Add more Machin-like formulae for computing π

Samayel · Nov 24, 2015 · 1122e6a · 1122e6a
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Showing 2 changed files with 28 additions and 16 deletions.
diff --git a/src/Math/Series/pi_machin.jl b/src/Math/Series/pi_machin.jl
@@ -2,16 +2,20 @@ module Machin
 
 using Brainstorm.Math.Series.Arctan: arctansum
 
-euler(digits::Integer)   = arctansum(digits, [2,   3], 4*[1,  1])
-hermann(digits::Integer) = arctansum(digits, [2,   7], 4*[2, -1])
-hutton(digits::Integer)  = arctansum(digits, [3,   7], 4*[2,  1])
-machin(digits::Integer)  = arctansum(digits, [5, 239], 4*[4, -1])
+euler(digits::Integer)           = arctansum(digits, [2,   3], 4*[1,  1])
+hermann(digits::Integer)         = arctansum(digits, [2,   7], 4*[2, -1])
+hutton(digits::Integer)          = arctansum(digits, [3,   7], 4*[2,  1])
+machin(digits::Integer)          = arctansum(digits, [5, 239], 4*[4, -1])
 
-gauss(digits::Integer)        = arctansum(digits, [18, 57, 239], 4*[12, 8, -5])
-strassnitzky(digits::Integer) = arctansum(digits, [ 2,  5,   8], 4*[ 1, 1,  1])
+gauss(digits::Integer)           = arctansum(digits, [18,  57,  239], 4*[12,  8, -5])
+strassnitzky(digits::Integer)    = arctansum(digits, [ 2,   5,    8], 4*[ 1,  1,  1])
+klingenstierna(digits::Integer)  = arctansum(digits, [10, 239,  515], 4*[ 8, -1, -4])
+euler3(digits::Integer)          = arctansum(digits, [ 5,  70,   99], 4*[ 4, -1,  1])
+loney(digits::Integer)           = arctansum(digits, [ 4,  20, 1985], 4*[ 3,  1,  1])
+stoermer(digits::Integer)        = arctansum(digits, [ 8,  57,  239], 4*[ 6,  2,  1])
 
-takano1982(digits::Integer)   = arctansum(digits, [49, 57, 239, 110443], 4*[12, 32,  -5, 12])
-stoermer1896(digits::Integer) = arctansum(digits, [57, 239, 682, 12943], 4*[44,  7, -12, 24])
+takano1982(digits::Integer)      = arctansum(digits, [49, 57, 239, 110443], 4*[12, 32,  -5, 12])
+stoermer1896(digits::Integer)    = arctansum(digits, [57, 239, 682, 12943], 4*[44,  7, -12, 24])
 
 hwang1997(digits::Integer)       = arctansum(digits, [239, 1023, 5832, 110443, 4841182, 6826318], 4*[183, 32, -68, 12, -12, -100])
 hwang2003(digits::Integer)       = arctansum(digits, BigInt[239, 1023, 5832, 113021, 6826318, 33366019650, 43599522992503626068], 4*[183, 32, -68, 12, -100, -12, 12])

diff --git a/test/Math/Series/pi.jl b/test/Math/Series/pi.jl
@@ -11,16 +11,20 @@ function test_pi_chudnovsky()
 end
 
 function test_pi_machin()
-    euler   = Brainstorm.Math.Series.Pi.Machin.euler
-    hermann = Brainstorm.Math.Series.Pi.Machin.hermann
-    hutton  = Brainstorm.Math.Series.Pi.Machin.hutton
-    machin  = Brainstorm.Math.Series.Pi.Machin.machin
+    euler           = Brainstorm.Math.Series.Pi.Machin.euler
+    hermann         = Brainstorm.Math.Series.Pi.Machin.hermann
+    hutton          = Brainstorm.Math.Series.Pi.Machin.hutton
+    machin          = Brainstorm.Math.Series.Pi.Machin.machin
 
-    gauss        = Brainstorm.Math.Series.Pi.Machin.gauss
-    strassnitzky = Brainstorm.Math.Series.Pi.Machin.strassnitzky
+    gauss           = Brainstorm.Math.Series.Pi.Machin.gauss
+    strassnitzky    = Brainstorm.Math.Series.Pi.Machin.strassnitzky
+    klingenstierna  = Brainstorm.Math.Series.Pi.Machin.klingenstierna
+    euler3          = Brainstorm.Math.Series.Pi.Machin.euler3
+    loney           = Brainstorm.Math.Series.Pi.Machin.loney
+    stoermer        = Brainstorm.Math.Series.Pi.Machin.stoermer
 
-    takano1982   = Brainstorm.Math.Series.Pi.Machin.takano1982
-    stoermer1896 = Brainstorm.Math.Series.Pi.Machin.stoermer1896
+    takano1982      = Brainstorm.Math.Series.Pi.Machin.takano1982
+    stoermer1896    = Brainstorm.Math.Series.Pi.Machin.stoermer1896
 
     hwang1997       = Brainstorm.Math.Series.Pi.Machin.hwang1997
     hwang2003       = Brainstorm.Math.Series.Pi.Machin.hwang2003
@@ -36,6 +40,10 @@ function test_pi_machin()
 
         @test all([gauss(d)           for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
         @test all([strassnitzky(d)    for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
+        @test all([klingenstierna(d)  for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
+        @test all([euler3(d)          for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
+        @test all([loney(d)           for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
+        @test all([stoermer(d)        for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
 
         @test all([takano1982(d)      for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)
         @test all([stoermer1896(d)    for d in (1, 10, 100, 1_000, 10_000)] - expected .== 0)