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| 1 | +# <!-- rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb --> |
| 2 | +# Provides mathematical functions. |
| 3 | +# |
| 4 | +# Example: |
| 5 | +# |
| 6 | +# require "bigdecimal/math" |
| 7 | +# |
| 8 | +# include BigMath |
| 9 | +# |
| 10 | +# a = BigDecimal((PI(100)/2).to_s) |
| 11 | +# puts sin(a,100) # => 0.99999999999999999999......e0 |
| 12 | +# |
| 13 | +module BigMath |
| 14 | + # <!-- |
| 15 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 16 | + # - E(numeric) -> BigDecimal |
| 17 | + # --> |
| 18 | + # Computes e (the base of natural logarithms) to the specified number of digits |
| 19 | + # of precision, `numeric`. |
| 20 | + # |
| 21 | + # BigMath.E(10).to_s |
| 22 | + # #=> "0.271828182845904523536028752390026306410273e1" |
| 23 | + # |
| 24 | + def self?.E: (Numeric prec) -> BigDecimal |
| 25 | + |
| 26 | + # <!-- |
| 27 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 28 | + # - PI(numeric) -> BigDecimal |
| 29 | + # --> |
| 30 | + # Computes the value of pi to the specified number of digits of precision, |
| 31 | + # `numeric`. |
| 32 | + # |
| 33 | + # BigMath.PI(10).to_s |
| 34 | + # #=> "0.3141592653589793238462643388813853786957412e1" |
| 35 | + # |
| 36 | + def self?.PI: (Numeric prec) -> BigDecimal |
| 37 | + |
| 38 | + # Computes the arccosine of `decimal` to the specified number of digits of |
| 39 | + # precision, `numeric`. |
| 40 | + # |
| 41 | + # If `decimal` is NaN, returns NaN. |
| 42 | + # |
| 43 | + # BigMath.acos(BigDecimal('0.5'), 32).to_s |
| 44 | + # #=> "0.10471975511965977461542144610932e1" |
| 45 | + # |
| 46 | + def self?.acos: (BigDecimal, Numeric) -> BigDecimal |
| 47 | + |
| 48 | + # Computes the inverse hyperbolic cosine of `decimal` to the specified number of |
| 49 | + # digits of precision, `numeric`. |
| 50 | + # |
| 51 | + # If `decimal` is NaN, returns NaN. |
| 52 | + # |
| 53 | + # BigMath.acosh(BigDecimal('2'), 32).to_s |
| 54 | + # #=> "0.1316957896924816708625046347308e1" |
| 55 | + # |
| 56 | + def self?.acosh: (BigDecimal, Numeric) -> BigDecimal |
| 57 | + |
| 58 | + # Computes the arcsine of `decimal` to the specified number of digits of |
| 59 | + # precision, `numeric`. |
| 60 | + # |
| 61 | + # If `decimal` is NaN, returns NaN. |
| 62 | + # |
| 63 | + # BigMath.asin(BigDecimal('0.5'), 32).to_s |
| 64 | + # #=> "0.52359877559829887307710723054658e0" |
| 65 | + # |
| 66 | + def self?.asin: (BigDecimal, Numeric) -> BigDecimal |
| 67 | + |
| 68 | + # Computes the inverse hyperbolic sine of `decimal` to the specified number of |
| 69 | + # digits of precision, `numeric`. |
| 70 | + # |
| 71 | + # If `decimal` is NaN, returns NaN. |
| 72 | + # |
| 73 | + # BigMath.asinh(BigDecimal('1'), 32).to_s |
| 74 | + # #=> "0.88137358701954302523260932497979e0" |
| 75 | + # |
| 76 | + def self?.asinh: (BigDecimal, Numeric) -> BigDecimal |
| 77 | + |
| 78 | + # <!-- |
| 79 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 80 | + # - atan(decimal, numeric) -> BigDecimal |
| 81 | + # --> |
| 82 | + # Computes the arctangent of `decimal` to the specified number of digits of |
| 83 | + # precision, `numeric`. |
| 84 | + # |
| 85 | + # If `decimal` is NaN, returns NaN. |
| 86 | + # |
| 87 | + # BigMath.atan(BigDecimal('-1'), 16).to_s |
| 88 | + # #=> "-0.785398163397448309615660845819878471907514682065e0" |
| 89 | + # |
| 90 | + def self?.atan: (BigDecimal x, Numeric prec) -> BigDecimal |
| 91 | + |
| 92 | + # Computes the arctangent of y and x to the specified number of digits of |
| 93 | + # precision, `numeric`. |
| 94 | + # |
| 95 | + # BigMath.atan2(BigDecimal('-1'), BigDecimal('1'), 32).to_s |
| 96 | + # #=> "-0.78539816339744830961566084581988e0" |
| 97 | + # |
| 98 | + def self?.atan2: (BigDecimal, BigDecimal, Numeric) -> BigDecimal |
