Module eos_rs::api::fixed

Dealing with fixed-point numbers used in the game.

Note that this module currently only deals with binary fixed-point representations. The game also sometimes uses decimal representations of fixed-point numbers (eg. 0x64 -> 100 -> ‘01.00’).

This pulls in parts of the fixed crate, which describes these numbers as follows:

An n-bit fixed-point number has f = Frac fractional bits where 0 ≤ f ≤ n, and n − f integer bits. For example, FixedI32<U24> is a 32-bit signed fixed-point number with n = 32 total bits, f = 24 fractional bits, and n − f = 8 integer bits. FixedI32<U0> behaves like [i32], and FixedU32<U0> behaves like [u32].

The difference between any two successive representable numbers is constant throughout the possible range for a fixed-point number: Δ = 1/2^f. When f = 0, like in FixedI32<U0>, Δ = 1 because representable numbers are integers, and the difference between two successive integers is 1. When f = n, Δ = 1/2ⁿ and the value lies in the range −0.5 ≤ x < 0.5 for signed numbers like FixedI32<U32>, and in the range 0 ≤ x < 1 for unsigned numbers like FixedU32<U32>.

Think of these similar to floats, but instead of having an arbitrary amount of fractional digits/bits and arbitrary precision, fixed-point numbers have a set amount of fractional digits/bits that are fully accurate.

Commonly used fixed numbers:

• I24F8: 32-bit number that has 24 integer bits and eight fractional bits.

You have several options to create a fixed-point number:

let n1 = I24F8::from_num(10);
assert_eq!(n1, 10.0);

// This will round to the nearest possible fixed representation. In this case,
// this value will fit, since 2 fits in a 24-bit integer and 75 fits in an
// 8-bit integer.
let n2 = I24F8::from_num(2.75);
// Note that due to precision differences this assertion can fail with some values.
assert_eq!(n2, 2.75);

// It's also possible (and probably faster) to directly use a number already encoded
// as a fixed number. This has the lower byte set to 0, which means the fractional
// bit will be 0, and the upper byte to 1, which means this is "1.0".
let n3 = I24F8::from_bits(0x01_00);
assert_eq!(n3, 1.0);

let n4 = I24F8::from_bits(0x01_AB);
// Using strings here to compare, due to the before mentioned accuracy issues.
assert_eq!(format!("{}", n4), "1.668");

let n5 = I24F8::from_bits(0x01_FF);
assert_eq!(format!("{}", n5), "1.996");

Modules

• extra
  Extra types that do not need to be handled directly.

Structs

• FixedI8
  An eight-bit signed number with Frac fractional bits.
• FixedI16
  A 16-bit signed number with Frac fractional bits.
• FixedI32
  A 32-bit signed number with Frac fractional bits.
• FixedU8
  An eight-bit unsigned number with Frac fractional bits.
• FixedU16
  A 16-bit unsigned number with Frac fractional bits.
• FixedU32
  A 32-bit unsigned number with Frac fractional bits.

