Fixed-Point Arithmetic

Fixed-Point Arithmetic. More...

Macros
#define	JAS_FIX_ZERO(fix_t, fracbits)    JAS_INTTOFIX(fix_t, fracbits, 0)
#define	JAS_FIX_ONE(fix_t, fracbits)    JAS_INTTOFIX(fix_t, fracbits, 1)
#define	JAS_FIX_HALF(fix_t, fracbits)    (JAS_CAST(fix_t, 1) << ((fracbits) - 1))
#define	JAS_INTTOFIX(fix_t, fracbits, x)    (JAS_CAST(fix_t, x) << (fracbits))
#define	JAS_FIXTOINT(fix_t, fracbits, x)    JAS_CAST(int, (x) >> (fracbits))
#define	JAS_FIXTODBL(fix_t, fracbits, x)    (JAS_CAST(double, x) / JAS_FIX_ONE(fix_t, fracbits))
#define	JAS_DBLTOFIX(fix_t, fracbits, x)    JAS_CAST(fix_t, ((x) * JAS_CAST(double, JAS_FIX_ONE(fix_t, fracbits))))
#define	JAS_FIX_ADD   JAS_FIX_ADD_FAST
#define	JAS_FIX_ADD_FAST(fix_t, fracbits, x, y)   ((x) + (y))
#define	JAS_FIX_ADD_OFLOW(fix_t, fracbits, x, y)
#define	JAS_FIX_MUL   JAS_FIX_MUL_FAST
#define	JAS_FIX_MUL_FAST(fix_t, fracbits, bigfix_t, x, y)
#define	JAS_FIX_MUL_OFLOW(fix_t, fracbits, bigfix_t, x, y)
#define	JAS_FIX_MULBYINT   JAS_FIX_MULBYINT_FAST
#define	JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)    JAS_CAST(fix_t, ((x) * (y)))
#define	JAS_FIX_MULBYINT_OFLOW(fix_t, fracbits, x, y)    JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)
#define	JAS_FIX_DIV   JAS_FIX_DIV_FAST
#define	JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)    JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) << (fracbits)) / (y))
#define	JAS_FIX_DIV_UFLOW(fix_t, fracbits, bigfix_t, x, y)    JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)
#define	JAS_FIX_NEG   JAS_FIX_NEG_FAST
#define	JAS_FIX_NEG_FAST(fix_t, fracbits, x)    (-(x))
#define	JAS_FIX_NEG_OFLOW(fix_t, fracbits, x)    (((x) < 0) ? (-(x) > 0 || JAS_FIX_OFLOW(), -(x)) : (-(x)))
#define	JAS_FIX_ASL   JAS_FIX_ASL_FAST
#define	JAS_FIX_ASL_FAST(fix_t, fracbits, x, n)    ((x) << (n))
#define	JAS_FIX_ASL_OFLOW(fix_t, fracbits, x, n)    ((((x) << (n)) >> (n)) == (x) || JAS_FIX_OFLOW(), (x) << (n))
#define	JAS_FIX_ASR   JAS_FIX_ASR_FAST
#define	JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)    ((x) >> (n))
#define	JAS_FIX_ASR_UFLOW(fix_t, fracbits, x, n)    JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
#define	JAS_FIX_SUB(fix_t, fracbits, x, y)    JAS_FIX_ADD(fix_t, fracbits, x, JAS_FIX_NEG(fix_t, fracbits, y))
#define	JAS_FIX_PLUSEQ(fix_t, fracbits, x, y)    ((x) = JAS_FIX_ADD(fix_t, fracbits, x, y))
#define	JAS_FIX_MINUSEQ(fix_t, fracbits, x, y)    ((x) = JAS_FIX_SUB(fix_t, fracbits, x, y))
#define	JAS_FIX_MULEQ(fix_t, fracbits, bigfix_t, x, y)    ((x) = JAS_FIX_MUL(fix_t, fracbits, bigfix_t, x, y))
#define	JAS_FIX_ABS(fix_t, fracbits, x)    (((x) >= 0) ? (x) : (JAS_FIX_NEG(fix_t, fracbits, x)))
#define	JAS_FIX_ISINT(fix_t, fracbits, x)    (JAS_FIX_FLOOR(fix_t, fracbits, x) == (x))
#define	JAS_FIX_SGN(fix_t, fracbits, x)    ((x) >= 0 ? 1 : (-1))
#define	JAS_FIX_CMP(fix_t, fracbits, x, y)    ((x) > (y) ? 1 : (((x) == (y)) ? 0 : (-1)))
#define	JAS_FIX_LT(fix_t, fracbits, x, y)    ((x) < (y))
#define	JAS_FIX_LTE(fix_t, fracbits, x, y)    ((x) <= (y))
#define	JAS_FIX_GT(fix_t, fracbits, x, y)    ((x) > (y))
#define	JAS_FIX_GTE(fix_t, fracbits, x, y)    ((x) >= (y))
#define	JAS_FIX_ROUND(fix_t, fracbits, x)
#define	JAS_FIX_FLOOR(fix_t, fracbits, x)    ((x) & (~(JAS_FIX_ONE(fix_t, fracbits) - 1)))