| 99 | + |
| 100 | + # Computes the inverse hyperbolic tangent of `decimal` to the specified number |
| 101 | + # of digits of precision, `numeric`. |
| 102 | + # |
| 103 | + # If `decimal` is NaN, returns NaN. |
| 104 | + # |
| 105 | + # BigMath.atanh(BigDecimal('0.5'), 32).to_s |
| 106 | + # #=> "0.54930614433405484569762261846126e0" |
| 107 | + # |
| 108 | + def self?.atanh: (BigDecimal, Numeric) -> BigDecimal |
| 109 | + |
| 110 | + # Computes the cube root of `decimal` to the specified number of digits of |
| 111 | + # precision, `numeric`. |
| 112 | + # |
| 113 | + # BigMath.cbrt(BigDecimal('2'), 32).to_s |
| 114 | + # #=> "0.12599210498948731647672106072782e1" |
| 115 | + # |
| 116 | + def self?.cbrt: (BigDecimal, Numeric) -> BigDecimal |
| 117 | + |
| 118 | + # <!-- |
| 119 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 120 | + # - cos(decimal, numeric) -> BigDecimal |
| 121 | + # --> |
| 122 | + # Computes the cosine of `decimal` to the specified number of digits of |
| 123 | + # precision, `numeric`. |
| 124 | + # |
| 125 | + # If `decimal` is Infinity or NaN, returns NaN. |
| 126 | + # |
| 127 | + # BigMath.cos(BigMath.PI(4), 16).to_s |
| 128 | + # #=> "-0.999999999999999999999999999999856613163740061349e0" |
| 129 | + # |
| 130 | + def self?.cos: (BigDecimal x, Numeric prec) -> BigDecimal |
| 131 | + |
| 132 | + # Computes the hyperbolic cosine of `decimal` to the specified number of digits |
| 133 | + # of precision, `numeric`. |
| 134 | + # |
| 135 | + # If `decimal` is NaN, returns NaN. |
| 136 | + # |
| 137 | + # BigMath.cosh(BigDecimal('1'), 32).to_s |
| 138 | + # #=> "0.15430806348152437784779056207571e1" |
| 139 | + # |
| 140 | + def self?.cosh: (BigDecimal, Numeric) -> BigDecimal |
| 141 | + |
| 142 | + # Computes the error function of +decimal+ to the specified number of digits of |
| 143 | + # precision, +numeric+. |
| 144 | + # |
| 145 | + # If +decimal+ is NaN, returns NaN. |
| 146 | + # |
| 147 | + # BigMath.erf(BigDecimal('1'), 32).to_s |
| 148 | + # #=> "0.84270079294971486934122063508261e0" |
| 149 | + # |
| 150 | + def self?.erf: (BigDecimal, Numeric) -> BigDecimal |
| 151 | + |
| 152 | + # Computes the complementary error function of +decimal+ to the specified number of digits of |
| 153 | + # precision, +numeric+. |
| 154 | + # |
| 155 | + # If +decimal+ is NaN, returns NaN. |
| 156 | + # |
| 157 | + # BigMath.erfc(BigDecimal('10'), 32).to_s |
| 158 | + # #=> "0.20884875837625447570007862949578e-44" |
| 159 | + # |
| 160 | + def self?.erfc: (BigDecimal, Numeric) -> BigDecimal |
| 161 | + |
| 162 | + # Computes the value of e (the base of natural logarithms) raised to the power |
| 163 | + # of `decimal`, to the specified number of digits of precision. |
| 164 | + # |
| 165 | + # If `decimal` is infinity, returns Infinity. |
| 166 | + # |
| 167 | + # If `decimal` is NaN, returns NaN. |
| 168 | + # |
| 169 | + def self?.exp: (BigDecimal, Numeric prec) -> BigDecimal |
| 170 | + |
| 171 | + # Decomposes +x+ into a normalized fraction and an integral power of ten. |
| 172 | + # |
| 173 | + # BigMath.frexp(BigDecimal(123.456)) |
| 174 | + # #=> [0.123456e0, 3] |
| 175 | + # |
| 176 | + def self?.frexp: (BigDecimal) -> [ BigDecimal, Integer ] |
| 177 | + |
| 178 | + # Computes the gamma function of +decimal+ to the specified number of |
| 179 | + # digits of precision, +numeric+. |
| 180 | + # |
| 181 | + # BigMath.gamma(BigDecimal('0.5'), 32).to_s |
| 182 | + # #=> "0.17724538509055160272981674833411e1" |
| 183 | + # |
| 184 | + def self?.gamma: (BigDecimal, Numeric) -> BigDecimal |
| 185 | + |
| 186 | + # Returns sqrt(x**2 + y**2) to the specified number of digits of precision, |
| 187 | + # `numeric`. |
| 188 | + # |
| 189 | + # BigMath.hypot(BigDecimal('1'), BigDecimal('2'), 32).to_s |