Type Definitions

• I0F8
  FixedI8 with no integer bits and eight fractional bits.
• I0F16
  FixedI16 with no integer bits and 16 fractional bits.
• I0F32
  FixedI32 with no integer bits and 32 fractional bits.
• I0F64
  FixedI64 with no integer bits and 64 fractional bits.
• I0F128
  FixedI128 with no integer bits and 128 fractional bits.
• I1F7
  FixedI8 with one integer bit and seven fractional bits.
• I1F15
  FixedI16 with one integer bit and 15 fractional bits.
• I1F31
  FixedI32 with one integer bit and 31 fractional bits.
• I1F63
  FixedI64 with one integer bit and 63 fractional bits.
• I1F127
  FixedI128 with one integer bit and 127 fractional bits.
• I2F6
  FixedI8 with two integer bits and six fractional bits.
• I2F14
  FixedI16 with two integer bits and 14 fractional bits.
• I2F30
  FixedI32 with two integer bits and 30 fractional bits.
• I2F62
  FixedI64 with two integer bits and 62 fractional bits.
• I2F126
  FixedI128 with two integer bits and 126 fractional bits.
• I3F5
  FixedI8 with three integer bits and five fractional bits.
• I3F13
  FixedI16 with three integer bits and 13 fractional bits.
• I3F29
  FixedI32 with three integer bits and 29 fractional bits.
• I3F61
  FixedI64 with three integer bits and 61 fractional bits.
• I3F125
  FixedI128 with three integer bits and 125 fractional bits.
• I4F4
  FixedI8 with four integer bits and four fractional bits.
• I4F12
  FixedI16 with four integer bits and 12 fractional bits.
• I4F28
  FixedI32 with four integer bits and 28 fractional bits.
• I4F60
  FixedI64 with four integer bits and 60 fractional bits.
• I4F124
  FixedI128 with four integer bits and 124 fractional bits.
• I5F3
  FixedI8 with five integer bits and three fractional bits.
• I5F11
  FixedI16 with five integer bits and 11 fractional bits.
• I5F27
  FixedI32 with five integer bits and 27 fractional bits.
• I5F59
  FixedI64 with five integer bits and 59 fractional bits.
• I5F123
  FixedI128 with five integer bits and 123 fractional bits.
• I6F2
  FixedI8 with six integer bits and two fractional bits.
• I6F10
  FixedI16 with six integer bits and 10 fractional bits.
• I6F26
  FixedI32 with six integer bits and 26 fractional bits.
• I6F58
  FixedI64 with six integer bits and 58 fractional bits.
• I6F122
  FixedI128 with six integer bits and 122 fractional bits.
• I7F1
  FixedI8 with seven integer bits and one fractional bit.
• I7F9
  FixedI16 with seven integer bits and nine fractional bits.
• I7F25
  FixedI32 with seven integer bits and 25 fractional bits.
• I7F57
  FixedI64 with seven integer bits and 57 fractional bits.
• I7F121
  FixedI128 with seven integer bits and 121 fractional bits.
• I8F0
  FixedI8 with eight integer bits and no fractional bits.
• I8F8
  FixedI16 with eight integer bits and eight fractional bits.
• I8F24
  FixedI32 with eight integer bits and 24 fractional bits.
• I8F56
  FixedI64 with eight integer bits and 56 fractional bits.
• I8F120
  FixedI128 with eight integer bits and 120 fractional bits.
• I9F7
  FixedI16 with nine integer bits and seven fractional bits.
• I9F23
  FixedI32 with nine integer bits and 23 fractional bits.
• I9F55
  FixedI64 with nine integer bits and 55 fractional bits.
• I9F119
  FixedI128 with nine integer bits and 119 fractional bits.
• I10F6
  FixedI16 with 10 integer bits and six fractional bits.
• I10F22
  FixedI32 with 10 integer bits and 22 fractional bits.
• I10F54
  FixedI64 with 10 integer bits and 54 fractional bits.
• I10F118
  FixedI128 with 10 integer bits and 118 fractional bits.
• I11F5
  FixedI16 with 11 integer bits and five fractional bits.
• I11F21
  FixedI32 with 11 integer bits and 21 fractional bits.
• I11F53
  FixedI64 with 11 integer bits and 53 fractional bits.
• I11F117
  FixedI128 with 11 integer bits and 117 fractional bits.
• I12F4
  FixedI16 with 12 integer bits and four fractional bits.
• I12F20
  FixedI32 with 12 integer bits and 20 fractional bits.
• I12F52
  FixedI64 with 12 integer bits and 52 fractional bits.
• I12F116
  FixedI128 with 12 integer bits and 116 fractional bits.
• I13F3
  FixedI16 with 13 integer bits and three fractional bits.
• I13F19
  FixedI32 with 13 integer bits and 19 fractional bits.
• I13F51
  FixedI64 with 13 integer bits and 51 fractional bits.
• I13F115
  FixedI128 with 13 integer bits and 115 fractional bits.
• I14F2
  FixedI16 with 14 integer bits and two fractional bits.
• I14F18
  FixedI32 with 14 integer bits and 18 fractional bits.
• I14F50
  FixedI64 with 14 integer bits and 50 fractional bits.
• I14F114
  FixedI128 with 14 integer bits and 114 fractional bits.
• I15F1
  FixedI16 with 15 integer bits and one fractional bit.
• I15F17
  FixedI32 with 15 integer bits and 17 fractional bits.
• I15F49
  FixedI64 with 15 integer bits and 49 fractional bits.
• I15F113
