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math_functions.nbt

math_functions.nbt 6.0 KB
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  1. # sqrt
    2. 

  2. 

  3. assert_eq(sqrt(0), 0)
    4. 

  4. assert_eq(sqrt(1), 1)
    5. 

  5. assert_eq(sqrt(4), 2)
    6. 

  6. 

  7. assert_eq(sqrt(0 m²), 0 m)
    8. 

  8. assert_eq(sqrt(1 m²), 1 m)
    9. 

  9. assert_eq(sqrt(4 m²), 2 m)
    10. 

  10. 

  11. # sqr
    12. 

  12. 

  13. assert_eq(sqr(0), 0)
    14. 

  14. assert_eq(sqr(1), 1)
    15. 

  15. assert_eq(sqr(4), 16)
    16. 

  16. 

  17. assert_eq(sqr(0 m), 0 m²)
    18. 

  18. assert_eq(sqr(1 m), 1 m²)
    19. 

  19. assert_eq(sqr(4 m), 16 m²)
    20. 

  20. 

  21. # exp
    22. 

  22. 

  23. assert_eq(exp(0), 1)
    24. 

  24. assert_eq(exp(1), e)
    25. 

  25. assert_eq(exp(2), e * e, 1e-8)
    26. 

  26. 

  27. # ln/log
    28. 

  28. 

  29. assert_eq(ln(1), 0)
    30. 

  30. assert_eq(ln(e), 1)
    31. 

  31. assert_eq(ln(e * e), 2, 1e-8)
    32. 

  32. 

  33. assert_eq(log(1), 0)
    34. 

  34. assert_eq(log(e), 1)
    35. 

  35. assert_eq(log(e * e), 2, 1e-8)
    36. 

  36. 

  37. # log10
    38. 

  38. 

  39. assert_eq(log10(1), 0)
    40. 

  40. assert_eq(log10(10), 1)
    41. 

  41. assert_eq(log10(100), 2)
    42. 

  42. 

  43. # log2
    44. 

  44. 

  45. assert_eq(log2(1), 0)
    46. 

  46. assert_eq(log2(2), 1)
    47. 

  47. assert_eq(log2(4), 2)
    48. 

  48. assert_eq(log2(1024), 10)
    49. 

  49. 

  50. # sin, cos, tan
    51. 

  51. 

  52. assert_eq(sin(0), 0, 1e-8)
    53. 

  53. assert_eq(sin(π / 2), 1, 1e-8)
    54. 

  54. assert_eq(sin(π), 0, 1e-8)
    55. 

  55. 

  56. assert_eq(cos(0), 1, 1e-8)
    57. 

  57. assert_eq(cos(π / 2), 0, 1e-8)
    58. 

  58. assert_eq(cos(π), -1, 1e-8)
    59. 

  59. 

  60. assert_eq(tan(0), 0, 1e-8)
    61. 

  61. assert_eq(tan(π / 4), 1, 1e-8)
    62. 

  62. 

  63. # asin, acos, atan
    64. 

  64. 

  65. assert_eq(asin(0), 0, 1e-8)
    66. 

  66. assert_eq(asin(1), π / 2, 1e-8)
    67. 

  67. 

  68. assert_eq(acos(0), π / 2, 1e-8)
    69. 

  69. assert_eq(acos(1), 0, 1e-8)
    70. 

  70. 

  71. assert_eq(atan(0), 0, 1e-8)
    72. 

  72. assert_eq(atan(1), π / 4, 1e-8)
    73. 

  73. 

  74. # atan2
    75. 

  75. 

  76. assert_eq(atan2(0, 1), 0, 1e-8)
    77. 

  77. assert_eq(atan2(1, 0), π / 2, 1e-8)
    78. 

  78. assert_eq(atan2(0, -1), π, 1e-8)
    79. 

  79. assert_eq(atan2(-1, 0), -π / 2, 1e-8)
    80. 

  80. 

