Drop BigDecimal (#46)

`BigDecimal` was introduced early in the project from my belief that high accuracy was needed.

It turns out that the number of digits in floats are enough to keep a precision up to 0.0001 arcseconds in most calculations.

Using `BigDecimal` has a cost over the overall performance of the library. If it is not absolutely necessary for the calculations, it's better not to use it. Calculations are performed 11 times faster using only floats, for the same precision (see benchmark below).

### Benchmark

The benchmark simply executes usual calculations enabled by the library at the moment, many times.

```rb
Benchmark.bmbm do |x|
  x.report do
    10_000.times do
      time = Time.utc(2023, 2, 17, 11, 0, 0)
      epoch = Astronoby::Epoch.from_time(time)

      observer = Astronoby::Observer.new(
        latitude: Astronoby::Angle.from_degrees(38),
        longitude: Astronoby::Angle.from_degrees(-78)
      )

      sun = Astronoby::Sun.new(epoch: epoch)

      sun
        .apparent_ecliptic_coordinates
        .to_apparent_equatorial(epoch: epoch)
        .to_horizontal(
          time: time,
          latitude: observer.latitude,
          longitude: observer.longitude
        )

      sun.rising_time(observer: observer)
      sun.rising_azimuth(observer: observer).str(:dms)
      sun.setting_time(observer: observer)
      sun.setting_azimuth(observer: observer).str(:dms)

      year = 2024
      Astronoby::EquinoxSolstice.march_equinox(year)
      Astronoby::EquinoxSolstice.june_solstice(year)
    end
  end
end
```

```
                         user    system      total         real
with BigDecimal     61.342663  0.351669  61.694332  (61.892873)
without BigDecimal   5.286487  0.004743   5.291230   (5.308093)
```