Typedefs
typedef int_least64_t	jas_fix_t

Detailed Description

Fixed-Point Arithmetic.

Macro Definition Documentation

JAS_DBLTOFIX

#define JAS_DBLTOFIX	(		fix_t,
			fracbits,
			x
	)		JAS_CAST(fix_t, ((x) * JAS_CAST(double, JAS_FIX_ONE(fix_t, fracbits))))

Convert a double to a fixed-point number.

JAS_FIX_ABS

#define JAS_FIX_ABS	(		fix_t,
			fracbits,
			x
	)		(((x) >= 0) ? (x) : (JAS_FIX_NEG(fix_t, fracbits, x)))

Calculate the absolute value of a fixed-point number.

JAS_FIX_ADD

#define JAS_FIX_ADD   JAS_FIX_ADD_FAST

Calculate the sum of two fixed-point numbers.

JAS_FIX_ADD_FAST

#define JAS_FIX_ADD_FAST	(		fix_t,
			fracbits,
			x,
			y
	)		((x) + (y))

Calculate the sum of two fixed-point numbers without overflow checking.

JAS_FIX_ADD_OFLOW

#define JAS_FIX_ADD_OFLOW	(		fix_t,
			fracbits,
			x,
			y
	)

Value:

        ((x) >= 0) ? \
          (((y) >= 0) ? ((x) + (y) >= 0 || JAS_FIX_OFLOW(), (x) + (y)) : \
          ((x) + (y))) : \
          (((y) >= 0) ? ((x) + (y)) : ((x) + (y) < 0 || JAS_FIX_OFLOW(), \
          (x) + (y)))

Calculate the sum of two fixed-point numbers with overflow checking.

JAS_FIX_ASL

#define JAS_FIX_ASL   JAS_FIX_ASL_FAST

Perform an arithmetic shift left of a fixed-point number.

JAS_FIX_ASL_FAST

#define JAS_FIX_ASL_FAST	(		fix_t,
			fracbits,
			x,
			n
	)		((x) << (n))

Perform an arithmetic shift left of a fixed-point number without overflow checking.

JAS_FIX_ASL_OFLOW

#define JAS_FIX_ASL_OFLOW	(		fix_t,
			fracbits,
			x,
			n
	)		((((x) << (n)) >> (n)) == (x) || JAS_FIX_OFLOW(), (x) << (n))

Perform an arithmetic shift left of a fixed-point number with overflow checking.

JAS_FIX_ASR

#define JAS_FIX_ASR   JAS_FIX_ASR_FAST

Perform an arithmetic shift right of a fixed-point number.

JAS_FIX_ASR_FAST

#define JAS_FIX_ASR_FAST	(		fix_t,
			fracbits,
			x,
			n
	)		((x) >> (n))

Perform an arithmetic shift right of a fixed-point number without underflow checking.

