Fixed Point Support

Fixed Point Support — Fixed Point API

Synopsis




typedef             ClutterFixed;
#define             CFX_Q
#define             CFX_ONE
#define             CFX_MAX
#define             CFX_MIN
typedef             ClutterAngle;
#define             CFX_PI
#define             CFX_2PI
#define             CFX_PI_2
#define             CFX_PI_4
#define             CFX_120
#define             CFX_180
#define             CFX_240
#define             CFX_360
#define             CFX_60
#define             CFX_255
#define             CFX_DIV
#define             CFX_INT
#define             CFX_MUL
#define             CFX_HALF
#define             CFX_QMUL                            (x,y)
#define             CLUTTER_FIXED_TO_FLOAT              (x)
#define             CLUTTER_FIXED_TO_DOUBLE             (x)
#define             CLUTTER_FLOAT_TO_FIXED              (x)
#define             CLUTTER_FLOAT_TO_INT                (x)
#define             CLUTTER_FLOAT_TO_UINT               (x)
#define             CLUTTER_INT_TO_FIXED                (x)
#define             CLUTTER_FIXED_INT                   (x)
#define             CLUTTER_FIXED_FRACTION              (x)
#define             CLUTTER_FIXED_FLOOR                 (x)
#define             CLUTTER_FIXED_CEIL                  (x)
#define             CLUTTER_FIXED_MUL                   (x,y)
#define             CLUTTER_FIXED_DIV                   (x,y)
#define             CLUTTER_ANGLE_FROM_DEG              (x)
#define             CLUTTER_ANGLE_FROM_DEGF             (x)
#define             CLUTTER_ANGLE_FROM_DEGX             (x)
#define             CLUTTER_ANGLE_TO_DEGF               (x)
#define             CLUTTER_ANGLE_TO_DEG                (x)
#define             CLUTTER_ANGLE_TO_DEGX               (x)
#define             CLUTTER_ANGLE_MAX_DEG
#define             clutter_cosi                        (angle)
#define             clutter_cosx                        (angle)
ClutterFixed        clutter_sini                        (ClutterAngle angle);
ClutterFixed        clutter_sinx                        (ClutterFixed angle);
gint                clutter_sqrti                       (gint x);
ClutterFixed        clutter_sqrtx                       (ClutterFixed x);
ClutterFixed        clutter_log2x                       (guint x);
guint               clutter_pow2x                       (ClutterFixed x);
guint               clutter_powx                        (guint x,
                                                         ClutterFixed y);
ClutterFixed        clutter_qmulx                       (ClutterFixed op1,
                                                         ClutterFixed op2);
ClutterFixed        clutter_tani                        (ClutterAngle angle);

Description

Clutter has a fixed point API targeted at platforms without a floating point unit, such as embedded devices. On such platforms this API should be preferred to the floating point one as it does not trigger the slow path of software emulation, relying on integer math for fixed-to-floating and floating-to-fixed conversion.

It is no recommened for use on platforms with a floating point unit (eg desktop systems) nor for use in bindings.

Basic rules of Fixed Point arithmethic:

  • Two fixed point numbers can be directly added and subtracted.

  • To add other numerical type to a fixed point number it has to be first converted to fixed point.

  • A fixed point number can be directly multiplied or divided by an integer.

  • Two fixed point numbers can only be multiplied and divided by the provided CLUTTER_FIXED_MUL and CLUTTER_FIXED_DIV macros.

Details

ClutterFixed

typedef gint32 ClutterFixed;

Fixed point number (16.16)


CFX_Q

#define CFX_Q      16		/* Decimal part size in bits */

Size in bits of decimal part of floating point value.


CFX_ONE

#define CFX_ONE    (1 << CFX_Q)	/* 1 */

1.0 represented as a fixed point value.


CFX_MAX

#define CFX_MAX    0x7fffffff

Maximum fixed point value.


CFX_MIN

#define CFX_MIN    0x80000000

Minimum fixed point value.


ClutterAngle

typedef gint32 ClutterAngle;    /* angle such that 1024 == 2*PI */

Integer representation of an angle such that 1024 corresponds to full circle (i.e., 2*Pi).


