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path: root/ext/bigdecimal/lib/bigdecimal/math.rb
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 ``` ``````# #-- # Contents: # sqrt(x, prec) # sin (x, prec) # cos (x, prec) # atan(x, prec) Note: |x|<1, x=0.9999 may not converge. # exp (x, prec) # log (x, prec) # PI (prec) # E (prec) == exp(1.0,prec) # # where: # x ... BigDecimal number to be computed. # |x| must be small enough to get convergence. # prec ... Number of digits to be obtained. #++ # # Provides mathematical functions. # # Example: # # require "bigdecimal" # require "bigdecimal/math" # # include BigMath # # a = BigDecimal((PI(100)/2).to_s) # puts sin(a,100) # -> 0.10000000000000000000......E1 # module BigMath # Computes the square root of x to the specified number of digits of # precision. # # BigDecimal.new('2').sqrt(16).to_s # -> "0.14142135623730950488016887242096975E1" # def sqrt(x,prec) x.sqrt(prec) end # Computes the sine of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. def sin(x, prec) raise ArgumentError, "Zero or negative precision for sin" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x1 = x x2 = x.mult(x,n) sign = 1 y = x d = y i = one z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z *= (i-one) * i d = sign * x1.div(z,m) y += d end y end # Computes the cosine of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. def cos(x, prec) raise ArgumentError, "Zero or negative precision for cos" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x1 = one x2 = x.mult(x,n) sign = 1 y = one d = y i = BigDecimal("0") z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z *= (i-one) * i d = sign * x1.div(z,m) y += d end y end # Computes the arctangent of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. # Raises an argument error if x > 1. def atan(x, prec) raise ArgumentError, "Zero or negative precision for atan" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? raise ArgumentError, "x.abs must be less than 1.0" if x.abs>=1 n = prec + BigDecimal.double_fig y = x d = y t = x r = BigDecimal("3") x2 = x.mult(x,n) while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = -t.mult(x2,n) d = t.div(r,m) y += d r += 2 end y end # Computes the value of e (the base of natural logarithms) raised to the # power of x, to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. # # BigMath::exp(BigDecimal.new('1'), 10).to_s # -> "0.271828182845904523536028752390026306410273E1" def exp(x, prec) raise ArgumentError, "Zero or negative precision for exp" if prec <= 0 return BigDecimal("NaN") if x.infinite? || x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") x1 = one y = one d = y z = one i = 0 while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig x1 = x1.mult(x,n) i += 1 z *= i d = x1.div(z,m) y += d end y end # Computes the natural logarithm of x to the specified number of digits # of precision. # # Returns x if x is infinite or NaN. # def log(x, prec) raise ArgumentError, "Zero or negative argument for log" if x <= 0 || prec <= 0 return x if x.infinite? || x.nan? one = BigDecimal("1") two = BigDecimal("2") n = prec + BigDecimal.double_fig x = (x - one).div(x + one,n) x2 = x.mult(x,n) y = x d = y i = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig x = x2.mult(x,n) i += two d = x.div(i,m) y += d end y*two end # Computes the value of pi to the specified number of digits of precision. def PI(prec) raise ArgumentError, "Zero or negative argument for PI" if prec <= 0 n = prec + BigDecimal.double_fig zero = BigDecimal("0") one = BigDecimal("1") two = BigDecimal("2") m25 = BigDecimal("-0.04") m57121 = BigDecimal("-57121") pi = zero d = one k = one w = one t = BigDecimal("-80") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = t*m25 d = t.div(k,m) k = k+two pi = pi + d end d = one k = one w = one t = BigDecimal("956") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = t.div(m57121,n) d = t.div(k,m) pi = pi + d k = k+two end pi end # Computes e (the base of natural logarithms) to the specified number of # digits of precision. def E(prec) raise ArgumentError, "Zero or negative precision for E" if prec <= 0 n = prec + BigDecimal.double_fig one = BigDecimal("1") y = one d = y z = one i = 0 while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig i += 1 z *= i d = one.div(z,m) y += d end y end end ``````