hendrik
/
wordclock
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
Browse Source

switched to fixed point arithmetic; saving 1046 byte and noticeable speedup

feature/2015
Christian Kroll 13 years ago
parent
028dea2b87
commit
af8a928123
1 changed files with 394 additions and 57 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 451
      animations/fpmath_patterns.c

451
animations/fpmath_patterns.c
View File

@ -1,30 +1,277 @@
#include <math.h> // Floating point math is dog slow on AVR, but I don't care.
#include <string.h>
/**
* Routines for drawing patterns generated by fixed point math functions.
*/
#include <assert.h>
#include <stdint.h>
#include <string.h>
#include "../config.h"
#include "../pixel.h"
#include "../util.h"
#include "fpmath_patterns.h"
/**
* \defgroup fixedpoint Fixed-point based animated plasma patterns.
*/
/*@{*/
/**
* Double buffering helps in reducing the effect of visibly redrawing every
* frame. With this option turned on, a frame is rendered into an off-screen
* buffer first and then copied to the actual frame buffer in one piece.
* However, given the borg's graphics architecture, half painted frames may
* still occur, but they are barely noticeable with this option enabled.
*
* Turn this off (#undef DOUBLE_BUFFERING) if you prefer speed over beauty.
*/
#define DOUBLE_BUFFERING
#ifdef DOUBLE_BUFFERING
#define BUFFER pixmap_buffer
#ifdef LOW_PRECISION
#undef LOW_PRECISION
#endif
#if NUM_COLS <= 16 && NUM_ROWS <= 16
/**
* Low precision means that we use Q10.5 values and 16 bit types for almost
* every calculation (with multiplication and division as notable exceptions
* as they and their interim results utilize 32 bit).
*
* Use this precision mode with care as image quality will suffer
* noticeably. It produces leaner and faster code, though. This mode should
* not be used with resolutions higher than 16x16 as overflows are likely to
* occur in interim calculations.
*
* Normal precision (i.e. #undef LOW_PRECISION) conforms to Q7.8 with the
* ability to store every interim result as Q23.8. Most operations like
* square root, sine, cosine, multiplication etc. utilize 32 bit types.
*/
#define LOW_PRECISION
#endif
#ifdef LOW_PRECISION
/** This is the type we expect ordinary integers to be. */
typedef int16_t ordinary_int_t;
/** This is the type which we use for fixed point values. */
typedef int16_t fixp_t;
/** This type covers arguments of fixSin() and fixCos(). */
typedef int16_t fixp_trig_t;
/** This type covers interim results of fixed point operations. */
typedef uint32_t fixp_interim_t;
/** This type covers interim results of the fixed point sqrt() function. */
typedef uint16_t ufixp_interim_t;
/** Amount of bits the fixed point sqrt() function can handle. */
#define SQRT_BITS 16
// NOTE: If you change the following values, don't forget to adapt the sine
// lookup table as well!
/** Multiply a number by this factor to convert it to a fixed point value.*/
#define FIX 32
/** Amount of fractional bits of a value (i.e. ceil(log_2(FIX))). */
#define FIX_FRACBITS 5
/**
* The amount of temporal quantization steps of the sine lookup table. It
* must be a divisor of (FIX * 2 * pi) and this divisor must be divisable by
* 4 itself. Approximate this value as close as possible to keep rounding
* errors at a minimum.
*/
#define FIX_SIN_COUNT 200
/** The rounded down quotient of (FIX * 2 * pi) and FIX_SIN_COUNT */
#define FIX_SIN_DIVIDER 1
/** Type of the lookup table elements. */
typedef uint8_t lut_t;
/**
* Lookup table of fractional parts which model the first quarter of a
* sine period. The rest of that period is calculated by mirroring those
* values. These values are intended for Q5 types.