README.md

@@ -32,7 +32,7 @@ major one is released.
 
 ```rb
 angle1 = Astronoby::Angle.from_degrees(90)
-angle2 = Astronoby::Angle.from_radians(Astronoby::Angle::PI / 2)
+angle2 = Astronoby::Angle.from_radians(Math::PI / 2)
 angle3 = Astronoby::Angle.from_hours(12)
 
 angle1 == angle2
@@ -83,8 +83,8 @@ horizontal_coordinates = sun.horizontal_coordinates(
   longitude: longitude
 )
 
-horizontal_coordinates.altitude.degrees.to_f
-# => 27.50008242057459
+horizontal_coordinates.altitude.degrees
+# => 27.500082420575094
 
 horizontal_coordinates.altitude.str(:dms)
 # => "+27° 30′ 0.2967″"

lib/astronoby/angle.rb

@@ -1,21 +1,18 @@
 # frozen_string_literal: true
 
-require "bigdecimal/math"
-
 module Astronoby
   class Angle
     include Comparable
 
-    PRECISION = 14
-    PI = BigMath.PI(PRECISION)
-    PI_IN_DEGREES = BigDecimal("180")
+    MIN_PRECISION = 10
+    PI_IN_DEGREES = 180.0
 
-    FULL_CIRCLE_IN_RADIANS = (2 * PI)
+    FULL_CIRCLE_IN_RADIANS = (2 * Math::PI)
 
-    RADIAN_PER_HOUR = PI / BigDecimal("12")
-    MINUTES_PER_DEGREE = BigDecimal("60")
-    MINUTES_PER_HOUR = BigDecimal("60")
-    SECONDS_PER_MINUTE = BigDecimal("60")
+    RADIAN_PER_HOUR = Math::PI / 12.0
+    MINUTES_PER_DEGREE = 60.0
+    MINUTES_PER_HOUR = 60.0
+    SECONDS_PER_MINUTE = 60.0
     SECONDS_PER_HOUR = MINUTES_PER_HOUR * SECONDS_PER_MINUTE
 
     FORMATS = %i[dms hms].freeze
@@ -31,7 +28,7 @@ def from_radians(radians)
       end
 
       def from_degrees(degrees)
-        radians = degrees / PI_IN_DEGREES * PI
+        radians = degrees / PI_IN_DEGREES * Math::PI
         from_radians(radians)
       end
 
@@ -70,16 +67,12 @@ def atan(ratio)
     attr_reader :radians
 
     def initialize(radians)
-      @radians = if radians.is_a?(Integer) || radians.is_a?(BigDecimal)
-        BigDecimal(radians)
-      else
-        BigDecimal(radians, PRECISION)
-      end
+      @radians = radians
       freeze
     end
 
     def degrees
-      @radians * PI_IN_DEGREES / PI
+      @radians * PI_IN_DEGREES / Math::PI
     end
 
     def hours
@@ -153,7 +146,7 @@ def to_dms(deg)
         absolute_decimal_minutes - absolute_decimal_minutes.floor
       )
 
-      Dms.new(sign, degrees, minutes, seconds.to_f.floor(4))
+      Dms.new(sign, degrees, minutes, seconds.floor(4))
     end
 
     def to_hms(hrs)
@@ -168,7 +161,7 @@ def to_hms(hrs)
         absolute_decimal_minutes - absolute_decimal_minutes.floor
       )
 
-      Hms.new(hours, minutes, seconds.to_f.floor(4))
+      Hms.new(hours, minutes, seconds.floor(4))
     end
   end
 end

lib/astronoby/bodies/sun.rb

@@ -4,7 +4,7 @@ module Astronoby
   class Sun
     SEMI_MAJOR_AXIS_IN_METERS = 149_598_500_000
     ANGULAR_DIAMETER = Angle.from_degrees(0.533128)
-    INTERPOLATION_FACTOR = BigDecimal("24.07")
+    INTERPOLATION_FACTOR = 24.07
 
     # Source:
     #  Title: Practical Astronomy with your Calculator or Spreadsheet

lib/astronoby/coordinates/equatorial.rb

@@ -39,7 +39,7 @@ def to_horizontal(time:, latitude:, longitude:)
         azimuth = Angle.acos(t2)
 
         if ha.sin.positive?
-          azimuth = Angle.from_degrees(BigDecimal("360") - azimuth.degrees)
+          azimuth = Angle.from_degrees(360 - azimuth.degrees)
         end
 
         Horizontal.new(

lib/astronoby/coordinates/horizontal.rb

@@ -31,7 +31,7 @@ def to_equatorial(time:)
 
         if @azimuth.sin.positive?
           hour_angle_degrees = Angle
-            .from_degrees(BigDecimal("360") - hour_angle_degrees)
+            .from_degrees(360 - hour_angle_degrees)
             .degrees
         end
 

lib/astronoby/geocentric_parallax.rb

@@ -9,8 +9,8 @@ class GeocentricParallax
     #  Chapter: 39 - Calculating correction for parallax
 
     ASTRONOMICAL_UNIT_IN_METERS = 149_597_870_700
-    EARTH_FLATTENING_CORRECTION = BigDecimal("0.996647")
-    EARTH_EQUATORIAL_RADIUS = BigDecimal("6378140")
+    EARTH_FLATTENING_CORRECTION = 0.996647
+    EARTH_EQUATORIAL_RADIUS = 6378140.0
 
     # Equatorial horizontal parallax
     # @param distance [Numeric] Distance of the body from the center of the

lib/astronoby/observer.rb

@@ -3,12 +3,12 @@
 module Astronoby
   class Observer
     DEFAULT_ELEVATION = 0
-    DEFAULT_TEMPERATURE = BigDecimal("283.15")
-    PRESSURE_AT_SEA_LEVEL = BigDecimal("1013.25")
-    PASCAL_PER_MILLIBAR = BigDecimal("0.01")
-    EARTH_GRAVITATIONAL_ACCELERATION = BigDecimal("9.80665")
-    MOLAR_MASS_OF_AIR = BigDecimal("0.0289644")
-    UNIVERSAL_GAS_CONSTANT = BigDecimal("8.31432")
+    DEFAULT_TEMPERATURE = 283.15
+    PRESSURE_AT_SEA_LEVEL = 1013.25
+    PASCAL_PER_MILLIBAR = 0.01
+    EARTH_GRAVITATIONAL_ACCELERATION = 9.80665
+    MOLAR_MASS_OF_AIR = 0.0289644
+    UNIVERSAL_GAS_CONSTANT = 8.31432
 
     attr_reader :latitude, :longitude, :elevation, :temperature
 
@@ -37,7 +37,7 @@ def initialize(
     # Compute an estimation of the atmospheric pressure based on the elevation
     # and temperature
     #
-    # @return [BigDecimal] the atmospheric pressure in millibars.
+    # @return [Float] the atmospheric pressure in millibars.
     def pressure
       @pressure ||= PRESSURE_AT_SEA_LEVEL * pressure_ratio
     end

lib/astronoby/time/greenwich_sidereal_time.rb

@@ -3,9 +3,9 @@
 module Astronoby
   class GreenwichSiderealTime
     JULIAN_CENTURIES_EXPONENTS = [
-      BigDecimal("6.697374558"),
-      BigDecimal("2400.051336"),
-      BigDecimal("0.000025862")
+      6.697374558,
+      2400.051336,
+      0.000025862
     ].freeze
 
     attr_reader :date, :time
@@ -29,7 +29,7 @@ def self.from_utc(utc)
         utc.min / 60.0 +
         (utc.sec + utc.subsec) / 3600.0
 
-      gmst = BigDecimal("1.002737909") * ut_in_hours + t0
+      gmst = 1.002737909 * ut_in_hours + t0
       gmst += 24 if gmst.negative?
       gmst -= 24 if gmst > 24
 
@@ -61,7 +61,7 @@ def to_utc
       a += 24 if a.negative?
       a -= 24 if a > 24
 
-      utc = BigDecimal("0.9972695663") * a
+      utc = 0.9972695663 * a
 
       decimal_hour_to_time(date, utc)
     end

lib/astronoby/util/trigonometry.rb

@@ -1,7 +1,5 @@
 # frozen_string_literal: true
 
-require "bigdecimal/math"
-
 module Astronoby
   module Util
     module Trigonometry