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* A Low Level GPU Graphics and Utilities API
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* Copyright (C) 2007,2008,2009 Intel Corporation.
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* Permission is hereby granted, free of charge, to any person
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* obtaining a copy of this software and associated documentation
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* files (the "Software"), to deal in the Software without
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* restriction, including without limitation the rights to use, copy,
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* modify, merge, publish, distribute, sublicense, and/or sell copies
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* of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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#if !defined(__COGL_H_INSIDE__) && !defined(COGL_COMPILATION)
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#error "Only <cogl/cogl.h> can be included directly."
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#ifndef __COGL_FIXED_H__
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#define __COGL_FIXED_H__
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#include <cogl/cogl-types.h>
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* @short_description: Fixed Point API
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* COGL has a fixed point API targeted at platforms without a floating
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* point unit, such as embedded devices. On such platforms this API should
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* be preferred to the floating point one as it does not trigger the slow
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* path of software emulation, relying on integer math for fixed-to-floating
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* and floating-to-fixed notations conversion.
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* It is not recommened for use on platforms with a floating point unit
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* (e.g. desktop systems), nor for use in language bindings.
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* Basic rules of Fixed Point arithmethic:
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* <para>Two fixed point numbers can be directly added, subtracted and
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* have their modulus taken.</para>
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* <para>To add other numerical type to a fixed point number it has to
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* be first converted to fixed point.</para>
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* <para>A fixed point number can be directly multiplied or divided by
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* <para>Two fixed point numbers can only be multiplied and divided by
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* the provided %COGL_FIXED_MUL and %COGL_FIXED_DIV macros.</para>
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* The fixed point API is available since COGL 1.0.
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* Evaluates to the number of bits used by the #CoglFixed type.
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#define COGL_FIXED_BITS (32)
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* Evaluates to the number of bits used for the non-integer part
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* of the #CoglFixed type.
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#define COGL_FIXED_Q (COGL_FIXED_BITS - 16)
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* The number 1 expressed as a #CoglFixed number.
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#define COGL_FIXED_1 (1 << COGL_FIXED_Q)
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* The number 0.5 expressed as a #CoglFixed number.
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#define COGL_FIXED_0_5 (32768)
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* COGL_FIXED_EPSILON:
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* A very small number expressed as a #CoglFixed number.
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#define COGL_FIXED_EPSILON (1)
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* The biggest number representable using #CoglFixed
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#define COGL_FIXED_MAX (0x7fffffff)
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* The smallest number representable using #CoglFixed
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#define COGL_FIXED_MIN (0x80000000)
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* The number pi, expressed as a #CoglFixed number.
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#define COGL_FIXED_PI (0x0003243f)
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* Two times pi, expressed as a #CoglFixed number.
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#define COGL_FIXED_2_PI (0x0006487f)
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* Half pi, expressed as a #CoglFixed number.
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#define COGL_FIXED_PI_2 (0x00019220)
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* pi / 4, expressed as #CoglFixed number.
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#define COGL_FIXED_PI_4 (0x0000c910)
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* Evaluates to the number 360 in fixed point notation.
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#define COGL_FIXED_360 (COGL_FIXED_FROM_INT (360))
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* Evaluates to the number 270 in fixed point notation.
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#define COGL_FIXED_270 (COGL_FIXED_FROM_INT (270))
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* Evaluates to the number 255 in fixed point notation.
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#define COGL_FIXED_255 (COGL_FIXED_FROM_INT (255))
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* Evaluates to the number 240 in fixed point notation.
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#define COGL_FIXED_240 (COGL_FIXED_FROM_INT (240))
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* Evaluates to the number 180 in fixed point notation.
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#define COGL_FIXED_180 (COGL_FIXED_FROM_INT (180))
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* Evaluates to the number 120 in fixed point notation.
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#define COGL_FIXED_120 (COGL_FIXED_FROM_INT (120))
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* Evaluates to the number 90 in fixed point notation.