  FixedI128 with 15 integer bits and 113 fractional bits.
• I16F0
  FixedI16 with 16 integer bits and no fractional bits.
• I16F16
  FixedI32 with 16 integer bits and 16 fractional bits.
• I16F48
  FixedI64 with 16 integer bits and 48 fractional bits.
• I16F112
  FixedI128 with 16 integer bits and 112 fractional bits.
• I17F15
  FixedI32 with 17 integer bits and 15 fractional bits.
• I17F47
  FixedI64 with 17 integer bits and 47 fractional bits.
• I17F111
  FixedI128 with 17 integer bits and 111 fractional bits.
• I18F14
  FixedI32 with 18 integer bits and 14 fractional bits.
• I18F46
  FixedI64 with 18 integer bits and 46 fractional bits.
• I18F110
  FixedI128 with 18 integer bits and 110 fractional bits.
• I19F13
  FixedI32 with 19 integer bits and 13 fractional bits.
• I19F45
  FixedI64 with 19 integer bits and 45 fractional bits.
• I19F109
  FixedI128 with 19 integer bits and 109 fractional bits.
• I20F12
  FixedI32 with 20 integer bits and 12 fractional bits.
• I20F44
  FixedI64 with 20 integer bits and 44 fractional bits.
• I20F108
  FixedI128 with 20 integer bits and 108 fractional bits.
• I21F11
  FixedI32 with 21 integer bits and 11 fractional bits.
• I21F43
  FixedI64 with 21 integer bits and 43 fractional bits.
• I21F107
  FixedI128 with 21 integer bits and 107 fractional bits.
• I22F10
  FixedI32 with 22 integer bits and 10 fractional bits.
• I22F42
  FixedI64 with 22 integer bits and 42 fractional bits.
• I22F106
  FixedI128 with 22 integer bits and 106 fractional bits.
• I23F9
  FixedI32 with 23 integer bits and nine fractional bits.
• I23F41
  FixedI64 with 23 integer bits and 41 fractional bits.
• I23F105
  FixedI128 with 23 integer bits and 105 fractional bits.
• I24F8
  FixedI32 with 24 integer bits and eight fractional bits.
• I24F40
  FixedI64 with 24 integer bits and 40 fractional bits.
• I24F104
  FixedI128 with 24 integer bits and 104 fractional bits.
• I25F7
  FixedI32 with 25 integer bits and seven fractional bits.
• I25F39
  FixedI64 with 25 integer bits and 39 fractional bits.
• I25F103
  FixedI128 with 25 integer bits and 103 fractional bits.
• I26F6
  FixedI32 with 26 integer bits and six fractional bits.
• I26F38
  FixedI64 with 26 integer bits and 38 fractional bits.
• I26F102
  FixedI128 with 26 integer bits and 102 fractional bits.
• I27F5
  FixedI32 with 27 integer bits and five fractional bits.
• I27F37
  FixedI64 with 27 integer bits and 37 fractional bits.
• I27F101
  FixedI128 with 27 integer bits and 101 fractional bits.
• I28F4
  FixedI32 with 28 integer bits and four fractional bits.
• I28F36
  FixedI64 with 28 integer bits and 36 fractional bits.
• I28F100
  FixedI128 with 28 integer bits and 100 fractional bits.
• I29F3
  FixedI32 with 29 integer bits and three fractional bits.
• I29F35
  FixedI64 with 29 integer bits and 35 fractional bits.
• I29F99
  FixedI128 with 29 integer bits and 99 fractional bits.
• I30F2
  FixedI32 with 30 integer bits and two fractional bits.
• I30F34
  FixedI64 with 30 integer bits and 34 fractional bits.
• I30F98
  FixedI128 with 30 integer bits and 98 fractional bits.
• I31F1
  FixedI32 with 31 integer bits and one fractional bit.
• I31F33
  FixedI64 with 31 integer bits and 33 fractional bits.
• I31F97
  FixedI128 with 31 integer bits and 97 fractional bits.
• I32F0
  FixedI32 with 32 integer bits and no fractional bits.
• I32F32
  FixedI64 with 32 integer bits and 32 fractional bits.
• I32F96
  FixedI128 with 32 integer bits and 96 fractional bits.
• I33F31
  FixedI64 with 33 integer bits and 31 fractional bits.
• I33F95
  FixedI128 with 33 integer bits and 95 fractional bits.
• I34F30
  FixedI64 with 34 integer bits and 30 fractional bits.
• I34F94
  FixedI128 with 34 integer bits and 94 fractional bits.
• I35F29
  FixedI64 with 35 integer bits and 29 fractional bits.
• I35F93
  FixedI128 with 35 integer bits and 93 fractional bits.
• I36F28
  FixedI64 with 36 integer bits and 28 fractional bits.
• I36F92
  FixedI128 with 36 integer bits and 92 fractional bits.
• I37F27
  FixedI64 with 37 integer bits and 27 fractional bits.
• I37F91
  FixedI128 with 37 integer bits and 91 fractional bits.
• I38F26
  FixedI64 with 38 integer bits and 26 fractional bits.
• I38F90
  FixedI128 with 38 integer bits and 90 fractional bits.
• I39F25
  FixedI64 with 39 integer bits and 25 fractional bits.
• I39F89
  FixedI128 with 39 integer bits and 89 fractional bits.
• I40F24
  FixedI64 with 40 integer bits and 24 fractional bits.
• I40F88
  FixedI128 with 40 integer bits and 88 fractional bits.
• I41F23
  FixedI64 with 41 integer bits and 23 fractional bits.
• I41F87
  FixedI128 with 41 integer bits and 87 fractional bits.
• I42F22
  FixedI64 with 42 integer bits and 22 fractional bits.
• I42F86
  FixedI128 with 42 integer bits and 86 fractional bits.
