Implement asin and acos

Author: tompng

lib/bigdecimal/math.rb

@@ -10,6 +10,8 @@
 #   sin (x, prec)
 #   cos (x, prec)
 #   tan (x, prec)
+#   asin(x, prec)
+#   acos(x, prec)
 #   atan(x, prec)
 #   atan2(y, x, prec)
 #   PI  (prec)
@@ -232,6 +234,55 @@ def tan(x, prec)
     sin(x, prec).div(cos, prec + BigDecimal.double_fig)
   end
 
+  # call-seq:
+  #   asin(decimal, numeric) -> BigDecimal
+  #
+  # Computes the arcsine of +decimal+ to the specified number of digits of
+  # precision, +numeric+.
+  #
+  # If +decimal+ is NaN, returns NaN.
+  #
+  #   BigMath.asin(BigDecimal('0.5'), 16).to_s
+  #   #=> "0.52359877559829887307710723054659e0"
+  #
+  def asin(x, prec)
+    raise ArgumentError, "Zero or negative precision for asin" if prec <= 0
+    raise Math::DomainError, "Out of domain argument for asin" if x < -1 || x > 1
+    return BigDecimal::NAN if x.nan?
+    prec2 = prec + BigDecimal.double_fig
+    cos = (BigDecimal("1") - x.mult(x, 2 * prec + BigDecimal.double_fig)).sqrt(prec2)
+    if cos.zero?
+      pi = PI(prec)
+      x > 0 ? pi / 2 : -pi / 2
+    else
+      atan(x.div(cos, prec2), prec)
+    end
+  end
+
+  # call-seq:
+  #   acos(decimal, numeric) -> BigDecimal
+  #
+  # Computes the arccosine of +decimal+ to the specified number of digits of
+  # precision, +numeric+.
+  #
+  # If +decimal+ is NaN, returns NaN.
+  #
+  #   BigMath.acos(BigDecimal('0.5'), 16).to_s
+  #   #=> "0.104719755119659771953607604646965e1"
+  #
+  def acos(x, prec)
+    raise ArgumentError, "Zero or negative precision for acos" if prec <= 0
+    raise Math::DomainError, "Out of domain argument for acos" if x < -1 || x > 1
+
+    return PI(prec) / 2 - asin(x, prec) if x < 0
+    return PI(prec) / 2 if x.zero?
+    return BigDecimal::NAN if x.nan?
+
+    prec2 = prec + BigDecimal.double_fig
+    sin = (1 - x**2).sqrt(prec2)
+    atan(sin.div(x, prec2), prec)
+  end
+
   # call-seq:
   #   atan(decimal, numeric) -> BigDecimal
   #
@@ -268,7 +319,7 @@ def atan(x, prec)
     y *= 2 if dbl
     y = pi / 2 - y if inv
     y = -y if neg
-    y
+    y.round(n + [-y.exponent, 0].max)
   end
 
   # call-seq:

test/bigdecimal/test_bigmath.rb

@@ -126,6 +126,39 @@ def test_tan
     assert_relative_precision {|n| tan(PI(200) * 101 / 2, n) }
   end
 
+  def test_asin
+    ["-1", "-0.9", "-0.1", "0", "0.1", "0.9", "1"].each do |x|
+      assert_in_delta(Math.asin(x.to_f), asin(BigDecimal(x), N))
+    end
+    assert_raise(Math::DomainError) { BigMath.asin(BigDecimal("1.1"), N) }
+    assert_raise(Math::DomainError) { BigMath.asin(BigDecimal("-1.1"), N) }
+    assert_in_delta(PI(100) / 6, asin(BigDecimal("0.5"), 100), BigDecimal("1e-100"))
+    assert_relative_precision {|n| asin(BigDecimal("-0.4"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("0.3"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("0.9"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("0.#{"9" * 50}"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("0.#{"9" * 100}"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("0.#{"9" * 195}"), n) }
+    assert_relative_precision {|n| asin(BigDecimal("1e-30"), n) }
+  end
+
+  def test_acos
+    ["-1", "-0.9", "-0.1", "0", "0.1", "0.9", "1"].each do |x|
+      assert_in_delta(Math.acos(x.to_f), acos(BigDecimal(x), N))
+    end
+    assert_raise(Math::DomainError) { BigMath.acos(BigDecimal("1.1"), N) }
+    assert_raise(Math::DomainError) { BigMath.acos(BigDecimal("-1.1"), N) }
+    assert_equal(0, acos(BigDecimal("1.0"), N))
+    assert_in_delta(PI(100) / 3, acos(BigDecimal("0.5"), 100), BigDecimal("1e-100"))
+    assert_relative_precision {|n| acos(BigDecimal("-0.4"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("0.3"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("0.9"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("0.#{"9" * 50}"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("0.#{"9" * 100}"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("0.#{"9" * 195}"), n) }
+    assert_relative_precision {|n| acos(BigDecimal("1e-30"), n) }
+  end
+
   def test_atan
     assert_equal(0.0, atan(BigDecimal("0.0"), N))
     assert_in_delta(Math::PI/4, atan(BigDecimal("1.0"), N))