package/cairo/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.patch

   1 From nobody Mon Sep 17 00:00:00 2001
   2 From: Dan Amelang <dan@amelang.net>
   3 Date: Sun Oct 29 21:31:23 2006 -0800
   4 Subject: [PATCH] Change _cairo_fixed_from_double to use the "magic number" technique
   5
   6 See long thread here:
   7 http://lists.freedesktop.org/archives/cairo/2006-October/008285.html
   8
   9 ---
  10
  11  src/cairo-fixed.c |   48 +++++++++++++++++++++++++++++++++++++++++++++++-
  12  1 files changed, 47 insertions(+), 1 deletions(-)
  13
  14 d88acddcabe770e17664b34a2d5f74d3926e1642
  15 diff --git a/src/cairo-fixed.c b/src/cairo-fixed.c
  16 index 604c9e7..fe6c2dc 100644
  17 --- a/src/cairo-fixed.c
  18 +++ b/src/cairo-fixed.c
  19 @@ -42,10 +42,56 @@ _cairo_fixed_from_int (int i)
  20      return i << 16;
  21  }
  22
  23 +/* This is the "magic number" approach to converting a double into fixed
  24 + * point as described here:
  25 + *
  26 + * http://www.stereopsis.com/sree/fpu2006.html (an overview)
  27 + * http://www.d6.com/users/checker/pdfs/gdmfp.pdf (in detail)
  28 + *
  29 + * The basic idea is to add a large enough number to the double that the
  30 + * literal floating point is moved up to the extent that it forces the
  31 + * double's value to be shifted down to the bottom of the mantissa (to make
  32 + * room for the large number being added in). Since the mantissa is, at a
  33 + * given moment in time, a fixed point integer itself, one can convert a
  34 + * float to various fixed point representations by moving around the point
  35 + * of a floating point number through arithmetic operations. This behavior
  36 + * is reliable on most modern platforms as it is mandated by the IEEE-754
  37 + * standard for floating point arithmetic.
  38 + *
  39 + * For our purposes, a "magic number" must be carefully selected that is
  40 + * both large enough to produce the desired point-shifting effect, and also
  41 + * has no lower bits in its representation that would interfere with our
  42 + * value at the bottom of the mantissa. The magic number is calculated as
  43 + * follows:
  44 + *
  45 + *          (2 ^ (MANTISSA_SIZE - FRACTIONAL_SIZE)) * 1.5
  46 + *
  47 + * where in our case:
  48 + *  - MANTISSA_SIZE for 64-bit doubles is 52
  49 + *  - FRACTIONAL_SIZE for 16.16 fixed point is 16
  50 + *
  51 + * Although this approach provides a very large speedup of this function
  52 + * on a wide-array of systems, it does come with two caveats:
  53 + *
  54 + * 1) It uses banker's rounding as opposed to arithmetic rounding.
  55 + * 2) It doesn't function properly if the FPU is in single-precision
  56 + *    mode.
  57 + */
  58 +#define CAIRO_MAGIC_NUMBER_FIXED_16_16 (103079215104.0)
  59  cairo_fixed_t
  60  _cairo_fixed_from_double (double d)
  61  {
  62 -    return (cairo_fixed_t) floor (d * 65536 + 0.5);
  63 +    union {
  64 +        double d;
  65 +        int32_t i[2];
  66 +    } u;
  67 +
  68 +    u.d = d + CAIRO_MAGIC_NUMBER_FIXED_16_16;
  69 +#ifdef FLOAT_WORDS_BIGENDIAN
  70 +    return u.i[1];
  71 +#else
  72 +    return u.i[0];
  73 +#endif
  74  }
  75
  76  cairo_fixed_t
  77 --
  78 1.2.6
  79