# NOTE: we could have an algorithm store all the residuals down to the format's emin but for f256, that would mean storing roughly 1000 f256 constants just to exhaust down to emin. for 30 constants that takes up about 1MiB. just for residuals no one will use. thats why daamath only stores constants up to 1 level of residue. its enough to make a bound interval and a ball interval anyway.

import math, mpmath
from daatypes import Float, Fixed
from typing import Any

def metallic(n, plus_else_minus_root: bool):
    return (n + mpmath.sqrt(n * n + 4)) / 2 if plus_else_minus_root else (n - mpmath.sqrt(n * n + 4)) / 2 

def liouville_10(n):
    factorials = {math.factorial(i) for i in range(n)}
    return '0.' + ''.join(str(int(i in factorials)) for i in range(1, math.factorial(n - 1) + 1))

def feigenbaum_alpha(digits: int):
    'https://sprott.physics.wisc.edu/phys505/feigen.htm'
    return '-2.5029078750958928222839028732182157863812713767271499773361920567792354631795902067032996497464338341295952318699958547239421823777854451792728633149933725781121635948795037447812609973805986712397117373289276654044010306698313834600094139322364490657889951220584317250787337746308785342428535198858750004235824691874082042817009017148230518216216194131998560661293827426497098440844701008054549677936760888126446406885181552709324007542506497157047047541993283178364533256241537869395712509706638797949265462313767459189098131167524342211101309131278371609511583412308415037164997020224681219644081216686527458043026245782561067150138521821644953254334987348741335279581535101658360545576351327650181078119483694595748502373982354526256327794753972699020128915166457939420198920248803394051699686551494477396533876979741232354061781989611249409599035312899773361184984737794610842883329383390395090089140863515256268033814146692799133107433497051435452013446434264752001621384610729922641994332772918977769053802596851'[:digits]

def feigenbaum_delta(digits: int):
    'https://sprott.physics.wisc.edu/phys505/feigen.htm'
    return '4.6692016091029906718532038204662016172581855774757686327456513430041343302113147371386897440239480138171659848551898151344086271420279325223124429888908908599449354632367134115324817142199474556443658237932020095610583305754586176522220703854106467494942849814533917262005687556659523398756038256372256480040951071283890611844702775854285419801113440175002428585382498335715522052236087250291678860362674527213399057131606875345083433934446103706309452019115876972432273589838903794946257251289097948986768334611626889116563123474460575179539122045562472807095202198199094558581946136877445617396074115614074243754435499204869180982648652368438702799649017397793425134723808737136211601860128186102056381818354097598477964173900328936171432159878240789776614391395764037760537119096932066998361984288981837003229412030210655743295550388845849737034727532121925706958414074661841981961006129640161487712944415901405467941800198133253378592493365883070459999938375411726563553016862529032210862320550634510679399023341675'[:digits]

mpmath.mp.dps = 300
# NOTE: "why do we need 300? this is madness!"
# madness? THIS    IS    SPARTAAAA!!!
# yes we genuinely need 300 because, assuming our constants have an exponent close to 0, f256 has 237 binary precision, which is roughly 237 * log10(2) ≈ 71.34 decimal digits. we will also want to store the residual. that means we need 71.34*2=142 or so. and remember that this is assuming our constants are close to 0 exponent. so yes, 300 is needed.

constants: dict[str, Any] = dict(
    zero                 = 0,
    liouville            = liouville_10(7),
    champernowne         = '0.' + ''.join(str(i) for i in range(1, 200)),
    meissel_mertens      = mpmath.mertens,
    half                 = 0.5,
    euler_mascheroni     = mpmath.euler,
    gompertz             = mpmath.e * mpmath.e1(1),    
    hardy_littlewood     = mpmath.twinprime,
    catalan              = mpmath.catalan,
    one                  = 1,
    apery                = mpmath.zeta(3),
    delian               = mpmath.cbrt(2),
    glaisher_kinkelin    = mpmath.glaisher,
    plastic              = mpmath.findroot(lambda x: x**3 - x - 1, 1.3),
    pythagoras           = mpmath.sqrt(2),
    ramanujan_soldner    = mpmath.findroot(mpmath.li, 1.45),
    golden_ratio         = metallic(1, True),
    theodorus            = mpmath.sqrt(3),
    two                  = 2, 
    wallis               = mpmath.findroot(lambda x: x ** 3 - 2 * x - 5, 2.09445),
    silver_ratio         = metallic(2, True),
    feigenbaum_alpha     = feigenbaum_alpha(mpmath.mp.dps),
    khinchin             = mpmath.khinchin,
    euler_bernoulli      = mpmath.e,
    archimedes           = mpmath.pi,
    bronze_ratio         = metallic(3, True),
    feigenbaum_delta     = feigenbaum_delta(mpmath.mp.dps),
    hartl                = mpmath.pi * 2,
    gelfond              = mpmath.e ** mpmath.pi,