*/
static lut_t const fix_sine_lut[FIX_SIN_COUNT / 4] =
{ 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15,
15, 16, 17, 18, 19, 20, 20, 21,
22, 22, 23, 24, 24, 25, 26, 26,
27, 27, 28, 28, 29, 29, 29, 30,
30, 30, 31, 31, 31, 31, 31, 31,
31, 31};
#else
#define BUFFER pixmap
/** This is the type we expect ordinary integers to be. */
typedef int16_t ordinary_int_t;
/** This is the type which we use for fixed point values. */
typedef int16_t fixp_t;
/** This type covers arguments of fixSin() and fixCos(). */
typedef int32_t fixp_trig_t;
/** This type covers interim results of fixed point operations. */
typedef int32_t fixp_interim_t;
/** This type covers interim results of the fixed point sqrt() function. */
typedef uint32_t ufixp_interim_t;
/** Amount of bits the fixed point sqrt() function can handle. */
#define SQRT_BITS 32
// NOTE: If you change the following values, don't forget to adapt the sine
// lookup table as well!
/** Multiply a number by this factor to convert it to a fixed point value.*/
#define FIX 256
/** Amount of fractional bits of a value (i.e. ceil(log_2(FIX))). */
#define FIX_FRACBITS 8
/**
* The amount of temporal quantization steps of the sine lookup table. It
* must be a divisor of (FIX * 2 * pi) and this divisor must be divisable by
* 4 itself. Approximate this value as close as possible to keep rounding
* errors at a minimum.
*/
#define FIX_SIN_COUNT 200
/** The rounded down quotient of (FIX * 2 * pi) and FIX_SIN_COUNT */
#define FIX_SIN_DIVIDER 8
/** Type of the lookup table elements. */
typedef uint8_t lut_t;
/**
* Lookup table of fractional parts which model the first quarter of a
* sine period. The rest of that period is calculated by mirroring those
* values. These values are intended for Q8 types.
*/
static lut_t const fix_sine_lut[FIX_SIN_COUNT / 4] =
{ 0, 9, 17, 24, 32, 40, 48, 56,
64, 72, 79, 87, 94, 102, 109, 116,
123, 130, 137, 144, 150, 157, 163, 169,
175, 181, 186, 192, 197, 202, 207, 211,
216, 220, 224, 228, 231, 235, 238, 240,
243, 245, 247, 249, 251, 252, 253, 254,
255, 255};
#endif
/** The ordinary pi constant. */
#define PI 3.14159265358979323846
/** Fixed point version of (pi / 2). */
#define FIX_PI_2 ((fixp_t)(PI * FIX / 2))
/** Fixed point version of pi. */
#define FIX_PI ((fixp_t)(PI * FIX))
/** Fixed point version of (2 * pi). */
#define FIX_2PI ((fixp_t)(2 * PI * FIX))
/**
* Pointer to a function which return a value depending on two-dimensional
* coordinates and a "step" value.
* @param x x-coordinate
* @param y y-coordinate
* @param t a step value which changes for each frame, allowing for animations
* @return
* Scales an ordinary integer up to its fixed point format.
* @param a an ordinary integer to be scaled up
* @return The given value in fixed point format.
*/
typedef unsigned char (*fpmath_pattern_func_t)(unsigned char const x,
unsigned char const y,
double t);
inline static fixp_t fixScaleUp(ordinary_int_t a)
{
return (fixp_t)a * FIX;
}
/**
* Scales a fixed point value down to an ordinary integer (omitting the
* fractional part).
* @param a fixed point value to be scaled down
* @return The given value in fixed point format.
*/
inline static ordinary_int_t fixScaleDown(fixp_t const a)
{
return a / FIX;
}
/**
* Multiplies two fixed point values.
* @param a operand a
* @param b operand b
* @return Product of a and b.
*/
inline static fixp_interim_t fixMul(fixp_t const a, fixp_t const b)
{
return ((fixp_interim_t)a * (fixp_interim_t)b) / FIX;
}
/**
* Divides two fixed point values.
* @param a operand a
* @param b operand b
* @return Quotient of a and b.
