/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
// This version is derived from the generic fma software implementation
// (__clc_sw_fma), but avoids the use of ulong in favor of uint2. The logic has
// been updated as appropriate.
#include <clc/clc.h>
#include "../../../generic/lib/clcmacro.h"
#include "../../../generic/lib/math/math.h"
struct fp {
uint2 mantissa;
int exponent;
uint sign;
};
static uint2 u2_set(uint hi, uint lo) {
uint2 res;
res.lo = lo;
res.hi = hi;
return res;
}
static uint2 u2_set_u(uint val) { return u2_set(0, val); }
static uint2 u2_mul(uint a, uint b) {
uint2 res;
res.hi = mul_hi(a, b);
res.lo = a * b;
return res;
}
static uint2 u2_sll(uint2 val, uint shift) {
if (shift == 0)
return val;
if (shift < 32) {
val.hi <<= shift;
val.hi |= val.lo >> (32 - shift);
val.lo <<= shift;
} else {
val.hi = val.lo << (shift - 32);
val.lo = 0;
}
return val;
}
static uint2 u2_srl(uint2 val, uint shift) {
if (shift == 0)
return val;
if (shift < 32) {
val.lo >>= shift;
val.lo |= val.hi << (32 - shift);
val.hi >>= shift;
} else {
val.lo = val.hi >> (shift - 32);
val.hi = 0;
}
return val;
}
static uint2 u2_or(uint2 a, uint b) {
a.lo |= b;
return a;
}
static uint2 u2_and(uint2 a, uint2 b) {
a.lo &= b.lo;
a.hi &= b.hi;
return a;
}
static uint2 u2_add(uint2 a, uint2 b) {
uint carry = (hadd(a.lo, b.lo) >> 31) & 0x1;
a.lo += b.lo;
a.hi += b.hi + carry;
return a;
}
static uint2 u2_add_u(uint2 a, uint b) { return u2_add(a, u2_set_u(b)); }
static uint2 u2_inv(uint2 a) {
a.lo = ~a.lo;
a.hi = ~a.hi;
return u2_add_u(a, 1);
}
static uint u2_clz(uint2 a) {
uint leading_zeroes = clz(a.hi);
if (leading_zeroes == 32) {
leading_zeroes += clz(a.lo);
}
return leading_zeroes;
}
static bool u2_eq(uint2 a, uint2 b) { return a.lo == b.lo && a.hi == b.hi; }
static bool u2_zero(uint2 a) { return u2_eq(a, u2_set_u(0)); }
static bool u2_gt(uint2 a, uint2 b) {
return a.hi > b.hi || (a.hi == b.hi && a.lo > b.lo);
}
_CLC_DEF _CLC_OVERLOAD float fma(float a, float b, float c) {
/* special cases */
if (isnan(a) || isnan(b) || isnan(c) || isinf(a) || isinf(b)) {
return mad(a, b, c);
}
/* If only c is inf, and both a,b are regular numbers, the result is c*/
if (isinf(c)) {
return c;
}
a = __clc_flush_denormal_if_not_supported(a);
b = __clc_flush_denormal_if_not_supported(b);
c = __clc_flush_denormal_if_not_supported(c);
if (a == 0.0f || b == 0.0f) {
return c;
}
if (c == 0) {
return a * b;
}
struct fp st_a, st_b, st_c;
st_a.exponent = a == .0f ? 0 : ((as_uint(a) & 0x7f800000) >> 23) - 127;
st_b.exponent = b == .0f ? 0 : ((as_uint(b) & 0x7f800000) >> 23) - 127;
st_c.exponent = c == .0f ? 0 : ((as_uint(c) & 0x7f800000) >> 23) - 127;
st_a.mantissa = u2_set_u(a == .0f ? 0 : (as_uint(a) & 0x7fffff) | 0x800000);
st_b.mantissa = u2_set_u(b == .0f ? 0 : (as_uint(b) & 0x7fffff) | 0x800000);
st_c.mantissa = u2_set_u(c == .0f ? 0 : (as_uint(c) & 0x7fffff) | 0x800000);
st_a.sign = as_uint(a) & 0x80000000;
st_b.sign = as_uint(b) & 0x80000000;
st_c.sign = as_uint(c) & 0x80000000;
// Multiplication.
// Move the product to the highest bits to maximize precision
// mantissa is 24 bits => product is 48 bits, 2bits non-fraction.
