MapleEvalhf - Maple Help

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MapleEvalhf

evaluate an object using hardware floats in external code

EvalhfMapleProc

evaluate a procedure using hardware floats in external code

 Calling Sequence MapleEvalhf(kv, s) EvalhfMapleProc(kv, fn, n, args)

Parameters

 kv - kernel handle of type MKernelVector s - type ALGEB object fn - Maple FUNCTION object n - number of arguments args - array of n hardware floats

Description

 • These functions can be used in external code with OpenMaple or define_external.
 • MapleEvalhf evaluates an expression to a numerical value using the hardware floating-point of the underlying system.  This command is equivalent to the Maple function, evalhf.
 • EvalhfMapleProc evaluates the function, f(args), to a numerical value using evalhf.  The n arguments provided are all 64-bit hardware floating-point numbers. 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.

Examples

 #include #include "maplec.h" ALGEB M_DECL MyNewton( MKernelVector kv, ALGEB *args ) { M_INT i; FLOAT64 guess[2], tolerance; 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 ); } guess[1] = MapleEvalhf(kv,args[2]); tolerance = MapleEvalhf(kv,args[3]); for( i=0; i<500; ++i ) { if( fabs(EvalhfMapleProc(kv,f,1,guess)) <= tolerance ) break; guess[1] = guess[1] - EvalhfMapleProc(kv,f,1,guess) / EvalhfMapleProc(kv,fprime,1,guess); } if( i == 500 ) { MapleRaiseError(kv,"unable to find root after 500 iterations"); return( NULL ); } return( ToMapleFloat(kv,guess[1]) ); }

Execute the external function from Maple.

 > $\mathrm{with}\left(\mathrm{ExternalCalling}\right):$
 > $\mathrm{dll}≔\mathrm{ExternalLibraryName}\left("HelpExamples"\right):$
 > $\mathrm{newton}≔\mathrm{DefineExternal}\left("MyNewton",\mathrm{dll}\right):$
 > $f≔{x}^{4}-5{x}^{2}+6x-2:$
 > $\mathrm{newton}\left(f,0,0.001\right)$
 ${0.731892751250226237}$ (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)
 > $\genfrac{}{}{0}{}{f}{\phantom{x=}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{f}}{x=}$
 ${0.000003833}$ (4)
 > $\mathrm{newton}\left(f,-\mathrm{π},1.{10}^{-10}\right)$
 ${-}{2.73205080756887719}$ (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)
 > $f≔\mathrm{unapply}\left(f,x\right):$
 > $\mathrm{newton}\left(f,-\mathrm{π},1.{10}^{-10}\right)$
 ${-}{2.73205080756887719}$ (7)
 > $\mathrm{evalhf}\left(f\left(\right)\right)$
 ${-}{7.10542735760100186}{}{{10}}^{{-15}}$ (8)