*/
inline static fixp_t fixDiv(fixp_interim_t const a, fixp_interim_t const b)
{
return (a * FIX) / b;
}
/**
* Fixed point variant of the sine function which receives a fixed point angle
* (radian). It uses a lookup table which models the first quarter of a full
* sine period and calculates the rest from that quarter.
* @param angle fixed point radian value
* @return Result of the sine function normalized to a range from -FIX to FIX.
*/
static fixp_t fixSin(fixp_t const fAngle)
{
// convert given angle to its corresponding lookup table quantization step
ordinary_int_t nNormAng = fAngle / FIX_SIN_DIVIDER;
// trim that value so that it fits into a range between [0, FIX_SIN_COUNT]
nNormAng = (nNormAng - (nNormAng / FIX_SIN_COUNT * FIX_SIN_COUNT) +
FIX_SIN_COUNT) % FIX_SIN_COUNT;
uint8_t nIndex = nNormAng % (FIX_SIN_COUNT / 2);
if (nIndex >= (FIX_SIN_COUNT / 4))
{
nIndex = (FIX_SIN_COUNT / 2 - 1) - nIndex;
}
assert(nIndex < (FIX_SIN_COUNT / 4));
return ((fixp_t)fix_sine_lut[nIndex]) *
(nNormAng < (FIX_SIN_COUNT / 2) ? 1 : -1);
}
/**
* Fixed point variant of the cosine function which takes a fixed point angle
* (radian). It adds FIX_PI_2 to the given angle and consults the fixSin()
* function for the final result.
* @param angle fixed point radian value
* @return Result of the cosine function normalized to a range from -FIX to FIX.
*/
static fixp_t fixCos(fixp_t const angle)
{
return fixSin(angle + FIX_PI_2);
}
/**
* Fixed point square root algorithm as proposed by Ken Turkowski:
* http://www.realitypixels.com/turk/computergraphics/FixedSqrt.pdf
* @param radicant we want the square root of
* @return The square root of the given value.
*/
static fixp_t fixSqrt(ufixp_interim_t const a)
{
ufixp_interim_t nRoot, nRemainingHigh, nRemainingLow, nTestDiv, nCount;
nRoot = 0; // clear root
nRemainingHigh = 0; // clear high part of partial remainder
nRemainingLow = a; // get argument into low part of partial remainder
nCount = (SQRT_BITS / 2 - 1) + (FIX_FRACBITS >> 1); // load loop counter
do
{
nRemainingHigh =
(nRemainingHigh << 2) | (nRemainingLow >> (SQRT_BITS - 2));
nRemainingLow <<= 2; // get 2 bits of the argument
nRoot <<= 1; // get ready for the next bit in the root
nTestDiv = (nRoot << 1) + 1; // test radical
if (nRemainingHigh >= nTestDiv)
{
nRemainingHigh -= nTestDiv;
nRoot++;
}
} while (nCount-- != 0);
return (nRoot);
}
/**
@ -33,41 +280,69 @@ typedef unsigned char (*fpmath_pattern_func_t)(unsigned char const x,
* @param y1 y coordinate of the first point
* @param x2 x coordinate of the second point
* @param y2 y coordinate of the second point
* @return distance between the points
* @return The distance between the given coordinates.
*/
static double dist(double x1, double y1, double x2, double y2)
static fixp_t fixDist(fixp_t const x1,
fixp_t const y1,
fixp_t const x2,
fixp_t const y2)
{
return sqrt(((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2)));
return fixSqrt(fixMul((x1 - x2), (x1 - x2)) + fixMul((y1 - y2), (y1 - y2)));
}
/**
* This pointer type covers functions which return a brightness value for the
* given coordinates and a "step" value. This actually results in a more or less
* "beautiful" pattern.
* @param x x-coordinate
* @param y y-coordinate
* @param t step value which changes for each frame, allowing for animations
* @param r pointer to persistent data required by the pattern function
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
typedef unsigned char (*fpmath_pattern_func_t)(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r);
#ifdef DOUBLE_BUFFERING
# define BUFFER pixmap_buffer
#else
# define BUFFER pixmap
#endif
/**
* Draws an animated two dimensional graph for a given function f(x, y, t).
