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ES-DE/external/lunasvg/3rdparty/plutovg/plutovg-ft-math.c

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/***************************************************************************/
/* */
/* fttrigon.c */
/* */
/* FreeType trigonometric functions (body). */
/* */
/* Copyright 2001-2005, 2012-2013 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used, */
/* modified, and distributed under the terms of the FreeType project */
/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
/* this file you indicate that you have read the license and */
/* understand and accept it fully. */
/* */
/***************************************************************************/
#include "plutovg-ft-math.h"
#if defined(_MSC_VER)
#include <intrin.h>
static unsigned int __inline clz(unsigned int x) {
unsigned long r = 0;
if (x != 0)
{
_BitScanReverse(&r, x);
}
return r;
}
#define PVG_FT_MSB(x) (clz(x))
#elif defined(__GNUC__)
#define PVG_FT_MSB(x) (31 - __builtin_clz(x))
#else
static unsigned int __inline clz(unsigned int x) {
int c = 31;
x &= ~x + 1;
if (n & 0x0000FFFF) c -= 16;
if (n & 0x00FF00FF) c -= 8;
if (n & 0x0F0F0F0F) c -= 4;
if (n & 0x33333333) c -= 2;
if (n & 0x55555555) c -= 1;
return c;
}
#define PVG_FT_MSB(x) (clz(x))
#endif
#define PVG_FT_PAD_FLOOR(x, n) ((x) & ~((n)-1))
#define PVG_FT_PAD_ROUND(x, n) PVG_FT_PAD_FLOOR((x) + ((n) / 2), n)
#define PVG_FT_PAD_CEIL(x, n) PVG_FT_PAD_FLOOR((x) + ((n)-1), n)
#define PVG_FT_BEGIN_STMNT do {
#define PVG_FT_END_STMNT } while (0)
/* transfer sign leaving a positive number */
#define PVG_FT_MOVE_SIGN(x, s) \
PVG_FT_BEGIN_STMNT \
if (x < 0) { \
x = -x; \
s = -s; \
} \
PVG_FT_END_STMNT
PVG_FT_Long PVG_FT_MulFix(PVG_FT_Long a, PVG_FT_Long b)
{
PVG_FT_Int s = 1;
PVG_FT_Long c;
PVG_FT_MOVE_SIGN(a, s);
PVG_FT_MOVE_SIGN(b, s);
c = (PVG_FT_Long)(((PVG_FT_Int64)a * b + 0x8000L) >> 16);
return (s > 0) ? c : -c;
}
PVG_FT_Long PVG_FT_MulDiv(PVG_FT_Long a, PVG_FT_Long b, PVG_FT_Long c)
{
PVG_FT_Int s = 1;
PVG_FT_Long d;
PVG_FT_MOVE_SIGN(a, s);
PVG_FT_MOVE_SIGN(b, s);
PVG_FT_MOVE_SIGN(c, s);
d = (PVG_FT_Long)(c > 0 ? ((PVG_FT_Int64)a * b + (c >> 1)) / c : 0x7FFFFFFFL);
return (s > 0) ? d : -d;
}
PVG_FT_Long PVG_FT_DivFix(PVG_FT_Long a, PVG_FT_Long b)
{
PVG_FT_Int s = 1;
PVG_FT_Long q;
PVG_FT_MOVE_SIGN(a, s);
PVG_FT_MOVE_SIGN(b, s);
q = (PVG_FT_Long)(b > 0 ? (((PVG_FT_UInt64)a << 16) + (b >> 1)) / b
: 0x7FFFFFFFL);
return (s < 0 ? -q : q);
}
/*************************************************************************/
/* */
/* This is a fixed-point CORDIC implementation of trigonometric */
/* functions as well as transformations between Cartesian and polar */
/* coordinates. The angles are represented as 16.16 fixed-point values */
/* in degrees, i.e., the angular resolution is 2^-16 degrees. Note that */
/* only vectors longer than 2^16*180/pi (or at least 22 bits) on a */
/* discrete Cartesian grid can have the same or better angular */
/* resolution. Therefore, to maintain this precision, some functions */
/* require an interim upscaling of the vectors, whereas others operate */
