String Math

[Pete]

My advice would be to pick any one of the many methods available, especially one you're comfortable with, and get it coded. I looked into it a while back, but I would extended my project into the time I wanted reserved for other projects. I mean square roots... and then... log, sine, cosign, etc. The list can get pretty long. I'm glad to see more bells and whistles are going into string math, as I do believe it is a valuable project for anyone who wants to work with very large figures, like Jenny Craig.

Pete

[jack]

bplus, maybe this could work

Code: QB64: [Select]

1. Declare CustomType Library
2.     Sub memcpy (ByVal dest As _Offset, Byval source As _Offset, Byval bytes As Long)
3. End Declare
4.  
5.  
6. Print approx_power(20000, 2#), Sqr(20000#)
7.  
8. x# = 1D100: y# = 7
9. Print approx_power(x#, y#), x# ^ (1 / y#)
10.  
11. Function ipow# (x As Double, e As Integer)
12.     'take x to an integer power
13.     Dim As Double z, y
14.     Dim As Integer n
15.     y = x
16.     n = Abs(e)
17.     z = 1#
18.     While n > 0
19.         While (n Mod 2) = 0
20.             n = n \ 2
21.             y = y * y
22.         Wend
23.         n = n - 1
24.         z = y * z
25.     Wend
26.     If e < 0 Then
27.         ipow = 1# / z
28.     Else
29.         ipow = z
30.     End If
31. End Function
32.  
33. Function approx_power# (x#, y#)
34.     Dim As Double a, b
35.     Dim As Long tmp
36.     a = x#: b = 1# / y#
37.     memcpy _Offset(tmp), _Offset(a) + 4, 4
38.     tmp = (tmp - 1072632447) * b
39.     tmp = tmp + 1072632447
40.     memcpy _Offset(a) + 4, _Offset(tmp), 4
41.     a = a - (ipow(a, y#) - x#) / (y# * ipow(a, y# - 1))
42.     a = a - (ipow(a, y#) - x#) / (y# * ipow(a, y# - 1))
43.     a = a - (ipow(a, y#) - x#) / (y# * ipow(a, y# - 1))
44.     a = a - (ipow(a, y#) - x#) / (y# * ipow(a, y# - 1))
45.     approx_power = a
46. End Function
47.  

[bplus]

I have the first sqrRoot$ compared side by side with the Square Root by Newton-Raphson Function (SRbyNR$) the first makes 3 calls to Mr$ Function while SRbyNR$ makes 5 per loop. I think it's noticeable but the real killer is . 20 0's 64, the first method returns a good result the 2nd is lost in infinite loop.

Code: QB64: [Select]