CFX_PI

#define CFX_PI     0x0003243f

Fixed point representation of Pi


CFX_2PI

#define CFX_2PI    0x0006487f

Fixed point representation of Pi*2


CFX_PI_2

#define CFX_PI_2   0x00019220   /* pi/2 */

Fixed point representation of Pi/2


CFX_PI_4

#define CFX_PI_4   0x0000c910   /* pi/4 */

Fixed point representation of Pi/4


CFX_120

#define CFX_120 CLUTTER_INT_TO_FIXED (120)

Fixed point representation of the number 120


CFX_180

#define CFX_180 CLUTTER_INT_TO_FIXED (180)

Fixed point representation of the number 180


CFX_240

#define CFX_240 CLUTTER_INT_TO_FIXED (240)

Fixed point representation of the number 240


CFX_360

#define CFX_360 CLUTTER_INT_TO_FIXED (360)

Fixed point representation of the number 360


CFX_60

#define CFX_60  CLUTTER_INT_TO_FIXED (60)

Fixed point representation of the number 60


CFX_255

#define CFX_255 CLUTTER_INT_TO_FIXED (255)

Fixed point representation of the number 255


CFX_DIV

#define CFX_DIV         CLUTTER_FIXED_DIV


CFX_INT

#define CFX_INT         CLUTTER_FIXED_INT


CFX_MUL

#define CFX_MUL         CLUTTER_FIXED_MUL


CFX_HALF

#define CFX_HALF   32768

0.5 represented as a fixed point value.


CFX_QMUL()

#define CFX_QMUL(x,y)   clutter_qmulx (x,y)

x :
y :

CLUTTER_FIXED_TO_FLOAT()

#define CLUTTER_FIXED_TO_FLOAT(x)       ((float) ((int)(x) / 65536.0))

Convert a fixed point value to float.

x : a fixed point value

CLUTTER_FIXED_TO_DOUBLE()

#define CLUTTER_FIXED_TO_DOUBLE(x)      ((double) ((int)(x) / 65536.0))

Convert a fixed point value to double.

x : a fixed point value

CLUTTER_FLOAT_TO_FIXED()

#define CLUTTER_FLOAT_TO_FIXED(x)       (_clutter_double_to_fixed ((x)))

Convert a float value to fixed.

x : a floating point value

CLUTTER_FLOAT_TO_INT()

#define CLUTTER_FLOAT_TO_INT(x)         (_clutter_double_to_int ((x)))

Convert a float value to int.

x : a floating point value

CLUTTER_FLOAT_TO_UINT()

#define CLUTTER_FLOAT_TO_UINT(x)         (_clutter_double_to_uint ((x)))

Convert a float value to unsigned int.

x : a floating point value

CLUTTER_INT_TO_FIXED()

#define CLUTTER_INT_TO_FIXED(x)         ((x) << CFX_Q)

Convert an integer value to fixed point.

x : an integer value

CLUTTER_FIXED_INT()

#define CLUTTER_FIXED_INT(x)            ((x) >> CFX_Q)

Convert a fixed point value to integer (removing decimal part).

x : a fixed point value

CLUTTER_FIXED_FRACTION()

#define CLUTTER_FIXED_FRACTION(x)       ((x) & ((1 << CFX_Q) - 1))

FIXME

x : a fixed point value

CLUTTER_FIXED_FLOOR()

#define             CLUTTER_FIXED_FLOOR(x)

Round down a fixed point value to an integer.

x : a fixed point value

CLUTTER_FIXED_CEIL()

#define CLUTTER_FIXED_CEIL(x)           (CLUTTER_FIXED_FLOOR (x + 0xffff))

Round up a fixed point value to an integer.

x : a fixed point value

CLUTTER_FIXED_MUL()

#define CLUTTER_FIXED_MUL(x,y) ((x) >> 8) * ((y) >> 8)

Multiply two fixed point values

x : a fixed point value
y : a fixed point value

CLUTTER_FIXED_DIV()

#define CLUTTER_FIXED_DIV(x,y) ((((x) << 8)/(y)) << 8)

Divide two fixed point values

x : a fixed point value
y : a fixed point value

CLUTTER_ANGLE_FROM_DEG()