/* with 24-bit long vectors directly. */
/* */
/*************************************************************************/
/* the Cordic shrink factor 0.858785336480436 * 2^32 */
#define PVG_FT_TRIG_SCALE 0xDBD95B16UL
/* the highest bit in overflow-safe vector components, */
/* MSB of 0.858785336480436 * sqrt(0.5) * 2^30 */
#define PVG_FT_TRIG_SAFE_MSB 29
/* this table was generated for PVG_FT_PI = 180L << 16, i.e. degrees */
#define PVG_FT_TRIG_MAX_ITERS 23
static const PVG_FT_Fixed ft_trig_arctan_table[] = {
1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, 14668L,
7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, 57L,
29L, 14L, 7L, 4L, 2L, 1L};
/* multiply a given value by the CORDIC shrink factor */
static PVG_FT_Fixed ft_trig_downscale(PVG_FT_Fixed val)
{
PVG_FT_Fixed s;
PVG_FT_Int64 v;
s = val;
val = PVG_FT_ABS(val);
v = (val * (PVG_FT_Int64)PVG_FT_TRIG_SCALE) + 0x100000000UL;
val = (PVG_FT_Fixed)(v >> 32);
return (s >= 0) ? val : -val;
}
/* undefined and never called for zero vector */
static PVG_FT_Int ft_trig_prenorm(PVG_FT_Vector* vec)
{
PVG_FT_Pos x, y;
PVG_FT_Int shift;
x = vec->x;
y = vec->y;
shift = PVG_FT_MSB(PVG_FT_ABS(x) | PVG_FT_ABS(y));
if (shift <= PVG_FT_TRIG_SAFE_MSB) {
shift = PVG_FT_TRIG_SAFE_MSB - shift;
vec->x = (PVG_FT_Pos)((PVG_FT_ULong)x << shift);
vec->y = (PVG_FT_Pos)((PVG_FT_ULong)y << shift);
} else {
shift -= PVG_FT_TRIG_SAFE_MSB;
vec->x = x >> shift;
vec->y = y >> shift;
shift = -shift;
}
return shift;
}
static void ft_trig_pseudo_rotate(PVG_FT_Vector* vec, PVG_FT_Angle theta)
{
PVG_FT_Int i;
PVG_FT_Fixed x, y, xtemp, b;
const PVG_FT_Fixed* arctanptr;
x = vec->x;
y = vec->y;
/* Rotate inside [-PI/4,PI/4] sector */
while (theta < -PVG_FT_ANGLE_PI4) {
xtemp = y;
y = -x;
x = xtemp;
theta += PVG_FT_ANGLE_PI2;
}
while (theta > PVG_FT_ANGLE_PI4) {
xtemp = -y;
y = x;
x = xtemp;
theta -= PVG_FT_ANGLE_PI2;
}
arctanptr = ft_trig_arctan_table;
/* Pseudorotations, with right shifts */
for (i = 1, b = 1; i < PVG_FT_TRIG_MAX_ITERS; b <<= 1, i++) {
PVG_FT_Fixed v1 = ((y + b) >> i);
PVG_FT_Fixed v2 = ((x + b) >> i);
if (theta < 0) {
xtemp = x + v1;
y = y - v2;
x = xtemp;
theta += *arctanptr++;
} else {
xtemp = x - v1;
y = y + v2;
x = xtemp;
theta -= *arctanptr++;
}
}
vec->x = x;
vec->y = y;
}
static void ft_trig_pseudo_polarize(PVG_FT_Vector* vec)
{
PVG_FT_Angle theta;
PVG_FT_Int i;
PVG_FT_Fixed x, y, xtemp, b;
const PVG_FT_Fixed* arctanptr;
x = vec->x;
y = vec->y;
/* Get the vector into [-PI/4,PI/4] sector */
if (y > x) {
if (y > -x) {
theta = PVG_FT_ANGLE_PI2;
xtemp = y;
y = -x;
x = xtemp;
} else {
theta = y > 0 ? PVG_FT_ANGLE_PI : -PVG_FT_ANGLE_PI;
x = -x;
y = -y;
}
} else {
if (y < -x) {
theta = -PVG_FT_ANGLE_PI2;
xtemp = -y;
y = x;
x = xtemp;
} else {
theta = 0;
}
}
arctanptr = ft_trig_arctan_table;
/* Pseudorotations, with right shifts */
for (i = 1, b = 1; i < PVG_FT_TRIG_MAX_ITERS; b <<= 1, i++) {
PVG_FT_Fixed v1 = ((y + b) >> i);
PVG_FT_Fixed v2 = ((x + b) >> i);
if (y > 0) {
xtemp = x + v1;
y = y - v2;
x = xtemp;
theta += *arctanptr++;
} else {
xtemp = x - v1;
y = y + v2;
x = xtemp;
theta -= *arctanptr++;
}
}
/* round theta */
if (theta >= 0)