1. Option _Explicit
2. _Title "Math regulator mr test sqr estimating" ' b+ start 2021-06-02
3. ' divide$ found fix? 2021-06-03 comment in that function
4. ' 2021-06-03 update with new sqrRoot$ Function
5.  
6. Randomize Timer 'now that it's seems to be running silent
7. Screen _NewImage(1200, 700, 32)
8. _Delay .25
9. _ScreenMove _Middle
10.  
11. Dim n$, result$
12. Do
13.     'remember everything is strings
14.     Input "Enter a number to find it's square root "; n$
15.     If n$ = "" Then End
16.     result$ = sqrRoot$(n$)
17.     Print result$
18.     Print "Length ="; Len(result$)
19.     _Delay 2
20.     result$ = SRbyNR$(n$)
21.     Print result$
22.     Print "Length ="; Len(result$)
23.     Print
24. Loop
25.  
26. Function sqrRoot$ (nmbr$)
27.     Dim n$, guess$, lastGuess$, other$, sum$, imaginary$, loopcnt
28.     If Left$(nmbr$, 1) = "-" Then 'handle neg numbers
29.         imaginary$ = "*i": n$ = Mid$(nmbr$, 2)
30.     Else
31.         imaginary$ = "": n$ = nmbr$
32.     End If
33.     guess$ = mr$(n$, "/", "2")
34.     other$ = n$
35.     Do
36.         loopcnt = loopcnt + 1
37.         Print "loop cnt"; loopcnt
38.  
39.         If (Mid$(guess$, 1, 105) = Mid$(lastGuess$, 1, 105)) Then ' go past 100 matching digits for 100 digit precision
40.             sqrRoot$ = Mid$(other$, 1, 101) + imaginary$ ' try other factor for guess$  sometimes it nails answer without all digits
41.             Exit Function
42.         Else
43.             lastGuess$ = guess$
44.             sum$ = mr$(guess$, "+", other$)
45.             guess$ = mr$(sum$, "/", "2")
46.             other$ = mr$(n$, "/", guess$)
47.         End If
48.     Loop
49. End Function
50.  
51. Function SRbyNR$ (nmbr$) ' square root by Newton - Ralphson method my interpretation of GeorgeMcGinn
52.  
53.     Dim n$, guess$, lastGuess$, dx$, imaginary$, other$, loopcnt
54.     If Left$(nmbr$, 1) = "-" Then 'handle neg numbers
55.         imaginary$ = "*i": n$ = Mid$(nmbr$, 2)
56.     Else
57.         imaginary$ = "": n$ = nmbr$
58.     End If
59.  
60.     guess$ = mr$(n$, "/", "2") ' get this going first and then try better starting guess later
61.  
62.     Do
63.         loopcnt = loopcnt + 1
64.         Print "loop cnt"; loopcnt
65.         If (Mid$(guess$, 1, 105) = Mid$(lastGuess$, 1, 105)) Then ' go past 100 matching digits for 100 digit precision
66.             SRbyNR$ = Mid$(other$, 1, 101) + imaginary$
67.             Exit Function
68.         Else
69.             'dx = (x - A / x) / 2: x = x - dx ' Thanks George
70.             lastGuess$ = guess$
71.             dx$ = mr$(mr$(guess$, "-", mr$(n$, "/", guess$)), "/", "2")
72.             guess$ = mr$(guess$, "-", dx$)
73.             other$ = mr$(n$, "/", guess$) ' try other factor for guess$  sometimes it nails answer without all digits
74.         End If
75.     Loop
76. End Function
77.  
78.  
79. Function mr$ (a$, op$, b$) ' catchy? mr$ for math regulator
80.     Dim ca$, cb$, aSgn$, bSgn$, postOp$, sgn$
81.     Dim adp As Integer, bdp As Integer, dp As Integer, lpop As Integer
82.  
83.     op$ = _Trim$(op$) 'save fixing each time
84.     ca$ = _Trim$(a$): cb$ = _Trim$(b$) 'make copies in case we change
85.     'strip signs and decimals
86.     If Left$(ca$, 1) = "-" Then
87.         aSgn$ = "-": ca$ = Mid$(ca$, 2)
88.     Else
89.         aSgn$ = "": ca$ = ca$
90.     End If
91.     dp = InStr(ca$, ".")
92.     If dp > 0 Then
93.         adp = Len(ca$) - dp
94.         ca$ = Mid$(ca$, 1, dp - 1) + Mid$(ca$, dp + 1)
95.     Else
96.         adp = 0
97.     End If
98.     If Left$(cb$, 1) = "-" Then
99.         bSgn$ = "-": cb$ = Mid$(cb$, 2)
100.     Else
101.         bSgn$ = "": cb$ = cb$
102.     End If
103.     dp = InStr(cb$, ".")
104.     If dp > 0 Then
105.         bdp = Len(cb$) - dp
106.         cb$ = Mid$(cb$, 1, dp - 1) + Mid$(cb$, dp + 1)
107.     Else
108.         bdp = 0
109.     End If
110.  
111.     If op$ = "+" Or op$ = "-" Or op$ = "/" Then 'add or subtr  even up strings on right of decimal
112.         'even up the right sides of decimals if any
113.         If adp > bdp Then dp = adp Else dp = bdp
114.         If adp < dp Then ca$ = ca$ + String$(dp - adp, "0")
115.         If bdp < dp Then cb$ = cb$ + String$(dp - bdp, "0")
116.     ElseIf op$ = "*" Then
117.         dp = adp + bdp
118.     End If
119.     If op$ = "*" Or op$ = "/" Then
120.         If aSgn$ = bSgn$ Then sgn$ = "" Else sgn$ = "-"
121.     End If
122.     'now according to signs and op$ call add$ or subtr$
123.     If op$ = "+" Then
124.         If aSgn$ = bSgn$ Then 'really add
125.             postOp$ = aSgn$ + add$(ca$, cb$)
126.         Else 'have a case of subtraction
127.             If aSgn$ = "-" Then postOp$ = subtr$(cb$, ca$) Else postOp$ = subtr$(ca$, cb$)
128.         End If
129.     ElseIf op$ = "-" Then
130.         If bSgn$ = "-" Then 'really add but switch b sign
131.             bSgn$ = ""
132.             If aSgn$ = "-" Then
133.                 postOp$ = subtr$(cb$, ca$)
134.             Else 'aSgn = ""
135.                 postOp$ = add$(ca$, cb$)
136.             End If
137.         Else 'bSgn$ =""
138.             If aSgn$ = "-" Then
139.                 bSgn$ = "-"
140.                 postOp$ = aSgn$ + add$(ca$, cb$)
141.             Else
142.                 postOp$ = subtr$(ca$, cb$)
143.             End If
144.         End If
145.     ElseIf op$ = "*" Then
146.         postOp$ = sgn$ + mult$(ca$, cb$)
147.     ElseIf op$ = "/" Then
148.         postOp$ = sgn$ + divide$(ca$, cb$)
149.     End If ' which op