• I43F21
  FixedI64 with 43 integer bits and 21 fractional bits.
• I43F85
  FixedI128 with 43 integer bits and 85 fractional bits.
• I44F20
  FixedI64 with 44 integer bits and 20 fractional bits.
• I44F84
  FixedI128 with 44 integer bits and 84 fractional bits.
• I45F19
  FixedI64 with 45 integer bits and 19 fractional bits.
• I45F83
  FixedI128 with 45 integer bits and 83 fractional bits.
• I46F18
  FixedI64 with 46 integer bits and 18 fractional bits.
• I46F82
  FixedI128 with 46 integer bits and 82 fractional bits.
• I47F17
  FixedI64 with 47 integer bits and 17 fractional bits.
• I47F81
  FixedI128 with 47 integer bits and 81 fractional bits.
• I48F16
  FixedI64 with 48 integer bits and 16 fractional bits.
• I48F80
  FixedI128 with 48 integer bits and 80 fractional bits.
• I49F15
  FixedI64 with 49 integer bits and 15 fractional bits.
• I49F79
  FixedI128 with 49 integer bits and 79 fractional bits.
• I50F14
  FixedI64 with 50 integer bits and 14 fractional bits.
• I50F78
  FixedI128 with 50 integer bits and 78 fractional bits.
• I51F13
  FixedI64 with 51 integer bits and 13 fractional bits.
• I51F77
  FixedI128 with 51 integer bits and 77 fractional bits.
• I52F12
  FixedI64 with 52 integer bits and 12 fractional bits.
• I52F76
  FixedI128 with 52 integer bits and 76 fractional bits.
• I53F11
  FixedI64 with 53 integer bits and 11 fractional bits.
• I53F75
  FixedI128 with 53 integer bits and 75 fractional bits.
• I54F10
  FixedI64 with 54 integer bits and 10 fractional bits.
• I54F74
  FixedI128 with 54 integer bits and 74 fractional bits.
• I55F9
  FixedI64 with 55 integer bits and nine fractional bits.
• I55F73
  FixedI128 with 55 integer bits and 73 fractional bits.
• I56F8
  FixedI64 with 56 integer bits and eight fractional bits.
• I56F72
  FixedI128 with 56 integer bits and 72 fractional bits.
• I57F7
  FixedI64 with 57 integer bits and seven fractional bits.
• I57F71
  FixedI128 with 57 integer bits and 71 fractional bits.
• I58F6
  FixedI64 with 58 integer bits and six fractional bits.
• I58F70
  FixedI128 with 58 integer bits and 70 fractional bits.
• I59F5
  FixedI64 with 59 integer bits and five fractional bits.
• I59F69
  FixedI128 with 59 integer bits and 69 fractional bits.
• I60F4
  FixedI64 with 60 integer bits and four fractional bits.
• I60F68
  FixedI128 with 60 integer bits and 68 fractional bits.
• I61F3
  FixedI64 with 61 integer bits and three fractional bits.
• I61F67
  FixedI128 with 61 integer bits and 67 fractional bits.
• I62F2
  FixedI64 with 62 integer bits and two fractional bits.
• I62F66
  FixedI128 with 62 integer bits and 66 fractional bits.
• I63F1
  FixedI64 with 63 integer bits and one fractional bit.
• I63F65
  FixedI128 with 63 integer bits and 65 fractional bits.
• I64F0
  FixedI64 with 64 integer bits and no fractional bits.
• I64F64
  FixedI128 with 64 integer bits and 64 fractional bits.
• I65F63
  FixedI128 with 65 integer bits and 63 fractional bits.
• I66F62
  FixedI128 with 66 integer bits and 62 fractional bits.
• I67F61
  FixedI128 with 67 integer bits and 61 fractional bits.
• I68F60
  FixedI128 with 68 integer bits and 60 fractional bits.
• I69F59
  FixedI128 with 69 integer bits and 59 fractional bits.
• I70F58
  FixedI128 with 70 integer bits and 58 fractional bits.
• I71F57
  FixedI128 with 71 integer bits and 57 fractional bits.
• I72F56
  FixedI128 with 72 integer bits and 56 fractional bits.
• I73F55
  FixedI128 with 73 integer bits and 55 fractional bits.
• I74F54
  FixedI128 with 74 integer bits and 54 fractional bits.
• I75F53
  FixedI128 with 75 integer bits and 53 fractional bits.
• I76F52
  FixedI128 with 76 integer bits and 52 fractional bits.
• I77F51
  FixedI128 with 77 integer bits and 51 fractional bits.
• I78F50
  FixedI128 with 78 integer bits and 50 fractional bits.
• I79F49
  FixedI128 with 79 integer bits and 49 fractional bits.
• I80F48
  FixedI128 with 80 integer bits and 48 fractional bits.
• I81F47
  FixedI128 with 81 integer bits and 47 fractional bits.
• I82F46
  FixedI128 with 82 integer bits and 46 fractional bits.
• I83F45
  FixedI128 with 83 integer bits and 45 fractional bits.
• I84F44
  FixedI128 with 84 integer bits and 44 fractional bits.
• I85F43
  FixedI128 with 85 integer bits and 43 fractional bits.
• I86F42
  FixedI128 with 86 integer bits and 42 fractional bits.
• I87F41
  FixedI128 with 87 integer bits and 41 fractional bits.
• I88F40
  FixedI128 with 88 integer bits and 40 fractional bits.
• I89F39
  FixedI128 with 89 integer bits and 39 fractional bits.
• I90F38
  FixedI128 with 90 integer bits and 38 fractional bits.
• I91F37
  FixedI128 with 91 integer bits and 37 fractional bits.
• I92F36
  FixedI128 with 92 integer bits and 36 fractional bits.
• I93F35
  FixedI128 with 93 integer bits and 35 fractional bits.
