path: root/splash/SplashMath.h

//========================================================================
//
// SplashMath.h
//
// Copyright 2003-2013 Glyph & Cog, LLC
//
//========================================================================

#ifndef SPLASHMATH_H
#define SPLASHMATH_H

#include <aconf.h>

#if USE_FIXEDPONT
#include "FixedPoint.h"
#else
#include <math.h>
#endif
#include "SplashTypes.h"

static inline SplashCoord splashAbs(SplashCoord x) {
#if USE_FIXEDPOINT
  return FixedPoint::abs(x);
#else
  return fabs(x);
#endif
}

static inline int splashFloor(SplashCoord x) {
#if USE_FIXEDPOINT
  return FixedPoint::floor(x);
#else
#if __GNUC__ && __i386__
  // floor() and (int)() are implemented separately, which results
  // in changing the FPCW multiple times - so we optimize it with
  // some inline assembly
  Gushort oldCW, newCW, t;
  int result;

  __asm__ volatile("fnstcw %0\n"
		   "movw   %0, %3\n"
		   "andw   $0xf3ff, %3\n"
		   "orw    $0x0400, %3\n"
		   "movw   %3, %1\n"       // round down
		   "fldcw  %1\n"
		   "fistl %2\n"
		   "fldcw  %0\n"
		   : "=m" (oldCW), "=m" (newCW), "=m" (result), "=r" (t)
		   : "t" (x));
  return result;
#elif defined(_WIN32) && defined(_M_IX86)
  // floor() and (int)() are implemented separately, which results
  // in changing the FPCW multiple times - so we optimize it with
  // some inline assembly
  Gushort oldCW, newCW;
  int result;

  __asm fld QWORD PTR x
  __asm fnstcw WORD PTR oldCW
  __asm mov ax, WORD PTR oldCW
  __asm and ax, 0xf3ff
  __asm or ax, 0x0400
  __asm mov WORD PTR newCW, ax     // round down
  __asm fldcw WORD PTR newCW
  __asm fistp DWORD PTR result
  __asm fldcw WORD PTR oldCW
  return result;
#else
  return (int)floor(x);
#endif
#endif
}

static inline int splashCeil(SplashCoord x) {
#if USE_FIXEDPOINT
  return FixedPoint::ceil(x);
#else
#if __GNUC__ && __i386__
  // ceil() and (int)() are implemented separately, which results
  // in changing the FPCW multiple times - so we optimize it with
  // some inline assembly
  Gushort oldCW, newCW, t;
  int result;

  __asm__ volatile("fnstcw %0\n"
		   "movw   %0, %3\n"
		   "andw   $0xf3ff, %3\n"
		   "orw    $0x0800, %3\n"
		   "movw   %3, %1\n"       // round up
		   "fldcw  %1\n"
		   "fistl %2\n"
		   "fldcw  %0\n"
		   : "=m" (oldCW), "=m" (newCW), "=m" (result), "=r" (t)
		   : "t" (x));
  return result;
#elif defined(_WIN32) && defined(_M_IX86)
  // ceil() and (int)() are implemented separately, which results
  // in changing the FPCW multiple times - so we optimize it with
  // some inline assembly
  Gushort oldCW, newCW;
  int result;

  __asm fld QWORD PTR x
  __asm fnstcw WORD PTR oldCW
  __asm mov ax, WORD PTR oldCW
  __asm and ax, 0xf3ff
  __asm or ax, 0x0800
  __asm mov WORD PTR newCW, ax     // round up
  __asm fldcw WORD PTR newCW
  __asm fistp DWORD PTR result
  __asm fldcw WORD PTR oldCW
  return result;
#else
  return (int)ceil(x);
#endif
#endif
}

static inline int splashRound(SplashCoord x) {
#if USE_FIXEDPOINT
  return FixedPoint::round(x);
#else
#if __GNUC__ && __i386__
  // this could use round-to-nearest mode and avoid the "+0.5",
  // but that produces slightly different results (because i+0.5
  // sometimes rounds up and sometimes down using the even rule)
  Gushort oldCW, newCW, t;
  int result;

  x += 0.5;
  __asm__ volatile("fnstcw %0\n"
		   "movw   %0, %3\n"
		   "andw   $0xf3ff, %3\n"
		   "orw    $0x0400, %3\n"
		   "movw   %3, %1\n"       // round down
		   "fldcw  %1\n"
		   "fistl %2\n"
		   "fldcw  %0\n"
		   : "=m" (oldCW), "=m" (newCW), "=m" (result), "=r" (t)
		   : "t" (x));
  return result;
#elif defined(_WIN32) && defined(_M_IX86)
  // this could use round-to-nearest mode and avoid the "+0.5",
  // but that produces slightly different results (because i+0.5
  // sometimes rounds up and sometimes down using the even rule)
  Gushort oldCW, newCW;
  int result;

