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Diffstat (limited to 'recipes/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff')

-rw-r--r-- | recipes/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff | 79 |

1 files changed, 79 insertions, 0 deletions

diff --git a/recipes/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff b/recipes/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/recipes/cairo/cairo-1.2.4/0002-Change-_cairo_fixed_from_double-to-use-the-magic-number-technique.diff @@ -0,0 +1,79 @@ +From nobody Mon Sep 17 00:00:00 2001 +From: Dan Amelang <dan@amelang.net> +Date: Sun Oct 29 21:31:23 2006 -0800 +Subject: [PATCH] Change _cairo_fixed_from_double to use the "magic number" technique + +See long thread here: +http://lists.freedesktop.org/archives/cairo/2006-October/008285.html + +--- + + src/cairo-fixed.c | 48 +++++++++++++++++++++++++++++++++++++++++++++++- + 1 files changed, 47 insertions(+), 1 deletions(-) + +d88acddcabe770e17664b34a2d5f74d3926e1642 +diff --git a/src/cairo-fixed.c b/src/cairo-fixed.c +index 604c9e7..fe6c2dc 100644 +--- a/src/cairo-fixed.c ++++ b/src/cairo-fixed.c +@@ -42,10 +42,56 @@ _cairo_fixed_from_int (int i) + return i << 16; + } + ++/* This is the "magic number" approach to converting a double into fixed ++ * point as described here: ++ * ++ * http://www.stereopsis.com/sree/fpu2006.html (an overview) ++ * http://www.d6.com/users/checker/pdfs/gdmfp.pdf (in detail) ++ * ++ * The basic idea is to add a large enough number to the double that the ++ * literal floating point is moved up to the extent that it forces the ++ * double's value to be shifted down to the bottom of the mantissa (to make ++ * room for the large number being added in). Since the mantissa is, at a ++ * given moment in time, a fixed point integer itself, one can convert a ++ * float to various fixed point representations by moving around the point ++ * of a floating point number through arithmetic operations. This behavior ++ * is reliable on most modern platforms as it is mandated by the IEEE-754 ++ * standard for floating point arithmetic. ++ * ++ * For our purposes, a "magic number" must be carefully selected that is ++ * both large enough to produce the desired point-shifting effect, and also ++ * has no lower bits in its representation that would interfere with our ++ * value at the bottom of the mantissa. The magic number is calculated as ++ * follows: ++ * ++ * (2 ^ (MANTISSA_SIZE - FRACTIONAL_SIZE)) * 1.5 ++ * ++ * where in our case: ++ * - MANTISSA_SIZE for 64-bit doubles is 52 ++ * - FRACTIONAL_SIZE for 16.16 fixed point is 16 ++ * ++ * Although this approach provides a very large speedup of this function ++ * on a wide-array of systems, it does come with two caveats: ++ * ++ * 1) It uses banker's rounding as opposed to arithmetic rounding. ++ * 2) It doesn't function properly if the FPU is in single-precision ++ * mode. ++ */ ++#define CAIRO_MAGIC_NUMBER_FIXED_16_16 (103079215104.0) + cairo_fixed_t + _cairo_fixed_from_double (double d) + { +- return (cairo_fixed_t) floor (d * 65536 + 0.5); ++ union { ++ double d; ++ int32_t i[2]; ++ } u; ++ ++ u.d = d + CAIRO_MAGIC_NUMBER_FIXED_16_16; ++#ifdef FLOAT_WORDS_BIGENDIAN ++ return u.i[1]; ++#else ++ return u.i[0]; ++#endif + } + + cairo_fixed_t +-- +1.2.6 + |