• I94F34
  FixedI128 with 94 integer bits and 34 fractional bits.
• I95F33
  FixedI128 with 95 integer bits and 33 fractional bits.
• I96F32
  FixedI128 with 96 integer bits and 32 fractional bits.
• I97F31
  FixedI128 with 97 integer bits and 31 fractional bits.
• I98F30
  FixedI128 with 98 integer bits and 30 fractional bits.
• I99F29
  FixedI128 with 99 integer bits and 29 fractional bits.
• I100F28
  FixedI128 with 100 integer bits and 28 fractional bits.
• I101F27
  FixedI128 with 101 integer bits and 27 fractional bits.
• I102F26
  FixedI128 with 102 integer bits and 26 fractional bits.
• I103F25
  FixedI128 with 103 integer bits and 25 fractional bits.
• I104F24
  FixedI128 with 104 integer bits and 24 fractional bits.
• I105F23
  FixedI128 with 105 integer bits and 23 fractional bits.
• I106F22
  FixedI128 with 106 integer bits and 22 fractional bits.
• I107F21
  FixedI128 with 107 integer bits and 21 fractional bits.
• I108F20
  FixedI128 with 108 integer bits and 20 fractional bits.
• I109F19
  FixedI128 with 109 integer bits and 19 fractional bits.
• I110F18
  FixedI128 with 110 integer bits and 18 fractional bits.
• I111F17
  FixedI128 with 111 integer bits and 17 fractional bits.
• I112F16
  FixedI128 with 112 integer bits and 16 fractional bits.
• I113F15
  FixedI128 with 113 integer bits and 15 fractional bits.
• I114F14
  FixedI128 with 114 integer bits and 14 fractional bits.
• I115F13
  FixedI128 with 115 integer bits and 13 fractional bits.
• I116F12
  FixedI128 with 116 integer bits and 12 fractional bits.
• I117F11
  FixedI128 with 117 integer bits and 11 fractional bits.
• I118F10
  FixedI128 with 118 integer bits and 10 fractional bits.
• I119F9
  FixedI128 with 119 integer bits and nine fractional bits.
• I120F8
  FixedI128 with 120 integer bits and eight fractional bits.
• I121F7
  FixedI128 with 121 integer bits and seven fractional bits.
• I122F6
  FixedI128 with 122 integer bits and six fractional bits.
• I123F5
  FixedI128 with 123 integer bits and five fractional bits.
• I124F4
  FixedI128 with 124 integer bits and four fractional bits.
• I125F3
  FixedI128 with 125 integer bits and three fractional bits.
• I126F2
  FixedI128 with 126 integer bits and two fractional bits.
• I127F1
  FixedI128 with 127 integer bits and one fractional bit.
• I128F0
  FixedI128 with 128 integer bits and no fractional bits.
• U0F8
  FixedU8 with no integer bits and eight fractional bits.
• U0F16
  FixedU16 with no integer bits and 16 fractional bits.
• U0F32
  FixedU32 with no integer bits and 32 fractional bits.
• U0F64
  FixedU64 with no integer bits and 64 fractional bits.
• U0F128
  FixedU128 with no integer bits and 128 fractional bits.
• U1F7
  FixedU8 with one integer bit and seven fractional bits.
• U1F15
  FixedU16 with one integer bit and 15 fractional bits.
• U1F31
  FixedU32 with one integer bit and 31 fractional bits.
• U1F63
  FixedU64 with one integer bit and 63 fractional bits.
• U1F127
  FixedU128 with one integer bit and 127 fractional bits.
• U2F6
  FixedU8 with two integer bits and six fractional bits.
• U2F14
  FixedU16 with two integer bits and 14 fractional bits.
• U2F30
  FixedU32 with two integer bits and 30 fractional bits.
• U2F62
  FixedU64 with two integer bits and 62 fractional bits.
• U2F126
  FixedU128 with two integer bits and 126 fractional bits.
• U3F5
  FixedU8 with three integer bits and five fractional bits.
• U3F13
  FixedU16 with three integer bits and 13 fractional bits.
• U3F29
  FixedU32 with three integer bits and 29 fractional bits.
• U3F61
  FixedU64 with three integer bits and 61 fractional bits.
• U3F125
  FixedU128 with three integer bits and 125 fractional bits.
• U4F4
  FixedU8 with four integer bits and four fractional bits.
• U4F12
  FixedU16 with four integer bits and 12 fractional bits.
• U4F28
  FixedU32 with four integer bits and 28 fractional bits.
• U4F60
  FixedU64 with four integer bits and 60 fractional bits.
• U4F124
  FixedU128 with four integer bits and 124 fractional bits.
• U5F3
  FixedU8 with five integer bits and three fractional bits.
• U5F11
  FixedU16 with five integer bits and 11 fractional bits.
• U5F27
  FixedU32 with five integer bits and 27 fractional bits.
• U5F59
  FixedU64 with five integer bits and 59 fractional bits.
• U5F123
  FixedU128 with five integer bits and 123 fractional bits.
• U6F2
  FixedU8 with six integer bits and two fractional bits.
• U6F10
  FixedU16 with six integer bits and 10 fractional bits.
• U6F26
  FixedU32 with six integer bits and 26 fractional bits.
• U6F58
  FixedU64 with six integer bits and 58 fractional bits.
• U6F122
  FixedU128 with six integer bits and 122 fractional bits.
• U7F1
  FixedU8 with seven integer bits and one fractional bit.
• U7F9