  81. # sinh, cosh, tanh
    82. 

  82. 

  83. assert_eq(sinh(0), 0, 1e-8)
    84. 

  84. assert_eq(sinh(1), (e - 1 / e) / 2, 1e-8)
    85. 

  85. 

  86. assert_eq(cosh(0), 1, 1e-8)
    87. 

  87. assert_eq(cosh(1), (e + 1 / e) / 2, 1e-8)
    88. 

  88. 

  89. assert_eq(tanh(0), 0, 1e-8)
    90. 

  90. assert_eq(tanh(1), (e * e - 1) / (e * e + 1), 1e-8)
    91. 

  91. 

  92. # asinh, acosh, atanh
    93. 

  93. 

  94. assert_eq(asinh(0), 0, 1e-8)
    95. 

  95. assert_eq(asinh(1), ln(1 + sqrt(2)), 1e-8)
    96. 

  96. 

  97. assert_eq(acosh(1), 0, 1e-8)
    98. 

  98. assert_eq(acosh(2), ln(2 + sqrt(3)), 1e-8)
    99. 

  99. 

  100. assert_eq(atanh(0), 0, 1e-8)
    101. 

  101. assert_eq(atanh(0.5), 0.549_306_144, 1e-8)
    102. 

  102. 

  103. # gamma
    104. 

  104. 

  105. assert_eq(gamma(1), 1)
    106. 

  106. assert_eq(gamma(2), 1)
    107. 

  107. assert_eq(gamma(2.5), 1.329_340_388, 1e-8)
    108. 

  108. assert_eq(gamma(3), 2)
    109. 

  109. assert_eq(gamma(4), 6)
    110. 

  110. 

  111. # factorial
    112. 

  112. 

  113. assert_eq(factorial(0), 1)
    114. 

  114. assert_eq(factorial(1), 1)
    115. 

  115. assert_eq(factorial(2), 2)
    116. 

  116. assert_eq(factorial(3), 6)
    117. 

  117. assert_eq(factorial(4), 24)
    118. 

  118. assert_eq(factorial(20), 2432902008176640000)
    119. 

  119. 

  120. # falling factorial
    121. 

  121. 

  122. assert_eq(falling_factorial(0, 0), 1)
    123. 

  123. assert_eq(falling_factorial(1, 0), 1)
    124. 

  124. assert_eq(falling_factorial(2, 0), 1)
    125. 

  125. assert_eq(falling_factorial(42.5, 0), 1)
    126. 

  126. 

  127. assert_eq(falling_factorial(0, 1), 0)
    128. 

  128. assert_eq(falling_factorial(1, 1), 1)
    129. 

  129. assert_eq(falling_factorial(2, 1), 2)
    130. 

  130. assert_eq(falling_factorial(42.5, 1), 42.5)
    131. 

  131. 

  132. assert_eq(falling_factorial(0, 2), 0)
    133. 

  133. assert_eq(falling_factorial(1, 2), 0)
    134. 

  134. assert_eq(falling_factorial(2, 2), 2)
    135. 

  135. assert_eq(falling_factorial(42.5, 2), 1763.75)
    136. 

  136. 

  137. assert_eq(falling_factorial(4, 0), 1)
    138. 

  138. assert_eq(falling_factorial(4, 1), 4)
    139. 

  139. assert_eq(falling_factorial(4, 2), 12)
    140. 

  140. assert_eq(falling_factorial(4, 3), 24)
    141. 

  141. assert_eq(falling_factorial(4, 4), 24)
    142. 

  142. assert_eq(falling_factorial(4, 5), 0)
    143. 

  143. assert_eq(falling_factorial(4, 6), 0)
    144. 

  144. 

  145. assert_eq(falling_factorial(20, 0), 1)
    146. 

  146. assert_eq(falling_factorial(20, 1), 20)
    147. 

  147. assert_eq(falling_factorial(20, 2), 380)
    148. 

