Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,41 +0,0 @@
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function Gamma (X : Long_Float) return Long_Float is
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A : constant array (0..29) of Long_Float :=
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( 1.00000_00000_00000_00000,
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0.57721_56649_01532_86061,
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-0.65587_80715_20253_88108,
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-0.04200_26350_34095_23553,
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0.16653_86113_82291_48950,
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-0.04219_77345_55544_33675,
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-0.00962_19715_27876_97356,
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0.00721_89432_46663_09954,
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-0.00116_51675_91859_06511,
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-0.00021_52416_74114_95097,
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0.00012_80502_82388_11619,
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-0.00002_01348_54780_78824,
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-0.00000_12504_93482_14267,
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0.00000_11330_27231_98170,
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-0.00000_02056_33841_69776,
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0.00000_00061_16095_10448,
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0.00000_00050_02007_64447,
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-0.00000_00011_81274_57049,
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0.00000_00001_04342_67117,
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0.00000_00000_07782_26344,
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-0.00000_00000_03696_80562,
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0.00000_00000_00510_03703,
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-0.00000_00000_00020_58326,
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-0.00000_00000_00005_34812,
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0.00000_00000_00001_22678,
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-0.00000_00000_00000_11813,
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0.00000_00000_00000_00119,
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0.00000_00000_00000_00141,
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-0.00000_00000_00000_00023,
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0.00000_00000_00000_00002
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);
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Y : constant Long_Float := X - 1.0;
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Sum : Long_Float := A (A'Last);
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begin
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for N in reverse A'First..A'Last - 1 loop
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Sum := Sum * Y + A (N);
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end loop;
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return 1.0 / Sum;
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end Gamma;
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@ -1,9 +0,0 @@
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with Ada.Text_IO; use Ada.Text_IO;
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with Gamma;
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procedure Test_Gamma is
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begin
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for I in 1..10 loop
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Put_Line (Long_Float'Image (Gamma (Long_Float (I) / 3.0)));
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end loop;
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end Test_Gamma;
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@ -20,13 +20,17 @@ ourGamma: function [x][
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return result
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]
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print repeat "-" 100
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loop 1..10 'z [
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v1: ourGamma z // 3
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v2: gamma z // 3
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print [
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pad (to :string z)++" =>" 10
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pad (to :string z)++" =>" 6
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pad (to :string v1)++" ~" 30
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pad (to :string v2)++" :" 30
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pad (to :string v1-v2) 30
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]
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]
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print repeat "-" 100
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@ -1,76 +0,0 @@
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program GammaTest;
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{$mode objfpc}{$H+}
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uses SysUtils;
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function Gamma( x : extended) : extended;
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const COF : array [0..14] of extended =
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( 0.999999999999997092, // may as well include this in the array