theta = PVG_FT_PAD_ROUND(theta, 32);
else
theta = -PVG_FT_PAD_ROUND(-theta, 32);
vec->x = x;
vec->y = theta;
}
/* documentation is in fttrigon.h */
PVG_FT_Fixed PVG_FT_Cos(PVG_FT_Angle angle)
{
PVG_FT_Vector v;
v.x = PVG_FT_TRIG_SCALE >> 8;
v.y = 0;
ft_trig_pseudo_rotate(&v, angle);
return (v.x + 0x80L) >> 8;
}
/* documentation is in fttrigon.h */
PVG_FT_Fixed PVG_FT_Sin(PVG_FT_Angle angle)
{
return PVG_FT_Cos(PVG_FT_ANGLE_PI2 - angle);
}
/* documentation is in fttrigon.h */
PVG_FT_Fixed PVG_FT_Tan(PVG_FT_Angle angle)
{
PVG_FT_Vector v;
v.x = PVG_FT_TRIG_SCALE >> 8;
v.y = 0;
ft_trig_pseudo_rotate(&v, angle);
return PVG_FT_DivFix(v.y, v.x);
}
/* documentation is in fttrigon.h */
PVG_FT_Angle PVG_FT_Atan2(PVG_FT_Fixed dx, PVG_FT_Fixed dy)
{
PVG_FT_Vector v;
if (dx == 0 && dy == 0) return 0;
v.x = dx;
v.y = dy;
ft_trig_prenorm(&v);
ft_trig_pseudo_polarize(&v);
return v.y;
}
/* documentation is in fttrigon.h */
void PVG_FT_Vector_Unit(PVG_FT_Vector* vec, PVG_FT_Angle angle)
{
vec->x = PVG_FT_TRIG_SCALE >> 8;
vec->y = 0;
ft_trig_pseudo_rotate(vec, angle);
vec->x = (vec->x + 0x80L) >> 8;
vec->y = (vec->y + 0x80L) >> 8;
}
void PVG_FT_Vector_Rotate(PVG_FT_Vector* vec, PVG_FT_Angle angle)
{
PVG_FT_Int shift;
PVG_FT_Vector v = *vec;
if ( v.x == 0 && v.y == 0 )
return;
shift = ft_trig_prenorm( &v );
ft_trig_pseudo_rotate( &v, angle );
v.x = ft_trig_downscale( v.x );
v.y = ft_trig_downscale( v.y );
if ( shift > 0 )
{
PVG_FT_Int32 half = (PVG_FT_Int32)1L << ( shift - 1 );
vec->x = ( v.x + half - ( v.x < 0 ) ) >> shift;
vec->y = ( v.y + half - ( v.y < 0 ) ) >> shift;
}
else
{
shift = -shift;
vec->x = (PVG_FT_Pos)( (PVG_FT_ULong)v.x << shift );
vec->y = (PVG_FT_Pos)( (PVG_FT_ULong)v.y << shift );
}
}
/* documentation is in fttrigon.h */
PVG_FT_Fixed PVG_FT_Vector_Length(PVG_FT_Vector* vec)
{
PVG_FT_Int shift;
PVG_FT_Vector v;
v = *vec;
/* handle trivial cases */
if (v.x == 0) {
return PVG_FT_ABS(v.y);
} else if (v.y == 0) {
return PVG_FT_ABS(v.x);
}
/* general case */
shift = ft_trig_prenorm(&v);
ft_trig_pseudo_polarize(&v);
v.x = ft_trig_downscale(v.x);
if (shift > 0) return (v.x + (1 << (shift - 1))) >> shift;
return (PVG_FT_Fixed)((PVG_FT_UInt32)v.x << -shift);
}
/* documentation is in fttrigon.h */
void PVG_FT_Vector_Polarize(PVG_FT_Vector* vec, PVG_FT_Fixed* length,
PVG_FT_Angle* angle)
{
PVG_FT_Int shift;
PVG_FT_Vector v;
v = *vec;
if (v.x == 0 && v.y == 0) return;
shift = ft_trig_prenorm(&v);
ft_trig_pseudo_polarize(&v);
v.x = ft_trig_downscale(v.x);
*length = (shift >= 0) ? (v.x >> shift)
: (PVG_FT_Fixed)((PVG_FT_UInt32)v.x << -shift);
*angle = v.y;
}
/* documentation is in fttrigon.h */
void PVG_FT_Vector_From_Polar(PVG_FT_Vector* vec, PVG_FT_Fixed length,
PVG_FT_Angle angle)
{
vec->x = length;
vec->y = 0;
PVG_FT_Vector_Rotate(vec, angle);
}
/* documentation is in fttrigon.h */
PVG_FT_Angle PVG_FT_Angle_Diff( PVG_FT_Angle angle1, PVG_FT_Angle angle2 )
{
PVG_FT_Angle delta = angle2 - angle1;
while ( delta <= -PVG_FT_ANGLE_PI )
delta += PVG_FT_ANGLE_2PI;
while ( delta > PVG_FT_ANGLE_PI )
delta -= PVG_FT_ANGLE_2PI;
return delta;
}
/* END */
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