JasPer: Fixed-Point Arithmetic

JasPer 4.2.9 |

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Fixed-Point Arithmetic

Fixed-Point Arithmetic. More...

## Macros
#define | JAS_FIX_ZERO(fix_t, fracbits)
#define | JAS_FIX_ONE(fix_t, fracbits)
#define | JAS_FIX_HALF(fix_t, fracbits)
#define | JAS_INTTOFIX(fix_t, fracbits, x)
#define | JAS_FIXTOINT(fix_t, fracbits, x)
#define | JAS_FIXTODBL(fix_t, fracbits, x)
#define | JAS_DBLTOFIX(fix_t, fracbits, x)
#define | JAS_FIX_ADD JAS_FIX_ADD_FAST
#define | JAS_FIX_ADD_FAST(fix_t, fracbits, 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)
#define | JAS_FIX_MULBYINT_OFLOW(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)
#define | JAS_FIX_DIV_UFLOW(fix_t, fracbits, bigfix_t, x, y)
#define | JAS_FIX_NEG JAS_FIX_NEG_FAST
#define | JAS_FIX_NEG_FAST(fix_t, fracbits, x)
#define | JAS_FIX_NEG_OFLOW(fix_t, fracbits, x)
#define | JAS_FIX_ASL JAS_FIX_ASL_FAST
#define | JAS_FIX_ASL_FAST(fix_t, fracbits, x, n)
#define | JAS_FIX_ASL_OFLOW(fix_t, fracbits, x, n)
#define | JAS_FIX_ASR JAS_FIX_ASR_FAST
#define | JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
#define | JAS_FIX_ASR_UFLOW(fix_t, fracbits, x, n)
#define | JAS_FIX_SUB(fix_t, fracbits, x, y)
#define | JAS_FIX_PLUSEQ(fix_t, fracbits, x, y)
#define | JAS_FIX_MINUSEQ(fix_t, fracbits, x, y)
#define | JAS_FIX_MULEQ(fix_t, fracbits, bigfix_t, x, y)
#define | JAS_FIX_ABS(fix_t, fracbits, x)
#define | JAS_FIX_ISINT(fix_t, fracbits, x)
#define | JAS_FIX_SGN(fix_t, fracbits, x)
#define | JAS_FIX_CMP(fix_t, fracbits, x, y)
#define | JAS_FIX_LT(fix_t, fracbits, x, y)
#define | JAS_FIX_LTE(fix_t, fracbits, x, y)
#define | JAS_FIX_GT(fix_t, fracbits, x, y)
#define | JAS_FIX_GTE(fix_t, fracbits, x, y)
#define | JAS_FIX_ROUND(fix_t, fracbits, x)
#define | JAS_FIX_FLOOR(fix_t, fracbits, x)

## 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 )

Value:
JAS_CAST(fix_t, ((x) * JAS_CAST(double, JAS_FIX_ONE(fix_t, fracbits))))
JAS_FIX_ONE
#define JAS_FIX_ONE(fix_t, fracbits)
Definition jas_fix.h:127

Convert a double to a fixed-point number.

## ◆ JAS_FIX_ABS

#define JAS_FIX_ABS | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
(((x) >= 0) ? (x) : (JAS_FIX_NEG(fix_t, fracbits, x)))
JAS_FIX_NEG
#define JAS_FIX_NEG
Definition jas_fix.h:240

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 )

Value:
((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 )

Value:
((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 )

Value:
((((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 )

Value:
((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 )

Value:
JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
JAS_FIX_ASR_FAST
#define JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
Definition jas_fix.h:281

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 )

Value:
((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 )

Value:
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 )

Value:
JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)
JAS_FIX_DIV_FAST
#define JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)
Definition jas_fix.h:230

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

## ◆ JAS_FIX_FLOOR

#define JAS_FIX_FLOOR | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
((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 )

Value:
((x) > (y))

Greater than.

## ◆ JAS_FIX_GTE

#define JAS_FIX_GTE | ( |  | fix_t,
|  |  | fracbits,
|  |  | x,
|  |  | y )

Value:
((x) >= (y))

Greater than or equal.

## ◆ JAS_FIX_HALF

#define JAS_FIX_HALF | ( |  | fix_t,
|  |  | fracbits )

Value:
(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 )

Value:
(JAS_FIX_FLOOR(fix_t, fracbits, x) == (x))
JAS_FIX_FLOOR
#define JAS_FIX_FLOOR(fix_t, fracbits, x)
Definition jas_fix.h:362

Is a fixed-point number an integer?

## ◆ JAS_FIX_LT

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

Value:
((x) < (y))

Less than.

## ◆ JAS_FIX_LTE

#define JAS_FIX_LTE | ( |  | fix_t,
|  |  | fracbits,
|  |  | x,
|  |  | y )

Value:
((x) <= (y))

Less than or equal.

## ◆ JAS_FIX_MINUSEQ

#define JAS_FIX_MINUSEQ | ( |  | fix_t,
|  |  | fracbits,
|  |  | x,
|  |  | y )

Value:
((x) = JAS_FIX_SUB(fix_t, fracbits, x, y))
JAS_FIX_SUB
#define JAS_FIX_SUB(fix_t, fracbits, x, y)
Definition jas_fix.h:294

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 )

Value:
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 )

Value:
JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)
JAS_FIX_MULBYINT_FAST
#define JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)
Definition jas_fix.h:213

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 )

Value:
((x) = JAS_FIX_MUL(fix_t, fracbits, bigfix_t, x, y))
JAS_FIX_MUL
#define JAS_FIX_MUL
Definition jas_fix.h:184

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 )

Value:
(-(x))

Negate a fixed-point number without overflow checking.

## ◆ JAS_FIX_NEG_OFLOW

#define JAS_FIX_NEG_OFLOW | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
(((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 )

Value:
JAS_INTTOFIX(fix_t, fracbits, 1)
JAS_INTTOFIX
#define JAS_INTTOFIX(fix_t, fracbits, x)
Definition jas_fix.h:139

The representation of the value one.

## ◆ JAS_FIX_PLUSEQ

#define JAS_FIX_PLUSEQ | ( |  | fix_t,
|  |  | fracbits,
|  |  | x,
|  |  | y )

Value:
((x) = JAS_FIX_ADD(fix_t, fracbits, x, y))
JAS_FIX_ADD
#define JAS_FIX_ADD
Definition jas_fix.h:166

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)))))
JAS_FIX_HALF
#define JAS_FIX_HALF(fix_t, fracbits)
Definition jas_fix.h:131

Round a fixed-point number to the nearest integer.

## ◆ JAS_FIX_SGN

#define JAS_FIX_SGN | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
((x) >= 0 ? 1 : (-1))

Get the sign of a fixed-point number.

## ◆ JAS_FIX_SUB

#define JAS_FIX_SUB | ( |  | fix_t,
|  |  | fracbits,
|  |  | x,
|  |  | y )

Value:
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 )

Value:
JAS_INTTOFIX(fix_t, fracbits, 0)

The representation of the value zero.

## ◆ JAS_FIXTODBL

#define JAS_FIXTODBL | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
(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 )

Value:
JAS_CAST(int, (x) >> (fracbits))

Convert a fixed-point number to an int.

## ◆ JAS_INTTOFIX

#define JAS_INTTOFIX | ( |  | fix_t,
|  |  | fracbits,
|  |  | x )

Value:
(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.