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
+