fixed31_32.h

/*
 * 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
 *
 */

#ifndef __DAL_FIXED31_32_H__
#define __DAL_FIXED31_32_H__

#ifndef LLONG_MAX
#define LLONG_MAX 9223372036854775807ll
#endif
#ifndef LLONG_MIN
#define LLONG_MIN (-LLONG_MAX - 1ll)
#endif

#define FIXED31_32_BITS_PER_FRACTIONAL_PART 32
#ifndef LLONG_MIN
#define LLONG_MIN (1LL<<63)
#endif
#ifndef LLONG_MAX
#define LLONG_MAX (-1LL>>1)
#endif

/*
 * @brief
 * Arithmetic operations on real numbers
 * represented as fixed-point numbers.
 * There are: 1 bit for sign,
 * 31 bit for integer part,
 * 32 bits for fractional part.
 *
 * @note
 * Currently, overflows and underflows are asserted;
 * no special result returned.
 */

struct fixed31_32 {
	long long value;
};


/*
 * @brief
 * Useful constants
 */

static const struct fixed31_32 dc_fixpt_zero = { 0 };
static const struct fixed31_32 dc_fixpt_epsilon = { 1LL };
static const struct fixed31_32 dc_fixpt_half = { 0x80000000LL };
static const struct fixed31_32 dc_fixpt_one = { 0x100000000LL };

/*
 * @brief
 * Initialization routines
 */

/*
 * @brief
 * result = numerator / denominator
 */
struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator);

/*
 * @brief
 * result = arg
 */
static inline struct fixed31_32 dc_fixpt_from_int(int arg)
{
	struct fixed31_32 res;

	res.value = (long long) arg << FIXED31_32_BITS_PER_FRACTIONAL_PART;

	return res;
}

/*
 * @brief
 * Unary operators
 */

/*
 * @brief
 * result = -arg
 */
static inline struct fixed31_32 dc_fixpt_neg(struct fixed31_32 arg)
{
	struct fixed31_32 res;

	res.value = -arg.value;

	return res;
}

/*
 * @brief
 * result = abs(arg) := (arg >= 0) ? arg : -arg
 */
static inline struct fixed31_32 dc_fixpt_abs(struct fixed31_32 arg)
{
	if (arg.value < 0)
		return dc_fixpt_neg(arg);
	else
		return arg;
}

/*
 * @brief
 * Binary relational operators
 */

/*
 * @brief
 * result = arg1 < arg2
 */
static inline bool dc_fixpt_lt(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	return arg1.value < arg2.value;
}

/*
 * @brief
 * result = arg1 <= arg2
 */
static inline bool dc_fixpt_le(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	return arg1.value <= arg2.value;
}

/*
 * @brief
 * result = arg1 == arg2
 */
static inline bool dc_fixpt_eq(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	return arg1.value == arg2.value;
}

/*
 * @brief
 * result = min(arg1, arg2) := (arg1 <= arg2) ? arg1 : arg2
 */
static inline struct fixed31_32 dc_fixpt_min(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	if (arg1.value <= arg2.value)
		return arg1;
	else
		return arg2;
}

/*
 * @brief
 * result = max(arg1, arg2) := (arg1 <= arg2) ? arg2 : arg1
 */
static inline struct fixed31_32 dc_fixpt_max(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	if (arg1.value <= arg2.value)
		return arg2;
	else
		return arg1;
}

/*
 * @brief
 *          | min_value, when arg <= min_value
 * result = | arg, when min_value < arg < max_value
 *          | max_value, when arg >= max_value
 */
static inline struct fixed31_32 dc_fixpt_clamp(
	struct fixed31_32 arg,
	struct fixed31_32 min_value,
	struct fixed31_32 max_value)
{
	if (dc_fixpt_le(arg, min_value))
		return min_value;
	else if (dc_fixpt_le(max_value, arg))
		return max_value;
	else
		return arg;
}

