Units part #1

Part way through writing a meta-library for units that cost nothing at runtime but give unit-type safety at compile time.

core/numeric/core.primes.stz

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+[ n seive-of-sundaram-into: primes | uint, &list of: uint -> ø |
+  limit = (n - 1) / 2
+
+  marked: (array of: bool length: limit + 1)
+  marked fill-with: false
+
+  1 to: limit do: [ i |
+    j = i
+    [(i + j + 2 * i * j) ≤ limit] while-true: [
+      marked[i + j + 2 * i * j] = true
+      j += 1]
+
+  n ≥ 2 then: [list add: 2]
+  1 to: limit do: [ i |
+    marked[i] then: [list add: 2 * i + 1] ] ]

core/unit/README.md

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+# Units and Quantities
+
+It is smarter to program with units than without. What is a 10 after all when it should be 10 bytes?
+We can create an array as either (array of: u8 length: 10) but how do we describe what we would create?
+with a quantity: {quantity of: u8 | magnitude: 10}
+
+SI units and their derived units exist as pre-made quantity classes which lets you write:
+100 seconds // returns a {quantity of: second | magniature: 100}
+
+You can describe the processing rate of your data with your own classes combined with SI units.
+processing-speed-type = person / second
+processing-speed-quantity = quantity of: processing-speed-type
+
+When adding or substracting two quantities if their base unit doesn't match there is a compile time error.
+This can avoid a lot of numerical type bugs. The unit system has no overhead on runtime, only compile time.
+
+When describing bytes or bits you can define an array type without having to specify a second parameter
+for length:
+my-buffer = array of: 4 kilobytes
+
+
+Every base and derived unit used is assigned a unique id that is a prime number allowing any combination
+of unit to be combined through multiplication and division. meter^2 is meter id * meter id while byte/second
+is byte id / second id. These id's are assigned lazily as they are needed in your code at compile time.

core/unit/quantity.stz

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+#package core
+
+quantity = (
+  #traits: (number-t,)
+  @of: (unit: unit-t)
+  magnitude: number-t )
+
+
+/* number-t */
+[ a + b
+| quantity of: a unit, quantity of: a unit -> quantity of: a unit
+| {magnitude: a magnitude + b magnitude} ]
+
+[ a + b
+| quantity of: a unit base, quantity of: a unit base -> quantity of: a unit base
+| {magnitude: a magnitude + b magnitude * b unit conversion / a unit conversion} ]
+
+[ a - b
+| quantity of: a unit, quantity of: a unit -> quantity of: a unit
+| {magnitude: a magnitude - b magnitude} ]
+
+[ a - b
+| quantity of: a unit base, quantity of: a unit base -> quantity of: a unit base
+| {magnitude: a magnitude - b magnitude * b unit conversion / a unit conversion} ]
+
+[ a * b
+| quantity, quantity -> quantity of: a unit * b unit
+| {magnitude: a magnitude * b magnitude} ]
+
+[ a * magnitude
+| quantity, number-t -> quantity of: a unit
+| {magnitude: a magnitude * magnitude} ]
+
+[ magnitude * a
+| number-t, quantity -> quantity of: a unit
+| {magnitude: magnitude * a magnitude} ]
+
+[ a / b
+| quantity, quantity -> quantity of: a unit / b unit
+| {magnitude: a magnitude / b magnitude} ]
+
+[ a / magnitude
+| quantity, number-t -> quantity of: a unit
+| {magnitude: a magnitude / magnitude} ]
+
+[ magnitude / a
+| number-t, quantity -> quantity of: 1 / a unit
+| {magnitude: magnitude * a magnitude} ]
+
+[ a floor
+| quantity -> a
+| {magnitude: magnitude floor} ]
+
+[ a ceiling
+| quantity -> a
+| {magnitude: magnitude ceiling} ]
+
+[ a round
+| quantity -> a
+| {magnitude: magnitude round} ]
+
+[ a truncate
+| quantity -> a
+| {magnitude: magnitude truncate} ]
+
+
+/* comparable-t */
+[ a < b
+| quantity of: a unit base, quantity of: a unit base -> bool
+| a magnitude < b magnitude ]
+
+[ a == b
+| quantity of: a unit base, quantity of: a unit base -> bool
+| a magnitude == b magnitude ]
+
+
+/* hashable-t */
+[ a hash | quantity | magnitude hash + unit hash ]
+
+
+/* convertable-t */
+[ a as: new-unit | quantity -> quantity | unit convert: magnitude to: new-unit ]

