I am playing with two new macros that use a variant of the Horner scheme:
SetPoly3 My3Pts() ; use three XY pairs to get a0...a2
GetPoly3(AllPts()) ; fill an array using y=a0+a1*(x-x0)+a2*(x-x0)*(x-x1)
Work in progress. In the attached executable, the two outer points are fixed, the middle one moves with the mouse.
very cool :t
i remember, long ago, i needed something like this
now, i can't remember what it was for - lol
that was back in the DOS days
it seems to hang up under certain conditions - hard to describe
i am sure you are aware of it - as you say, work in progress
Quote from: dedndave on March 19, 2013, 01:52:09 PM
it seems to hang up under certain conditions - hard to describe
Usually you can unblock it by moving around the lower right corner.
Here is a variant that uses the three red points to define the bounding rectangle. The only difference is that now the other points can go outside the rect.
if 1 ; optional: use the "biggest" array to define a common range
ArrayPlot My3Pts(XY), 0, 0, MyMargins, SetRange ; the three red points define the range
else
ArrayPlot AllPts(XY), 0, 0, MyMargins, SetRange ; the big array defines the range
endif
Quote from: jj2007 on March 19, 2013, 11:11:03 PM
Seeing your code would be nice indeed ;-)
it is an assembler forum, afterall :P
I somehow like the idea and looked up for an robust algorithm for getting polynomials through arbitrary points and found the method of divided differences (similar: hermite interpolation ).
An C implementation can be found here (http://people.sc.fsu.edu/~jburkardt/c_src/divdif/divdif.c) (functions: data_to_dif and dif_val).
In the attachment a example (sry, no source): with the left mouse button you can add and drag points, which are used for interpolation. With the right mouse button selected points are removed.
qWord
Quote from: qWord on March 22, 2013, 12:56:02 PMmethod of divided differences (similar: hermite interpolation )
Nice link :t
Reference:
Carl deBoor,
A Practical Guide to Splines,
Springer, 2001The reference for my macros is Dubbel, Taschenbuch für den Maschinenbau (http://de.wikipedia.org/wiki/Taschenbuch_f%C3%BCr_den_Maschinenbau),
Springer 19xx (can't find the book right now, but it must be before 1981).
If I find time over the weekend, I'll post a new edition of MasmBasic with the sources.
EDIT: Sources are online, see here (http://masm32.com/board/index.php?topic=94.msg17181#msg17181)
Pretty good video explanation of Horner's Method here (https://youtu.be/zEvfkSuPqWk).
Quote from: NoCforMe on December 19, 2023, 10:10:02 AMPretty good video explanation of Horner's Method here (https://youtu.be/zEvfkSuPqWk).
Great :biggrin:
So the basics of FastMath (https://www.jj2007.eu/MasmBasicQuickReference.htm#Mb1520) were invented 1000 years ago by Jia Xian (1010...1070) :cool:
:thumbsup: Just take into acount that precision drop from 10-12 (or so) to 10-4 making interpolations.
Quote from: HSE on December 19, 2023, 10:59:31 AMprecision drop
Which precision drop?
include \masm32\MasmBasic\MasmBasic.inc
SetGlobals fct:REAL10
Init
Cls 5
FastMath FastLog10 ; define a math function
For_ fct=0.001 To 10.0 Step 0.01 ; max 10,000 iterations
fld fct ; X
fstp REAL10 ptr [edi]
void Log10(fct) ; Y (built-in MasmBasic function)
fstp REAL10 ptr [edi+REAL10]
add edi, 2*REAL10
Next
FastMath
For_ fct=0.001 To 7.5 Step 0.5
Print Str$("Log(%3f):\t", fct), Str$("%Gf = ", FastLog10(fct)v), Str$("%Gf\n", Log10(fct)v)
Next
EndOfCodeLog(0.00100): -3.000000000000000 = -3.000000000000000
Log(0.501): -0.3001622741327543 = -0.3001622741327543
Log(1.00): 4.340774793186407e-04 = 4.340774793186407e-04
Log(1.50): 0.1763806922432704 = 0.1763806922432704
Log(2.00): 0.3012470886362114 = 0.3012470886362114
Log(2.50): 0.3981136917305025 = 0.3981136917305025
Log(3.00): 0.4772659954248526 = 0.4772659954248526
Log(3.50): 0.5441921107650326 = 0.5441921107650326
Log(4.00): 0.6021685513789972 = 0.6021685513789972
Log(4.50): 0.6533090129384789 = 0.6533090129384789
Log(5.00): 0.6990568545476678 = 0.6990568545476678
Log(5.50): 0.7404416449497660 = 0.7404416449497660
Log(6.00): 0.7782236267660965 = 0.7782236267660965
Log(6.50): 0.8129801660394804 = 0.8129801660394804
Log(7.00): 0.8451600776519458 = 0.8451600776519458
:biggrin:
Quote from: HSE on December 19, 2023, 10:59:31 AMprecision drop ... making interpolations.
Using the table values is just table precision :thumbsup:
include \masm32\MasmBasic\MasmBasic.inc
SetGlobals fct:REAL10
Init
Cls 5
FastMath FastLog10 ; define a math function
For_ fct=1.0 To 10.0 Step 1.0 ; max 10,000 iterations
fld fct ; X
fstp REAL10 ptr [edi]
void Log10(fct) ; Y (built-in MasmBasic function)
fstp REAL10 ptr [edi+REAL10]
add edi, 2*REAL10
Next
FastMath
For_ fct=1.5 To 7.5 Step 1.0
Print Str$("Log(%3f):\t", fct), Str$("%Gf = ", FastLog10(fct)v), Str$("%Gf\n", Log10(fct)v)
Next
EndOfCode
Log(1.50): 0.1661323399080281 = 0.1760912590556812
Log(2.50): 0.3954696904977445 = 0.3979400086720376
Log(3.50): 0.5430942134738429 = 0.5440680443502756
Log(4.50): 0.6527310937020445 = 0.6532125137753437
Log(5.50): 0.7413197895734896 = 0.7403626894942438
Log(6.50): 0.8135372823265489 = 0.8129133566428556
Log(7.50): 0.8754905888107381 = 0.8750612633917000
Sure, but why a table with only 10 entries? What stops you from creating a bigger table?
664 µs for creating a table with 6400 entries
Log(0.00100): -3.000000000000000 = -3.000000000000000
Log(0.251): -0.6003262785189619 = -0.6003262785189619
Log(0.501): -0.3001622741327543 = -0.3001622741327543
Log(0.751): -0.1243600629958316 = -0.1243600629958316
Log(1.00): 4.340774793186407e-04 = 4.340774793186407e-04
...
Less than one millisecond for the creation of the table, which is done only once at program start...
Quote from: jj2007 on December 19, 2023, 10:30:49 PMSure, but why a table with only 10 entries? What stops you from creating a bigger table?
:thumbsup: That is the point: No problem using table values, be careful using interpolation.