150.     'put dp back
151.     If op$ <> "/" Then
152.         lpop = Len(postOp$) ' put decimal back
153.         postOp$ = Mid$(postOp$, 1, lpop - dp) + "." + Mid$(postOp$, lpop - dp + 1)
154.     End If
155.     mr$ = trim0$(postOp$)
156. End Function
157.  
158. Function divide$ (n$, d$) ' goal here is 100 digits precision not 100 digits past decimal
159.     Dim di$, ndi$, nD As Integer
160.     If trim0$(n$) = "0" Then divide$ = "0": Exit Function
161.     If trim0$(d$) = "0" Then divide$ = "div 0": Exit Function
162.     If trim0$(d$) = "1" Then divide$ = trim0$(n$): Exit Function '8/17 add trim0$
163.  
164.     ' aha! found a bug when d$ gets really huge 100 is no where near enough!!!!
165.     ' 2021-06-03 fix by adding 100 to len(d$), plus have to go a little past 100 for 100 digit precision
166.     ' need to go past 100 for 100 precise digits (not decimal places)
167.     di$ = Mid$(nInverse$(d$, Len(d$) + 200), 2) 'chop off decimal point after
168.     nD = Len(di$)
169.     ndi$ = mult$(n$, di$)
170.     ndi$ = Mid$(ndi$, 1, Len(ndi$) - nD) + "." + Right$(String$(nD, "0") + Right$(ndi$, nD), nD)
171.     divide$ = trim0$(ndi$)
172. End Function
173.  
174. Function nInverse$ (n$, DP As Integer) 'assume decimal at very start of the string of digits returned, no rounding
175.     Dim m$(1 To 9), si$, r$, outstr$, d$
176.     Dim i As Integer
177.     For i = 1 To 9
178.         si$ = _Trim$(Str$(i))
179.         m$(i) = mult$(si$, n$)
180.     Next
181.     outstr$ = ""
182.     If n$ = "0" Then nInverse$ = "Div 0": Exit Function
183.     If n$ = "1" Then nInverse$ = "1": Exit Function
184.     outstr$ = "." 'everything else n > 1 is decimal 8/17
185.     r$ = "10"
186.     Do
187.         While Left$(subtr$(r$, n$), 1) = "-" '   r - n < 0
188.             outstr$ = outstr$ + "0" '            add 0 to the  output string
189.             If Len(outstr$) = DP Then nInverse$ = outstr$: Exit Function 'check if we've reached DP length
190.             r$ = r$ + "0"
191.         Wend
192.         For i = 9 To 1 Step -1
193.             If LTE(m$(i), r$) Then d$ = _Trim$(Str$(i)): Exit For
194.         Next
195.         outstr$ = outstr$ + d$
196.         If Len(outstr$) = DP Then nInverse$ = outstr$: Exit Function
197.         r$ = subtr$(r$, mult$(d$, n$)) 'r = r -d*n
198.         If r$ = "0" Then nInverse$ = outstr$: Exit Function 'found a perfect divisor
199.         r$ = r$ + "0" 'add another place
200.     Loop
201. End Function
202.  
203. Function mult$ (a$, b$) 'assume both positive integers prechecked as all digits strings
204.     Dim la As Integer, lb As Integer, m As Integer, g As Integer, dp As Integer
205.     Dim v18 As _Unsigned _Integer64, sd As _Unsigned _Integer64, co As _Unsigned _Integer64
206.     Dim f18$, f1$, t$, build$, accum$
207.  
208.     If trim0$(a$) = "0" Then mult$ = "0": Exit Function
209.     If trim0$(b$) = "0" Then mult$ = "0": Exit Function
210.     If trim0$(a$) = "1" Then mult$ = trim0$(b$): Exit Function
211.     If trim0$(b$) = "1" Then mult$ = trim0$(a$): Exit Function
212.     'find the longer number and make it a mult of 18 to take 18 digits at a time from it
213.     la = Len(a$): lb = Len(b$)
214.     If la > lb Then
215.         m = Int(la / 18) + 1
216.         f18$ = Right$(String$(m * 18, "0") + a$, m * 18)
217.         f1$ = b$
218.     Else
219.         m = Int(lb / 18) + 1
220.         f18$ = Right$(String$(m * 18, "0") + b$, m * 18)
221.         f1$ = a$
222.     End If
223.     For dp = Len(f1$) To 1 Step -1 'dp = digit position of the f1$
224.         build$ = "" 'line builder
225.         co = 0
226.         'now taking 18 digits at a time Thanks Steve McNeill
227.         For g = 1 To m
228.             v18 = Val(Mid$(f18$, m * 18 - g * 18 + 1, 18))
229.             sd = Val(Mid$(f1$, dp, 1))
230.             t$ = Right$(String$(19, "0") + _Trim$(Str$(v18 * sd + co)), 19)
231.             co = Val(Mid$(t$, 1, 1))
232.             build$ = Mid$(t$, 2) + build$
233.         Next g
234.         If co Then build$ = _Trim$(Str$(co)) + build$
235.         If dp = Len(f1$) Then
236.             accum$ = build$
237.         Else
238.             accum$ = add$(accum$, build$ + String$(Len(f1$) - dp, "0"))
239.         End If
240.     Next dp
241.     mult$ = accum$
242. End Function
243.  
244. Function subtr$ (sum$, minus$) ' assume both numbers are positive all digits
245.     Dim m As Integer, g As Integer, p As Integer
246.     Dim VB As _Unsigned _Integer64, vs As _Unsigned _Integer64, tenE18 As _Unsigned _Integer64
247.     Dim ts$, tm$, sign$, LG$, sm$, t$, result$
248.  
249.     ts$ = TrimLead0$(sum$): tm$ = TrimLead0$(minus$)
250.     If trim0(ts$) = trim0$(tm$) Then subtr$ = "0": Exit Function 'OK proceed with function knowing they are not equal
251.     tenE18 = 1000000000000000000 'yes!!! no dang E's
252.     If LTE(ts$, tm$) Then ' which is bigger? minus is bigger
253.         sign$ = "-"
254.         m = Int(Len(tm$) / 18) + 1
255.         LG$ = Right$(String$(m * 18, "0") + tm$, m * 18)
256.         sm$ = Right$(String$(m * 18, "0") + ts$, m * 18)
257.     Else 'sum is bigger
258.         sign$ = ""
259.         m = Int(Len(ts$) / 18) + 1
260.         LG$ = Right$(String$(m * 18, "0") + ts$, m * 18)
261.         sm$ = Right$(String$(m * 18, "0") + tm$, m * 18)
262.     End If
263.     'now taking 18 digits at a time From Steve I learned we can do more than 1 digit at a time
264.     For g = 1 To m
265.         VB = Val(Mid$(LG$, m * 18 - g * 18 + 1, 18))