  x += 0.5;
  __asm fld QWORD PTR x
  __asm fnstcw WORD PTR oldCW
  __asm mov ax, WORD PTR oldCW
  __asm and ax, 0xf3ff
  __asm or ax, 0x0400
  __asm mov WORD PTR newCW, ax     // round down
  __asm fldcw WORD PTR newCW
  __asm fistp DWORD PTR result
  __asm fldcw WORD PTR oldCW
  return result;
#else
  return (int)floor(x + 0.5);
#endif
#endif
}

static inline SplashCoord splashAvg(SplashCoord x, SplashCoord y) {
#if USE_FIXEDPOINT
  return FixedPoint::avg(x, y);
#else
  return 0.5 * (x + y);
#endif
}

static inline SplashCoord splashSqrt(SplashCoord x) {
#if USE_FIXEDPOINT
  return FixedPoint::sqrt(x);
#else
  return sqrt(x);
#endif
}

static inline SplashCoord splashPow(SplashCoord x, SplashCoord y) {
#if USE_FIXEDPOINT
  return FixedPoint::pow(x, y);
#else
  return pow(x, y);
#endif
}

static inline SplashCoord splashDist(SplashCoord x0, SplashCoord y0,
				     SplashCoord x1, SplashCoord y1) {
  SplashCoord dx, dy;
  dx = x1 - x0;
  dy = y1 - y0;
#if USE_FIXEDPOINT
  // this handles the situation where dx*dx or dy*dy is too large to
  // fit in the 16.16 fixed point format
  SplashCoord dxa, dya, d;
  dxa = splashAbs(dx);
  dya = splashAbs(dy);
  if (dxa == 0 && dya == 0) {
    return 0;
  } else if (dxa > dya) {
    d = dya / dxa;
    return dxa * FixedPoint::sqrt(d*d + 1);
  } else {
    d = dxa / dya;
    return dya * FixedPoint::sqrt(d*d + 1);
  }
#else
  return sqrt(dx * dx + dy * dy);
#endif
}

static inline GBool splashCheckDet(SplashCoord m11, SplashCoord m12,
				   SplashCoord m21, SplashCoord m22,
				   SplashCoord epsilon) {
#if USE_FIXEDPOINT
  return FixedPoint::checkDet(m11, m12, m21, m22, epsilon);
#else
  return fabs(m11 * m22 - m12 * m21) >= epsilon;
#endif
}

// Perform stroke adjustment on a SplashCoord range [xMin, xMax),
// resulting in an int range [*xMinI, *xMaxI).
//
// There are several options:
//
// 1. Round both edge coordinates.
//    Pro: adjacent strokes/fills line up without any gaps or
//         overlaps
//    Con: lines with the same original floating point width can
//         end up with different integer widths, e.g.:
//               xMin  = 10.1   xMax  = 11.3   (width = 1.2)
//           --> xMinI = 10     xMaxI = 11     (width = 1)
//         but
//               xMin  = 10.4   xMax  = 11.6   (width = 1.2)
//           --> xMinI = 10     xMaxI = 12     (width = 2)
//
// 2. Round the min coordinate; add the ceiling of the width.
//    Pro: lines with the same original floating point width will
//         always end up with the same integer width
//    Con: adjacent strokes/fills can have overlaps (which is
//         problematic with transparency)
//    (This could use floor on the min coordinate, instead of
//    rounding, with similar results.)
//    (If the width is rounded instead of using ceiling, the results
//    Are similar, except that adjacent strokes/fills can have gaps
//    as well as overlaps.)
//
// 3. Use floor on the min coordinate and ceiling on the max
//    coordinate.
//    Pro: lines always end up at least as wide as the original
//         floating point width
//    Con: adjacent strokes/fills can have overlaps, and lines with
//         the same original floating point width can end up with
//         different integer widths; the integer width can be more
//         than one pixel wider than the original width, e.g.:
//               xMin  = 10.9   xMax  = 12.1   (width = 1.2)
//           --> xMinI = 10     xMaxI = 13     (width = 3)
//         but
//               xMin  = 10.1   xMax  = 11.3   (width = 1.2)
//           --> xMinI = 10     xMaxI = 12     (width = 2)
static inline void splashStrokeAdjust(SplashCoord xMin, SplashCoord xMax,
				      int *xMinI, int *xMaxI) {
  int x0, x1;

  // NB: enable exactly one of these.
#if 1 // 1. Round both edge coordinates.
  x0 = splashRound(xMin);
  x1 = splashRound(xMax);
#endif
#if 0 // 2. Round the min coordinate; add the ceiling of the width.
  x0 = splashRound(xMin);
  x1 = x0 + splashCeil(xMax - xMin);
#endif
#if 0 // 3. Use floor on the min coord and ceiling on the max coord.
  x0 = splashFloor(xMin);
  x1 = splashCeil(xMax);
#endif
  if (x1 == x0) {
    ++x1;
  }
  *xMinI = x0;
  *xMaxI = x1;
}

#endif