// Add one bit for future addition overflow,
// add another bit to detect subtraction underflow
struct fp st_mul;
st_mul.sign = st_a.sign ^ st_b.sign;
st_mul.mantissa = u2_sll(u2_mul(st_a.mantissa.lo, st_b.mantissa.lo), 14);
st_mul.exponent =
!u2_zero(st_mul.mantissa) ? st_a.exponent + st_b.exponent : 0;
// FIXME: Detecting a == 0 || b == 0 above crashed GCN isel
if (st_mul.exponent == 0 && u2_zero(st_mul.mantissa))
return c;
// Mantissa is 23 fractional bits, shift it the same way as product mantissa
#define C_ADJUST 37ul
// both exponents are bias adjusted
int exp_diff = st_mul.exponent - st_c.exponent;
st_c.mantissa = u2_sll(st_c.mantissa, C_ADJUST);
uint2 cutoff_bits = u2_set_u(0);
uint2 cutoff_mask = u2_add(u2_sll(u2_set_u(1), abs(exp_diff)),
u2_set(0xffffffff, 0xffffffff));
if (exp_diff > 0) {
cutoff_bits =
exp_diff >= 64 ? st_c.mantissa : u2_and(st_c.mantissa, cutoff_mask);
st_c.mantissa =
exp_diff >= 64 ? u2_set_u(0) : u2_srl(st_c.mantissa, exp_diff);
} else {
cutoff_bits = -exp_diff >= 64 ? st_mul.mantissa
: u2_and(st_mul.mantissa, cutoff_mask);
st_mul.mantissa =
-exp_diff >= 64 ? u2_set_u(0) : u2_srl(st_mul.mantissa, -exp_diff);
}
struct fp st_fma;
st_fma.sign = st_mul.sign;
st_fma.exponent = max(st_mul.exponent, st_c.exponent);
if (st_c.sign == st_mul.sign) {
st_fma.mantissa = u2_add(st_mul.mantissa, st_c.mantissa);
} else {
// cutoff bits borrow one
st_fma.mantissa =
u2_add(u2_add(st_mul.mantissa, u2_inv(st_c.mantissa)),
(!u2_zero(cutoff_bits) && (st_mul.exponent > st_c.exponent)
? u2_set(0xffffffff, 0xffffffff)
: u2_set_u(0)));
}
// underflow: st_c.sign != st_mul.sign, and magnitude switches the sign
if (u2_gt(st_fma.mantissa, u2_set(0x7fffffff, 0xffffffff))) {
st_fma.mantissa = u2_inv(st_fma.mantissa);
st_fma.sign = st_mul.sign ^ 0x80000000;
}
// detect overflow/underflow
int overflow_bits = 3 - u2_clz(st_fma.mantissa);
// adjust exponent
st_fma.exponent += overflow_bits;
// handle underflow
if (overflow_bits < 0) {
st_fma.mantissa = u2_sll(st_fma.mantissa, -overflow_bits);
overflow_bits = 0;
}
// rounding
uint2 trunc_mask = u2_add(u2_sll(u2_set_u(1), C_ADJUST + overflow_bits),
u2_set(0xffffffff, 0xffffffff));
uint2 trunc_bits =
u2_or(u2_and(st_fma.mantissa, trunc_mask), !u2_zero(cutoff_bits));
uint2 last_bit =
u2_and(st_fma.mantissa, u2_sll(u2_set_u(1), C_ADJUST + overflow_bits));
uint2 grs_bits = u2_sll(u2_set_u(4), C_ADJUST - 3 + overflow_bits);
// round to nearest even
if (u2_gt(trunc_bits, grs_bits) ||
(u2_eq(trunc_bits, grs_bits) && !u2_zero(last_bit))) {
st_fma.mantissa =
u2_add(st_fma.mantissa, u2_sll(u2_set_u(1), C_ADJUST + overflow_bits));
}
// Shift mantissa back to bit 23
st_fma.mantissa = u2_srl(st_fma.mantissa, C_ADJUST + overflow_bits);
// Detect rounding overflow
if (u2_gt(st_fma.mantissa, u2_set_u(0xffffff))) {
++st_fma.exponent;
st_fma.mantissa = u2_srl(st_fma.mantissa, 1);
}
if (u2_zero(st_fma.mantissa)) {
return 0.0f;
}
// Flating point range limit
if (st_fma.exponent > 127) {
return as_float(as_uint(INFINITY) | st_fma.sign);
}
// Flush denormals
if (st_fma.exponent <= -127) {
return as_float(st_fma.sign);
}
return as_float(st_fma.sign | ((st_fma.exponent + 127) << 23) |
((uint)st_fma.mantissa.lo & 0x7fffff));
}
_CLC_TERNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, fma, float, float, float)
#ifdef cl_khr_fp16
#pragma OPENCL EXTENSION cl_khr_fp16 : enable
_CLC_DEF _CLC_OVERLOAD half fma(half a, half b, half c) {
return (half)mad((float)a, (float)b, (float)c);
}
_CLC_TERNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, half, fma, half, half, half)
#endif
Codebase Browser
llvm