decfloat 2.0

[bplus]

if someone were to actually use this

I have this thread book marked to return to later to study more closely.

Is the Bernoulli thing for his equation used in physics for fluid flow?

[jack]

bplus, the example program simply computes the Bernoulli numbers, as you may know the numbers come up frequently in power series, aside from that I don't know.
but thank you for your interest :-)
here's a Float version, should be easier to follow the flow
notice how quickly the numbers become inaccurate

Code: QB64: [Select]

1. Dim As String f: f = "###  ####.############"
2. Print "  Bn      computed"
3. Const n = 20
4. Dim As Long i, j
5. Dim As _Float b(0 To n)
6. For i = 0 To n
7.     b(i) = 1 / (i + 1)
8.     For j = i To 1 Step -1
9.         b(j - 1) = j * (b(j - 1) - b(j))
10.     Next j
11.     Print Using f; i; b(0)
12. Next i
13.  

[bplus]

the example program simply computes the Bernoulli numbers, as you may know the numbers come up frequently in power series,

Ah even better, always liked Taylor series. That was how I was going to do higher functions for String Math.

[jack]

did a major upgrade, fixed several bugs and renamed the sub's and functions to be easier to remember
added trig functions see https://www.qb64.org/forum/index.php?topic=4276.msg136873#msg136873
list of sub's/functions

Code: [Select]

Sub fpadd (result As decfloat, x As decfloat, y As decfloat, digits_in As Long)
Sub fpsub (result As decfloat, x As decfloat, y As decfloat, digits_in As Long)
Sub fpmul (result As decfloat, x As decfloat, y As decfloat, digits_in As Long)
Sub fpmul_si (result As decfloat, x As decfloat, y As Integer64, digits_in As Long)
Sub fpdiv (result As decfloat, x As decfloat, y As decfloat, digits_in As Long)
Sub fpdiv_si (result As decfloat, num As decfloat, den As Long, digits_in As Long)
Sub fpinv (result As decfloat, m As decfloat, digits_in As Long)
Sub fpipow (result As decfloat, x As decfloat, e As Integer64, digits_in As Long)
Sub fppow (result As decfloat, lhs As decfloat, rhs As decfloat)
Sub fpnroot (result As decfloat, x As decfloat, p As Long, digits_in As Long)
Sub fpsqr (result As decfloat, num As decfloat, digits_in As Long)
Sub fplog (result As decfloat, x As decfloat, digits_in As Long)
Sub fpexp (result As decfloat, x As decfloat, digits_in As Long)
Sub fpsin (result As decfloat, x As decfloat, digits_in As Unsigned Long)
Sub fpcos (result As decfloat, z As decfloat, digits_in As Unsigned Long)
Sub fptan (result As decfloat, z As decfloat, digits_in As Unsigned Long)
Sub fpasin (result As decfloat, x As decfloat, digits_in As Unsigned Long)
Sub fpacos (result As decfloat, x As decfloat, digits_in As Unsigned Long)
Sub fpatn (result As decfloat, x As decfloat, digits_in As Unsigned Long)
Sub fpabs (result As decfloat, n As decfloat)
Sub fpneg (result As decfloat, n As decfloat)
Sub fpfix (result As decfloat, num As decfloat)
Sub fpfrac (result As decfloat, num As decfloat, digits_in As Long)

Sub si2fp (result As decfloat, m As Integer64, digits_in As Long)
Sub str2fp (result As decfloat, value As String)
Function fp2dbl# (n As decfloat)
Function fp2str$ (n As decfloat, places As Long)
Function fp2str_exp$ (n As decfloat, places As Long)
Function fp2str_fix$ (n As decfloat, places As Long)


[jack]

here's a program that calculates the first and last 40 digits of insanely huge Fibonacci numbers, in this example it's for Fibonacci( 2 ^ 1024)
the fib program is based on a program in page 14 of this document https://www.uni-math.gwdg.de/tschinkel/gauss/Fibon.pdf
result on my PC
you will need the bi and bm from  https://www.qb64.org/forum/index.php?topic=4276.msg136873#msg136873

Code: [Select]

2116996771162424982619007079477296709285
 5727677983280861229066251547465117987387
 4.023000000001048


Code: QB64: [Select]