266.         vs = Val(Mid$(sm$, m * 18 - g * 18 + 1, 18))
267.         If vs > VB Then
268.             t$ = Right$(String$(18, "0") + _Trim$(Str$(tenE18 - vs + VB)), 18)
269.             p = (m - g) * 18
270.             While p > 0 And Mid$(LG$, p, 1) = "0"
271.                 Mid$(LG$, p, 1) = "9"
272.                 p = p - 1
273.             Wend
274.             If p > 0 Then Mid$(LG$, p, 1) = _Trim$(Str$(Val(Mid$(LG$, p, 1)) - 1))
275.         Else
276.             t$ = Right$(String$(18, "0") + _Trim$(Str$(VB - vs)), 18)
277.         End If
278.         result$ = t$ + result$
279.     Next
280.     subtr$ = sign$ + result$
281. End Function
282.  
283. Function add$ (a$, b$) 'add 2 positive integers assume a and b are just numbers no spaces or - signs
284.     'first thing is to set a and b numbers to same length and multiple of 18 so can take 18 digits at a time
285.     Dim la As Integer, lb As Integer, m As Integer, g As Integer
286.     Dim sa As _Unsigned _Integer64, sb As _Unsigned _Integer64, co As _Unsigned _Integer64
287.     Dim fa$, fb$, t$, new$, result$
288.     la = Len(a$): lb = Len(b$)
289.     If la > lb Then m = Int(la / 18) + 1 Else m = Int(lb / 18) + 1
290.     fa$ = Right$(String$(m * 18, "0") + a$, m * 18)
291.     fb$ = Right$(String$(m * 18, "0") + b$, m * 18)
292.  
293.     'now taking 18 digits at a time Thanks Steve McNeill
294.     For g = 1 To m
295.         sa = Val(Mid$(fa$, m * 18 - g * 18 + 1, 18))
296.         sb = Val(Mid$(fb$, m * 18 - g * 18 + 1, 18))
297.         t$ = Right$(String$(36, "0") + _Trim$(Str$(sa + sb + co)), 36)
298.         co = Val(Mid$(t$, 1, 18))
299.         new$ = Mid$(t$, 19)
300.         result$ = new$ + result$
301.     Next
302.     If co Then result$ = Str$(co) + result$
303.     add$ = result$
304. End Function
305.  
306. ' String Math Helpers -----------------------------------------------
307.  
308. 'this function needs TrimLead0$(s$)
309. Function LTE (a$, b$) ' a$ Less Than or Equal b$  comparison of 2 strings
310.     Dim ca$, cb$, la As Integer, lb As Integer, i As Integer
311.     ca$ = TrimLead0$(a$): cb$ = TrimLead0(b$)
312.     la = Len(ca$): lb = Len(cb$)
313.     If ca$ = cb$ Then
314.         LTE = -1
315.     ElseIf la < lb Then ' a is smaller
316.         LTE = -1
317.     ElseIf la > lb Then ' a is bigger
318.         LTE = 0
319.     ElseIf la = lb Then ' equal lengths
320.         For i = 1 To Len(ca$)
321.             If Val(Mid$(ca$, i, 1)) > Val(Mid$(cb$, i, 1)) Then
322.                 LTE = 0: Exit Function
323.             ElseIf Val(Mid$(ca$, i, 1)) < Val(Mid$(cb$, i, 1)) Then
324.                 LTE = -1: Exit Function
325.             End If
326.         Next
327.     End If
328. End Function
329.  
330. ' ------------------------------------- use these for final display
331.  
332. Function TrimLead0$ (s$) 'for treating strings as number (pos integers)
333.     Dim copys$, i As Integer, find As Integer
334.     copys$ = _Trim$(s$) 'might as well remove spaces too
335.     i = 1: find = 0
336.     While i < Len(copys$) And Mid$(copys$, i, 1) = "0"
337.         i = i + 1: find = 1
338.     Wend
339.     If find = 1 Then copys$ = Mid$(copys$, i)
340.     If copys$ = "" Then TrimLead0$ = "0" Else TrimLead0$ = copys$
341. End Function
342.  
343. Function TrimTail0$ (s$)
344.     Dim copys$, dp As Integer, i As Integer, find As Integer
345.     copys$ = _Trim$(s$) 'might as well remove spaces too
346.     TrimTail0$ = copys$
347.     dp = InStr(copys$, ".")
348.     If dp > 0 Then
349.         i = Len(copys$): find = 0
350.         While i > dp And Mid$(copys$, i, 1) = "0"
351.             i = i - 1: find = 1
352.         Wend
353.         If find = 1 Then
354.             If i = dp Then
355.                 TrimTail0$ = Mid$(copys$, 1, dp - 1)
356.             Else
357.                 TrimTail0$ = Mid$(copys$, 1, i)
358.             End If
359.         End If
360.     End If
361. End Function
362.  
363. Function trim0$ (s$)
364.     Dim cs$, si$
365.     cs$ = s$
366.     si$ = Left$(cs$, 1)
367.     If si$ = "-" Then cs$ = Mid$(cs$, 2)
368.     cs$ = TrimLead0$(cs$)
369.     cs$ = TrimTail0$(cs$)
370.     If Right$(cs$, 1) = "." Then cs$ = Mid$(cs$, 1, Len(cs$) - 1)
371.     If si$ = "-" Then trim0$ = si$ + cs$ Else trim0$ = cs$
372. End Function
373.  
374. ' for displaying truncated numbers say to 60 digits
375. Function showDP$ (num$, nDP As Integer)
376.     Dim cNum$, dp As Integer, d As Integer, i As Integer
377.     cNum$ = num$ 'since num$ could get changed
378.     showDP$ = num$
379.     dp = InStr(num$, ".")
380.     If dp > 0 Then
381.         If Len(Mid$(cNum$, dp + 1)) > nDP Then
382.             d = Val(Mid$(cNum$, dp + nDP + 1, 1))
383.             If d > 4 Then
384.                 cNum$ = "0" + cNum$ ' tack on another 0 just in case 9's all the way to left
385.                 dp = dp + 1
386.                 i = dp + nDP
387.                 While Mid$(cNum$, i, 1) = "9" Or Mid$(cNum$, i, 1) = "."
388.                     If Mid$(cNum$, i, 1) = "9" Then
389.                         Mid$(cNum$, i, 1) = "0"
390.                     End If
391.                     i = i - 1
392.                 Wend
393.                 Mid$(cNum$, i, 1) = _Trim$(Str$(Val(Mid$(cNum$, i, 1)) + 1)) 'last non 9 digit
394.                 cNum$ = Mid$(cNum$, 1, dp + nDP) 'chop it
395.                 showDP$ = trim0$(cNum$)
396.             Else
397.                 showDP$ = Mid$(cNum$, 1, dp + nDP)
398.             End If
399.         End If
400.     End If
401. End Function
402.  