  FixedU16 with seven integer bits and nine fractional bits.
• U7F25
  FixedU32 with seven integer bits and 25 fractional bits.
• U7F57
  FixedU64 with seven integer bits and 57 fractional bits.
• U7F121
  FixedU128 with seven integer bits and 121 fractional bits.
• U8F0
  FixedU8 with eight integer bits and no fractional bits.
• U8F8
  FixedU16 with eight integer bits and eight fractional bits.
• U8F24
  FixedU32 with eight integer bits and 24 fractional bits.
• U8F56
  FixedU64 with eight integer bits and 56 fractional bits.
• U8F120
  FixedU128 with eight integer bits and 120 fractional bits.
• U9F7
  FixedU16 with nine integer bits and seven fractional bits.
• U9F23
  FixedU32 with nine integer bits and 23 fractional bits.
• U9F55
  FixedU64 with nine integer bits and 55 fractional bits.
• U9F119
  FixedU128 with nine integer bits and 119 fractional bits.
• U10F6
  FixedU16 with 10 integer bits and six fractional bits.
• U10F22
  FixedU32 with 10 integer bits and 22 fractional bits.
• U10F54
  FixedU64 with 10 integer bits and 54 fractional bits.
• U10F118
  FixedU128 with 10 integer bits and 118 fractional bits.
• U11F5
  FixedU16 with 11 integer bits and five fractional bits.
• U11F21
  FixedU32 with 11 integer bits and 21 fractional bits.
• U11F53
  FixedU64 with 11 integer bits and 53 fractional bits.
• U11F117
  FixedU128 with 11 integer bits and 117 fractional bits.
• U12F4
  FixedU16 with 12 integer bits and four fractional bits.
• U12F20
  FixedU32 with 12 integer bits and 20 fractional bits.
• U12F52
  FixedU64 with 12 integer bits and 52 fractional bits.
• U12F116
  FixedU128 with 12 integer bits and 116 fractional bits.
• U13F3
  FixedU16 with 13 integer bits and three fractional bits.
• U13F19
  FixedU32 with 13 integer bits and 19 fractional bits.
• U13F51
  FixedU64 with 13 integer bits and 51 fractional bits.
• U13F115
  FixedU128 with 13 integer bits and 115 fractional bits.
• U14F2
  FixedU16 with 14 integer bits and two fractional bits.
• U14F18
  FixedU32 with 14 integer bits and 18 fractional bits.
• U14F50
  FixedU64 with 14 integer bits and 50 fractional bits.
• U14F114
  FixedU128 with 14 integer bits and 114 fractional bits.
• U15F1
  FixedU16 with 15 integer bits and one fractional bit.
• U15F17
  FixedU32 with 15 integer bits and 17 fractional bits.
• U15F49
  FixedU64 with 15 integer bits and 49 fractional bits.
• U15F113
  FixedU128 with 15 integer bits and 113 fractional bits.
• U16F0
  FixedU16 with 16 integer bits and no fractional bits.
• U16F16
  FixedU32 with 16 integer bits and 16 fractional bits.
• U16F48
  FixedU64 with 16 integer bits and 48 fractional bits.
• U16F112
  FixedU128 with 16 integer bits and 112 fractional bits.
• U17F15
  FixedU32 with 17 integer bits and 15 fractional bits.
• U17F47
  FixedU64 with 17 integer bits and 47 fractional bits.
• U17F111
  FixedU128 with 17 integer bits and 111 fractional bits.
• U18F14
  FixedU32 with 18 integer bits and 14 fractional bits.
• U18F46
  FixedU64 with 18 integer bits and 46 fractional bits.
• U18F110
  FixedU128 with 18 integer bits and 110 fractional bits.
• U19F13
  FixedU32 with 19 integer bits and 13 fractional bits.
• U19F45
  FixedU64 with 19 integer bits and 45 fractional bits.
• U19F109
  FixedU128 with 19 integer bits and 109 fractional bits.
• U20F12
  FixedU32 with 20 integer bits and 12 fractional bits.
• U20F44
  FixedU64 with 20 integer bits and 44 fractional bits.
• U20F108
  FixedU128 with 20 integer bits and 108 fractional bits.
• U21F11
  FixedU32 with 21 integer bits and 11 fractional bits.
• U21F43
  FixedU64 with 21 integer bits and 43 fractional bits.
• U21F107
  FixedU128 with 21 integer bits and 107 fractional bits.
• U22F10
  FixedU32 with 22 integer bits and 10 fractional bits.
• U22F42
  FixedU64 with 22 integer bits and 42 fractional bits.
• U22F106
  FixedU128 with 22 integer bits and 106 fractional bits.
• U23F9
  FixedU32 with 23 integer bits and nine fractional bits.
• U23F41
  FixedU64 with 23 integer bits and 41 fractional bits.
• U23F105
  FixedU128 with 23 integer bits and 105 fractional bits.
• U24F8
  FixedU32 with 24 integer bits and eight fractional bits.
• U24F40
  FixedU64 with 24 integer bits and 40 fractional bits.
• U24F104
  FixedU128 with 24 integer bits and 104 fractional bits.
• U25F7
  FixedU32 with 25 integer bits and seven fractional bits.
• U25F39
  FixedU64 with 25 integer bits and 39 fractional bits.
• U25F103
  FixedU128 with 25 integer bits and 103 fractional bits.
• U26F6
  FixedU32 with 26 integer bits and six fractional bits.
• U26F38
  FixedU64 with 26 integer bits and 38 fractional bits.
• U26F102
  FixedU128 with 26 integer bits and 102 fractional bits.
• U27F5
  FixedU32 with 27 integer bits and five fractional bits.
• U27F37