* @param t_start start value for the function's time variable
* @param t_stop stop value for the function's time variable
* @param t_delta value by which the function's timing variable gets incremented
* @param frame_delay frame delay in ms
* @param fpPattern function which generates a pattern depending on x, y, t
*/
static void fpmath_pattern(double const t_start,
double const t_stop,
double const t_delta,
unsigned int const frame_delay,
fpmath_pattern_func_t fpPattern)
* @param t_start start value for the function's step variable
* @param t_stop stop value for the function's step variable
* @param t_delta value by which the function's step variable gets incremented
* @param frame_delay frame delay in milliseconds
* @param fpPattern function which generates a pattern depending on x, y and t
* @param r pointer to persistent data required by the fpPattern function
*/
static void fixPattern(fixp_t const t_start,
fixp_t const t_stop,
fixp_t const t_delta,
int const frame_delay,
fpmath_pattern_func_t fpPattern,
void *r)
{
#ifdef DOUBLE_BUFFERING
// double buffering to reduce half painted pictures
unsigned char pixmap_buffer[NUMPLANE][NUM_ROWS][LINEBYTES];
#endif
for (double t = t_start; t < t_stop; t += t_delta)
for (fixp_t t = t_start; t < t_stop; t += t_delta)
{
for (unsigned char y = 0; y < NUM_ROWS; ++y)
{
unsigned char nChunk[NUMPLANE + 1][LINEBYTES] = {{0}};
for (unsigned char x = 0; x < (LINEBYTES * 8); ++x)
{
nChunk[fpPattern(x, y, t) - 1][x / 8u] |= shl_table[x % 8u];
assert (y < 16);
nChunk[fpPattern(x, y, t, r) - 1][x / 8u] |= shl_table[x % 8u];
}
for (unsigned char p = NUMPLANE; p--;)
{
@ -89,71 +364,133 @@ static void fpmath_pattern(double const t_start,
#ifdef ANIMATION_PLASMA
#define PLASMA_X (1.0 / (NUM_COLS / (2.0 * M_PI)))
/**
* Draws a simple plasma like pattern.
* This type maintains values relevant for the Plasma animation which need to be
* persistent over consecutive invocations.
*/
static unsigned char fpmath_plasma(unsigned char x, unsigned char y, double t)
typedef struct fixp_plasma_s
{
fixp_t fFunc1[NUM_COLS]; /**< Result of 1st trig. func. depending on x. */
fixp_t fFunc2CosArg; /**< Arg. of 2st trig. func. depending on the frame. */
fixp_t fFunc2SinArg; /**< Arg. of 2st trig. func. depending on the frame. */
} fixp_plasma_t;
/**
* Draws a plasma like pattern (sort of... four shades of grey are pretty
* scarce for a neat plasma animation).