core/unit/unit-init.stz

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+#package core
+
+unitless = base-unit-t symbol: empty'empty'
+primary-unit-library = {&unit-library | new init}
+primary-unit-library unit-ids[unitless]: 1
+
+meter    = base-unit-t symbol: 'm'
+second   = base-unit-t symbol: 's'
+gram     = base-unit-t symbol: 'g'   // the si unit is kilogram but that makes the init code harder
+mole     = base-unit-t symbol: 'mol'
+kelvin   = base-unit-t symbol: 'L'
+ampere   = base-unit-t symbol: 'A'
+candela  = base-unit-t symbol: 'cd'
+
+// useful but not an SI unit
+byte     = base-unit-t symbol: 'B'
+
+// controversial apparently
+
+// si scaled versions of base units
+( meter, second, gram, mole, kelvin, ampere, candela, ) do: [ unit | register-derived-si-prefixes: si-negative-prefixes ]
+( meter,         gram, mole, kelvin, ampere, candela, byte ) do: [ unit | register-derived-si-prefixes: si-positive-prefixes ]
+
+// si approved derived units
+hertz = derived-unit-t base: 1 / second symbol: 'Hz'
+newton = derived-unit-t base: kilogram * meter * (second ** -2) symbol: 'N'
+pascal = derived-unit-t base: newton * (meter ** -2) symbol: 'Pa'
+joule = derived-unit-t base: newton * meter symbol: 'J'
+watt = derived-unit-t base: joule / second symbol: 'W'
+coulomb = derived-unit-t base: ampere * second symbol: 'C'
+volt = derived-unit-t base: watt / ampere symbol: 'V'
+farad = derived-unit-t base: coulomb / volt symbol: 'F'
+ohm = derived-unit-t base: volt / ampere symbol: 'Ω'
+siemens = derived-unit-t base: ampere / volt symbol: 'S'
+webere = derived-unit-t base: volt * second symbol: 'Wb'
+tesla = derived-unit-t base: weber * (meter ** -2) symbol: 'T'
+henry = derived-unit-t base: weber / ampere symbol: 'H'
+celcius = derived-unit-t base: kelvin symbol: 'ºC' offset: -273.15
+radian = base-unit-t symbol: 'rad'
+steradian = base-unit-t symbol: 'sr'
+lumen = derived-unit-t base: candela * steradian symbol: 'lm'
+lux = derived-unit-t base: lumen * (meter ** -2) symbol: 'lx'
+becquerel = derived-unit-t base: 1 / second symbol: 'Bq'
+gray = derived-unit-t base: joule / kilogram symbol: 'Gy'
+katal = derived-unit-t base: mole / second symbol: 'kat'
+
+( hertz, newton, pascal, joule, watt, coulomb, volt, farad, ohm, siemens, weber,
+  tesla, henry, celcius, radian, steradian, lumen, lux, becquerl, gray, katal, ) do: [ unit |
+    register-derived-si-prefixes: si-negative-prefixes
+    register-derived-si-prefixes: si-positive-prefixes ]
+
+// derived distance
+inch = derived-unit-t base: meter symbol: 'in' scale: 254 / 10_000
+foot = derived-unit-t base: meter symbol: "ft" scale: 3_048 / 10_000
+yard = derived-unit-t base: meter symbol: 'yd' scale: 9_144 / 10_000
+mile = derived-unit-t base: meter symbol: 'mi' scale: 1_609_344 / 1_000
+light-year = derived-unit-t base: meter symbol: 'lightyear' scale: 9_460_500_000_000_000
+parsec = derived-unit-t base: meter symbol: 'parsec' scale: 30_856_770_000_000_000
+
+// derived time
+minute    = derived-unit-t base: second symbol: 'min' scale: 60
+hour      = derived-unit-t base: second symbol: 'hr' scale: 60
+day       = derived-unit-t base: second symbol: 'd' scale: 24
+week      = derived-unit-t base: second symbol: 'wk' scale: 7
+year      = derived-unit-t base: second symbol: 'y' scale: 315_569_259_747 / 10_000
+decade    = derived-unit-t base: second symbol: 'decade' symbol: 'decade' scale: 315_569_259_747 / 1_000
+century   = derived-unit-t base: second symbol: 'century' symbol: 'century' scale: 315_569_259_747 / 100
+millenium = derived-unit-t base: second symbol: 'millenium' symbol: 'millenium' scale: 315_569_259_747 / 10
+
+// derived weight
+tonne = derived-unit-t base: gram symbol: 't' scale: 1_000_000
+stone = derived-unit-t base: gram symbol: 'st' scale: 6_350_29_318 / 100_000
+pound = derived-unit-t base: gram symbol: 'lb' scale: 453_59_237 / 100_000
+ounce = derived-unit-t base: gram symbol: 'oz' scale: 28_349_523_125 / 1_000_000_000
+carat = derived-unit-t base: gram symbol: 'ct' scale: 2 / 10
+
+// derived information
+bit = derived-unit-t base: byte symbol: 'b' scale: 1 / 8
+bit register-si-derived-units: si-positive-prefixes scale: 1 / 8
+
+// derived angle
+degree = derived-unit-t base: radian symbol: 'º' scale: 1_000_000_000_000 / 57_295_779_513_082
+arc-minute = derived-unit-t base: radian symbol: "'" scale: 1000000000000 / 57295779513082 / 60
+arc-second = derived-unit-t base: radian symbol: '"' scale: 1000000000000 / 57295779513082 / 3600
+
+// derived areas
+meter-squared = meter * meter
+acre = derived-unit-t base: meter-squared symbol: 'ac' scale: 40_468_564_224 / 10_000_000
+hectare = derived-unit-t base: meter-squared symbol: 'ha' scale: 10_000
+
+// derived powers
+horse-power = derived-unit-t base: watt base symbol: 'hp' scale: 7457 / 10
+
+// derived pressures
+atmosphere = derived-unit-t base: pascal base symbol: 'atm' scale: 101_325
+bar = derived-unit-t base: pascal base symbol: 'bar' scale: 100_000
+psi = derived-unit-t base: pascal base symbol: 'psi' scale: 6_894_757 / 1_000
+
+// derived volumes
+litre = derived-unit-t base: m ** -3 symbol: 'L' scale: 1 / 1_000

