Module: BigMath

Defined in:
lib/bigdecimal/math.rb

Overview

– Contents:

sqrt(x, prec)
sin (x, prec)
cos (x, prec)
atan(x, prec)  Note: |x|<1, x=0.9999 may not converge.
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/math"

include BigMath

a = BigDecimal((PI(100)/2).to_s)
puts sin(a,100) # => 0.10000000000000000000......E1

Class Method Summary collapse

Class Method Details

.atan(x, prec) ⇒ Object

call-seq:

atan(decimal, numeric) -> BigDecimal

Computes the arctangent of decimal to the specified number of digits of precision, numeric.

If decimal is NaN, returns NaN.

BigMath::atan(BigDecimal.new('-1'), 16).to_s
#=> "-0.785398163397448309615660845819878471907514682065E0"

Raises:

  • (ArgumentError) 


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
 
# File 'lib/bigdecimal/math.rb', line 145

def atan(x, prec)
  raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
  return BigDecimal("NaN") if x.nan?
  pi = PI(prec)
  x = -x if neg = x < 0
  return pi.div(neg ? -2 : 2, prec) if x.infinite?
  return pi / (neg ? -4 : 4) if x.round(prec) == 1
  x = BigDecimal("1").div(x, prec) if inv = x > 1
  x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5
  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 *= 2 if dbl
  y = pi / 2 - y if inv
  y = -y if neg
  y
end

.cos(x, prec) ⇒ Object

call-seq:

cos(decimal, numeric) -> BigDecimal

Computes the cosine of decimal to the specified number of digits of precision, numeric.

If decimal is Infinity or NaN, returns NaN.

BigMath::cos(BigMath::PI(4), 16).to_s
#=> "-0.999999999999999999999999999999856613163740061349E0"

Raises:

  • (ArgumentError) 


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
 
# File 'lib/bigdecimal/math.rb', line 101

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")
  x = -x if x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x %= twopi
    else
      x -= twopi while x > twopi
    end
  end
  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

.E(prec) ⇒ Object

call-seq:

E(numeric) -> BigDecimal

Computes e (the base of natural logarithms) to the specified number of digits of precision, numeric.

BigMath::E(10).to_s
#=> "0.271828182845904523536028752390026306410273E1"

Raises:

  • (ArgumentError) 


227
228
229
230
 
# File 'lib/bigdecimal/math.rb', line 227

def E(prec)
  raise ArgumentError, "Zero or negative precision for E" if prec <= 0
  BigMath.exp(1, prec)
end

.PI(prec) ⇒ Object

call-seq:

PI(numeric) -> BigDecimal

Computes the value of pi to the specified number of digits of precision, numeric.

BigMath::PI(10).to_s
#=> "0.3141592653589793238462643388813853786957412E1"

Raises:

  • (ArgumentError) 


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
 
# File 'lib/bigdecimal/math.rb', line 182

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
  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
  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

.sin(x, prec) ⇒ Object

call-seq:

sin(decimal, numeric) -> BigDecimal

Computes the sine of decimal to the specified number of digits of precision, numeric.

If decimal is Infinity or NaN, returns NaN.

BigMath::sin(BigMath::PI(5)/4, 5).to_s
#=> "0.70710678118654752440082036563292800375E0"

Raises:

  • (ArgumentError) 


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
 
# File 'lib/bigdecimal/math.rb', line 57

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")
  x = -x if neg = x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x %= twopi
    else
      x -= twopi while x > twopi
    end
  end
  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
  neg ? -y : y
end

.sqrt(x, prec) ⇒ Object

call-seq:

sqrt(decimal, numeric) -> BigDecimal

Computes the square root of decimal to the specified number of digits of precision, numeric.

BigMath::sqrt(BigDecimal.new('2'), 16).to_s
#=> "0.14142135623730950488016887242096975E1"



42
43
44
 
# File 'lib/bigdecimal/math.rb', line 42

def sqrt(x, prec)
  x.sqrt(prec)
end