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57.1562356658629235,
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-59.5979603554754912,
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14.1360979747417471,
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-0.491913816097620199,
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0.339946499848118887e-4,
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0.465236289270485756e-4,
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-0.983744753048795646e-4,
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0.158088703224912494e-3,
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-0.210264441724104883e-3,
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0.217439618115212643e-3,
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-0.164318106536763890e-3,
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0.844182239838527433e-4,
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-0.261908384015814087e-4,
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0.368991826595316234e-5);
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const
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K = 2.5066282746310005;
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PI_OVER_K = PI / K;
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var
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j : integer;
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tmp, w, ser : extended;
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reflect : boolean;
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begin
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reflect := (x < 0.5);
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if reflect then w := 1.0 - x else w := x;
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tmp := w + 5.2421875;
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tmp := (w + 0.5)*Ln(tmp) - tmp;
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ser := COF[0];
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for j := 1 to 14 do ser := ser + COF[j]/(w + j);
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try
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if reflect then
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result := PI_OVER_K * w * Exp(-tmp) / (Sin(PI*x) * ser)
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else
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result := K * Exp(tmp) * ser / w;
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except
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raise SysUtils.Exception.CreateFmt(
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'Gamma(%g) is undefined or out of floating-point range', [x]);
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end;
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end;
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// Main routine for testing the Gamma function
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var
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x, k : extended;
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begin
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WriteLn( 'Is it seamless at x = 1/2 ?');
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x := 0.49999999999999;
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WriteLn( SysUtils.Format( 'Gamma(%g) = %g', [x, Gamma(x)]));
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x := 0.50000000000001;
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WriteLn( SysUtils.Format( 'Gamma(%g) = %g', [x, Gamma(x)]));
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WriteLn( 'Test a few values:');
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WriteLn( SysUtils.Format( 'Gamma(1) = %g', [Gamma(1)]));
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WriteLn( SysUtils.Format( 'Gamma(2) = %g', [Gamma(2)]));
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WriteLn( SysUtils.Format( 'Gamma(3) = %g', [Gamma(3)]));
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WriteLn( SysUtils.Format( 'Gamma(10) = %g', [Gamma(10)]));
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WriteLn( SysUtils.Format( 'Gamma(101) = %g', [Gamma(101)]));
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WriteLn( ' 100! = 9.33262154439442E157');
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WriteLn( SysUtils.Format( 'Gamma(1/2) = %g', [Gamma(0.5)]));
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WriteLn( SysUtils.Format( 'Sqrt(pi) = %g', [Sqrt(PI)]));
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WriteLn( SysUtils.Format( 'Gamma(-7/2) = %g', [Gamma(-3.5)]));
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(*
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Note here a bug or misfeature in Lazarus (doesn't occur in Delphi):
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Putting (16.0/105.0)*Sqrt(PI) does not give the required precision.
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We have to explicitly define the integers as extended floating-point.
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*)
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k := extended(16.0)/extended(105.0);
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WriteLn( SysUtils.Format( ' (16/105)Sqrt(pi) = %g', [k*Sqrt(PI)]));
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WriteLn( SysUtils.Format( 'Gamma(-9/2) = %g', [Gamma(-4.5)]));
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k := extended(32.0)/extended(945.0);
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WriteLn( SysUtils.Format( '-(32/945)Sqrt(pi) = %g', [-k*Sqrt(PI)]));