/*
 * @brief
 * Binary shift operators
 */

/*
 * @brief
 * result = arg << shift
 */
static inline struct fixed31_32 dc_fixpt_shl(struct fixed31_32 arg, unsigned char shift)
{
	ASSERT(((arg.value >= 0) && (arg.value <= LLONG_MAX >> shift)) ||
		((arg.value < 0) && (arg.value >= ~(LLONG_MAX >> shift))));

	arg.value = arg.value << shift;

	return arg;
}

/*
 * @brief
 * result = arg >> shift
 */
static inline struct fixed31_32 dc_fixpt_shr(struct fixed31_32 arg, unsigned char shift)
{
	bool negative = arg.value < 0;

	if (negative)
		arg.value = -arg.value;
	arg.value = arg.value >> shift;
	if (negative)
		arg.value = -arg.value;
	return arg;
}

/*
 * @brief
 * Binary additive operators
 */

/*
 * @brief
 * result = arg1 + arg2
 */
static inline struct fixed31_32 dc_fixpt_add(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	struct fixed31_32 res;

	ASSERT(((arg1.value >= 0) && (LLONG_MAX - arg1.value >= arg2.value)) ||
		((arg1.value < 0) && (LLONG_MIN - arg1.value <= arg2.value)));

	res.value = arg1.value + arg2.value;

	return res;
}

/*
 * @brief
 * result = arg1 + arg2
 */
static inline struct fixed31_32 dc_fixpt_add_int(struct fixed31_32 arg1, int arg2)
{
	return dc_fixpt_add(arg1, dc_fixpt_from_int(arg2));
}

/*
 * @brief
 * result = arg1 - arg2
 */
static inline struct fixed31_32 dc_fixpt_sub(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	struct fixed31_32 res;

	ASSERT(((arg2.value >= 0) && (LLONG_MIN + arg2.value <= arg1.value)) ||
		((arg2.value < 0) && (LLONG_MAX + arg2.value >= arg1.value)));

	res.value = arg1.value - arg2.value;

	return res;
}

/*
 * @brief
 * result = arg1 - arg2
 */
static inline struct fixed31_32 dc_fixpt_sub_int(struct fixed31_32 arg1, int arg2)
{
	return dc_fixpt_sub(arg1, dc_fixpt_from_int(arg2));
}


/*
 * @brief
 * Binary multiplicative operators
 */

/*
 * @brief
 * result = arg1 * arg2
 */
struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2);


/*
 * @brief
 * result = arg1 * arg2
 */
static inline struct fixed31_32 dc_fixpt_mul_int(struct fixed31_32 arg1, int arg2)
{
	return dc_fixpt_mul(arg1, dc_fixpt_from_int(arg2));
}

/*
 * @brief
 * result = square(arg) := arg * arg
 */
struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg);

/*
 * @brief
 * result = arg1 / arg2
 */
static inline struct fixed31_32 dc_fixpt_div_int(struct fixed31_32 arg1, long long arg2)
{
	return dc_fixpt_from_fraction(arg1.value, dc_fixpt_from_int((int)arg2).value);
}

/*
 * @brief
 * result = arg1 / arg2
 */
static inline struct fixed31_32 dc_fixpt_div(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	return dc_fixpt_from_fraction(arg1.value, arg2.value);
}

/*
 * @brief
 * Reciprocal function
 */

/*
 * @brief
 * result = reciprocal(arg) := 1 / arg
 *
 * @note
 * No special actions taken in case argument is zero.
 */
struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg);

/*
 * @brief
 * Trigonometric functions
 */

/*
 * @brief
 * result = sinc(arg) := sin(arg) / arg
 *
 * @note
 * Argument specified in radians,
 * internally it's normalized to [-2pi...2pi] range.
 */
struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg);

/*
 * @brief
 * result = sin(arg)
 *
 * @note
 * Argument specified in radians,
 * internally it's normalized to [-2pi...2pi] range.
 */
struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg);