    #ramanujan            = mpmath.e ** (mpmath.pi * mpmath.sqrt(163)), # probably not very useful
    ln_2                 = mpmath.ln(2),
    #'degree' = mpmath.pi * 2 / 360,
    #'gradian'= mpmath.pi * 2 / 400,
    #'minute' = mpmath.pi * 2 / 21600,
    #'second' = mpmath.pi * 2 / 129600,
    sqrt_5 = mpmath.sqrt(5),
    cbrt_3 = mpmath.cbrt(3),
    root_2_12 = mpmath.root(2, 12),
    supergolden = mpmath.findroot(lambda x: x ** 3 - x ** 2 - 1, 1.46),


    connective = mpmath.sqrt(2 + mpmath.sqrt(2)),
)

# sort alphabetically
constants: dict[str, Any] = dict(sorted(constants.items()))

# convert to Float
for constant_name, v in constants.items():
    constants[constant_name] = Float.from_str(str(v), radix = 10)

for constant_name, constant in constants.items():
    if len(str(constant)) < mpmath.mp.dps:
        raise Exception(f'{constant} has <{mpmath.mp.dps} digits. idk bro go fix it')
    print(constant_name, str(constant))

# (radix, precision) of the five basic IEEE 754 formats
formats = {'f32' : ( 2,  24),
           'f64' : ( 2,  53),
           'f128': ( 2, 113),
           'd64' : (10,  16),
           'd128': (10,  34)}

# stored as lines
markdown_table: list[str] = []

for constant_name, constant in constants.items():
    print(f'\n{constant_name}:')

    for format_name, format_details in formats.items():
        radix, precision = format_details
        nearest = Float.from_rational(constant, radix, precision)
        residual = Float.from_rational(constant - nearest, radix, precision)

        print(f'  {format_name}:')
        print(f'    nearest:')
        print(f'      significand: {nearest.significand}')
        print(f'      radix: {nearest.radix}')
        print(f'      exponent: {nearest.exponent}')
        print(f'    residual:')
        print(f'      significand: {residual.significand}')
        print(f'      radix: {residual.radix}')
        print(f'      exponent: {residual.exponent}')

        #markdown_table.append(str(Fixed.from_rational(nearest, nearest.radix)))
        #markdown_table.append(str(constant))

for line in markdown_table:
    print(line)

- name: zero
  link: https://en.wikipedia.org/wiki/Zero
  oeis: 
  eponyms: []
  formula: $0 = ∃!x ∈ \href{https://en.wikipedia.org/wiki/Complex_numbers}{ℂ} \mid ∀a ∈ \href{https://en.wikipedia.org/wiki/Complex_numbers}{ℂ}, x \href{https://en.wikipedia.org/wiki/Addition}{+} a = a$
  decimal: 0

- name: liouville
  link: https://fr.wikipedia.org/wiki/Nombre_de_Liouville#Constante_de_Liouville
  oeis: 
  eponyms: 
    - name: Joseph Liouville
      link: https://fr.wikipedia.org/wiki/Joseph_Liouville
  formula: '$L = \displaystyle\sum_{k=1}^∞ \dfrac{1}{10^{k!}}$'
  decimal: 0.11000100000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000…

- name: champernowne
  link: https://en.wikipedia.org/wiki/Champernowne_constant
  oeis: 
  eponyms: 
    - name: David Gawen Champernowne
      link: https://en.wikipedia.org/wiki/D._G._Champernowne
  formula: $C_10 = $
  decimal: 0.1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545…