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end.
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@ -1,116 +1,114 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">accm</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- (k - 1)!*(-1)^k with 0!==1</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">k1_factrl</span>
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<span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">accm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]/(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #000000;">accm</span> <span style="color: #0000FF;">*=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">))*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Gamma(z+1)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">/</span><span style="color: #000000;">z</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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sequence c = repeat(0,12)
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function spouge_gamma(atom z)
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atom accm = c[1]
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if accm=0 then
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accm = sqrt(2*PI)
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c[1] = accm
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atom k1_factrl = 1 -- (k - 1)!*(-1)^k with 0!==1
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for k=2 to 12 do
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c[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl
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k1_factrl *= -(k-1)
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end for
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end if
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for k=2 to 12 do
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accm += c[k]/(z+k-1)
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end for
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accm *= exp(-(z+12))*power(z+12,z+0.5) -- Gamma(z+1)
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return accm/z
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">taylor_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- (good for values between 0 and 1, apparently)</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">1.00000_00000_00000_00000</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.57721_56649_01532_86061</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.65587_80715_20253_88108</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.04200_26350_34095_23553</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.16653_86113_82291_48950</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.04219_77345_55544_33675</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00962_19715_27876_97356</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00721_89432_46663_09954</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00116_51675_91859_06511</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00021_52416_74114_95097</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00012_80502_82388_11619</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00002_01348_54780_78824</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_12504_93482_14267</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_11330_27231_98170</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_02056_33841_69776</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00061_16095_10448</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00050_02007_64447</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00011_81274_57049</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00001_04342_67117</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_07782_26344</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_03696_80562</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_00510_03703</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00020_58326</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00005_34812</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_00001_22678</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00000_11813</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_00000_00119</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_00000_00141</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00000_00023</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">0.00000_00000_00000_00002</span> <span style="color: #0000FF;">}</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[$]</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">s</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function taylor_gamma(atom x)
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-- (good for values between 0 and 1, apparently)
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constant t = { 1.00000_00000_00000_00000,
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0.57721_56649_01532_86061,
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-0.65587_80715_20253_88108,
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-0.04200_26350_34095_23553,
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0.16653_86113_82291_48950,
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-0.04219_77345_55544_33675,
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-0.00962_19715_27876_97356,
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0.00721_89432_46663_09954,
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-0.00116_51675_91859_06511,
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-0.00021_52416_74114_95097,
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0.00012_80502_82388_11619,