  148. assert_eq(falling_factorial(20, 20), 2432902008176640000)
    149. 

  149. assert_eq(falling_factorial(20, 21), 0)
    150. 

  150. 

  151. # binomial coefficient
    152. 

  152. assert_eq(binom(0, -1), 0)
    153. 

  153. assert_eq(binom(0, 0), 1)
    154. 

  154. assert_eq(binom(0, 1), 0)
    155. 

  155. 

  156. assert_eq(binom(1, -1), 0)
    157. 

  157. assert_eq(binom(1, 0), 1)
    158. 

  158. assert_eq(binom(1, 1), 1)
    159. 

  159. assert_eq(binom(1, 2), 0)
    160. 

  160. 

  161. assert_eq(binom(2, -1), 0)
    162. 

  162. assert_eq(binom(2, 0), 1)
    163. 

  163. assert_eq(binom(2, 1), 2)
    164. 

  164. assert_eq(binom(2, 2), 1)
    165. 

  165. assert_eq(binom(2, 3), 0)
    166. 

  166. 

  167. assert_eq(binom(3, -1), 0)
    168. 

  168. assert_eq(binom(3, 0), 1)
    169. 

  169. assert_eq(binom(3, 1), 3)
    170. 

  170. assert_eq(binom(3, 2), 3)
    171. 

  171. assert_eq(binom(3, 3), 1)
    172. 

  172. assert_eq(binom(3, 4), 0)
    173. 

  173. 

  174. assert_eq(binom(4, -1), 0)
    175. 

  175. assert_eq(binom(4, 0), 1)
    176. 

  176. assert_eq(binom(4, 1), 4)
    177. 

  177. assert_eq(binom(4, 2), 6)
    178. 

  178. assert_eq(binom(4, 3), 4)
    179. 

  179. assert_eq(binom(4, 4), 1)
    180. 

  180. assert_eq(binom(4, 5), 0)
    181. 

  181. 

  182. assert_eq(binom(1.5, -1), 0)
    183. 

  183. assert_eq(binom(1.5, 0), 1)
    184. 

  184. assert_eq(binom(1.5, 1), 1.5)
    185. 

  185. assert_eq(binom(1.5, 2), 0.375)
    186. 

  186. assert_eq(binom(1.5, 3), -0.0625)
    187. 

  187. assert_eq(binom(1.5, 4), 0.0234375)
    188. 

  188. 

  189. # combinatoric sequences
    190. 

  190. assert_eq(fibonacci(0), 0)
    191. 

  191. assert_eq(fibonacci(1), 1)
    192. 

  192. assert_eq(fibonacci(5), 5)
    193. 

  193. 

  194. assert_eq(lucas(0), 2)
    195. 

  195. assert_eq(lucas(1), 1)
    196. 

  196. assert_eq(lucas(5), 11)
    197. 

  197. 

  198. assert_eq(catalan(0), 1)
    199. 

  199. assert_eq(catalan(1), 1)
    200. 

  200. assert_eq(catalan(5), 42)
    201. 

  201. 

  202. # maximum
    203. 

  203. 

  204. assert_eq(maximum([1]), 1)
    205. 

  205. assert_eq(maximum([1, 3]), 3)
    206. 

  206. assert_eq(maximum([3, 1]), 3)
    207. 

  207. assert_eq(maximum([100 cm, 3 m]), 3 m)
    208. 

  208. 

  209. # minimum
    210. 

  210. 

  211. assert_eq(minimum([1]), 1)
    212. 

  212. assert_eq(minimum([1, 3]), 1)
    213. 

  213. assert_eq(minimum([3, 1]), 1)
    214. 

  214. assert_eq(minimum([100 cm, 3 m]), 100 cm)
    215. 

  215. 

  216. # mean
    217. 

  217. 

  218. assert_eq(mean([]), 0)
    219. 

  219. assert_eq(mean([1]), 1)
    220. 

