/*
* Copyright 2012-15 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 COPYRIGHT HOLDER(S) OR AUTHOR(S) 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.
*
* Authors: AMD
*
*/
#include "dm_services.h"
#include "include/fixed31_32.h"
static const struct fixed31_32 dc_fixpt_two_pi = { 26986075409LL };
static const struct fixed31_32 dc_fixpt_ln2 = { 2977044471LL };
static const struct fixed31_32 dc_fixpt_ln2_div_2 = { 1488522236LL };
static inline unsigned long long abs_i64(
long long arg)
{
if (arg > 0)
return (unsigned long long)arg;
else
return (unsigned long long)(-arg);
}
/*
* @brief
* result = dividend / divisor
* *remainder = dividend % divisor
*/
static inline unsigned long long complete_integer_division_u64(
unsigned long long dividend,
unsigned long long divisor,
unsigned long long *remainder)
{
unsigned long long result;
ASSERT(divisor);
result = div64_u64_rem(dividend, divisor, remainder);
return result;
}
#define FRACTIONAL_PART_MASK \
((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1)
#define GET_INTEGER_PART(x) \
((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART)
#define GET_FRACTIONAL_PART(x) \
(FRACTIONAL_PART_MASK & (x))
struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator)
{
struct fixed31_32 res;
bool arg1_negative = numerator < 0;
bool arg2_negative = denominator < 0;
unsigned long long arg1_value = arg1_negative ? -numerator : numerator;
unsigned long long arg2_value = arg2_negative ? -denominator : denominator;
unsigned long long remainder;
/* determine integer part */
unsigned long long res_value = complete_integer_division_u64(
arg1_value, arg2_value, &remainder);
ASSERT(res_value <= LONG_MAX);
/* determine fractional part */
{
unsigned int i = FIXED31_32_BITS_PER_FRACTIONAL_PART;
do {
remainder <<= 1;
res_value <<= 1;
if (remainder >= arg2_value) {
res_value |= 1;
remainder -= arg2_value;
}
} while (--i != 0);
}
/* round up LSB */
{
unsigned long long summand = (remainder << 1) >= arg2_value;
ASSERT(res_value <= LLONG_MAX - summand);
res_value += summand;
}
res.value = (long long)res_value;
if (arg1_negative ^ arg2_negative)
res.value = -res.value;
return res;
}
struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
struct fixed31_32 res;
bool arg1_negative = arg1.value < 0;
bool arg2_negative = arg2.value < 0;
unsigned long long arg1_value = arg1_negative ? -arg1.value : arg1.value;
unsigned long long arg2_value = arg2_negative ? -arg2.value : arg2.value;
unsigned long long arg1_int = GET_INTEGER_PART(arg1_value);
unsigned long long arg2_int = GET_INTEGER_PART(arg2_value);
unsigned long long arg1_fra = GET_FRACTIONAL_PART(arg1_value);
unsigned long long arg2_fra = GET_FRACTIONAL_PART(arg2_value);
unsigned long long tmp;
res.value = arg1_int * arg2_int;
res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
tmp = arg1_int * arg2_fra;
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
tmp = arg2_int * arg1_fra;
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
tmp = arg1_fra * arg2_fra;
tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
(tmp >= (unsigned long long)dc_fixpt_half.value);
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
if (arg1_negative ^ arg2_negative)
res.value = -res.value;
return res;
}
struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg)
{
struct fixed31_32 res;
unsigned long long arg_value = abs_i64(arg.value);
unsigned long long arg_int = GET_INTEGER_PART(arg_value);
unsigned long long arg_fra = GET_FRACTIONAL_PART(arg_value);
unsigned long long tmp;
res.value = arg_int * arg_int;
res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
tmp = arg_int * arg_fra;
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
tmp = arg_fra * arg_fra;
tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
(tmp >= (unsigned long long)dc_fixpt_half.value);
ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
res.value += tmp;
return res;
}
struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg)
{
/*
* @note
* Good idea to use Newton's method
*/
ASSERT(arg.value);
return dc_fixpt_from_fraction(
dc_fixpt_one.value,
arg.value);
}
struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg)
{
struct fixed31_32 square;
struct fixed31_32 res = dc_fixpt_one;
int n = 27;
struct fixed31_32 arg_norm = arg;
if (dc_fixpt_le(
dc_fixpt_two_pi,
dc_fixpt_abs(arg))) {
arg_norm = dc_fixpt_sub(
arg_norm,
dc_fixpt_mul_int(
dc_fixpt_two_pi,
(int)div64_s64(
arg_norm.value,
dc_fixpt_two_pi.value)));
}
square = dc_fixpt_sqr(arg_norm);
do {
res = dc_fixpt_sub(
dc_fixpt_one,
dc_fixpt_div_int(
dc_fixpt_mul(
square,
res),
n * (n - 1)));
n -= 2;
} while (n > 2);
if (arg.value != arg_norm.value)
res = dc_fixpt_div(
dc_fixpt_mul(res, arg_norm),
arg);
return res;
}
struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg)
{
return dc_fixpt_mul(
arg,
dc_fixpt_sinc(arg));
}
struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg)
{
/* TODO implement argument normalization */
const struct fixed31_32 square = dc_fixpt_sqr(arg);
struct fixed31_32 res = dc_fixpt_one;
int n = 26;
do {
res = dc_fixpt_sub(
dc_fixpt_one,
dc_fixpt_div_int(
dc_fixpt_mul(
square,
res),
n * (n - 1)));
n -= 2;
} while (n != 0);
return res;
}
/*
* @brief
* result = exp(arg),
* where abs(arg) < 1
*
* Calculated as Taylor series.