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-0.00002_01348_54780_78824,
|
||||
-0.00000_12504_93482_14267,
|
||||
0.00000_11330_27231_98170,
|
||||
-0.00000_02056_33841_69776,
|
||||
0.00000_00061_16095_10448,
|
||||
0.00000_00050_02007_64447,
|
||||
-0.00000_00011_81274_57049,
|
||||
0.00000_00001_04342_67117,
|
||||
0.00000_00000_07782_26344,
|
||||
-0.00000_00000_03696_80562,
|
||||
0.00000_00000_00510_03703,
|
||||
-0.00000_00000_00020_58326,
|
||||
-0.00000_00000_00005_34812,
|
||||
0.00000_00000_00001_22678,
|
||||
-0.00000_00000_00000_11813,
|
||||
0.00000_00000_00000_00119,
|
||||
0.00000_00000_00000_00141,
|
||||
-0.00000_00000_00000_00023,
|
||||
0.00000_00000_00000_00002 }
|
||||
atom y = x-1,
|
||||
s = t[$]
|
||||
for n=length(t)-1 to 1 by -1 do
|
||||
s = s*y + t[n]
|
||||
end for
|
||||
return 1/s
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">z</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0.5</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #004600;">PI</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- use a lanczos approximation:</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.99999999999980993</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">6.5</span><span style="color: #0000FF;">;</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">676.5203681218851</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">-</span><span style="color: #000000;">1259.1392167224028</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">771.32342877765313</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">-</span><span style="color: #000000;">176.61502916214059</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">12.507343278686905</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.13857109526572012</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">9.9843695780195716e-6</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">1.5056327351493116e-7</span> <span style="color: #0000FF;">}</span>
|
||||
<span style="color: #000000;">z</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">z</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">x</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function lanczos_gamma(atom z)
|
||||
if z<0.5 then
|
||||
return PI / (sin(PI*z)*lanczos_gamma(1-z))
|
||||
end if
|
||||
-- use a lanczos approximation:
|
||||
atom x = 0.99999999999980993,
|
||||
t = z + 6.5;
|
||||
sequence p = { 676.5203681218851,
|
||||
-1259.1392167224028,
|
||||
771.32342877765313,
|
||||
-176.61502916214059,
|
||||
12.507343278686905,
|
||||
-0.13857109526572012,
|
||||
9.9843695780195716e-6,
|
||||
1.5056327351493116e-7 }
|
||||
z -= 1
|
||||
for i=1 to length(p) do
|
||||
x += p[i] / (z + i)
|
||||
end for
|
||||
return sqrt(2*PI) * power(t,z+0.5) * exp(-t) * x
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">sqPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
|
||||
constant sqPI = sqrt(PI)
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">sq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zm</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">mul</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">taylor_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)},</span>
|
||||
<span style="color: #000000;">error</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">", "</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">bdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">smallest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">error</span><span style="color: #0000FF;">,</span><span style="color: #000000;">return_index</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bdx</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bdx</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">mul</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (potentially mark >1)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">best</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">22</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">22</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"*,"</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">es</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%5g: %s %s, %19.16f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure sq(sequence zm, string fmt="%19.16f")
|
||||
atom {z, mul} = zm
|
||||
atom e = sqPI/mul
|
||||
sequence s = {spouge_gamma(z),
|
||||
taylor_gamma(z),
|
||||
lanczos_gamma(z)},
|
||||
error = sq_abs(sq_sub(s,e))
|
||||
string t = join(s,", ",fmt:=fmt)&", "
|
||||
integer bdx = smallest(error,return_index:=true)
|
||||
atom best = s[bdx],
|
||||
p = s[bdx]*mul
|
||||
for i=1 to length(s) do -- (potentially mark >1)
|
||||
if s[i]=best then
|
||||
t[i*22-2..i*22-1] = "*,"
|
||||
end if
|
||||
end for
|
||||
string es = sprintf(fmt,e)
|
||||
printf(1,"%5g: %s %s, %19.16f\n",{z,t,es,p*p})
|
||||
end procedure
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" z ------ spouge ----- ----- taylor ------ ----- lanczos ----- ---- expected ----- %19.16f\n"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">/</span><span style="color: #000000;">15</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">sq</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">999.4237725</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.15f"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.01</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">99.43258512</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9.513507699</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.12f"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9.332621544e155</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.13g"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">64</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">150</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3.808922638e260</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.13g"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (fatal power overflow error on 32 bits)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<!--