[jack]

hi bplus
here's my version of the Newton-Raphson, I had to use a for loop for the iterations as I found no way to use a do loop but it's much faster especially as the input numbers are larger

Code: QB64: [Select]

1. Option _Explicit
2. _Title "Math regulator mr test sqr estimating" ' b+ start 2021-06-02
3. ' divide$ found fix? 2021-06-03 comment in that function
4. ' 2021-06-03 update with new sqrRoot$ Function
5.  
6. Randomize Timer 'now that it's seems to be running silent
7. Screen _NewImage(1200, 700, 32)
8. _Delay .25
9. _ScreenMove _Middle
10.  
11. Dim n$, result$
12. Dim t#
13. Do
14.     'remember everything is strings
15.     Input "Enter a number to find it's square root "; n$
16.     If n$ = "" Then End
17.     t# = Timer
18.     result$ = sqrRoot$(n$)
19.     Print Timer - t#, result$
20.     t# = Timer
21.     result$ = sqrt$(n$)
22.     Print Timer - t#, result$
23.     Print "Length ="; Len(result$)
24.     Print
25. Loop
26.  
27. Function sqrRoot$ (nmbr$)
28.     Dim n$, guess$, lastGuess$, other$, sum$, imaginary$
29.     If Left$(nmbr$, 1) = "-" Then 'handle neg numbers
30.         imaginary$ = "*i": n$ = Mid$(nmbr$, 2)
31.     Else
32.         imaginary$ = "": n$ = nmbr$
33.     End If
34.     guess$ = mr$(n$, "/", "2")
35.     other$ = n$
36.     Do
37.         If (Mid$(guess$, 1, 105) = Mid$(lastGuess$, 1, 105)) Then ' go past 100 matching digits for 100 digit precision
38.             sqrRoot$ = Mid$(other$, 1, 101) + imaginary$
39.             Exit Function
40.         Else
41.             lastGuess$ = guess$
42.             sum$ = mr$(guess$, "+", other$)
43.             guess$ = mr$(sum$, "/", "2")
44.             other$ = mr$(n$, "/", guess$)
45.         End If
46.     Loop
47. End Function
48.  
49. Function sqrt$ (n$)
50.     Dim As String r, tmp, r2
51.     Dim As Integer k
52.     r = _Trim$(Str$(Sqr(Val(n$))))
53.     For k = 1 To 3
54.         tmp = mr$(r, "*", r)
55.         tmp = mr$(tmp, "-", n$)
56.         r2 = mr$(r, "+", r)
57.         tmp = mr$(tmp, "/", r2)
58.         r = mr$(r, "-", tmp)
59.         If Len(r) > 101 Then r = Left$(r, 101)
60.     Next k 'Loop Until Abs(Val(tmp)) < 1D-100
61.     sqrt$ = r
62. End Function
63.  
64. Function mr$ (a$, op$, b$) ' catchy? mr$ for math regulator
65.     Dim ca$, cb$, aSgn$, bSgn$, postOp$, sgn$
66.     Dim adp As Integer, bdp As Integer, dp As Integer, lpop As Integer
67.  
68.     op$ = _Trim$(op$) 'save fixing each time
69.     ca$ = _Trim$(a$): cb$ = _Trim$(b$) 'make copies in case we change
70.     'strip signs and decimals
71.     If Left$(ca$, 1) = "-" Then
72.         aSgn$ = "-": ca$ = Mid$(ca$, 2)
73.     Else
74.         aSgn$ = "": ca$ = ca$
75.     End If
76.     dp = InStr(ca$, ".")
77.     If dp > 0 Then
78.         adp = Len(ca$) - dp
79.         ca$ = Mid$(ca$, 1, dp - 1) + Mid$(ca$, dp + 1)
80.     Else
81.         adp = 0
82.     End If
83.     If Left$(cb$, 1) = "-" Then
84.         bSgn$ = "-": cb$ = Mid$(cb$, 2)
85.     Else
86.         bSgn$ = "": cb$ = cb$
87.     End If
88.     dp = InStr(cb$, ".")
89.     If dp > 0 Then
90.         bdp = Len(cb$) - dp
91.         cb$ = Mid$(cb$, 1, dp - 1) + Mid$(cb$, dp + 1)
92.     Else
93.         bdp = 0
94.     End If
95.  
96.     If op$ = "+" Or op$ = "-" Or op$ = "/" Then 'add or subtr  even up strings on right of decimal
97.         'even up the right sides of decimals if any
98.         If adp > bdp Then dp = adp Else dp = bdp
99.         If adp < dp Then ca$ = ca$ + String$(dp - adp, "0")
100.         If bdp < dp Then cb$ = cb$ + String$(dp - bdp, "0")
101.     ElseIf op$ = "*" Then
102.         dp = adp + bdp
103.     End If
104.     If op$ = "*" Or op$ = "/" Then
105.         If aSgn$ = bSgn$ Then sgn$ = "" Else sgn$ = "-"
106.     End If
107.     'now according to signs and op$ call add$ or subtr$
108.     If op$ = "+" Then
109.         If aSgn$ = bSgn$ Then 'really add
110.             postOp$ = aSgn$ + add$(ca$, cb$)
111.         Else 'have a case of subtraction
112.             If aSgn$ = "-" Then postOp$ = subtr$(cb$, ca$) Else postOp$ = subtr$(ca$, cb$)
113.         End If
114.     ElseIf op$ = "-" Then
115.         If bSgn$ = "-" Then 'really add but switch b sign
116.             bSgn$ = ""
117.             If aSgn$ = "-" Then
118.                 postOp$ = subtr$(cb$, ca$)
119.             Else 'aSgn = ""
120.                 postOp$ = add$(ca$, cb$)
121.             End If
122.         Else 'bSgn$ =""
123.             If aSgn$ = "-" Then
124.                 bSgn$ = "-"
125.                 postOp$ = aSgn$ + add$(ca$, cb$)
126.             Else
127.                 postOp$ = subtr$(ca$, cb$)
128.             End If
129.         End If
130.     ElseIf op$ = "*" Then
131.         postOp$ = sgn$ + mult$(ca$, cb$)
132.     ElseIf op$ = "/" Then
133.         postOp$ = sgn$ + divide$(ca$, cb$)
134.     End If ' which op
135.     'put dp back
136.     If op$ <> "/" Then
137.         lpop = Len(postOp$) ' put decimal back
138.         postOp$ = Mid$(postOp$, 1, lpop - dp) + "." + Mid$(postOp$, lpop - dp + 1)
139.     End If
140.     mr$ = trim0$(postOp$)
141. End Function
142.  
143. Function divide$ (n$, d$) ' goal here is 100 digits precision not 100 digits past decimal
144.     Dim di$, ndi$, nD As Integer
145.     If trim0$(n$) = "0" Then divide$ = "0": Exit Function
146.     If trim0$(d$) = "0" Then divide$ = "div 0": Exit Function
147.     If trim0$(d$) = "1" Then divide$ = trim0$(n$): Exit Function '8/17 add trim0$
148.  
149.     ' aha! found a bug when d$ gets really huge 100 is no where near enough!!!!
150.     ' 2021-06-03 fix by adding 100 to len(d$), plus have to go a little past 100 for 100 digit precision
151.     ' need to go past 100 for 100 precise digits (not decimal places)
152.     di$ = Mid$(nInverse$(d$, Len(d$) + 200), 2) 'chop off decimal point after
153.     nD = Len(di$)
154.     ndi$ = mult$(n$, di$)
155.     ndi$ = Mid$(ndi$, 1, Len(ndi$) - nD) + "." + Right$(String$(nD, "0") + Right$(ndi$, nD), nD)
156.     divide$ = trim0$(ndi$)
157. End Function
158.  
159. Function nInverse$ (n$, DP As Integer) 'assume decimal at very start of the string of digits returned, no rounding
160.     Dim m$(1 To 9), si$, r$, outstr$, d$
161.     Dim i As Integer
162.     For i = 1 To 9
163.         si$ = _Trim$(Str$(i))
164.         m$(i) = mult$(si$, n$)
165.     Next
166.     outstr$ = ""
167.     If n$ = "0" Then nInverse$ = "Div 0": Exit Function
168.     If n$ = "1" Then nInverse$ = "1": Exit Function
169.     outstr$ = "." 'everything else n > 1 is decimal 8/17
170.     r$ = "10"
171.     Do
172.         While Left$(subtr$(r$, n$), 1) = "-" '   r - n < 0
173.             outstr$ = outstr$ + "0" '            add 0 to the  output string
174.             If Len(outstr$) = DP Then nInverse$ = outstr$: Exit Function 'check if we've reached DP length
175.             r$ = r$ + "0"
176.         Wend
177.         For i = 9 To 1 Step -1
178.             If LTE(m$(i), r$) Then d$ = _Trim$(Str$(i)): Exit For
179.         Next
180.         outstr$ = outstr$ + d$
181.         If Len(outstr$) = DP Then nInverse$ = outstr$: Exit Function
182.         r$ = subtr$(r$, mult$(d$, n$)) 'r = r -d*n
183.         If r$ = "0" Then nInverse$ = outstr$: Exit Function 'found a perfect divisor
184.         r$ = r$ + "0" 'add another place
185.     Loop
186. End Function
187.  
188. Function mult$ (a$, b$) 'assume both positive integers prechecked as all digits strings
189.     Dim la As Integer, lb As Integer, m As Integer, g As Integer, dp As Integer
190.     Dim v18 As _Unsigned _Integer64, sd As _Unsigned _Integer64, co As _Unsigned _Integer64
191.     Dim f18$, f1$, t$, build$, accum$
192.  
193.     If trim0$(a$) = "0" Then mult$ = "0": Exit Function
194.     If trim0$(b$) = "0" Then mult$ = "0": Exit Function
195.     If trim0$(a$) = "1" Then mult$ = trim0$(b$): Exit Function
196.     If trim0$(b$) = "1" Then mult$ = trim0$(a$): Exit Function
