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Diffstat (limited to 'meta/packages/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff')
-rw-r--r-- | meta/packages/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff | 79 |
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diff --git a/meta/packages/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff b/meta/packages/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff new file mode 100644 index 0000000000..56d8b7e99a --- /dev/null +++ b/meta/packages/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff | |||
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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 | |||