1. 'you must use $NoPrefix
2. $NoPrefix
3. $Console:Only
4. Dest Console
5.  
6. Option Explicit
7.  
8. Const NUMBER_OF_DIGITS = 620 ' you must have NUMBER_OF_DIGITS defined -- not to exceed 1024
9. '                             before including decfloat.bi
10. '$include: 'decfloat.bi'
11.  
12. '======================================================================
13. ' your code follows
14.  
15. Dim As decfloat first, last, fn, m, x, y, z, v
16. Dim As String s
17. Dim As Double t
18. Dim As Long dp
19. t = Timer(.001)
20. 'str2fp fn, "4784969" ' "4784969"
21. si2fp fn, 2, NUM_DWORDS
22. fpipow fn, fn, 1024, NUM_DWORDS
23. str2fp m, "10000000000000000000000000000000000000000"
24. si2fp x, 5, NUM_DWORDS
25. fpsqr x, x, NUM_DWORDS
26. si2fp z, 1, NUM_DWORDS
27. fpadd y, x, z, NUM_DWORDS
28. fpdiv_si y, y, 2, NUM_DWORDS
29. fplog y, y, NUM_DWORDS
30. fpmul y, y, fn, NUM_DWORDS
31. fplog z, x, NUM_DWORDS
32. fpsub y, y, z, NUM_DWORDS
33. si2fp x, 10, NUM_DWORDS
34. fplog v, x, NUM_DWORDS
35. fpdiv y, y, v, NUM_DWORDS
36. fpfrac z, y, NUM_DWORDS
37. fppow y, x, z
38. s = fp2str(y, 40)
39. dp = InStr(s, ".")
40. s = Left$(s, dp - 1) + Mid$(s, dp + 1)
41. Print s
42. fib fn, m, last
43. t = Timer - t
44. s = fp2str(last, NUMBER_OF_DIGITS)
45. dp = InStr(s, ".")
46. Print Left$(s, dp - 1)
47. Print t
48.  
49.  
50. Sub fib (k As decfloat, m As decfloat, fibonacci As decfloat)
51.     Dim As decfloat b, x, y, xx, temp, tmp, rn
52.     Dim As Long i, bit_length
53.     str2fp rn, ".05"
54.     si2fp tmp, 1, NUM_DWORDS
55.     If fpcmp(k, tmp, NUM_DWORDS) <= 0 Then
56.         fibonacci = k
57.         Exit Sub
58.     End If
59.     si2fp x, 1, NUM_DWORDS
60.     si2fp y, 0, NUM_DWORDS
61.     fplog tmp, k, NUM_DWORDS
62.     si2fp temp, 2, NUM_DWORDS
63.     fplog xx, temp, NUM_DWORDS
64.     fpdiv b, tmp, xx, NUM_DWORDS
65.     fpfix tmp, b
66.     bit_length = fp2dbl(tmp)
67.     si2fp b, 2, NUM_DWORDS
68.     fpipow b, b, bit_length - 1, NUM_DWORDS
69.     For i = bit_length - 1 To 0 Step -1
70.         fpmul xx, x, x, NUM_DWORDS
71.         fpdiv xx, xx, m, NUM_DWORDS
72.         fpfrac xx, xx, NUM_DWORDS
73.         fpmul xx, xx, m, NUM_DWORDS
74.         fpadd xx, xx, rn, NUM_DWORDS
75.         fpfix xx, xx
76.         fpmul x, x, y, NUM_DWORDS
77.         fpmul_si x, x, 2, NUM_DWORDS
78.         fpadd x, xx, x, NUM_DWORDS
79.         fpdiv x, x, m, NUM_DWORDS
80.         fpfrac x, x, NUM_DWORDS
81.         fpmul x, x, m, NUM_DWORDS
82.         fpadd x, x, rn, NUM_DWORDS
83.         fpfix x, x
84.         fpmul y, y, y, NUM_DWORDS
85.         fpadd y, y, xx, NUM_DWORDS
86.         fpdiv y, y, m, NUM_DWORDS
87.         fpfrac y, y, NUM_DWORDS
88.         fpmul y, y, m, NUM_DWORDS
89.         fpadd y, y, rn, NUM_DWORDS
90.         fpfix y, y
91.         fpdiv temp, k, b, NUM_DWORDS
92.         If fpfix_is_odd(temp) Then
93.             temp = x
94.             fpadd x, x, y, NUM_DWORDS
95.             fpdiv x, x, m, NUM_DWORDS
96.             fpfrac x, x, NUM_DWORDS
97.             fpmul x, x, m, NUM_DWORDS
98.             fpadd x, x, rn, NUM_DWORDS
99.             fpfix x, x
100.             y = temp
101.         End If
102.         fpdiv_si b, b, 2, NUM_DWORDS
103.     Next
104.     fibonacci = x
105. End Sub
106.  
107. ' end of your code
108. ' you must include decfloat.bm
109. '$include: 'decfloat.bm'
110.