197.     'find the longer number and make it a mult of 18 to take 18 digits at a time from it
198.     la = Len(a$): lb = Len(b$)
199.     If la > lb Then
200.         m = Int(la / 18) + 1
201.         f18$ = Right$(String$(m * 18, "0") + a$, m * 18)
202.         f1$ = b$
203.     Else
204.         m = Int(lb / 18) + 1
205.         f18$ = Right$(String$(m * 18, "0") + b$, m * 18)
206.         f1$ = a$
207.     End If
208.     For dp = Len(f1$) To 1 Step -1 'dp = digit position of the f1$
209.         build$ = "" 'line builder
210.         co = 0
211.         'now taking 18 digits at a time Thanks Steve McNeill
212.         For g = 1 To m
213.             v18 = Val(Mid$(f18$, m * 18 - g * 18 + 1, 18))
214.             sd = Val(Mid$(f1$, dp, 1))
215.             t$ = Right$(String$(19, "0") + _Trim$(Str$(v18 * sd + co)), 19)
216.             co = Val(Mid$(t$, 1, 1))
217.             build$ = Mid$(t$, 2) + build$
218.         Next g
219.         If co Then build$ = _Trim$(Str$(co)) + build$
220.         If dp = Len(f1$) Then
221.             accum$ = build$
222.         Else
223.             accum$ = add$(accum$, build$ + String$(Len(f1$) - dp, "0"))
224.         End If
225.     Next dp
226.     mult$ = accum$
227. End Function
228.  
229. Function subtr$ (sum$, minus$) ' assume both numbers are positive all digits
230.     Dim m As Integer, g As Integer, p As Integer
231.     Dim VB As _Unsigned _Integer64, vs As _Unsigned _Integer64, tenE18 As _Unsigned _Integer64
232.     Dim ts$, tm$, sign$, LG$, sm$, t$, result$
233.  
234.     ts$ = TrimLead0$(sum$): tm$ = TrimLead0$(minus$)
235.     If trim0(ts$) = trim0$(tm$) Then subtr$ = "0": Exit Function 'OK proceed with function knowing they are not equal
236.     tenE18 = 1000000000000000000 'yes!!! no dang E's
237.     If LTE(ts$, tm$) Then ' which is bigger? minus is bigger
238.         sign$ = "-"
239.         m = Int(Len(tm$) / 18) + 1
240.         LG$ = Right$(String$(m * 18, "0") + tm$, m * 18)
241.         sm$ = Right$(String$(m * 18, "0") + ts$, m * 18)
242.     Else 'sum is bigger
243.         sign$ = ""
244.         m = Int(Len(ts$) / 18) + 1
245.         LG$ = Right$(String$(m * 18, "0") + ts$, m * 18)
246.         sm$ = Right$(String$(m * 18, "0") + tm$, m * 18)
247.     End If
248.     'now taking 18 digits at a time From Steve I learned we can do more than 1 digit at a time
249.     For g = 1 To m
250.         VB = Val(Mid$(LG$, m * 18 - g * 18 + 1, 18))
251.         vs = Val(Mid$(sm$, m * 18 - g * 18 + 1, 18))
252.         If vs > VB Then
253.             t$ = Right$(String$(18, "0") + _Trim$(Str$(tenE18 - vs + VB)), 18)
254.             p = (m - g) * 18
255.             While p > 0 And Mid$(LG$, p, 1) = "0"
256.                 Mid$(LG$, p, 1) = "9"
257.                 p = p - 1
258.             Wend
259.             If p > 0 Then Mid$(LG$, p, 1) = _Trim$(Str$(Val(Mid$(LG$, p, 1)) - 1))
260.         Else
261.             t$ = Right$(String$(18, "0") + _Trim$(Str$(VB - vs)), 18)
262.         End If
263.         result$ = t$ + result$
264.     Next
265.     subtr$ = sign$ + result$
266. End Function
267.  
268. Function add$ (a$, b$) 'add 2 positive integers assume a and b are just numbers no spaces or - signs
269.     'first thing is to set a and b numbers to same length and multiple of 18 so can take 18 digits at a time
270.     Dim la As Integer, lb As Integer, m As Integer, g As Integer
271.     Dim sa As _Unsigned _Integer64, sb As _Unsigned _Integer64, co As _Unsigned _Integer64
272.     Dim fa$, fb$, t$, new$, result$
273.     la = Len(a$): lb = Len(b$)
274.     If la > lb Then m = Int(la / 18) + 1 Else m = Int(lb / 18) + 1
275.     fa$ = Right$(String$(m * 18, "0") + a$, m * 18)
276.     fb$ = Right$(String$(m * 18, "0") + b$, m * 18)
277.  
278.     'now taking 18 digits at a time Thanks Steve McNeill
279.     For g = 1 To m
280.         sa = Val(Mid$(fa$, m * 18 - g * 18 + 1, 18))
281.         sb = Val(Mid$(fb$, m * 18 - g * 18 + 1, 18))
282.         t$ = Right$(String$(36, "0") + _Trim$(Str$(sa + sb + co)), 36)
283.         co = Val(Mid$(t$, 1, 18))
284.         new$ = Mid$(t$, 19)
285.         result$ = new$ + result$
286.     Next
287.     If co Then result$ = Str$(co) + result$
288.     add$ = result$
289. End Function
290.  
291. ' String Math Helpers -----------------------------------------------
292.  
293. 'this function needs TrimLead0$(s$)
294. Function LTE (a$, b$) ' a$ Less Than or Equal b$  comparison of 2 strings
295.     Dim ca$, cb$, la As Integer, lb As Integer, i As Integer
296.     ca$ = TrimLead0$(a$): cb$ = TrimLead0(b$)
297.     la = Len(ca$): lb = Len(cb$)
298.     If ca$ = cb$ Then
299.         LTE = -1
300.     ElseIf la < lb Then ' a is smaller
301.         LTE = -1
302.     ElseIf la > lb Then ' a is bigger
303.         LTE = 0
304.     ElseIf la = lb Then ' equal lengths
305.         For i = 1 To Len(ca$)
306.             If Val(Mid$(ca$, i, 1)) > Val(Mid$(cb$, i, 1)) Then
307.                 LTE = 0: Exit Function
308.             ElseIf Val(Mid$(ca$, i, 1)) < Val(Mid$(cb$, i, 1)) Then
309.                 LTE = -1: Exit Function
310.             End If
311.         Next
312.     End If
313. End Function
314.  
315. ' ------------------------------------- use these for final display
316.  
317. Function TrimLead0$ (s$) 'for treating strings as number (pos integers)
318.     Dim copys$, i As Integer, find As Integer
319.     copys$ = _Trim$(s$) 'might as well remove spaces too
320.     i = 1: find = 0
321.     While i < Len(copys$) And Mid$(copys$, i, 1) = "0"
322.         i = i + 1: find = 1
323.     Wend
324.     If find = 1 Then copys$ = Mid$(copys$, i)
325.     If copys$ = "" Then TrimLead0$ = "0" Else TrimLead0$ = copys$
326. End Function
327.  
328. Function TrimTail0$ (s$)
329.     Dim copys$, dp As Integer, i As Integer, find As Integer
330.     copys$ = _Trim$(s$) 'might as well remove spaces too
331.     TrimTail0$ = copys$
332.     dp = InStr(copys$, ".")
333.     If dp > 0 Then
334.         i = Len(copys$): find = 0
335.         While i > dp And Mid$(copys$, i, 1) = "0"
336.             i = i - 1: find = 1
337.         Wend
338.         If find = 1 Then
339.             If i = dp Then
340.                 TrimTail0$ = Mid$(copys$, 1, dp - 1)
341.             Else
342.                 TrimTail0$ = Mid$(copys$, 1, i)
343.             End If
344.         End If
345.     End If
346. End Function
347.  
348. Function trim0$ (s$)
349.     Dim cs$, si$
350.     cs$ = s$
351.     si$ = Left$(cs$, 1)
352.     If si$ = "-" Then cs$ = Mid$(cs$, 2)
353.     cs$ = TrimLead0$(cs$)
354.     cs$ = TrimTail0$(cs$)
355.     If Right$(cs$, 1) = "." Then cs$ = Mid$(cs$, 1, Len(cs$) - 1)
356.     If si$ = "-" Then trim0$ = si$ + cs$ Else trim0$ = cs$
357. End Function
358.  
359. ' for displaying truncated numbers say to 60 digits
360. Function showDP$ (num$, nDP As Integer)
361.     Dim cNum$, dp As Integer, d As Integer, i As Integer
362.     cNum$ = num$ 'since num$ could get changed
363.     showDP$ = num$
364.     dp = InStr(num$, ".")
365.     If dp > 0 Then
366.         If Len(Mid$(cNum$, dp + 1)) > nDP Then
367.             d = Val(Mid$(cNum$, dp + nDP + 1, 1))
368.             If d > 4 Then
369.                 cNum$ = "0" + cNum$ ' tack on another 0 just in case 9's all the way to left
370.                 dp = dp + 1
371.                 i = dp + nDP
372.                 While Mid$(cNum$, i, 1) = "9" Or Mid$(cNum$, i, 1) = "."
373.                     If Mid$(cNum$, i, 1) = "9" Then
374.                         Mid$(cNum$, i, 1) = "0"
375.                     End If
376.                     i = i - 1
377.                 Wend
378.                 Mid$(cNum$, i, 1) = _Trim$(Str$(Val(Mid$(cNum$, i, 1)) + 1)) 'last non 9 digit
379.                 cNum$ = Mid$(cNum$, 1, dp + nDP) 'chop it
380.                 showDP$ = trim0$(cNum$)
381.             Else
382.                 showDP$ = Mid$(cNum$, 1, dp + nDP)
383.             End If
384.         End If
385.     End If
386. End Function
387.  