/*
 * @brief
 * result = cos(arg)
 *
 * @note
 * Argument specified in radians
 * and should be in [-2pi...2pi] range -
 * passing arguments outside that range
 * will cause incorrect result!
 */
struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg);

/*
 * @brief
 * Transcendent functions
 */

/*
 * @brief
 * result = exp(arg)
 *
 * @note
 * Currently, function is verified for abs(arg) <= 1.
 */
struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg);

/*
 * @brief
 * result = log(arg)
 *
 * @note
 * Currently, abs(arg) should be less than 1.
 * No normalization is done.
 * Currently, no special actions taken
 * in case of invalid argument(s). Take care!
 */
struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg);

/*
 * @brief
 * Power function
 */

/*
 * @brief
 * result = pow(arg1, arg2)
 *
 * @note
 * Currently, abs(arg1) should be less than 1. Take care!
 */
static inline struct fixed31_32 dc_fixpt_pow(struct fixed31_32 arg1, struct fixed31_32 arg2)
{
	if (arg1.value == 0)
		return arg2.value == 0 ? dc_fixpt_one : dc_fixpt_zero;

	return dc_fixpt_exp(
		dc_fixpt_mul(
			dc_fixpt_log(arg1),
			arg2));
}

/*
 * @brief
 * Rounding functions
 */

/*
 * @brief
 * result = floor(arg) := greatest integer lower than or equal to arg
 */
static inline int dc_fixpt_floor(struct fixed31_32 arg)
{
	unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;

	if (arg.value >= 0)
		return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
	else
		return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
}

/*
 * @brief
 * result = round(arg) := integer nearest to arg
 */
static inline int dc_fixpt_round(struct fixed31_32 arg)
{
	unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;

	const long long summand = dc_fixpt_half.value;

	ASSERT(LLONG_MAX - (long long)arg_value >= summand);

	arg_value += summand;

	if (arg.value >= 0)
		return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
	else
		return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
}

/*
 * @brief
 * result = ceil(arg) := lowest integer greater than or equal to arg
 */
static inline int dc_fixpt_ceil(struct fixed31_32 arg)
{
	unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;

	const long long summand = dc_fixpt_one.value -
		dc_fixpt_epsilon.value;

	ASSERT(LLONG_MAX - (long long)arg_value >= summand);

	arg_value += summand;

	if (arg.value >= 0)
		return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
	else
		return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
}

/* the following two function are used in scaler hw programming to convert fixed
 * point value to format 2 bits from integer part and 19 bits from fractional
 * part. The same applies for u0d19, 0 bits from integer part and 19 bits from
 * fractional
 */

unsigned int dc_fixpt_u4d19(struct fixed31_32 arg);

unsigned int dc_fixpt_u3d19(struct fixed31_32 arg);

unsigned int dc_fixpt_u2d19(struct fixed31_32 arg);

unsigned int dc_fixpt_u0d19(struct fixed31_32 arg);

unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg);

unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg);

int dc_fixpt_s4d19(struct fixed31_32 arg);

static inline struct fixed31_32 dc_fixpt_truncate(struct fixed31_32 arg, unsigned int frac_bits)
{
	bool negative = arg.value < 0;

	if (frac_bits >= FIXED31_32_BITS_PER_FRACTIONAL_PART) {
		ASSERT(frac_bits == FIXED31_32_BITS_PER_FRACTIONAL_PART);
		return arg;
	}

	if (negative)
		arg.value = -arg.value;
	arg.value &= (~0ULL) << (FIXED31_32_BITS_PER_FRACTIONAL_PART - frac_bits);
	if (negative)
		arg.value = -arg.value;
	return arg;
}

struct fixed31_32 dc_fixpt_from_ux_dy(unsigned int value, unsigned int integer_bits, unsigned int fractional_bits);
struct fixed31_32 dc_fixpt_from_int_dy(unsigned int int_value,
		unsigned int frac_value,
		unsigned int integer_bits,
		unsigned int fractional_bits);

#endif