| 190 | + # #=> "0.22360679774997896964091736687313e1" |
| 191 | + # |
| 192 | + def self?.hypot: (BigDecimal, BigDecimal, Numeric) -> BigDecimal |
| 193 | + |
| 194 | + # Inverse of +frexp+. |
| 195 | + # Returns the value of fraction * 10**exponent. |
| 196 | + # |
| 197 | + # BigMath.ldexp(BigDecimal("0.123456e0"), 3) |
| 198 | + # #=> 0.123456e3 |
| 199 | + # |
| 200 | + def self?.ldexp: (BigDecimal, Integer) -> BigDecimal |
| 201 | + |
| 202 | + # Computes the natural logarithm of the absolute value of the gamma function |
| 203 | + # of +decimal+ to the specified number of digits of precision, +numeric+ and its sign. |
| 204 | + # |
| 205 | + # BigMath.lgamma(BigDecimal('0.5'), 32) |
| 206 | + # #=> [0.57236494292470008707171367567653e0, 1] |
| 207 | + # |
| 208 | + def self?.lgamma: (BigDecimal, Numeric) -> [BigDecimal, Integer] |
| 209 | + |
| 210 | + # Computes the natural logarithm of `decimal` to the specified number of digits |
| 211 | + # of precision, `numeric`. |
| 212 | + # |
| 213 | + # If `decimal` is zero or negative, raises Math::DomainError. |
| 214 | + # |
| 215 | + # If `decimal` is positive infinity, returns Infinity. |
| 216 | + # |
| 217 | + # If `decimal` is NaN, returns NaN. |
| 218 | + # |
| 219 | + def self?.log: (BigDecimal, Numeric prec) -> BigDecimal |
| 220 | + |
| 221 | + # Computes the base 2 logarithm of `decimal` to the specified number of digits |
| 222 | + # of precision, `numeric`. |
| 223 | + # |
| 224 | + # If `decimal` is zero or negative, raises Math::DomainError. |
| 225 | + # |
| 226 | + # If `decimal` is positive infinity, returns Infinity. |
| 227 | + # |
| 228 | + # If `decimal` is NaN, returns NaN. |
| 229 | + # |
| 230 | + # BigMath.log2(BigDecimal('3'), 32).to_s |
| 231 | + # #=> "0.15849625007211561814537389439478e1" |
| 232 | + # |
| 233 | + def self?.log2: (BigDecimal, Numeric) -> BigDecimal |
| 234 | + |
| 235 | + # <!-- |
| 236 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 237 | + # - sin(decimal, numeric) -> BigDecimal |
| 238 | + # --> |
| 239 | + # Computes the sine of `decimal` to the specified number of digits of precision, |
| 240 | + # `numeric`. |
| 241 | + # |
| 242 | + # If `decimal` is Infinity or NaN, returns NaN. |
| 243 | + # |
| 244 | + # BigMath.sin(BigMath.PI(5)/4, 5).to_s |
| 245 | + # #=> "0.70710678118654752440082036563292800375e0" |
| 246 | + # |
| 247 | + def self?.sin: (BigDecimal x, Numeric prec) -> BigDecimal |
| 248 | + |
| 249 | + # Computes the hyperbolic sine of `decimal` to the specified number of digits of |
| 250 | + # precision, `numeric`. |
| 251 | + # |
| 252 | + # If `decimal` is NaN, returns NaN. |
| 253 | + # |
| 254 | + # BigMath.sinh(BigDecimal('1'), 32).to_s |
| 255 | + # #=> "0.11752011936438014568823818505956e1" |
| 256 | + # |
| 257 | + def self?.sinh: (BigDecimal, Numeric) -> BigDecimal |
| 258 | + |
| 259 | + # <!-- |
| 260 | + # rdoc-file=ext/bigdecimal/lib/bigdecimal/math.rb |
| 261 | + # - sqrt(decimal, numeric) -> BigDecimal |
| 262 | + # --> |
| 263 | + # Computes the square root of `decimal` to the specified number of digits of |
| 264 | + # precision, `numeric`. |
| 265 | + # |
| 266 | + # BigMath.sqrt(BigDecimal('2'), 16).to_s |
| 267 | + # #=> "0.1414213562373095048801688724e1" |
| 268 | + # |
| 269 | + def self?.sqrt: (BigDecimal x, Numeric prec) -> BigDecimal |
| 270 | + |
| 271 | + # Computes the hyperbolic tangent of `decimal` to the specified number of digits |
| 272 | + # of precision, `numeric`. |
| 273 | + # |
| 274 | + # If `decimal` is NaN, returns NaN. |
| 275 | + # |
| 276 | + # BigMath.tanh(BigDecimal('1'), 32).to_s |
| 277 | + # #=> "0.76159415595576488811945828260479e0" |
| 278 | + # |
| 279 | + def self?.tanh: (BigDecimal, Numeric) -> BigDecimal |
| 280 | +end |
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