Module: BigMath
Relationships & Source Files | |
Defined in: | ext/bigdecimal/lib/bigdecimal/math.rb, ext/bigdecimal/bigdecimal.c |
Overview
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
-
.exp(decimal, numeric) ⇒ BigDecimal
Computes the value of e (the base of natural logarithms) raised to the power of
decimal
, to the specified number of digits of precision. -
.log(decimal, numeric) ⇒ BigDecimal
Computes the natural logarithm of
decimal
to the specified number of digits of precision,numeric
. -
.atan(decimal, numeric) ⇒ BigDecimal
mod_func
Computes the arctangent of
decimal
to the specified number of digits of precision,numeric
. -
.cos(decimal, numeric) ⇒ BigDecimal
mod_func
Computes the cosine of
decimal
to the specified number of digits of precision,numeric
. -
E(numeric) ⇒ BigDecimal
mod_func
Computes e (the base of natural logarithms) to the specified number of digits of precision,
numeric
. -
PI(numeric) ⇒ BigDecimal
mod_func
Computes the value of pi to the specified number of digits of precision,
numeric
. -
.sin(decimal, numeric) ⇒ BigDecimal
mod_func
Computes the sine of
decimal
to the specified number of digits of precision,numeric
. -
.sqrt(decimal, numeric) ⇒ BigDecimal
mod_func
Computes the square root of
decimal
to the specified number of digits of precision,numeric
.
Class Method Details
.atan(decimal, numeric) ⇒ BigDecimal (mod_func)
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"
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 146
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(decimal, numeric) ⇒ BigDecimal (mod_func)
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 102
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(numeric) ⇒ BigDecimal (mod_func)
Computes e (the base of natural logarithms) to the specified number of digits of precision, numeric
.
BigMath.E(10).to_s
#=> "0.271828182845904523536028752390026306410273E1"
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 228
def E(prec) raise ArgumentError, "Zero or negative precision for E" if prec <= 0 BigMath.exp(1, prec) end
.exp(decimal, numeric) ⇒ BigDecimal
Computes the value of e (the base of natural logarithms) raised to the power of decimal
, to the specified number of digits of precision.
If decimal
is infinity, returns Infinity.
If decimal
is NaN, returns NaN.
.log(decimal, numeric) ⇒ BigDecimal
Computes the natural logarithm of decimal
to the specified number of digits of precision, numeric
.
If decimal
is zero or negative, raises Math::DomainError
.
If decimal
is positive infinity, returns Infinity.
If decimal
is NaN, returns NaN.
PI(numeric) ⇒ BigDecimal (mod_func)
Computes the value of pi to the specified number of digits of precision, numeric
.
BigMath.PI(10).to_s
#=> "0.3141592653589793238462643388813853786957412E1"
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 183
def PI(prec) raise ArgumentError, "Zero or negative precision 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(decimal, numeric) ⇒ BigDecimal (mod_func)
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 58
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(decimal, numeric) ⇒ BigDecimal (mod_func)
Computes the square root of decimal
to the specified number of digits of precision, numeric
.
BigMath.sqrt(BigDecimal.new('2'), 16).to_s
#=> "0.1414213562373095048801688724E1"
# File 'ext/bigdecimal/lib/bigdecimal/math.rb', line 43
def sqrt(x, prec) x.sqrt(prec) end