*/
static struct fixed31_32 fixed31_32_exp_from_taylor_series(struct fixed31_32 arg)
{
unsigned int n = 9;
struct fixed31_32 res = dc_fixpt_from_fraction(
n + 2,
n + 1);
/* TODO find correct res */
ASSERT(dc_fixpt_lt(arg, dc_fixpt_one));
do
res = dc_fixpt_add(
dc_fixpt_one,
dc_fixpt_div_int(
dc_fixpt_mul(
arg,
res),
n));
while (--n != 1);
return dc_fixpt_add(
dc_fixpt_one,
dc_fixpt_mul(
arg,
res));
}
struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg)
{
/*
* @brief
* Main equation is:
* exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r),
* where m = round(x / ln(2)), r = x - m * ln(2)
*/
if (dc_fixpt_le(
dc_fixpt_ln2_div_2,
dc_fixpt_abs(arg))) {
int m = dc_fixpt_round(
dc_fixpt_div(
arg,
dc_fixpt_ln2));
struct fixed31_32 r = dc_fixpt_sub(
arg,
dc_fixpt_mul_int(
dc_fixpt_ln2,
m));
ASSERT(m != 0);
ASSERT(dc_fixpt_lt(
dc_fixpt_abs(r),
dc_fixpt_one));
if (m > 0)
return dc_fixpt_shl(
fixed31_32_exp_from_taylor_series(r),
(unsigned char)m);
else
return dc_fixpt_div_int(
fixed31_32_exp_from_taylor_series(r),
1LL << -m);
} else if (arg.value != 0)
return fixed31_32_exp_from_taylor_series(arg);
else
return dc_fixpt_one;
}
struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg)
{
struct fixed31_32 res = dc_fixpt_neg(dc_fixpt_one);
/* TODO improve 1st estimation */
struct fixed31_32 error;
ASSERT(arg.value > 0);
/* TODO if arg is negative, return NaN */
/* TODO if arg is zero, return -INF */
do {
struct fixed31_32 res1 = dc_fixpt_add(
dc_fixpt_sub(
res,
dc_fixpt_one),
dc_fixpt_div(
arg,
dc_fixpt_exp(res)));
error = dc_fixpt_sub(
res,
res1);
res = res1;
/* TODO determine max_allowed_error based on quality of exp() */
} while (abs_i64(error.value) > 100ULL);
return res;
}
/* this function is a generic helper to translate fixed point value to
* specified integer format that will consist of integer_bits integer part and
* fractional_bits fractional part. For example it is used in
* dc_fixpt_u2d19 to receive 2 bits integer part and 19 bits fractional
* part in 32 bits. It is used in hw programming (scaler)
*/
static inline unsigned int ux_dy(
long long value,
unsigned int integer_bits,
unsigned int fractional_bits)
{
/* 1. create mask of integer part */
unsigned int result = (1 << integer_bits) - 1;
/* 2. mask out fractional part */
unsigned int fractional_part = FRACTIONAL_PART_MASK & value;
/* 3. shrink fixed point integer part to be of integer_bits width*/
result &= GET_INTEGER_PART(value);
/* 4. make space for fractional part to be filled in after integer */
result <<= fractional_bits;
/* 5. shrink fixed point fractional part to of fractional_bits width*/
fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits;
/* 6. merge the result */
return result | fractional_part;
}
static inline unsigned int clamp_ux_dy(
long long value,
unsigned int integer_bits,
unsigned int fractional_bits,
unsigned int min_clamp)
{
unsigned int truncated_val = ux_dy(value, integer_bits, fractional_bits);
if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART)))
return (1 << (integer_bits + fractional_bits)) - 1;
else if (truncated_val > min_clamp)
return truncated_val;
else
return min_clamp;
}
unsigned int dc_fixpt_u4d19(struct fixed31_32 arg)
{
return ux_dy(arg.value, 4, 19);
}
unsigned int dc_fixpt_u3d19(struct fixed31_32 arg)
{
return ux_dy(arg.value, 3, 19);
}
unsigned int dc_fixpt_u2d19(struct fixed31_32 arg)
{
return ux_dy(arg.value, 2, 19);
}
unsigned int dc_fixpt_u0d19(struct fixed31_32 arg)
{
return ux_dy(arg.value, 0, 19);
}
unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg)
{
return clamp_ux_dy(arg.value, 0, 14, 1);
}
unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg)
{
return clamp_ux_dy(arg.value, 0, 10, 1);
}
int dc_fixpt_s4d19(struct fixed31_32 arg)
{
if (arg.value < 0)
return -(int)ux_dy(dc_fixpt_abs(arg).value, 4, 19);
else
return ux_dy(arg.value, 4, 19);
}
struct fixed31_32 dc_fixpt_from_ux_dy(unsigned int value,
unsigned int integer_bits,
unsigned int fractional_bits)
{
struct fixed31_32 fixpt_value = dc_fixpt_zero;
struct fixed31_32 fixpt_int_value = dc_fixpt_zero;
long long frac_mask = ((long long)1 << (long long)integer_bits) - 1;
fixpt_value.value = (long long)value << (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits);
frac_mask = frac_mask << fractional_bits;
fixpt_int_value.value = value & frac_mask;
fixpt_int_value.value <<= (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits);
fixpt_value.value |= fixpt_int_value.value;
return fixpt_value;
}
struct fixed31_32 dc_fixpt_from_int_dy(unsigned int int_value,
unsigned int frac_value,
unsigned int integer_bits,
unsigned int fractional_bits)
{
struct fixed31_32 fixpt_value = dc_fixpt_from_int(int_value);
fixpt_value.value |= (long long)frac_value << (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits);
return fixpt_value;
}
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