  FixedU64 with 27 integer bits and 37 fractional bits.
• U27F101
  FixedU128 with 27 integer bits and 101 fractional bits.
• U28F4
  FixedU32 with 28 integer bits and four fractional bits.
• U28F36
  FixedU64 with 28 integer bits and 36 fractional bits.
• U28F100
  FixedU128 with 28 integer bits and 100 fractional bits.
• U29F3
  FixedU32 with 29 integer bits and three fractional bits.
• U29F35
  FixedU64 with 29 integer bits and 35 fractional bits.
• U29F99
  FixedU128 with 29 integer bits and 99 fractional bits.
• U30F2
  FixedU32 with 30 integer bits and two fractional bits.
• U30F34
  FixedU64 with 30 integer bits and 34 fractional bits.
• U30F98
  FixedU128 with 30 integer bits and 98 fractional bits.
• U31F1
  FixedU32 with 31 integer bits and one fractional bit.
• U31F33
  FixedU64 with 31 integer bits and 33 fractional bits.
• U31F97
  FixedU128 with 31 integer bits and 97 fractional bits.
• U32F0
  FixedU32 with 32 integer bits and no fractional bits.
• U32F32
  FixedU64 with 32 integer bits and 32 fractional bits.
• U32F96
  FixedU128 with 32 integer bits and 96 fractional bits.
• U33F31
  FixedU64 with 33 integer bits and 31 fractional bits.
• U33F95
  FixedU128 with 33 integer bits and 95 fractional bits.
• U34F30
  FixedU64 with 34 integer bits and 30 fractional bits.
• U34F94
  FixedU128 with 34 integer bits and 94 fractional bits.
• U35F29
  FixedU64 with 35 integer bits and 29 fractional bits.
• U35F93
  FixedU128 with 35 integer bits and 93 fractional bits.
• U36F28
  FixedU64 with 36 integer bits and 28 fractional bits.
• U36F92
  FixedU128 with 36 integer bits and 92 fractional bits.
• U37F27
  FixedU64 with 37 integer bits and 27 fractional bits.
• U37F91
  FixedU128 with 37 integer bits and 91 fractional bits.
• U38F26
  FixedU64 with 38 integer bits and 26 fractional bits.
• U38F90
  FixedU128 with 38 integer bits and 90 fractional bits.
• U39F25
  FixedU64 with 39 integer bits and 25 fractional bits.
• U39F89
  FixedU128 with 39 integer bits and 89 fractional bits.
• U40F24
  FixedU64 with 40 integer bits and 24 fractional bits.
• U40F88
  FixedU128 with 40 integer bits and 88 fractional bits.
• U41F23
  FixedU64 with 41 integer bits and 23 fractional bits.
• U41F87
  FixedU128 with 41 integer bits and 87 fractional bits.
• U42F22
  FixedU64 with 42 integer bits and 22 fractional bits.
• U42F86
  FixedU128 with 42 integer bits and 86 fractional bits.
• U43F21
  FixedU64 with 43 integer bits and 21 fractional bits.
• U43F85
  FixedU128 with 43 integer bits and 85 fractional bits.
• U44F20
  FixedU64 with 44 integer bits and 20 fractional bits.
• U44F84
  FixedU128 with 44 integer bits and 84 fractional bits.
• U45F19
  FixedU64 with 45 integer bits and 19 fractional bits.
• U45F83
  FixedU128 with 45 integer bits and 83 fractional bits.
• U46F18
  FixedU64 with 46 integer bits and 18 fractional bits.
• U46F82
  FixedU128 with 46 integer bits and 82 fractional bits.
• U47F17
  FixedU64 with 47 integer bits and 17 fractional bits.
• U47F81
  FixedU128 with 47 integer bits and 81 fractional bits.
• U48F16
  FixedU64 with 48 integer bits and 16 fractional bits.
• U48F80
  FixedU128 with 48 integer bits and 80 fractional bits.
• U49F15
  FixedU64 with 49 integer bits and 15 fractional bits.
• U49F79
  FixedU128 with 49 integer bits and 79 fractional bits.
• U50F14
  FixedU64 with 50 integer bits and 14 fractional bits.
• U50F78
  FixedU128 with 50 integer bits and 78 fractional bits.
• U51F13
  FixedU64 with 51 integer bits and 13 fractional bits.
• U51F77
  FixedU128 with 51 integer bits and 77 fractional bits.
• U52F12
  FixedU64 with 52 integer bits and 12 fractional bits.
• U52F76
  FixedU128 with 52 integer bits and 76 fractional bits.
• U53F11
  FixedU64 with 53 integer bits and 11 fractional bits.
• U53F75
  FixedU128 with 53 integer bits and 75 fractional bits.
• U54F10
  FixedU64 with 54 integer bits and 10 fractional bits.
• U54F74
  FixedU128 with 54 integer bits and 74 fractional bits.
• U55F9
  FixedU64 with 55 integer bits and nine fractional bits.
• U55F73
  FixedU128 with 55 integer bits and 73 fractional bits.
• U56F8
  FixedU64 with 56 integer bits and eight fractional bits.
• U56F72
  FixedU128 with 56 integer bits and 72 fractional bits.
• U57F7
  FixedU64 with 57 integer bits and seven fractional bits.
• U57F71
  FixedU128 with 57 integer bits and 71 fractional bits.
• U58F6
  FixedU64 with 58 integer bits and six fractional bits.
• U58F70
  FixedU128 with 58 integer bits and 70 fractional bits.
• U59F5
  FixedU64 with 59 integer bits and five fractional bits.
• U59F69
  FixedU128 with 59 integer bits and 69 fractional bits.
• U60F4
  FixedU64 with 60 integer bits and four fractional bits.
• U60F68
  FixedU128 with 60 integer bits and 68 fractional bits.
• U61F3
