define machine epsilon constants #9
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These are the IEEE-prescribed values already used in this library. I have assigned them names and also implemented the named versions in the Hasher class which already uses them. Their descriptions might need more elaboration regarding their properties.
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There's some docs that I don't think are quite accurate as they stand now. I do really like reusing the common values instead of having yet another magic number, heh. It would be really nice to mention in the docs that EPSILON is 2 to the -24, and EPSILON_D is 2 to the -53, which could save some source-diving.
| @@ -314,7 +317,7 @@ public static int randomize3Bounded(long state, int bound) { | |||
| * @return a pseudo-random float between 0f (inclusive) and 1f (exclusive), determined by {@code state} | |||
| */ | |||
| public static float randomize1Float(long state) { | |||
| return ((((state = (((state * 0x632BE59BD9B4E019L) ^ 0x9E3779B97F4A7C15L) * 0xC6BC279692B5CC83L)) ^ state >>> 27) * 0xAEF17502108EF2D9L) >>> 40) * 0x1p-24f; | |||
| return ((((state = (((state * 0x632BE59BD9B4E019L) ^ 0x9E3779B97F4A7C15L) * 0xC6BC279692B5CC83L)) ^ state >>> 27) * 0xAEF17502108EF2D9L) >>> 40) * EPSILON; | |||
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It's interesting that the multiplier used to produce the most valid zero-to-one floats with uniform spacing is also the machine epsilon; I am guessing that this isn't a coincidence.
| @@ -53,6 +53,18 @@ private MathTools() { | |||
| * false-positive equivalence with very small inputs. | |||
| */ | |||
| public static final float FLOAT_ROUNDING_ERROR = 0x1p-20f; // was 0.000001f | |||
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| /** | |||
| * The smallest measurable difference between a given {@code float} value and a directly adjacent value. | |||
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I don't think this is right; the smallest measurable difference varies a lot based on the magnitude of the floats, and would be measured as one ulp. This is, however, the smallest non-zero distance possible between two floats returned by Random#nextFloat(), if my math is right.
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| /** | ||
| * The smallest measurable difference between a given {@code float} value and a directly adjacent value. | ||
| * Useful for converting a 64-bit {@code long} value to a gradient between 0 and 1. |
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Also a bit of a nit-pick here, this is useful for converting non-negative up-to-24-bit ints or longs to fit in a uniformly-spaced 0 to 1 range. It can work on more than just long, and it probably doesn't do what you want if you multiply an arbitrary (possibly negative) long by this.
| public static final float EPSILON = 0x1p-24f; | ||
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| /** | ||
| * The smallest measurable difference between a given {@code double} value and a directly adjacent value. |
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Also the comment about an ulp above applies here. This might be the smallest non-zero distance possible between two doubles returned by Random#nextDouble(), but Random specifically might not be so precise. All of the EnhancedRandom classes in juniper have a nextDouble() that matches this precision.
These are the IEEE-prescribed values already used in this library. I have assigned them names and also implemented the named versions in the Hasher class which already uses them. Their descriptions might need more elaboration regarding their properties.