EvalhfDataProc - Maple Help

EvalhfDataProc

evaluate a procedure using the hardware floats evaluator with floats, procedures and rtables as arguments

 Calling Sequence EvalhfDataProc(kv, fn, n, args)

Parameters

 kv - kernel handle of type MKernelVector fn - Maple FUNCTION object n - number of arguments args - array of n hfdata structs

Description

 • These functions can be used in external code with OpenMaple or define_external.
 • EvalhfDataProc evaluates the function, f(args), to a numerical value using evalhf.  The n arguments provided are all hfdata structures representing complex floating point values, Maple procedures or rtables of type float[8].  The first argument must be inserted at args[1].  For example, to call f(3.14,2.718), set args[1] = 3.14, and args[2] = 2.718.  The value at args[0] is not used.
 • The MapleTohfData function can be used to initialize the hfdata from a Maple procedure or rtable.  The DoubleTohfData and ComplexTohfData routines can be used to initialize an hfdata variable from doubles or pairs of doubles.
 • The return value of EvalhfDataProc is an hfdata object.  Currently this will always represent a real double.  The real component of an hfData structure can be accessed using the RealhfData function.

Examples

 #include #include "maplec.h" ALGEB MyNewtonData( MKernelVector kv, ALGEB *args ) { M_INT i; FLOAT64 tolerance, newguess, res; hfdata guess[2]; ALGEB f, fprime, x; if( 3 != MapleNumArgs(kv,(ALGEB)args) ) { MapleRaiseError(kv,"three arguments expected"); return( NULL ); } if( IsMapleProcedure(kv,args[1]) ) { f = args[1]; } else { ALGEB indets; indets = EvalMapleProc(kv,ToMapleName(kv,"indets",TRUE),1,args[1]); if( !IsMapleSet(kv,indets) || MapleNumArgs(kv,indets) != 1 ) { MapleRaiseError(kv,"unable to find roots"); return( NULL ); } i = 1; f = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2,args[1], MapleSelectIndexed(kv,indets,1,&i)); if( !f || !IsMapleProcedure(kv,f) ) { MapleRaiseError(kv,"unable to convert first arg to a procedure"); return( NULL ); } } x = ToMapleName(kv,"x",FALSE); fprime = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2, EvalMapleProc(kv,ToMapleName(kv,"diff",TRUE),2, ToMapleFunction(kv,f,1,x),x),x); if( !fprime || !IsMapleProcedure(kv,fprime) ) { MapleRaiseError(kv,"unable to compute derivative"); return( NULL ); } DoubleTohfData( kv, MapleEvalhf( kv, args[2] ), 0, guess+1 ); tolerance = MapleEvalhf(kv,args[3]); res = 0.0; for( i=0; i<500; ++i ) { res = RealhfData( kv, EvalhfDataProc(kv,f,1,guess) ); if( fabs( res ) <= tolerance ) break; newguess = RealhfData( kv, guess[1] ) - res / RealhfData( kv, EvalhfDataProc(kv,fprime,1,guess) ); DoubleTohfData( kv, newguess, 0, guess+1 ); } if( i == 500 ) { MapleRaiseError(kv,"unable to find root after 500 iterations"); return( NULL ); } return( ToMapleFloat(kv, RealhfData( kv, guess[1] ) ) ); }

Execute the external function from Maple.

 > $\mathrm{with}\left(\mathrm{ExternalCalling}\right):$
 > $\mathrm{dll}≔\mathrm{ExternalLibraryName}\left("HelpExamples"\right):$
 > $\mathrm{newton}≔\mathrm{DefineExternal}\left("MyNewtonData",\mathrm{dll}\right):$
 > $f≔{x}^{4}-5{x}^{2}+6x-2:$
 > $\mathrm{newton}\left(f,0,0.001\right)$
 ${0.731892751250226237}$ (1)
 > $\genfrac{}{}{0}{}{f}{\phantom{x=}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{f}}{x=}$
 ${-0.000039355}$ (2)
 > $\mathrm{newton}\left(f,\sqrt{2},0.00001\right)$
 ${1.00195003210012135}$ (3)
 > $\genfrac{}{}{0}{}{f}{\phantom{x=}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{f}}{x=}$
 ${3.833}{×}{{10}}^{{-6}}$ (4)
 > $\mathrm{newton}\left(f,-\mathrm{Pi},1.{10}^{-10}\right)$
 ${-2.73205080756887719}$ (5)
 > $\mathrm{Digits}≔15:$
 > $\genfrac{}{}{0}{}{f}{\phantom{x=}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{f}}{x=}$
 ${1.5}{×}{{10}}^{{-13}}$ (6)
 > $f≔\mathrm{unapply}\left(f,x\right):$
 > $\mathrm{newton}\left(f,-\mathrm{Pi},1.{10}^{-10}\right)$
 ${-2.73205080756887719}$ (7)
 > $\mathrm{evalhf}\left(f\left(\right)\right)$
 ${-7.10542735760100186}{×}{{10}}^{{-15}}$ (8)