* @param x x-coordinate
* @param y y-coordinate
* @param t step value which changes for each frame, allowing for animations
* @param r pointer to persistent interim results
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
static unsigned char fixAnimPlasma(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r)
{
assert(x < NUM_COLS);
assert(y < NUM_ROWS);
static double fFunc1[NUM_COLS];
static double fFunc2CosArg;
static double fFunc2SinArg;
// scaling factor
static fixp_t const fPlasmaX = (2 * PI * FIX) / NUM_COLS;
// reentrant data
fixp_plasma_t *const p = (fixp_plasma_t *)r;
if (x == 0 && y == 0)
{
fFunc2CosArg = NUM_ROWS * cos(t) + NUM_ROWS;
fFunc2SinArg = NUM_COLS * sin(t) + NUM_COLS;
p->fFunc2CosArg = NUM_ROWS * fixCos(t) + fixScaleUp(NUM_ROWS);
p->fFunc2SinArg = NUM_COLS * fixSin(t) + fixScaleUp(NUM_COLS);
}
if (y == 0)
{
fFunc1[x] = sin(x * PLASMA_X + t);
p->fFunc1[x] = fixSin(fixMul(fixScaleUp(x), fPlasmaX) + t);
}
return (fFunc1[x] + sin(dist(x, y, fFunc2SinArg, fFunc2CosArg) * PLASMA_X)
+ 2) * (NUMPLANE - 1) / 2;
fixp_t const fFunc2 = fixSin(fixMul(fixDist(fixScaleUp(x), fixScaleUp(y),
p->fFunc2SinArg, p->fFunc2CosArg), fPlasmaX));
uint8_t const nRes = fixScaleDown(fixDiv(fixMul(p->fFunc1[x] + fFunc2 +
fixScaleUp(2), fixScaleUp(NUMPLANE - 1)), fixScaleUp(2)));
assert (nRes <= 3);
return nRes;
}
void plasma(void)
{
fixp_plasma_t r;
#ifndef __AVR__
fpmath_pattern(0.0, 75, 0.1, 80, fpmath_plasma);
fixPattern(0, fixScaleUp(75), 0.1 * FIX, 80, fixAnimPlasma, &r);
#else
fpmath_pattern(0.0, 60.0, 0.1, 1, fpmath_plasma);
#endif
fixPattern(0, fixScaleUp(60), 0.1 * FIX, 1, fixAnimPlasma, &r);
#endif /* __AVR__ */
}
#endif
#endif /* ANIMATION_PLASMA */
#ifdef ANIMATION_PSYCHEDELIC
/**
* This type maintains values relevant for the Psychedelic animation which need
* to be persistent over consecutive invocations.
*/
typedef struct fixp_psychedelic_s
{
fixp_t fCos; /** column factor for the circle calculation */
fixp_t fSin; /** row factor for the circle calculation */
fixp_interim_t ft10; /** value involved in rotating the animation's center*/
} fixp_psychedelic_t;
/**
* Draws flowing circular waves with a rotating center.
* @param x x-coordinate
* @param y y-coordinate
* @param t step value which changes for each frame, allowing for animations
* @param r pointer to persistent interim results
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
static unsigned char fpmath_psycho(unsigned char x, unsigned char y, double t)
static unsigned char fixAnimPsychedelic(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r)
{
assert(x < NUM_COLS);
assert(y < NUM_ROWS);
fixp_psychedelic_t *p = (fixp_psychedelic_t *)r;
static double fCosinus;
static double fSinus;
static double t10;
if (x == 0 && y == 0)
{
fCosinus = NUM_COLS * cos(t);
fSinus = NUM_ROWS * sin(t);
t10 = t * 10;
p->fCos = NUM_COLS/2 * fixCos(t);
p->fSin = NUM_ROWS/2 * fixSin(t);
p->ft10 = fixMul(t, fixScaleUp(10));
}
return (sin(dist(x, y, fCosinus, fSinus) - t10) + 1) * (NUMPLANE - 1);
uint8_t const nResult =
fixScaleDown(fixMul(fixSin((fixp_interim_t)fixDist(fixScaleUp(x),
fixScaleUp(y), p->fCos, p->fSin) - p->ft10) + fixScaleUp(1),
fixScaleUp(NUMPLANE - 1)));
assert(nResult <= NUMPLANE);
return nResult;
}
void psychedelic(void)
{
fixp_psychedelic_t r;
#ifndef __AVR__
fpmath_pattern(0.0, 75, 0.1, 80, fpmath_psycho);
fixPattern(0, fixScaleUp(75), 0.1 * FIX, 80, fixAnimPsychedelic, &r);
#else
fpmath_pattern(0.0, 60.0, 0.1, 1, fpmath_psycho);
#endif
fixPattern(0, fixScaleUp(60), 0.1 * FIX, 15, fixAnimPsychedelic, &r);
#endif /* __AVR__ */
}
#endif
#endif /* ANIMATION_PSYCHEDELIC */
/*@}*/

Write Preview
Loading…
Cancel
Save