JAS_FIX_ASR_UFLOW

#define JAS_FIX_ASR_UFLOW	(		fix_t,
			fracbits,
			x,
			n
	)		JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)

Perform an arithmetic shift right of a fixed-point number with underflow checking.

JAS_FIX_CMP

#define JAS_FIX_CMP	(		fix_t,
			fracbits,
			x,
			y
	)		((x) > (y) ? 1 : (((x) == (y)) ? 0 : (-1)))

Compare two fixed-point numbers.

JAS_FIX_DIV

#define JAS_FIX_DIV   JAS_FIX_DIV_FAST

Calculate the quotient of two fixed-point numbers.

JAS_FIX_DIV_FAST

#define JAS_FIX_DIV_FAST	(		fix_t,
			fracbits,
			bigfix_t,
			x,
			y
	)		JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) << (fracbits)) / (y))

Calculate the quotient of two fixed-point numbers without underflow checking.

JAS_FIX_DIV_UFLOW

#define JAS_FIX_DIV_UFLOW	(		fix_t,
			fracbits,
			bigfix_t,
			x,
			y
	)		JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)

Calculate the quotient of two fixed-point numbers with underflow checking.

JAS_FIX_FLOOR

#define JAS_FIX_FLOOR	(		fix_t,
			fracbits,
			x
	)		((x) & (~(JAS_FIX_ONE(fix_t, fracbits) - 1)))

Round a fixed-point number to the nearest integer in the direction of negative infinity (i.e., the floor function).

JAS_FIX_GT

#define JAS_FIX_GT	(		fix_t,
			fracbits,
			x,
			y
	)		((x) > (y))

Greater than.

JAS_FIX_GTE

#define JAS_FIX_GTE	(		fix_t,
			fracbits,
			x,
			y
	)		((x) >= (y))

Greater than or equal.

JAS_FIX_HALF

#define JAS_FIX_HALF	(		fix_t,
			fracbits
	)		(JAS_CAST(fix_t, 1) << ((fracbits) - 1))

The representation of the value one half.

JAS_FIX_ISINT

#define JAS_FIX_ISINT	(		fix_t,
			fracbits,
			x
	)		(JAS_FIX_FLOOR(fix_t, fracbits, x) == (x))

Is a fixed-point number an integer?

JAS_FIX_LT

#define JAS_FIX_LT	(		fix_t,
			fracbits,
			x,
			y
	)		((x) < (y))

Less than.

JAS_FIX_LTE

#define JAS_FIX_LTE	(		fix_t,
			fracbits,
			x,
			y
	)		((x) <= (y))

Less than or equal.

JAS_FIX_MINUSEQ

#define JAS_FIX_MINUSEQ	(		fix_t,
			fracbits,
			x,
			y
	)		((x) = JAS_FIX_SUB(fix_t, fracbits, x, y))

Subtract one fixed-point number from another.

JAS_FIX_MUL

#define JAS_FIX_MUL   JAS_FIX_MUL_FAST

Calculate the product of two fixed-point numbers.

JAS_FIX_MUL_FAST

#define JAS_FIX_MUL_FAST	(		fix_t,
			fracbits,
			bigfix_t,
			x,
			y
	)

Value:

        JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y)) >> \
          (fracbits))

Calculate the product of two fixed-point numbers without overflow checking.

JAS_FIX_MUL_OFLOW

#define JAS_FIX_MUL_OFLOW	(		fix_t,
			fracbits,
			bigfix_t,
			x,
			y
	)

Value:

        ((JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> (fracbits)) == \
          JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
          (fracbits))) ? \
          JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
          (fracbits))) : JAS_FIX_OFLOW())

Calculate the product of two fixed-point numbers with overflow checking.

JAS_FIX_MULBYINT

#define JAS_FIX_MULBYINT   JAS_FIX_MULBYINT_FAST

Calculate the product of a fixed-point number and an int.

