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