|
||||
printf(1," z ------ spouge ----- ----- taylor ------ ----- lanczos ----- ---- expected ----- %19.16f\n",PI)
|
||||
papply({{-3/2,3/4},{-1/2,-1/2},{1/2,1},{1,sqPI},{3/2,2},{2,sqPI},{5/2,4/3},{3,sqPI/2},{7/2,8/15},{4,sqPI/6}},sq)
|
||||
sq({0.001,sqPI/999.4237725},"%19.15f")
|
||||
sq({0.01,sqPI/99.43258512},"%19.16f")
|
||||
sq({0.1,sqPI/9.513507699},"%19.16f")
|
||||
sq({10,sqPI/362880},"%19.12f")
|
||||
sq({100,sqPI/9.332621544e155},"%19.13g")
|
||||
if machine_bits()=64 then
|
||||
sq({150,sqPI/3.808922638e260},"%19.13g") -- (fatal power overflow error on 32 bits)
|
||||
end if
|
||||
|
|
|
|||
|
|
@ -1,109 +1,107 @@
|
|||
-->
|
||||
<span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span> <span style="color: #000080;font-style:italic;">-- (no mpfr_exp(), mpfr_gamma() in pwa/p2js)</span>
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">dp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">30</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"%5s: %33s, %33s, %32s\n"</span>
|
||||
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_get_fixed(maxlen), mpfr_gamma)</span>
|
||||
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
|
||||
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">87</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 87 decimal places. </span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">40</span><span style="color: #0000FF;">)</span>
|
||||
without javascript_semantics -- (no mpfr_exp(), mpfr_gamma() in pwa/p2js)
|
||||
constant dp = 30
|
||||
string fmt = "%5s: %33s, %33s, %32s\n"
|
||||
requires("1.0.2") -- (mpfr_get_fixed(maxlen), mpfr_gamma)
|
||||
include mpfr.e
|
||||
mpfr_set_default_precision(-87) -- 87 decimal places.
|
||||
sequence mc = mpfr_inits(40)
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpfr_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000080;font-style:italic;">-- mc[1] := sqrt(2*PI)</span>
|
||||
<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- k1_factrl = (k - 1)!*(-1)^k with 0!==1</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">tmk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
|
||||
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000080;font-style:italic;">-- mc[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl</span>
|
||||
<span style="color: #7060A8;">mpfr_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- k1_factrl *= -(k-1)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,-(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000080;font-style:italic;">-- accm += mc[k]/(z+k-1)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">ck</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]),</span>
|
||||
<span style="color: #000000;">zk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">-- atom zc = z+length(mc)
|
||||
-- accm *= exp(-zc)*power(zc,z+0.5) -- Gamma(z+1)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">ez</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
|
||||
<span style="color: #000000;">zh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #7060A8;">mpfr_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- return accm/z</span>
|
||||
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">accm</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function mpfr_spouge_gamma(mpfr z)
|
||||
mpfr accm = mc[1]
|
||||
if mpfr_cmp_si(accm,0)=0 then
|
||||
-- mc[1] := sqrt(2*PI)
|
||||
mpfr_const_pi(accm)
|
||||
mpfr_mul_si(accm,accm,2)
|
||||
mpfr_sqrt(accm,accm)
|
||||
-- k1_factrl = (k - 1)!*(-1)^k with 0!==1
|
||||
mpfr k1_factrl = mpfr_init(1),
|
||||
tmk = mpfr_init(),
|
||||
p = mpfr_init()
|
||||
for k=2 to length(mc) do
|
||||
-- mc[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl
|
||||
mpfr_set_si(tmk,length(mc)+1-k)
|
||||
mpfr_exp(mc[k],tmk)
|
||||
mpfr_set_d(p,k-1.5)
|
||||
mpfr_pow(p,tmk,p)
|
||||
mpfr_div(p,p,k1_factrl)
|
||||
mpfr_mul(mc[k],mc[k],p)
|
||||
-- k1_factrl *= -(k-1)
|
||||
mpfr_mul_si(k1_factrl,k1_factrl,-(k-1))
|
||||
end for
|
||||
end if
|
||||
accm = mpfr_init_set(accm)
|
||||
for k=2 to length(mc) do
|
||||
-- accm += mc[k]/(z+k-1)
|
||||
mpfr ck = mpfr_init_set(mc[k]),
|
||||
zk = mpfr_init_set(z)
|
||||
mpfr_add_si(zk,zk,k-1)
|
||||
mpfr_div(ck,ck,zk)
|
||||
mpfr_add(accm,accm,ck)
|
||||
end for
|
||||
-- atom zc = z+length(mc)
|
||||
-- accm *= exp(-zc)*power(zc,z+0.5) -- Gamma(z+1)
|
||||
mpfr p = mpfr_init_set(z),
|
||||
ez = mpfr_init(),
|
||||
zh = mpfr_init(0.5)
|
||||
mpfr_add_si(p,p,length(mc))
|
||||
mpfr_neg(ez,p)
|
||||
mpfr_exp(ez,ez)
|
||||
mpfr_add(zh,zh,z)
|
||||
mpfr_pow(p,p,zh)
|
||||
mpfr_mul(accm,accm,ez)
|
||||
mpfr_mul(accm,accm,p)
|
||||
-- return accm/z
|
||||
mpfr_div(accm,accm,z)
|
||||
return accm
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">mPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
|
||||
<span style="color: #000000;">mqPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">pistr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
|
||||
constant mPI = mpfr_init(),
|
||||
mqPI = mpfr_init()
|
||||
mpfr_const_pi(mPI)
|
||||
string pistr = mpfr_get_fixed(mPI,dp)
|
||||
mpfr_sqrt(mqPI,mPI)