  FixedU64 with 61 integer bits and three fractional bits.
• U61F67
  FixedU128 with 61 integer bits and 67 fractional bits.
• U62F2
  FixedU64 with 62 integer bits and two fractional bits.
• U62F66
  FixedU128 with 62 integer bits and 66 fractional bits.
• U63F1
  FixedU64 with 63 integer bits and one fractional bit.
• U63F65
  FixedU128 with 63 integer bits and 65 fractional bits.
• U64F0
  FixedU64 with 64 integer bits and no fractional bits.
• U64F64
  FixedU128 with 64 integer bits and 64 fractional bits.
• U65F63
  FixedU128 with 65 integer bits and 63 fractional bits.
• U66F62
  FixedU128 with 66 integer bits and 62 fractional bits.
• U67F61
  FixedU128 with 67 integer bits and 61 fractional bits.
• U68F60
  FixedU128 with 68 integer bits and 60 fractional bits.
• U69F59
  FixedU128 with 69 integer bits and 59 fractional bits.
• U70F58
  FixedU128 with 70 integer bits and 58 fractional bits.
• U71F57
  FixedU128 with 71 integer bits and 57 fractional bits.
• U72F56
  FixedU128 with 72 integer bits and 56 fractional bits.
• U73F55
  FixedU128 with 73 integer bits and 55 fractional bits.
• U74F54
  FixedU128 with 74 integer bits and 54 fractional bits.
• U75F53
  FixedU128 with 75 integer bits and 53 fractional bits.
• U76F52
  FixedU128 with 76 integer bits and 52 fractional bits.
• U77F51
  FixedU128 with 77 integer bits and 51 fractional bits.
• U78F50
  FixedU128 with 78 integer bits and 50 fractional bits.
• U79F49
  FixedU128 with 79 integer bits and 49 fractional bits.
• U80F48
  FixedU128 with 80 integer bits and 48 fractional bits.
• U81F47
  FixedU128 with 81 integer bits and 47 fractional bits.
• U82F46
  FixedU128 with 82 integer bits and 46 fractional bits.
• U83F45
  FixedU128 with 83 integer bits and 45 fractional bits.
• U84F44
  FixedU128 with 84 integer bits and 44 fractional bits.
• U85F43
  FixedU128 with 85 integer bits and 43 fractional bits.
• U86F42
  FixedU128 with 86 integer bits and 42 fractional bits.
• U87F41
  FixedU128 with 87 integer bits and 41 fractional bits.
• U88F40
  FixedU128 with 88 integer bits and 40 fractional bits.
• U89F39
  FixedU128 with 89 integer bits and 39 fractional bits.
• U90F38
  FixedU128 with 90 integer bits and 38 fractional bits.
• U91F37
  FixedU128 with 91 integer bits and 37 fractional bits.
• U92F36
  FixedU128 with 92 integer bits and 36 fractional bits.
• U93F35
  FixedU128 with 93 integer bits and 35 fractional bits.
• U94F34
  FixedU128 with 94 integer bits and 34 fractional bits.
• U95F33
  FixedU128 with 95 integer bits and 33 fractional bits.
• U96F32
  FixedU128 with 96 integer bits and 32 fractional bits.
• U97F31
  FixedU128 with 97 integer bits and 31 fractional bits.
• U98F30
  FixedU128 with 98 integer bits and 30 fractional bits.
• U99F29
  FixedU128 with 99 integer bits and 29 fractional bits.
• U100F28
  FixedU128 with 100 integer bits and 28 fractional bits.
• U101F27
  FixedU128 with 101 integer bits and 27 fractional bits.
• U102F26
  FixedU128 with 102 integer bits and 26 fractional bits.
• U103F25
  FixedU128 with 103 integer bits and 25 fractional bits.
• U104F24
  FixedU128 with 104 integer bits and 24 fractional bits.
• U105F23
  FixedU128 with 105 integer bits and 23 fractional bits.
• U106F22
  FixedU128 with 106 integer bits and 22 fractional bits.
• U107F21
  FixedU128 with 107 integer bits and 21 fractional bits.
• U108F20
  FixedU128 with 108 integer bits and 20 fractional bits.
• U109F19
  FixedU128 with 109 integer bits and 19 fractional bits.
• U110F18
  FixedU128 with 110 integer bits and 18 fractional bits.
• U111F17
  FixedU128 with 111 integer bits and 17 fractional bits.
• U112F16
  FixedU128 with 112 integer bits and 16 fractional bits.
• U113F15
  FixedU128 with 113 integer bits and 15 fractional bits.
• U114F14
  FixedU128 with 114 integer bits and 14 fractional bits.
• U115F13
  FixedU128 with 115 integer bits and 13 fractional bits.
• U116F12
  FixedU128 with 116 integer bits and 12 fractional bits.
• U117F11
  FixedU128 with 117 integer bits and 11 fractional bits.
• U118F10
  FixedU128 with 118 integer bits and 10 fractional bits.
• U119F9
  FixedU128 with 119 integer bits and nine fractional bits.
• U120F8
  FixedU128 with 120 integer bits and eight fractional bits.
• U121F7
  FixedU128 with 121 integer bits and seven fractional bits.
• U122F6
  FixedU128 with 122 integer bits and six fractional bits.
• U123F5
  FixedU128 with 123 integer bits and five fractional bits.
• U124F4
  FixedU128 with 124 integer bits and four fractional bits.
• U125F3
  FixedU128 with 125 integer bits and three fractional bits.
• U126F2
  FixedU128 with 126 integer bits and two fractional bits.
• U127F1
  FixedU128 with 127 integer bits and one fractional bit.
• U128F0
  FixedU128 with 128 integer bits and no fractional bits.