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#define COGL_FIXED_90 (COGL_FIXED_FROM_INT (90))
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* Evaluates to the number 60 in fixed point notation.
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#define COGL_FIXED_60 (COGL_FIXED_FROM_INT (60))
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* Evaluates to the number 45 in fixed point notation.
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#define COGL_FIXED_45 (COGL_FIXED_FROM_INT (45))
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* Evaluates to the number 30 in fixed point notation.
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#define COGL_FIXED_30 (COGL_FIXED_FROM_INT (30))
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* COGL_RADIANS_TO_DEGREES:
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* Evaluates to 180 / pi in fixed point notation.
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#define COGL_RADIANS_TO_DEGREES (0x394bb8)
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* COGL_FIXED_FROM_FLOAT:
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* @x: a floating point number
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* Converts @x from a floating point to a fixed point notation.
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#define COGL_FIXED_FROM_FLOAT(x) ((float) cogl_double_to_fixed (x))
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* COGL_FIXED_TO_FLOAT:
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* @x: a #CoglFixed number
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* Converts @x from a fixed point to a floating point notation, in
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#define COGL_FIXED_TO_FLOAT(x) ((float) ((int)(x) / 65536.0))
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* COGL_FIXED_FROM_DOUBLE:
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* @x: a floating point number
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* Converts @x from a double precision, floating point to a fixed
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#define COGL_FIXED_FROM_DOUBLE(x) (cogl_double_to_fixed (x))
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* COGL_FIXED_TO_DOUBLE:
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* @x: a #CoglFixed number
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* Converts @x from a fixed point to a floating point notation, in
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#define COGL_FIXED_TO_DOUBLE(x) ((double) ((int)(x) / 65536.0))
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* COGL_FIXED_FROM_INT:
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* @x: an integer number
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* Converts @x from an integer to a fixed point notation.
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#define COGL_FIXED_FROM_INT(x) ((x) << COGL_FIXED_Q)
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* @x: a #CoglFixed number
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* Converts @x from a fixed point notation to an integer, dropping
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* the fractional part without rounding.
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#define COGL_FIXED_TO_INT(x) ((x) >> COGL_FIXED_Q)
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* @x: a floatint point number
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* Converts @x from a floating point notation to a signed integer.
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#define COGL_FLOAT_TO_INT(x) (cogl_double_to_int ((x)))
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* COGL_FLOAT_TO_UINT:
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* @x: a floatint point number
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* Converts @x from a floating point notation to an unsigned integer.
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#define COGL_FLOAT_TO_UINT(x) (cogl_double_to_uint ((x)))
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* fixed point math functions
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* COGL_FIXED_FRACTION:
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* @x: a #CoglFixed number
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* Retrieves the fractionary part of @x.
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#define COGL_FIXED_FRACTION(x) ((x) & ((1 << COGL_FIXED_Q) - 1))
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* @x: a #CoglFixed number
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* Rounds down a fixed point number to the previous integer.
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#define COGL_FIXED_FLOOR(x) (((x) >= 0) ? ((x) >> COGL_FIXED_Q) \
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: ~((~(x)) >> COGL_FIXED_Q))
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* @x: a #CoglFixed number
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* Rounds up a fixed point number to the next integer.
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#define COGL_FIXED_CEIL(x) (COGL_FIXED_FLOOR ((x) + 0xffff))
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* @a: a #CoglFixed number
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* @b: a #CoglFixed number
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#define COGL_FIXED_MUL(a,b) (cogl_fixed_mul ((a), (b)))
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* @a: a #CoglFixed number
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* @b: a #CoglFixed number
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#define COGL_FIXED_DIV(a,b) (cogl_fixed_div ((a), (b)))
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* COGL_FIXED_MUL_DIV:
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* @a: a #CoglFixed number
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* @b: a #CoglFixed number
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* @c: a #CoglFixed number
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* Computes ((a * b) / c). It is logically equivalent to:
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* res = COGL_FIXED_DIV (COGL_FIXED_MUL (a, b), c);
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* But it is shorter to type.
