Some mathematical functions like sine, cosine, tangens etc are a little bit slow, so a speedier alternative might be useful. This is what the new FastMath macro is good for: You feed it with a range of y=f(x) values, and then you can use a new fast function. Example:
FastMath MyBessel ; -------- create the MyBessel function --------
xor ecx, ecx ; counter for the arrays
For_ fct=-10.0 To 20.0 Step 0.1
fld fct
fst x(ecx) ; assign to x() array
fstp REAL10 ptr [edi] ; and to the FastMath macro
void gsl_sf_bessel_J0(fct) ; see GNU Scientific Library Reference (http://www.gnu.org/software/gsl/manual/gsl-ref.html)
fst y(ecx) ; assign to y() array
fstp REAL10 ptr [edi+REAL10] ; and to the FastMath macro
add edi, 2*REAL10
inc ecx
Next
FastMath
The usage of the new function is pretty simple, for example:
Print Str$("MyBessel(10.0)=%f\n", MyBessel(10.0))
Attached a full example with a graphical interface. Building requires MasmBasic version 3 September 2020 (http://masm32.com/board/index.php?topic=94.0). It may ask you at a certain point to install the GSL dlls; if that works (it should, it's only 3MB), you'll see them afterwards in \masm32\MasmBasic\GnuScLib\DLL\*.dll
New version, needs MasmBasic version 4 September (http://masm32.com/board/index.php?topic=94.0) to build. The attachment does no longer need the Gnu Scientific Library because I discovered that the ordinary CRT has a Bessel function, too :cool:
Now there are two versions of FastMath available:
a) FastMath FastLog10 ; define a math function
For_ fct=0.0 To 10.0 Step 0.5 ; max 10,000 iterations
fld fct ; X
fstp REAL10 ptr [edi]
void Log10(fct) ; Y (built-in MasmBasic function)
fstp REAL10 ptr [edi+REAL10]
add edi, 2*REAL10
Next
FastMath
Print Str$("Log(5.0)=%Jf", FastLog10(5)v)
b) if you save the REAL10 X/Y pairs to disk, you can use e.g. the one-liner FastMath MyLog10, "log10.dat"
For the one-liner, the second arg is a filename or a resource ID (data are in a RCDATA resource), or even a URL.
Inspired by srvaldez at the FreeBasic forum: (https://www.freebasic.net/forum/viewtopic.php?f=3&t=29147#p279617)
Intel(R) Core(TM) i5-2450M CPU @ 2.50GHz
ExpE_slow: 1987 ms for the sum 3.3071e+300
ExpE_fast: 699 ms for the sum 3.3074e+300
ExpE_slow: 1974 ms for the sum 3.3071e+300
ExpE_fast: 701 ms for the sum 3.3074e+300
ExpE_slow: 1982 ms for the sum 3.3071e+300
ExpE_fast: 692 ms for the sum 3.3074e+300
ExpE_slow: 1952 ms for the sum 3.3071e+300
ExpE_fast: 691 ms for the sum 3.3074e+300
Speed gain factor: 2.83
Source (attached):
include \masm32\MasmBasic\MasmBasic.inc
SetGlobals ct, sum:REAL10, fct:REAL8, timeSlow, timeFast
Init
PrintCpu 0
FastMath ExpE_fast
For_ fct=0.0 To 680.0 Step 0.08
fld fct ; X
fstp REAL10 ptr [edi]
void ExpE(fct) ; Y (ExpE is a built-in MasmBasic function)
fstp REAL10 ptr [edi+REAL10]
add edi, 2*REAL10
Next
FastMath
push 4
.Repeat
NanoTimer()
Clr sum
For_ ct=1 To 100000-1
xor ecx, ecx
.Repeat
void ExpE(ecx) ; calculates ExpE(ecx) and leaves the result in ST(0)
fld sum
fadd ; sum+=ExpE(ecx)
fstp sum
inc ecx
.Until ecx>680
Next
add timeSlow, NanoTimer(ms)
Print Str$("ExpE_slow: %___i ms", eax), Str$(" for the sum %5e\n", sum) ; expected sum = 3.31e+300
fldz
fstp sum ; Clr sum
NanoTimer()
Clr sum
For_ ct=1 To 100000-1
xor ecx, ecx
.Repeat
void ExpE_fast(ecx) ; calculates ExpE(ecx) approximately and leaves the result in ST(0)
fld sum
fadd
fstp sum
inc ecx
.Until ecx>680
Next
add timeFast, NanoTimer(ms)
Print Str$("ExpE_fast: %___i ms", eax), Str$(" for the sum %5e\n\n", sum) ; expected sum = 3.31e+300
dec stack
.Until Sign?
Inkey Str$("Speed gain factor: %3f", timeSlow/timeFast)
EndOfCode