[George McGinn]

@bplus - Here is my version of the Square Root using strings.

I have integrated it into your MR program. However, as you will see from the result screen, it seems like it does not clear out what is in the decimal places.

I am using your add, subtract and divide routines, and I'm not yet sure if it is an error with your routines not clearing out the decimal places, or that they are not designed to be nested in a formula (the ones my friend and I wrote for the iPad/iPhone does work properly), or I just don't understand how your program fully works.

I created an OP code ">" to represent Square Root, and the second number is set to "" (can be any value really, as it is never referenced in my routine.

Because the iterations do not stop when dx$ = "10" I get an erroneous result. As you will see I have both the original formula expressed properly in your mr$ format, as well as it broken out in its components based on the order of operations. I get the same results in both, that is I get a carryover of the decimals from the prior iteration.

Code: QB64: [Select]

1. PRINT "Square Root of 100 equals "; mr$("100", ">", "")    

Code: QB64: [Select]

1. '*** Add in Square Root Function
2.     ELSEIF op$ = ">" THEN
3.         postOp$ = root_2$(ca$)
4.  
5.  

Code: QB64: [Select]

1. FUNCTION root_2$ (A$)
2.     DIM x$, dx$
3.     DIM precision, max_iterations
4.     DIM i AS INTEGER
5.  
6.     x$ = mr$(A$, "/", "2"): precision = 0.001: max_iterations = 30
7.     FOR i = 1 TO max_iterations
8. '*** Formula: dx = (x - A / x) / 2
9. '*** Reduce x by dx:  x = x - dx
10.  
11.          dx$ = mr$(mr$(x$, "-", mr$(A$, "/", x$)), "/", "2")
12.  
13. '         dx$ = mr$(A$, "/", x$)
14. '         dx$ = mr$(x$, "-", dx$)
15. '         dx$ = mr$(dx$, "/", "2")
16.          x$ = mr$(x$, "-", dx$)
17.          PRINT "DX$ = "; dx$
18.          PRINT "X$  = "; x$: PRINT
19.          IF ABS(VAL(dx$)) < precision THEN i = max_iterations
20.     NEXT i
21.     root_2$ = x$
22. END FUNCTION

Here is my run of the function above. You will see that dx$ is right, but x$ should be just 10. If you want, I can post the entire MR program.
 

[jack]

@bplus
your string math does not understand numbers in exponential format so when the input number get big and the Sqr of the number is expressed in exponential format then my version fails, I suppose there may be a way to fix that

[jack]

the Newton-Raphson formula for the square root is
r = r - (r^2-x)/(2*r)
in general the inverse function approximation is found by
Xi = Xi - ( f(Xi) -x)/ f ' (Xi)

[bplus]

@bplus
your string math does not understand numbers in exponential format so when the input number get big and the Sqr of the number is expressed in exponential format then my version fails, I suppose there may be a way to fix that

Right! String Math means no exponents, it's straight digits and though it takes longer it's accurate with the biggest and smallest of numbers
@jack your code here:

Code: QB64: [Select]

1. Function sqrt$ (n$)
2.     Dim As String r, tmp, r2
3.     Dim As Integer k
4.     r = _Trim$(Str$(Sqr(Val(n$)))) ' <<<<<<<<<<<<
5.     For k = 1 To 3
6.         tmp = mr$(r, "*", r)
7.         tmp = mr$(tmp, "-", n$)
8.         r2 = mr$(r, "+", r)
9.         tmp = mr$(tmp, "/", r2)
10.         r = mr$(r, "-", tmp)
11.         If Len(r) > 101 Then r = Left$(r, 101)
12.     Next k 'Loop Until Abs(Val(tmp)) < 1D-100
13.     sqrt$ = r
14. End Function
15.  

Uses 2 functions not available to String Math,
 
VAL() because there are only string type variables
EDIT: well maybe VAL() will work on smaller strings but I don't see it handling a string a 100 digits long?

SQR() heck! that's exactly what we are looking for, of course it's faster but only works for regular type numbers, integers, longs, single, double... not a string of digits.
EDIT: Unless you are somehow dividing the string into workable sections and taking SQR() of those and string together a giant construction like we do with the add$, mult$, subtract$ then I am misunderstanding, apologies.
In fact I have something like that from way back doing SQR, like we learned in school.

 

[bplus]

the Newton-Raphson formula for the square root is
r = r - (r^2-x)/(2*r)
in general the inverse function approximation is found by
Xi = Xi - ( f(Xi) -x)/ f ' (Xi)

I was going by George McGinn example which did seem to be working for big numbers (but not dot 20-0's64 or .0000000000000000000064).

[bplus]

@bplus - Here is my version of the Square Root using strings.

I have integrated it into your MR program. However, as you will see from the result screen, it seems like it does not clear out what is in the decimal places.

I am using your add, subtract and divide routines, and I'm not yet sure if it is an error with your routines not clearing out the decimal places, or that they are not designed to be nested in a formula (the ones my friend and I wrote for the iPad/iPhone does work properly), or I just don't understand how your program fully works.

I created an OP code ">" to represent Square Root, and the second number is set to "" (can be any value really, as it is never referenced in my routine.

Because the iterations do not stop when dx$ = "10" I get an erroneous result. As you will see I have both the original formula expressed properly in your mr$ format, as well as it broken out in its components based on the order of operations. I get the same results in both, that is I get a carryover of the decimals from the prior iteration.