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">makempfr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'/'</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #7060A8;">mpfr_div_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">to_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]))</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #7060A8;">mpfr_div_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function makempfr(object x)
|
||||
mpfr res
|
||||
if string(x) then
|
||||
x = split(x,'/')
|
||||
res = mpfr_init(x[1])
|
||||
mpfr_div_si(res,res,to_integer(x[2]))
|
||||
elsif sequence(x) then
|
||||
{mpfr x1, object x2} = x
|
||||
res = mpfr_init_set(x1)
|
||||
if string(x2) then
|
||||
mpfr d = mpfr_init(x2)
|
||||
mpfr_div(res,res,d)
|
||||
else
|
||||
mpfr_div_d(res,res,x2)
|
||||
end if
|
||||
else
|
||||
res = mpfr_init(x)
|
||||
end if
|
||||
return res
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">mq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">makempfr</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #7060A8;">mpfr_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mul</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">zs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">es</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">zs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure mq(sequence zm, integer d=dp)
|
||||
mpfr {z, mul} = apply(zm,makempfr)
|
||||
mpfr s = mpfr_spouge_gamma(z)
|
||||
string t = mpfr_get_fixed(s,d,10,maxlen:=dp+2)
|
||||
mpfr e = mpfr_init()
|
||||
mpfr_gamma(e,z)
|
||||
mpfr p = mpfr_init_set(s)
|
||||
mpfr_mul(p,p,mul)
|
||||
mpfr_mul(p,p,p)
|
||||
string zs = mpfr_get_fixed(z,3),
|
||||
es = mpfr_get_fixed(e,d,10,maxlen:=dp+2),
|
||||
ps = mpfr_get_fixed(p,dp,10)
|
||||
printf(1,fmt,{zs,t,es,ps})
|
||||
end procedure
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" z %s %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" spouge "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" expected "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #000000;">pistr</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.75</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">2.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"4/3"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">3.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"8/15"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}},</span><span style="color: #000000;">mq</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/1000"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"999.4237724845954661149822012996"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/100"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"99.43258511915060371353298887051"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">29</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/10"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.513507698668731836292487177265"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">25</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.332621544394415268169923885627e155"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">150</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"3.80892263763056972698595524350735e260"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
printf(1," z %s %s %s\n",{pad(" spouge ",dp+2,"BOTH",'-'),pad(" expected ",dp+2,"BOTH",'-'),pistr})
|
||||
papply({{-1.5,0.75},{-0.5,-0.5},{0.5,1},{1,{mqPI,1}},{1.5,2},{2,{mqPI,1}},{2.5,"4/3"},{3,{mqPI,2}},{3.5,"8/15"},{4,{mqPI,6}}},mq)
|
||||
mq({"1/1000",{mqPI,"999.4237724845954661149822012996"}},28)
|
||||
mq({"1/100",{mqPI,"99.43258511915060371353298887051"}},29)
|
||||
mq({"1/10",{mqPI,"9.513507698668731836292487177265"}},30)
|
||||
mq({10,{mqPI,362880}},25)
|
||||
mq({100,{mqPI,"9.332621544394415268169923885627e155"}},0)
|
||||
mq({150,{mqPI,"3.80892263763056972698595524350735e260"}},0)
|
||||
|
|
|
|||
|
|
@ -1,3 +0,0 @@
|
|||
Add-Type -Path "C:\Program Files (x86)\Math\MathNet.Numerics.3.12.0\lib\net40\MathNet.Numerics.dll"
|
||||
|
||||
1..20 | ForEach-Object {[MathNet.Numerics.SpecialFunctions]::Gamma($_ / 10)}
|
||||
|
|
@ -1,5 +1,5 @@
|
|||
-- 28 Jul 2025
|
||||
include Settings
|
||||
-- 23 Aug 2025
|
||||
include Setting
|
||||
arg n
|
||||
if n = '' then
|
||||
n = 100
|
||||
|
|
|
|||
|
|
@ -1,50 +0,0 @@
|
|||
function real Gamma (X);
|
||||
real X, A, Y, Sum;
|
||||
integer N;
|
||||
begin
|
||||
A \constant array (0..29) of Long_Float\ :=
|
||||
[ 1.00000_00000_00000_00000,
|
||||
0.57721_56649_01532_86061,
|
||||
-0.65587_80715_20253_88108,
|
||||
-0.04200_26350_34095_23553,
|
||||
0.16653_86113_82291_48950,
|
||||
-0.04219_77345_55544_33675,
|
||||
-0.00962_19715_27876_97356,
|
||||
0.00721_89432_46663_09954,
|
||||
-0.00116_51675_91859_06511,
|
||||
-0.00021_52416_74114_95097,
|
||||
0.00012_80502_82388_11619,
|
||||
-0.00002_01348_54780_78824,
|
||||
-0.00000_12504_93482_14267,
|
||||
0.00000_11330_27231_98170,
|
||||
-0.00000_02056_33841_69776,
|
||||
0.00000_00061_16095_10448,
|
||||
0.00000_00050_02007_64447,
|
||||
-0.00000_00011_81274_57049,
|
||||
0.00000_00001_04342_67117,
|
||||
0.00000_00000_07782_26344,
|
||||
-0.00000_00000_03696_80562,
|
||||
0.00000_00000_00510_03703,
|
||||
-0.00000_00000_00020_58326,
|
||||
-0.00000_00000_00005_34812,
|
||||
0.00000_00000_00001_22678,
|
||||
-0.00000_00000_00000_11813,
|
||||
0.00000_00000_00000_00119,
|
||||
0.00000_00000_00000_00141,
|
||||
-0.00000_00000_00000_00023,
|
||||
0.00000_00000_00000_00002
|
||||
];
|
||||
Y := X - 1.0;
|
||||
Sum := A (29);
|
||||
for N:= 29-1 downto 0 do
|
||||
Sum := Sum * Y + A (N);
|
||||
return 1.0 / Sum;
|
||||
end \Gamma\;
|
||||
|
||||
\Test program:
|
||||
integer I;
|
||||
begin
|
||||
Format(0, 14);
|
||||
for I:= 1 to 10 do
|
||||
[RlOut(0, Gamma (Float (I) / 3.0)); CrLf(0)];
|
||||
end
|
||||
Loading…
Add table
Add a link
Reference in a new issue