- name: meissel_mertens
  link: https://de.wikipedia.org/wiki/Meissel-Mertens-Konstante
  oeis: 
  eponyms: 
    - name: Daniel Friedrich Ernst Meissel
      link: https://de.wikipedia.org/wiki/Ernst_Meissel
    - name: Franciszek Carl Josef Mertens
      link: https://de.wikipedia.org/wiki/Franz_Mertens_(Mathematiker)
  formula: $M$
  decimal: 0.26149721284764278375542683860869585905156664826119920619206421392492451089736820971414263143424665…

- name: one_half
  link: https://en.wikipedia.org/wiki/One_half
  oeis: 
  eponyms: []
  formula: $0.5 = \dfrac{1}{2}$
  decimal: 0.5
- name: euler_mascheroni
  link: https://en.wikipedia.org/wiki/Euler%27s_constant
  oeis: 
  eponyms: 
    - name: Leonhard Euler
      link: https://als.wikipedia.org/wiki/Leonhard_Euler
    - name: Lorenzo Mascheroni
      link: https://it.wikipedia.org/wiki/Lorenzo_Mascheroni
  formula: γ
  decimal: 0.57721566490153286060651209008240243104215933593992359880576723488486772677766467093694706329174674…

- name: gompertz
  link: https://en.wikipedia.org/wiki/Gompertz_constant
  oeis: 
  eponyms: 
    - name: Benjamin Gompertz
      link: https://en.wikipedia.org/wiki/Benjamin_Gompertz
  formula: δ
  decimal: 0.59634736232319407434107849936927937607417786015254878157348491048232721911487441747043049709361276…

- name: hardy_littlewood
  link: https://en.wikipedia.org/wiki/Twin_prime#First_Hardy%E2%80%93Littlewood_conjecture
  oeis: 
  eponyms: 
    - name: Godfrey Harold Hardy
      link: https://en.wikipedia.org/wiki/G._H._Hardy
    - name: John Edensor Littlewood
      link: https://en.wikipedia.org/wiki/John_Edensor_Littlewood
  formula: C~2~
  decimal: 0.66016181584686957392781211001455577843262336028473341331944842333540564230449527714376003141383986…

- name: catalan
  link: https://fr.wikipedia.org/wiki/Constante_de_Catalan
  oeis: 
  eponyms: 
    - name: Eugène Charles Catalan
      link: https://fr.wikipedia.org/wiki/Eug%C3%A8ne_Charles_Catalan
  formula: G
  decimal: 0.91596559417721901505460351493238411077414937428167213426649811962176301977625476947935651292611510…

- name: one
  link: https://en.wikipedia.org/wiki/1
  oeis: 
  eponyms: []
  formula: $1 = ∃!x ∈ ℂ \mid ∀a ∈ ℂ, x × a = a$
  decimal: 1

- name: apery
  link: https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant
  oeis: 
  eponyms: 
    - name: Roger Apéry
      link: https://en.wikipedia.org/wiki/Roger_Ap%C3%A9ry
  formula: $\href{https://en.wikipedia.org/wiki/Riemann_zeta_function}{ζ}(3)$
  decimal: 1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525…

- name: delian
  link: https://el.wikipedia.org/wiki/%CE%94%CE%B9%CF%80%CE%BB%CE%B1%CF%83%CE%B9%CE%B1%CF%83%CE%BC%CF%8C%CF%82_%CF%84%CE%BF%CF%85_%CE%BA%CF%8D%CE%B2%CE%BF%CF%85
  oeis: 
  eponyms: 
    - name: Δῆλος
      link: https://el.wikipedia.org/wiki/%CE%94%CE%AE%CE%BB%CE%BF%CF%82
  formula: $\sqrt[3]{2}$
  decimal: 1.25992104989487316476…

- name: glaisher_kinkelin
  link: https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant
  oeis: 
  eponyms:
    - name: James Whitbread Lee Glaisher
      link: https://en.wikipedia.org/wiki/James_Whitbread_Lee_Glaisher
    - name: Hermann Kinkelin
      link: https://en.wikipedia.org/wiki/Hermann_Kinkelin
  formula: A
  decimal: 1.28242712910062263687534256886979172776768892732500119206374002174040630885882646112973649195820237…

