Add bin and edit workflow

bin/gems/bigdecimal-3.1.9/lib/bigdecimal/math.rb

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+# frozen_string_literal: false
+require 'bigdecimal'
+
+#
+#--
+# 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) # => 0.99999999999999999999......e0
+#
+module BigMath
+  module_function
+
+  # call-seq:
+  #   sqrt(decimal, numeric) -> BigDecimal
+  #
+  # Computes the square root of +decimal+ to the specified number of digits of
+  # precision, +numeric+.
+  #
+  #   BigMath.sqrt(BigDecimal('2'), 16).to_s
+  #   #=> "0.1414213562373095048801688724e1"
+  #
+  def sqrt(x, prec)
+    x.sqrt(prec)
+  end
+
+  # 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"
+  #
+  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
+
+  # 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"
+  #
+  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
+
+  # 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('-1'), 16).to_s
+  #   #=> "-0.785398163397448309615660845819878471907514682065e0"
+  #
+  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
+
+  # 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"
+  #
+  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
+
+  # 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"
+  #
+  def E(prec)
+    raise ArgumentError, "Zero or negative precision for E" if prec <= 0
+    BigMath.exp(1, prec)
+  end
+end