  220. assert_eq(mean([1, 3]), 2)
    221. 

  221. assert_eq(mean([1 m, 300 cm]), 2 m)
    222. 

  222. 

  223. # variance
    224. 

  224. 

  225. assert_eq(variance([]), 0)
    226. 

  226. assert_eq(variance([1]), 0)
    227. 

  227. assert_eq(variance([1, 1, 1, 1]), 0)
    228. 

  228. assert_eq(variance([1, 2, 3, 4, 5]), 2.0)
    229. 

  229. assert_eq(variance([1, -1, 1, -1]), 1.0)
    230. 

  230. assert_eq(variance([-2, -4, -6, -8]), 5.0)
    231. 

  231. 

  232. # standard deviation
    233. 

  233. 

  234. assert_eq(stdev([]), 0)
    235. 

  235. assert_eq(stdev([1]), 0)
    236. 

  236. assert_eq(stdev([1, 1, 1, 1]), 0)
    237. 

  237. assert_eq(stdev([1, 2, 3, 4, 5]), sqrt(2.0))
    238. 

  238. 

  239. # median
    240. 

  240. 

  241. assert_eq(median([1]), 1)
    242. 

  242. assert_eq(median([1, 2]), 1.5)
    243. 

  243. assert_eq(median([1, 2, 3]), 2)
    244. 

  244. assert_eq(median([1, 2, 3, 4]), 2.5)
    245. 

  245. assert_eq(median([1, 2, 3, 4, 5]), 3)
    246. 

  246. 

  247. # gcd
    248. 

  248. 

  249. assert_eq(gcd(0, 0), 0)
    250. 

  250. assert_eq(gcd(0, 1), 1)
    251. 

  251. assert_eq(gcd(1, 0), 1)
    252. 

  252. assert_eq(gcd(1, 1), 1)
    253. 

  253. assert_eq(gcd(2, 3), 1)
    254. 

  254. assert_eq(gcd(2, 4), 2)
    255. 

  255. assert_eq(gcd(3, 6), 3)
    256. 

  256. assert_eq(gcd(4, 6), 2)
    257. 

  257. assert_eq(gcd(4, 8), 4)
    258. 

  258. assert_eq(gcd(6, 35), 1)
    259. 

  259. assert_eq(gcd(1071, 462), 21)
    260. 

  260. assert_eq(gcd(-8, 4), 4)
    261. 

  261. assert_eq(gcd(-8, -4), 4)
    262. 

  262. assert_eq(gcd(8, -4), 4)
    263. 

  263. 

  264. # lcm
    265. 

  265. 

  266. assert_eq(lcm(1, 1), 1)
    267. 

  267. assert_eq(lcm(2, 3), 6)
    268. 

  268. assert_eq(lcm(2, 4), 4)
    269. 

  269. assert_eq(lcm(3, 6), 6)
    270. 

  270. assert_eq(lcm(21, 6), 42)
    271. 

  271. assert_eq(lcm(-8, 4), 8)
    272. 

  272. assert_eq(lcm(8, -4), 8)
    273. 

  273. 

  274. # hypot2, hypot3
    275. 

  275. 

  276. assert_eq(hypot2(3, 4), 5)
    277. 

  277. assert_eq(hypot2(3 m, 4 m), 5 m)
    278. 

  278. 

  279. assert_eq(hypot3(8, 9, 12), 17)
    280. 

  280. assert_eq(hypot3(8 m, 9 m, 12 m), 17 m)
    281. 

  281. 

  282. # circle_area, circle_circumference, sphere_area, sphere_volume
    283. 

  283. 

  284. assert_eq(circle_area(2 m), 4 π m²)
    285. 

  285. assert_eq(circle_circumference(2 m), 4 π m)
    286. 

  286. assert_eq(sphere_area(2 m), 16 π m²)
    287. 

  287. assert_eq(sphere_volume(2 m), 32/3 * π m³)
    288.