- name: plastic
  link: https://en.wikipedia.org/wiki/Plastic_ratio
  oeis: 
  eponyms: []
  formula: ρ
  decimal: 1.32471795724474602596090885447809734073440405690173336453401505030282785124554759405469934798178728… 

- name: pythagoras
  link: https://en.wikipedia.org/wiki/Square_root_of_2
  oeis: 
  eponyms:
    - name: Πυθαγόρας
      link: https://en.wikipedia.org/wiki/Pythagoras
  formula: '[√](https://en.wikipedia.org/wiki/Square_root)2'
  decimal: 1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157…

- name: ramanujan_soldner
  link: https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant
  oeis: 
  eponyms:
    - name: ஶ்ரீநிவாஸ ராமாநுஜையங்கார்
      link: https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
    - name: Johann Georg von Soldner
      link: https://en.wikipedia.org/wiki/Johann_Georg_von_Soldner
  formula: μ
  decimal: 1.45136923488338105028396848589202744949303228364801586309300455766242559575451783565953135771108682884704075157097064920307143357020423478488319003911084098422088650348382593759733331313969041108938752002714096930942987193069514832776410872163829967084223691265784528427072307722410618111313183181245…

- name: golden_ratio
  link: https://en.wikipedia.org/wiki/Golden_ratio
  oeis: 
  eponyms: []
  formula: $φ = n + \sqrt{n^2+4} / 2, n = 1$
  decimal: 1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113…

- name: theodorus
  link: https://en.wikipedia.org/wiki/Square_root_of_3
  oeis: 
  eponyms: 
    - name: Θεόδωρος
      link: https://en.wikipedia.org/wiki/Theodorus_of_Cyrene
  formula: '\href{https://en.wikipedia.org/wiki/Square_root}{√}3'
  decimal: 1.73205080756887729352744634150587236694280525381038062805580697945193301690880003708114618675724857…

- name: connective
  link: https://en.wikipedia.org/wiki/Connective_constant
  oeis: 
  eponyms: []
  formula: μ
  decimal: 

- name: brun
  link: https://en.wikipedia.org/wiki/Brun%27s_theorem
  oeis: https://oeis.org/A065421
  eponyms: 
    - name: Viggo Brun
      link: https://no.wikipedia.org/wiki/Viggo_Brun
  formula: $\begin{aligned} B_2 &= \sum_{p \in \mathbb P_2}\left(\frac 1p + \frac 1 {p + 2}\right) \\ \href{https://en.wikipedia.org/wiki/Twin_prime}{\mathbb P_2} &= \{p \in \mathbb P \mid p + 2 \in \mathbb P\}\end{aligned}$
  #formula: $B_2 = \displaystyle\sum_{p \in \href{https://en.wikipedia.org/wiki/Twin_prime}{\mathbb P_2}} \left(\frac 1p + \frac 1 {p + 2}\right)$
  decimal: 

- name: two
  link: https://en.wikipedia.org/wiki/2
  oeis: 
  eponyms: []
  formula: $2 = 1 \href{https://en.wikipedia.org/wiki/Addition}{+} 1$
  decimal: 2

- name: wallis
  link: https://mathworld.wolfram.com/WallissConstant.html
  oeis: 
  eponyms: 
    - name: John Wallis
      link: https://en.wikipedia.org/wiki/John_Wallis
  formula: 
  decimal: 2.09455148154232659148238654057930296385730610562823918030412852904531218998348366714626728177715775786083952118906296345984514039842081282370173965531394055476160225828188949144397222665915595450399332426472256800938699177395882894016181834927454149608941225576642742318917626635375670383400596997798…

- name: silver_ratio
  link: https://en.wikipedia.org/wiki/Silver_ratio
  oeis: 
  eponyms: []
  formula: $σ = \href{}{}, n = 2$
  decimal: 2.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157…