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#define COGL_FIXED_MUL_DIV(a,b,c) (cogl_fixed_mul_div ((a), (b), (c)))
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* COGL_FIXED_FAST_MUL:
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* @a: a #CoglFixed number
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* @b: a #CoglFixed number
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* Fast version of %COGL_FIXED_MUL, implemented as a macro.
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* <note>This macro might lose precision. If the precision of the result
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* is important use %COGL_FIXED_MUL instead.</note>
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#define COGL_FIXED_FAST_MUL(a,b) ((a) >> 8) * ((b) >> 8)
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* COGL_FIXED_FAST_DIV:
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* @a: a #CoglFixed number
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* @b: a #CoglFixed number
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* Fast version of %COGL_FIXED_DIV, implemented as a macro.
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* <note>This macro might lose precision. If the precision of the result
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* is important use %COGL_FIXED_DIV instead.</note>
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#define COGL_FIXED_FAST_DIV(a,b) ((((a) << 8) / (b)) << 8)
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* @angle: a #CoglFixed number
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* Computes the sine of @angle.
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* Return value: the sine of the passed angle, in fixed point notation
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cogl_fixed_sin (CoglFixed angle);
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* @angle: a #CoglFixed number
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* Computes the tangent of @angle.
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* Return value: the tangent of the passed angle, in fixed point notation
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cogl_fixed_tan (CoglFixed angle);
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* @angle: a #CoglFixed number
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* Computes the cosine of @angle.
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* Return value: the cosine of the passed angle, in fixed point notation
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CoglFixed cogl_fixed_cos (CoglFixed angle);
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* @a: a #CoglFixed number
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* Computes the arc tangent of @a.
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* Return value: the arc tangent of the passed value, in fixed point notation
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cogl_fixed_atan (CoglFixed a);
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* @a: the numerator as a #CoglFixed number
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* @b: the denominator as a #CoglFixed number
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* Computes the arc tangent of @a / @b but uses the sign of both
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* arguments to return the angle in right quadrant.
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* Return value: the arc tangent of the passed fraction, in fixed point
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cogl_fixed_atan2 (CoglFixed a,
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/* Fixed point math routines */
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G_INLINE_FUNC CoglFixed
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cogl_fixed_mul (CoglFixed a,
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G_INLINE_FUNC CoglFixed
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cogl_fixed_div (CoglFixed a,
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G_INLINE_FUNC CoglFixed
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cogl_fixed_mul_div (CoglFixed a,
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* COGL_SQRTI_ARG_MAX:
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* Maximum argument that can be passed to cogl_sqrti() function.
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#define COGL_SQRTI_ARG_MAX 0x3fffff
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#define COGL_SQRTI_ARG_MAX INT_MAX
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* COGL_SQRTI_ARG_5_PERCENT:
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* Maximum argument that can be passed to cogl_sqrti() for which the
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* resulting error is < 5%
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#define COGL_SQRTI_ARG_5_PERCENT 210
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#define COGL_SQRTI_ARG_5_PERCENT INT_MAX
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* COGL_SQRTI_ARG_10_PERCENT:
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* Maximum argument that can be passed to cogl_sqrti() for which the
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* resulting error is < 10%
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#define COGL_SQRTI_ARG_10_PERCENT 5590
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#define COGL_SQRTI_ARG_10_PERCENT INT_MAX
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* @x: a #CoglFixed number
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* Computes the square root of @x.
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* Return value: the square root of the passed value, in floating point
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cogl_fixed_sqrt (CoglFixed x);
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* @x: value to calculate base 2 logarithm from
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* Calculates base 2 logarithm.
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* This function is some 2.5 times faster on x86, and over 12 times faster on
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* fpu-less arm, than using libc log().
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* Return value: base 2 logarithm.
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cogl_fixed_log2 (unsigned int x);
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* @x: a #CoglFixed number
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* Calculates 2 to the @x power.
629
* This function is around 11 times faster on x86, and around 22 times faster
630
* on fpu-less arm than libc pow(2, x).
632
* Return value: the power of 2 to the passed value
637
cogl_fixed_pow2 (CoglFixed x);
642
* @y: #CoglFixed exponent
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* Calculates @x to the @y power.
646
* Return value: the power of @x to the @y
651
cogl_fixed_pow (unsigned int x,
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* Very fast fixed point implementation of square root for integers.
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* This function is at least 6x faster than clib sqrt() on x86, and (this is
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* not a typo!) about 500x faster on ARM without FPU. It's error is less than
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* 5% for arguments smaller than %COGL_SQRTI_ARG_5_PERCENT and less than 10%
663
* for narguments smaller than %COGL_SQRTI_ARG_10_PERCENT. The maximum
664
* argument that can be passed to this function is %COGL_SQRTI_ARG_MAX.
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* Return value: integer square root.
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* COGL_ANGLE_FROM_DEG:
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* @x: an angle in degrees in floating point notation
677
* Converts an angle in degrees into a #CoglAngle.
681
#define COGL_ANGLE_FROM_DEG(x) (COGL_FLOAT_TO_INT (((float)(x) * 1024.0f) / 360.0f))
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* Converts a #CoglAngle into an angle in degrees, using floatint point
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#define COGL_ANGLE_TO_DEG(x) (((float)(x) * 360.0) / 1024.0)
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* COGL_ANGLE_FROM_DEGX:
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* @x: an angle in degrees in fixed point notation
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* Converts an angle in degrees into a #CoglAngle.
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#define COGL_ANGLE_FROM_DEGX(x) (COGL_FIXED_TO_INT ((((x) / 360) * 1024) + COGL_FIXED_0_5))
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* COGL_ANGLE_TO_DEGX:
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* Converts a #CoglAngle into an angle in degrees, using fixed point notation
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#define COGL_ANGLE_TO_DEGX(x) (COGL_FIXED_FROM_INT ((x) * 45) / 128)
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* @angle: an angle expressed using #CoglAngle
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* Computes the sine of @angle
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* Return value: the sine of the passed angle
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cogl_angle_sin (CoglAngle angle);
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* @angle: an angle expressed using #CoglAngle
731
* Computes the tangent of @angle
733
* Return value: the tangent of the passed angle
738
cogl_angle_tan (CoglAngle angle);
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* @angle: an angle expressed using #CoglAngle
744
* Computes the cosine of @angle
746
* Return value: the cosine of the passed angle
751
cogl_angle_cos (CoglAngle angle);
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#if defined (G_CAN_INLINE)
756
G_INLINE_FUNC CoglFixed
757
cogl_fixed_mul (CoglFixed a,
763
__asm__ ("smull %0, %1, %2, %3 \n"
764
"mov %0, %0, lsr %4 \n"
765
"add %1, %0, %1, lsl %5 \n"
766
: "=r"(res_hi), "=r"(res_low)\
767
: "r"(a), "r"(b), "i"(COGL_FIXED_Q), "i"(32 - COGL_FIXED_Q));
769
return (CoglFixed) res_low;
771
long long r = (long long) a * (long long) b;
773
return (unsigned int)(r >> COGL_FIXED_Q);
778
#if defined (G_CAN_INLINE)
779
G_INLINE_FUNC CoglFixed
780
cogl_fixed_div (CoglFixed a,
783
return (CoglFixed) ((((int64_t) a) << COGL_FIXED_Q) / b);
787
#if defined(G_CAN_INLINE)
788
G_INLINE_FUNC CoglFixed
789
cogl_fixed_mul_div (CoglFixed a,
793
CoglFixed ab = cogl_fixed_mul (a, b);
794
CoglFixed quo = cogl_fixed_div (ab, c);
801
cogl_double_to_fixed (double value);
804
cogl_double_to_int (double value);
807
cogl_double_to_uint (double value);
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#endif /* __COGL_FIXED_H__ */
added
removed
cogl/cogl/deprecated/cogl-fixed.h