Code: QB64: [Select]

1. PRINT "Square Root of 100 equals "; mr$("100", ">", "")    

Code: QB64: [Select]

1. '*** Add in Square Root Function
2.     ELSEIF op$ = ">" THEN
3.         postOp$ = root_2$(ca$)
4.  
5.  

Code: QB64: [Select]

1. FUNCTION root_2$ (A$)
2.     DIM x$, dx$
3.     DIM precision, max_iterations
4.     DIM i AS INTEGER
5.  
6.     x$ = mr$(A$, "/", "2"): precision = 0.001: max_iterations = 30
7.     FOR i = 1 TO max_iterations
8. '*** Formula: dx = (x - A / x) / 2
9. '*** Reduce x by dx:  x = x - dx
10.  
11.          dx$ = mr$(mr$(x$, "-", mr$(A$, "/", x$)), "/", "2")
12.  
13. '         dx$ = mr$(A$, "/", x$)
14. '         dx$ = mr$(x$, "-", dx$)
15. '         dx$ = mr$(dx$, "/", "2")
16.          x$ = mr$(x$, "-", dx$)
17.          PRINT "DX$ = "; dx$
18.          PRINT "X$  = "; x$: PRINT
19.          IF ABS(VAL(dx$)) < precision THEN i = max_iterations
20.     NEXT i
21.     root_2$ = x$
22. END FUNCTION

Here is my run of the function above. You will see that dx$ is right, but x$ should be just 10. If you want, I can post the entire MR program.
 

@George McGinn are we so different?

Code: QB64: [Select]

1. Function SRbyNR$ (nmbr$) ' square root by Newton - Ralphson method my interpretation of GeorgeMcGinn
2.  
3.     Dim n$, guess$, lastGuess$, dx$, imaginary$, other$, loopcnt
4.     If Left$(nmbr$, 1) = "-" Then 'handle neg numbers
5.         imaginary$ = "*i": n$ = Mid$(nmbr$, 2)
6.     Else
7.         imaginary$ = "": n$ = nmbr$
8.     End If
9.  
10.     guess$ = mr$(n$, "/", "2") ' get this going first and then try better starting guess later
11.  
12.     Do
13.         loopcnt = loopcnt + 1
14.         Print "loop cnt"; loopcnt
15.         If (Mid$(guess$, 1, 105) = Mid$(lastGuess$, 1, 105)) Then ' go past 100 matching digits for 100 digit precision
16.             SRbyNR$ = Mid$(other$, 1, 101) + imaginary$
17.             Exit Function
18.         Else
19.             'dx = (x - A / x) / 2: x = x - dx ' Thanks George
20.             lastGuess$ = guess$
21.             dx$ = mr$(mr$(guess$, "-", mr$(n$, "/", guess$)), "/", "2")
22.             guess$ = mr$(guess$, "-", dx$)
23.             other$ = mr$(n$, "/", guess$) ' try other factor for guess$  sometimes it nails answer without all digits
24.         End If
25.     Loop
26. End Function

dx$ = mr$(mr$(guess$, "-", mr$(n$, "/", guess$)), "/", "2") ' yes you can team functions up like this that is fine!
dx$ = mr$(mr$(x$, "-", mr$(A$, "/", x$)), "/", "2")

We just use different variables with the main formula.

This is where we differ, Finished conditional-
yours:

Code: QB64: [Select]

1. IF ABS(VAL(dx$)) < precision THEN i = max_iterations

ABS() needs a number type and I don't trust VAL() to handle 100 plus digit strings.
Hence I don't trust < to work as expected.

mine:

Code: QB64: [Select]

1. If (Mid$(guess$, 1, 105) = Mid$(lastGuess$, 1, 105)) Then

So I went the route of matching strings down until the first 100 digits of last guess match first 100 digits of current guess. Oddly our method would rather go 100-9's, 1.9999999...'s, than go to 2.0 for the square root of 4!
If guess is always growing larger towards 2, the other factor is gaining 0's after decimal such that it looks exactly right when we cut off after 100 digits of 0's (for 2.0000000000...) have been accumulated.

[bplus]

@jack no exponents, is that a paradigm shift? do you feel the freedom or do you feel like you lost your best friend? like you are dealing with stone age folks!

Obviously it's slow as hell but the accuracy!

[George McGinn]

@bplus - DUH, you're right. I saw the word 'guess" which threw me off.

I put your routine in with mine to test it out.

Both produces 2 as the square root of 4, but when I do SRQ(100) I get 5. ... from mine (which is the issue I outlined) but yours does not produce a result.

Are we having the same issue?

[George McGinn]

This was the reason why my friend and I decided to add a precision check.

As for the question about VAL working on a string of 100 digits/decimal places, it works fine from my testing on both mobile devices (from the original code) to what I ported over to QB64.

I was going by George McGinn example which did seem to be working for big numbers (but not dot 20-0's64 or .0000000000000000000064).

[jack]

@bplus it seems that you didn't bother to run the code I posted, instead you jump to conclusions.
but for completeness here my sqrt$ function that takes care of any exponential notation and is many times faster

Code: QB64: [Select]

1. Function sqrt$ (n$)
2.     Dim As String r, tmp, r2
3.     Dim As Integer d, e, k, l
4.     r = _Trim$(Str$(Sqr(Val(n$))))
5.     d = InStr(r, "D")
6.     If d > 0 Then
7.         e = Val(Mid$(r, d + 1))
8.         r = Left$(r, 1) + Mid$(Left$(r, d - 1), 3)
9.         l = Len(r)
10.         If e > 0 Then
11.             r = r + String$(e - l + 1, "0")
12.         ElseIf e < 0 Then
13.             r = "0." + String$(Abs(e) - 1, "0") + r
14.         End If
15.     End If
16.     For k = 1 To 3
17.         tmp = mr$(r, "*", r)
18.         tmp = mr$(tmp, "-", n$)
19.         r2 = mr$(r, "+", r)
20.         tmp = mr$(tmp, "/", r2)
21.         r = mr$(r, "-", tmp)
22.         If Len(r) > 101 Then r = Left$(r, 101)
23.     Next k 'Loop Until Abs(Val(tmp)) < 1D-100
24.     sqrt$ = r
25. End Function
26.  

Enter a number to find it's square root ?  20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 26.375  141421356237309504880168872420969807856967187537694807317667.9737990732478462107038850387534327641572
 .0546875          141421356237309504880168872420969807856967187537694807317667.9737990732478462107038850387534327641572

about 482 times faster

[jack]

bplus, there's a bug in your subtract routine

Code: QB64: [Select]

1. result$ = mr$(".00000000000000000000000000000000000000000000200000000000000054307978001764", "-", ".000000000000000000000000000000000000000000002")
2. Print result$
3.  

the output

.000000000000000000000054307978001764

it should be

.00000000000000000000000000000000000000000000000000000000000054307978001764