Newly added.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@4388 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

ext/bigdecimal/lib/bigdecimal/math.rb

@@ -0,0 +1,147 @@
+#
+# Contents:
+#   sin(x, prec)
+#   cos(x, prec)
+#   exp(x, prec)
+#   log(x, prec)
+#   PI (prec)
+#
+# where:
+#   x    ... BigDecimal number to be computed.
+#   prec ... Number of digits to be obtained.
+#
+module BigMath
+  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
+    n2   = n+n
+    one  = BigDecimal("1")
+    two  = BigDecimal("2")
+    x1   = x
+    x2   = x * x
+    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,n2)
+      i  += two
+      z  *= (i-one) * i
+      d   = sign * x1.div(z,m)
+      y  += d
+    end
+    y
+  end
+
+  def cos(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
+    n2   = n+n
+    one  = BigDecimal("1")
+    two  = BigDecimal("2")
+    x1 = one
+    x2 = x * x
+    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,n2)
+      i  += two
+      z  *= (i-one) * i
+      d   = sign * x1.div(z,m)
+      y  += d
+    end
+    y
+  end
+
+  def exp(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
+    n2   = n+n
+    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,n2)
+      i += 1
+      z *= i
+      d  = x1.div(z,m)
+      y += d
+    end
+    y
+  end
+
+  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
+    n2 = n + n
+    x  = (x - one).div(x + one,n)
+    x2 = x   * x
+    y  = two * 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,n2)
+      i += two
+      d  = (two * x).div(i,m)
+      y += d
+    end
+    y
+  end
+
+  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,m)
+      d   = t.div(k,m)
+      pi  = pi + d
+      k   = k+two
+    end
+    pi
+  end
+end