(math::mad(local_a, one, zero), fast_case);
result.merge(xor_sign(local_a, sgn_a), fast_case);
filled_out |= fast_case;
if (filled_out.all())
return result;
}
auto rem_body_res = __impl_rem_body(a, b, q, sgn_a, filled_out);
result.merge(rem_body_res, (filled_out == 0));
return result;
}
} // namespace
CM_NODEBUG CM_NOINLINE extern "C" float __vc_builtin_frem_f32__rte_(float a,
float b) {
vector<float, 1> va = a;
vector<float, 1> vb = b;
return __impl_rem_f32(va, vb)[0];
}
#define FREM(WIDTH) \
CM_NODEBUG CM_NOINLINE extern "C" cl_vector<float, WIDTH> \
__vc_builtin_frem_v##WIDTH##f32__rte_(cl_vector<float, WIDTH> a, \
cl_vector<float, WIDTH> b) { \
vector<float, WIDTH> va{a}; \
vector<float, WIDTH> vb{b}; \
auto r = __impl_rem_f32(va, vb); \
return r.cl_vector(); \
}
FREM(1)
FREM(2)
FREM(4)
FREM(8)
FREM(16)
FREM(32)
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