From aafd6b025cdd52c3ef97796a6dc2bda02011f670 Mon Sep 17 00:00:00 2001 From: shigek Date: Fri, 25 Jul 2003 02:26:56 +0000 Subject: ver method added. Spec for div changed. add,sub,mult,div now can specify exact digits number. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@4153 b2dd03c8-39d4-4d8f-98ff-823fe69b080e --- ext/bigdecimal/bigdecimal_en.html | 80 ++++++++++++++++++++++----------------- 1 file changed, 46 insertions(+), 34 deletions(-) (limited to 'ext/bigdecimal/bigdecimal_en.html') diff --git a/ext/bigdecimal/bigdecimal_en.html b/ext/bigdecimal/bigdecimal_en.html index cfdff51f79..ed192fca58 100644 --- a/ext/bigdecimal/bigdecimal_en.html +++ b/ext/bigdecimal/bigdecimal_en.html @@ -108,13 +108,13 @@ where:
s: Initial value string.
n: Maximum number of significant digits of a. n must be a Fixnum object. If n is omitted or is equal to 0,then the maximum number of significant digits of a is determined from the length of s. +Actual number of digits handled in computations are usually gretaer than n.
n is useful when performing divisions like 
 BigDecimal("1")    / BigDecimal("3")    # => 0.3333333333 33E0
 BigDecimal("1",10) / BigDecimal("3",10) # => 0.3333333333 3333333333 33333333E0
-but the result may differ in future version. - +but the resulting digits obtained may differ in future version.
  • mode
    • @@ -168,14 +168,17 @@ where flag must be one of: nil is returned if any argument is illegal.
    The digit location for rounding operation can not be specified by mode method, -use truncate/round/ceil/floor mthods for each instance instead. - +use truncate/round/ceil/floor/add/sub/mult/div mthods for each instance instead.
  • limit[(n)]
    • Limits the maximum digits that the newly created BigDecimal objects can hold -never exceed n. Returns maximum value before set. +never exceed n+? (Currently,? can not be determined beforehand,but not so big). +This means the rounding operation specified by BigDecimal.mode is +performed if necessary. +limit returns maximum value before set. Zero,the default value,means no upper limit.
    +Except for zero,the limit has more priority than instance methods such as truncate,round,ceil,floor,add,sub,mult,and div.
    mf = BigDecimal::limit(n)
    @@ -230,31 +233,28 @@ For the resulting number of significant digits of c,see Resultin c = a.add(b,n)
    c = a.add(b,n) performs c = a + b. If n is less than the actual significant digits of a + b, -then c is rounded properly. +then c is rounded properly according to the BigDecimal.limit.
  • sub
    • c = a.sub(b,n)
    c = a.sub(b,n) performs c = a - b. If n is less than the actual significant digits of a - b, -then c is rounded properly. +then c is rounded properly according to the BigDecimal.limit.
  • mult
    • c = a.mult(b,n)
    c = a.mult(b,n) performs c = a * b. If n is less than the actual significant digits of a * b, -then c is rounded properly. +then c is rounded properly according to the BigDecimal.limit.
  • div
    • -c,r = a.div(b,n)
    -c,r = a.div(b,n) performs c = a / b, r is the residue of a / b. -If necessary,the divide operation continues to n digits which c - can hold. -Unlike the divmod method,c is not always an integer. -c is never rounded,and the equation a = c*b + r is always -valid unless c is NaN or Infinity. +c = a.div(b,n)
    +c = a.div(b,n) performs c = a / b. +If n is less than the actual significant digits of a / b, +then c is rounded properly according to the BigDecimal.limit.
  • %
    • @@ -724,32 +724,40 @@ maximum significant digits of both side of the operator.
    For example, c has more than 100 siginificant digits if c is computed as:
    c = 0.1+0.1*10**(-100)

    -As +,-,and * are always exact(no round operation is performed), +As +,-,and * are always exact(no round operation is performed unless BigDecimal.limit is specified), which means more momories are required to keep computation results. - -Division such as c=1.0/3.0 will be rounded.
    +But,the division such as c=1.0/3.0 will always be rounded.

    2. assign,add,sub,mult,div

    The length of the significant digits obtained from +,-,*,/ is always defined by that of right and left side of the operator. To specify the length of the significant digits by your self, -use methos assign,add,sub,mult,div, or limit(class method). +use methos assign,add,sub,mult,div. +
    + BigDecimal("2").div(3,12) # 2.0/3.0 => 0.6666666666 67E0
+
     +
    + +

    3. truncate,round,ceil,floor

    +Using these methods,you can specify rounding location relatively from +decimal point. +
    + BigDecimal("6.66666666666666").round(12) # => 0.6666666666 667E1
+
     + + + +

    4. Example

    Following example compute the ratio of the circumference of a circle to its dirmeter(pi=3.14159265358979....) using J.Machin's formula. 

     #!/usr/local/bin/ruby
 
-#
-# pi.rb
-#  USAGE: ruby pi.rb n
-#   where n is the number of digits required.
-#  EX.: ruby pi.rb 1000
-#
-
 require "bigdecimal"
 #
-# Calculates 3.1415.... using J. Machin's formula.
+# Calculates 3.1415.... (the number of times that a circle's diameter
+# will fit around the circle) using J. Machin's formula.
 #
 def big_pi(sig) # sig: Number of significant figures
   exp    = -sig
@@ -762,9 +770,9 @@ def big_pi(sig) # sig: Number of significant figures
   k = BigDecimal::new("1")
   w = BigDecimal::new("1")
   t = BigDecimal::new("-80")
-  while (u.exponent >= exp) 
+  while (u.nonzero? && u.exponent >= exp) 
     t   = t*m25
-    u,r = t.div(k,sig)
+    u   = t.div(k,sig)
     pi  = pi + u
     k   = k+two
   end
@@ -773,9 +781,9 @@ def big_pi(sig) # sig: Number of significant figures
   k = BigDecimal::new("1")
   w = BigDecimal::new("1")
   t = BigDecimal::new("956")
-  while (u.exponent >= exp )
-    t,r = t.div(m57121,sig)
-    u,r = t.div(k,sig)
+  while (u.nonzero? && u.exponent >= exp )
+    t   = t.div(m57121,sig)
+    u   = t.div(k,sig)
     pi  = pi + u
     k   = k+two
   end
@@ -783,8 +791,12 @@ def big_pi(sig) # sig: Number of significant figures
 end
 
 if $0 == __FILE__
-  print "PI("+ARGV[0]+"):\n"
-  p pi(ARGV[0].to_i)
+  if ARGV.size == 1
+    print "PI("+ARGV[0]+"):\n"
+    p big_pi(ARGV[0].to_i)
+  else
+    print "TRY: ruby pi.rb 1000 \n"
+  end
 end
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