- name: feigenbaum_alpha
  link: https://en.wikipedia.org/wiki/Feigenbaum_constants#The_second_constant
  oeis: 
  eponyms: 
    - name: Mitchell Jay Feigenbaum
      link: https://en.wikipedia.org/wiki/Mitchell_J._Feigenbaum
  formula: α 
  decimal: 2.5029078750958928222839028732182157863812713767271499773361920567792354631795902067032996497464338…

- name: khinchin
  link: https://en.wikipedia.org/wiki/Khinchin's_constant
  oeis: 
  eponyms: 
    - name: Алекса́ндр Я́ковлевич Хи́нчи
      link: https://en.wikipedia.org/wiki/Aleksandr_Khinchin
  formula: K~0~ 
  decimal: 2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769…

- name: euler_bernoulli
  link: https://en.wikipedia.org/wiki/E_(mathematical_constant)
  oeis: 
  eponyms:
    - name: Leonhard Euler
      link: https://als.wikipedia.org/wiki/Leonhard_Euler
    - name: Jakob Bernoulli
      link: https://als.wikipedia.org/wiki/Jakob_Bernoulli
  formula: e
  decimal: 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642…

- name: archimedes
  link: https://el.wikipedia.org/wiki/%CE%A0_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AE_%CF%83%CF%84%CE%B1%CE%B8%CE%B5%CF%81%CE%AC)
  oeis: https://oeis.org/A000796
  eponyms:
    - name: Ἀρχιμήδης
      link: https://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B9%CE%BC%CE%AE%CE%B4%CE%B7%CF%82
  formula: π
  decimal: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706… 

- name: bronze_ratio
  link: https://en.wikipedia.org/wiki/Metallic_mean
  oeis: 
  eponyms: []
  formula: S~3~ 
  decimal: 3.30277563773199464655961063373524797312564828692262310635522652811358347414650522260230954100924535…

- name: feigenbaum_delta
  link: https://en.wikipedia.org/wiki/Feigenbaum_constants#The_first_constant
  oeis: 
  eponyms: 
    - name: Mitchell Jay Feigenbaum
      link: https://en.wikipedia.org/wiki/Mitchell_J._Feigenbaum
  formula: δ 
  decimal: 4.66920160910299067185320382046620161725818557747576863274565134300413433021131473713868974402394801…

- name: hartl
  link: https://en.wikipedia.org/wiki/Tau_(mathematics) 
  oeis: https://oeis.org/A019692
  eponyms: 
    - name: Michael Hartl
      link: https://en.wikipedia.org/wiki/Michael_Hartl
  formula: τ 
  decimal: 6.28318530717958647692528676655900576839433879875021164194988918461563281257241799725606965068423413…

- name: gelfond
  link: https://en.wikipedia.org/wiki/Gelfond%27s_constant
  oeis: 
  eponyms: 
    - name: Алекса́ндр О́сипович Ге́льфонд
      link: https://en.wikipedia.org/wiki/Alexander_Gelfond
  formula: e^π^
  decimal: 23.1406926327792690057290863679485473802661062426002119934450464095243423506904527835169719970675492196759527048010877731444280444146938358447174458796098493653279658636692422302689910137417646844014103951838684772430680595881624498444914309667784136716319634147840382165112876377314703473538331628213…

# [`landau_ramanujan`](https://en.wikipedia.org/wiki/Landau%E2%80%93Ramanujan_constant) | [Edmund Georg Hermann Landau](https://en.wikipedia.org/wiki/Edmund_Landau), [ஶ்ரீநிவாஸ ராமாநுஜையங்கார்](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan) | b =  |

- name: supergolden
  link: https://en.wikipedia.org/wiki/Supergolden_ratio
  oeis: 
  eponyms: []
  formula: ψ 
  decimal: 

- name: kepler_bouwkamp
  link: https://en.wikipedia.org/wiki/Kepler%E2%80%93Bouwkamp_constant
  oeis: 
  eponyms: 
    - name: Johannes Kepler
      link: https://de.wikipedia.org/wiki/Johannes_Kepler
    - name: Christoffel Jacob Bouwkamp
      link: https://de.wikipedia.org/wiki/Christoffel_Jacob_Bouwkamp
  formula: K'
  decimal: