diff options
author | Dan Amelang <dan@amelang.net> | 2006-10-29 21:31:23 -0800 |
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committer | Carl Worth <cworth@cworth.org> | 2006-11-06 09:37:40 -0800 |
commit | 4cd50965a1935bf934f39f9e35b7d1a055ae7e16 (patch) | |
tree | 8db676c9599b7ef5bc2008a986f53c309bd49d2c /src/cairo-fixed.c | |
parent | 5376e474255b80d084dd250cab6ea5c14220a3f3 (diff) |
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
This patch provides a 3x performance improvement (on x86) for the
conversion of floating-point to fixed-point values as measured by
the recent pattern_create_radial performance test:
image-rgba pattern_create_radial-16 8.98 3.36% -> 2.97 1.03%: 3.38x speedup
██▍
image-rgb pattern_create_radial-16 8.94 3.21% -> 2.97 0.18%: 3.36x speedup
██▍
xlib-rgb pattern_create_radial-16 9.55 3.17% -> 3.64 0.51%: 2.93x speedup
█▉
xlib-rgba pattern_create_radial-16 9.63 3.53% -> 3.69 0.66%: 2.91x speedup
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Diffstat (limited to 'src/cairo-fixed.c')
-rw-r--r-- | src/cairo-fixed.c | 48 |
1 files changed, 47 insertions, 1 deletions
diff --git a/src/cairo-fixed.c b/src/cairo-fixed.c index 604c9e72..fe6c2dc3 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 |