#define CLUTTER_ANGLE_FROM_DEG(x)  (CLUTTER_FLOAT_TO_INT (((x) * 1024.0) / 360.0))

x :

CLUTTER_ANGLE_FROM_DEGF()

#define CLUTTER_ANGLE_FROM_DEGF(x) (CLUTTER_FLOAT_TO_INT (((float)(x) * 1024.0f) / 360.0f))

x :

CLUTTER_ANGLE_FROM_DEGX()

#define CLUTTER_ANGLE_FROM_DEGX(x) (CFX_INT((((x)/360)*1024) + CFX_HALF))

x :

CLUTTER_ANGLE_TO_DEGF()

#define CLUTTER_ANGLE_TO_DEGF(x)   (((float)(x) * 360.0)/ 1024.0)

x :

CLUTTER_ANGLE_TO_DEG()

#define CLUTTER_ANGLE_TO_DEG(x)    (((x) * 360.0)/ 1024.0)

x :

CLUTTER_ANGLE_TO_DEGX()

#define CLUTTER_ANGLE_TO_DEGX(x)   (CLUTTER_INT_TO_FIXED((x) * 45)/128)

x :

CLUTTER_ANGLE_MAX_DEG

#define CLUTTER_ANGLE_MAX_DEG 1509949439.6


clutter_cosi()

#define clutter_cosi(angle) (clutter_sini ((angle) + 256))

Very fast fixed point implementation of cosine function.

ClutterAngle is an integer such that 1024 represents full circle.

angle : a ClutterAngle angle

Since 0.2


clutter_cosx()

#define clutter_cosx(angle) (clutter_sinx((angle) + CFX_PI_2))

Fixed point cosine function

angle : a ClutterFixed angle in radians

Since 0.2


clutter_sini ()

ClutterFixed        clutter_sini                        (ClutterAngle angle);

Very fast fixed point implementation of sine function.

ClutterAngle is an integer such that 1024 represents full circle.

angle : a ClutterAngle
Returns : ClutterFixed sine value.

Since 0.2


clutter_sinx ()

ClutterFixed        clutter_sinx                        (ClutterFixed angle);

Fixed point implementation of sine function

angle : a ClutterFixed angle in radians
Returns : ClutterFixed sine value.

Since 0.2


clutter_sqrti ()

gint                clutter_sqrti                       (gint x);

Very fast fixed point implementation of square root for integers.

This function is about 10x faster than clib sqrt() on x86, and (this is not a typo!) more than 800x faster on ARM without FPU. It's error is < 5% for arguments < 132 and < 10% for arguments < 5591.

x : integer value
Returns : integer square root.

Since 0.2


clutter_sqrtx ()

ClutterFixed        clutter_sqrtx                       (ClutterFixed x);

A fixed point implementation of squre root

x : a ClutterFixed
Returns : ClutterFixed square root.

Since 0.2


clutter_log2x ()

ClutterFixed        clutter_log2x                       (guint x);

Calculates base 2 logarithm.

This function is some 2.5 times faster on x86, and over 12 times faster on fpu-less arm, than using libc log().

x : value to calculate base 2 logarithm from
Returns : base 2 logarithm.

Since 0.4


clutter_pow2x ()

guint               clutter_pow2x                       (ClutterFixed x);

Calculates 2 to x power.

This function is around 11 times faster on x86, and around 22 times faster on fpu-less arm than libc pow(2, x).

x : exponent
Returns : 2 in x power.

Since 0.4


clutter_powx ()

guint               clutter_powx                        (guint x,
                                                         ClutterFixed y);

Calculates x to y power. (Note, if x is a constant it will be faster to calculate the power as clutter_pow2x (CLUTTER_FIXED_MUL(y, log2 (x)))

x : base
y : ClutterFixed exponent
Returns : x in y power.

Since 0.4


clutter_qmulx ()

ClutterFixed        clutter_qmulx                       (ClutterFixed op1,
                                                         ClutterFixed op2);

op1 :
op2 :
Returns :

clutter_tani ()

ClutterFixed        clutter_tani                        (ClutterAngle angle);

Very fast fixed point implementation of tan function.

ClutterAngle is an integer such that 1024 represents full circle.

angle : a ClutterAngle
Returns : ClutterFixed sine value.

Since 0.3