JAS_FIX_MULBYINT_FAST

#define JAS_FIX_MULBYINT_FAST	(		fix_t,
			fracbits,
			x,
			y
	)		JAS_CAST(fix_t, ((x) * (y)))

Calculate the product of a fixed-point number and an int without overflow checking.

JAS_FIX_MULBYINT_OFLOW

#define JAS_FIX_MULBYINT_OFLOW	(		fix_t,
			fracbits,
			x,
			y
	)		JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)

Calculate the product of a fixed-point number and an int with overflow checking.

JAS_FIX_MULEQ

#define JAS_FIX_MULEQ	(		fix_t,
			fracbits,
			bigfix_t,
			x,
			y
	)		((x) = JAS_FIX_MUL(fix_t, fracbits, bigfix_t, x, y))

Multiply one fixed-point number by another.

JAS_FIX_NEG

#define JAS_FIX_NEG   JAS_FIX_NEG_FAST

Negate a fixed-point number.

JAS_FIX_NEG_FAST

#define JAS_FIX_NEG_FAST	(		fix_t,
			fracbits,
			x
	)		(-(x))

Negate a fixed-point number without overflow checking.

JAS_FIX_NEG_OFLOW

#define JAS_FIX_NEG_OFLOW	(		fix_t,
			fracbits,
			x
	)		(((x) < 0) ? (-(x) > 0 || JAS_FIX_OFLOW(), -(x)) : (-(x)))

Negate a fixed-point number with overflow checking.

JAS_FIX_ONE

#define JAS_FIX_ONE	(		fix_t,
			fracbits
	)		JAS_INTTOFIX(fix_t, fracbits, 1)

The representation of the value one.

JAS_FIX_PLUSEQ

#define JAS_FIX_PLUSEQ	(		fix_t,
			fracbits,
			x,
			y
	)		((x) = JAS_FIX_ADD(fix_t, fracbits, x, y))

Add one fixed-point number to another.

JAS_FIX_ROUND

#define JAS_FIX_ROUND	(		fix_t,
			fracbits,
			x
	)

Value:

        (((x) < 0) ? JAS_FIX_FLOOR(fix_t, fracbits, JAS_FIX_ADD(fix_t, fracbits, \
          (x), JAS_FIX_HALF(fix_t, fracbits))) : \
          JAS_FIX_NEG(fix_t, fracbits, JAS_FIX_FLOOR(fix_t, fracbits, \
          JAS_FIX_ADD(fix_t, fracbits, (-(x)), JAS_FIX_HALF(fix_t, fracbits)))))

Round a fixed-point number to the nearest integer.

JAS_FIX_SGN

#define JAS_FIX_SGN	(		fix_t,
			fracbits,
			x
	)		((x) >= 0 ? 1 : (-1))

Get the sign of a fixed-point number.

JAS_FIX_SUB

#define JAS_FIX_SUB	(		fix_t,
			fracbits,
			x,
			y
	)		JAS_FIX_ADD(fix_t, fracbits, x, JAS_FIX_NEG(fix_t, fracbits, y))

Calculate the difference between two fixed-point numbers.

JAS_FIX_ZERO

#define JAS_FIX_ZERO	(		fix_t,
			fracbits
	)		JAS_INTTOFIX(fix_t, fracbits, 0)

The representation of the value zero.

JAS_FIXTODBL

#define JAS_FIXTODBL	(		fix_t,
			fracbits,
			x
	)		(JAS_CAST(double, x) / JAS_FIX_ONE(fix_t, fracbits))

Convert a fixed-point number to a double.

JAS_FIXTOINT

#define JAS_FIXTOINT	(		fix_t,
			fracbits,
			x
	)		JAS_CAST(int, (x) >> (fracbits))

Convert a fixed-point number to an int.

JAS_INTTOFIX

#define JAS_INTTOFIX	(		fix_t,
			fracbits,
			x
	)		(JAS_CAST(fix_t, x) << (fracbits))

Convert an int to a fixed-point number.

Typedef Documentation

jas_fix_t

typedef int_least64_t jas_fix_t

Integral type used for fixed-point representations.