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define machine epsilon constants #9

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Aug 8, 2022
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define machine epsilon constants #9

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15 changes: 9 additions & 6 deletions src/main/java/com/github/tommyettinger/digital/Hasher.java
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Original file line number Diff line number Diff line change
Expand Up @@ -22,6 +22,9 @@
import static com.github.tommyettinger.digital.BitConversion.doubleToRawLongBits;
import static com.github.tommyettinger.digital.BitConversion.floatToRawIntBits;

import static com.github.tommyettinger.digital.MathTools.EPSILON;
import static com.github.tommyettinger.digital.MathTools.EPSILON_D;

/**
* 64-bit and 32-bit hashing functions that we can rely on staying the same cross-platform.
* This uses a family of algorithms all based on Wang Yi's wyhash, but using at most 64-bit
Expand Down Expand Up @@ -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.

}

/**
Expand Down Expand Up @@ -345,7 +348,7 @@ public static float randomize1Float(long state) {
*/
public static float randomize2Float(long state) {
state ^= 0xD1B54A32D192ED03L;
return ((((state = (state ^ (state << 39 | state >>> 25) ^ (state << 17 | state >>> 47)) * 0x9E6C63D0676A9A99L) ^ state >>> 23 ^ state >>> 51) * 0x9E6D62D06F6A9A9BL) >>> 40) * 0x1p-24f;
return ((((state = (state ^ (state << 39 | state >>> 25) ^ (state << 17 | state >>> 47)) * 0x9E6C63D0676A9A99L) ^ state >>> 23 ^ state >>> 51) * 0x9E6D62D06F6A9A9BL) >>> 40) * EPSILON;
}

/**
Expand Down Expand Up @@ -382,7 +385,7 @@ public static float randomize3Float(long state) {
state *= 0xBEA225F9EB34556DL;
state ^= state >>> 32;
state *= 0xBEA225F9EB34556DL;
return (state >>> 40) * 0x1p-24f;
return (state >>> 40) * EPSILON;
}

/**
Expand Down Expand Up @@ -410,7 +413,7 @@ public static float randomize3Float(long state) {
* @return a pseudo-random double between 0.0 (inclusive) and 1.0 (exclusive), determined by {@code state}
*/
public static double randomize1Double(long state) {
return (((state = ((state = (((state * 0x632BE59BD9B4E019L) ^ 0x9E3779B97F4A7C15L) * 0xC6BC279692B5CC83L)) ^ state >>> 27) * 0xAEF17502108EF2D9L) ^ state >>> 25) & 0x1FFFFFFFFFFFFFL) * 0x1p-53;
return (((state = ((state = (((state * 0x632BE59BD9B4E019L) ^ 0x9E3779B97F4A7C15L) * 0xC6BC279692B5CC83L)) ^ state >>> 27) * 0xAEF17502108EF2D9L) ^ state >>> 25) & 0x1FFFFFFFFFFFFFL) * EPSILON_D;
}

/**
Expand Down Expand Up @@ -440,7 +443,7 @@ public static double randomize1Double(long state) {
*/
public static double randomize2Double(long state) {
state ^= 0xD1B54A32D192ED03L;
return (((state = ((state = (state ^ (state << 39 | state >>> 25) ^ (state << 17 | state >>> 47)) * 0x9E6C63D0676A9A99L) ^ state >>> 23 ^ state >>> 51) * 0x9E6D62D06F6A9A9BL) ^ state >>> 23) >>> 11) * 0x1p-53;
return (((state = ((state = (state ^ (state << 39 | state >>> 25) ^ (state << 17 | state >>> 47)) * 0x9E6C63D0676A9A99L) ^ state >>> 23 ^ state >>> 51) * 0x9E6D62D06F6A9A9BL) ^ state >>> 23) >>> 11) * EPSILON_D;
}

/**
Expand Down Expand Up @@ -476,7 +479,7 @@ public static double randomize3Double(long state) {
state *= 0xBEA225F9EB34556DL;
state ^= state >>> 32;
state *= 0xBEA225F9EB34556DL;
return (state >>> 11 ^ state >>> 40) * 0x1p-53;
return (state >>> 11 ^ state >>> 40) * EPSILON_D;
}

/**
Expand Down
12 changes: 12 additions & 0 deletions src/main/java/com/github/tommyettinger/digital/MathTools.java
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Original file line number Diff line number Diff line change
Expand Up @@ -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

/**
* 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.

* 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;

/**
* 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.

* Useful for converting a 64-bit {@code long} value to a gradient between 0 and 1.
*/
public static final double EPSILON_D = 0x1p-53;

/**
* The {@code float} value that is closer than any other to
Expand Down