core/unit/unit-library.stz

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+#package core
+
+unit-library = (
+  next-id: uint = 2
+  ids: ( class, uint | ) )
+
+[ library unit-id-for: unit | &!unit-library, class -> fraction |
+  ^ids[unit] else [
+    id = next-id
+    next-id = next-id next-prime
+    ids[unit]: id ] ]
+
+#scope private
+[ library unit-suffix-for: unit | &unit-library, class -> string |
+  ^unit name ]
+
+[ library unit-suffix-for: unit | &unit-library, base-unit-t -> string |
+  ^unit class symbol ]
+
+[ library unit-suffix-for: unit | &unit-library, derived-unit-t -> string |
+  ^unit class symbol ]
+
+[ library unit-scaling-for: unit | &unit-library, class -> int |
+  ^1 ]
+
+[ library unit-scaling-for: unit | &unit-library, derived-unit-t -> int |
+  ^unit class scale ]
+
+[ library unit-base-for: unit | &unit-library, class -> base-unit-t |
+  ^unit ]
+
+[ library unit-base-for: unit | &unit-library, derived-unit-t -> base-unit-t |
+  ^unit base ]
+
+
+#scope package
+
+si-unit-prefix = (prefix: string, symbol: string, scale: int)
+
+positive-prefixes = ( si-unit-prefix |
+  {prefix: "quetta", symbol: "Q",  base: 10 ** 30},
+  {prefix: "ronna",  symbol: "R",  base: 10 ** 27},
+  {prefix: "yotta",  symbol: "Y",  base: 10 ** 24},
+  {prefix: "zetta",  symbol: "Z",  base: 10 ** 21},
+  {prefix: "exa",    symbol: "E",  base: 10 ** 18},
+  {prefix: "peta",   symbol: "P",  base: 10 ** 15},
+  {prefix: "tera",   symbol: "T",  base: 10 ** 12},
+  {prefix: "giga",   symbol: "G",  base: 10 ** 9},
+  {prefix: "mega",   symbol: "M",  base: 10 ** 6},
+  {prefix: "kilo",   symbol: "K",  base: 10 ** 3},
+  {prefix: "hecto",  symbol: "h",  base: 10 ** 2},
+  {prefix: "deca",   sybmol: "da", base: 10})
+
+negative-prefixes = ( si-unit-prefix |
+  {prefix: "deci",   symbol: "d",  base: -10},
+  {prefix: "centi",  symbol: "c",  base: 10 ** -2},
+  {prefix: "milli",  symbol: "m",  base: 10 ** -3},
+  {prefix: "micro",  symbol: "µ",  base: 10 ** -6},
+  {prefix: "nano",   symbol: "n",  base: 10 ** -9},
+  {prefix: "pico",   symbol: "p",  base: 10 ** -12},
+  {prefix: "femto",  symbol: "f",  base: 10 ** -15},
+  {prefix: "atto",   symbol: "a",  base: 10 ** -18},
+  {prefix: "zepto",  symbol: "z",  base: 10 ** -21},
+  {prefix: "yocto",  symbol: "y",  base: 10 ** -24},
+  {prefix: "ronto",  symbol: "r",  base: 10 ** -27},
+  {prefix: "quecto", symbol: "q",  base: 10 ** -30})
+
+si-prefixes = positive-prefixes + negative-prefixes
+
+[ base-unit register-derived-unit: unit-name symbol: unit-symbol | unit-t, string, string, int |
+  base-unit register-derived-unit: unit-name symbol: unit-symbol scale: 1 ]
+
+[ base-unit register-derived-unit: unit-name symbol: unit-symbol scale: scale | unit-t, string, string, int |
+  #context public[unit-name]: (derived-unit base: base-unit symbol: unit-symbol scale: scale) ] ]
+
+[ base-unit register-derived-si-prefixes: prefixes | base-unit-t, &list of: si-unit-prefix |
+  base-unit register-derived-si-prefixes: prefixes scale: 1 ]
+
+[ base-unit register-derived-si-prefixes: prefixes scale: scale | base-unit-t, &list of: si-unit-prefix, int |
+  base-unit-name = #context public key-for: base-unit
+  prefixes do: [ prefix |
+    unit-name = prefix name + base-unit-name
+    unit-symbol = prefix symbol + base-unit symbol
+    base-unit register-derived-unit: unit-name symbol: unit-symbol scale: prefix base * int ] ]

core/unit/unit-t.stz

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+#package core
+
+base-unit-t    = (@symbol: string,)
+derived-unit-t = (@base: base-unit-t, @scale: int, @symbol: string)