/* monotl.c Floating point function test vectors . Arguments and function values are synthesized for NPTS points in the vicinity of each given tabulated test point . The points are chosen to be near and on either side of the likely function algorithm domain boundaries . Since the function programs change their methods at these points , major coding errors or monotonicity failures might be detected . August , 1998 /* Unit of error tolerance in test[i].thresh. */ static long double MACHEPL =5 .42101086242752217003726400434970855712890625 E-20 L;/* How many times the above error to allow before printing a complaint. #define TOL 8 /* Number of test points to generate on each side of tabulated point. */ #define NPTS 100 #include <stdio.h>/* Avoid including math.h. */ long double frexpl (long double , int *);long double ldexpl (long double , int );/* Functions of one variable. */ long double expl (long double );long double logl (long double );long double sinl (long double );long double cosl (long double );long double tanl (long double );long double atanl (long double );long double asinl (long double );long double acosl (long double );long double sinhl (long double );long double coshl (long double );long double tanhl (long double );long double asinhl (long double );long double acoshl (long double );long double atanhl (long double );#if 1 long double lgaml (long double );long double gammal (long double );#define lgammal lgaml#else long double lgammal (long double );long double tgammal (long double );#define lgammal lgaml#define gammal tgammal#endif long double fabsl (long double );long double floorl (long double );long double j0l (long double );long double y0l (long double );long double j1l (long double );long double y1l (long double );/* Data structure of the test. */ struct oneargumentchar *name; /* Name of the function. */ long double (*func) (long double ); /* Function call. */ long double arg1; /* Function argument, assumed exact. */ long double answer1; /* Exact number, close to function value. */ long double answer2; /* answer1 + answer2 has extended precision. */ long double derivative; /* dy/dx evaluated at x = arg1. */ /* Error report threshold. 2 => 1 ulp approximately int thresh;struct oneargument test1[] ="exp" , expl, 1 .0 L, 2 .7182769775390625 L,4 .85091998273536028747 e-6 L, 2 .71828182845904523536 L, TOL},"exp" , expl, -1 .0 L, 3 .678741455078125 e-1 L,5 .29566362982159552377 e-6 L, 3 .678794411714423215955 e-1 L, TOL},"exp" , expl, 0 .5 L, 1 .648712158203125 L,9 .1124970031468486507878 e-6 L, 1 .64872127070012814684865 L, TOL},"exp" , expl, -0 .5 L, 6 .065216064453125 e-1 L,9 .0532673209236037995 e-6 L, 6 .0653065971263342360 e-1 L, TOL},"exp" , expl, 2 .0 L, 7 .3890533447265625 L,2 .75420408772723042746 e-6 L, 7 .38905609893065022723 L, TOL},"exp" , expl, -2 .0 L, 1 .353302001953125 e-1 L,5 .08304130019189399949 e-6 L, 1 .3533528323661269189 e-1 L, TOL},"log" , logl, 1 .41421356237309492343 L, 3 .465728759765625 e-1 L,7 .1430341006605745676897 e-7 L, 7 .0710678118654758708668 e-1 L, TOL},"log" , logl, 7 .07106781186547461715 e-1 L, -3 .46588134765625 e-1 L,1 .45444856522566402246 e-5 L, 1 .41421356237309517417 L, TOL},"sin" , sinl, 7 .85398163397448278999 e-1 L, 7 .0709228515625 e-1 L,1 .4496030297502751942956 e-5 L, 7 .071067811865475460497 e-1 L, TOL},"sin" , sinl, -7 .85398163397448501044 e-1 L, -7 .071075439453125 e-1 L,7 .62758764840238811175 e-7 L, 7 .07106781186547389040 e-1 L, TOL},"sin" , sinl, 1 .570796326794896558 L, 9 .999847412109375 e-1 L,1 .52587890625 e-5 L, 6 .12323399573676588613 e-17 L, TOL},"sin" , sinl, -1 .57079632679489678004 L, -1 .0 L,1 .29302922820150306903 e-32 L, -1 .60812264967663649223 e-16 L, TOL},"sin" , sinl, 4 .712388980384689674 L, -1 .0 L,1 .68722975549458979398 e-32 L, -1 .83697019872102976584 e-16 L, TOL},"sin" , sinl, -4 .71238898038468989604 L, 9 .999847412109375 e-1 L,1 .52587890625 e-5 L, 3 .83475850529283315008 e-17 L, TOL},"cos" , cosl, 3 .92699081698724139500 E-1 L, 9 .23873901367187500000 E-1 L,5 .63114409926198633370 E-6 L, -3 .82683432365089757586 E-1 L, TOL},"cos" , cosl, 7 .85398163397448278999 E-1 L, 7 .07092285156250000000 E-1 L,1 .44960302975460497458 E-5 L, -7 .07106781186547502752 E-1 L, TOL},"cos" , cosl, 1 .17809724509617241850 E0L, 3 .82675170898437500000 E-1 L,8 .26146665231415693919 E-6 L, -9 .23879532511286738554 E-1 L, TOL},"cos" , cosl, 1 .96349540849362069750 E0L, -3 .82690429687500000000 E-1 L,6 .99732241029898567203 E-6 L, -9 .23879532511286785419 E-1 L, TOL},"cos" , cosl, 2 .35619449019234483700 E0L, -7 .07107543945312500000 E-1 L,7 .62758765040545859856 E-7 L, -7 .07106781186547589348 E-1 L, TOL},"cos" , cosl, 2 .74889357189106897650 E0L, -9 .23889160156250000000 E-1 L,9 .62764496328487887036 E-6 L, -3 .82683432365089870728 E-1 L, TOL},"cos" , cosl, 3 .14159265358979311600 E0L, -1 .00000000000000000000 E0L,7 .49879891330928797323 E-33 L, -1 .22464679914735317723 E-16 L, TOL},"tan" , tanl, 7 .85398163397448278999 E-1 L, 9 .999847412109375 e-1 L,1 .52587890624387676600 E-5 L, 1 .99999999999999987754 E0L, TOL},"tan" , tanl, 1 .17809724509617241850 E0L, 2 .41419982910156250000 E0L,1 .37332715322352112604 E-5 L, 6 .82842712474618858345 E0L, TOL},"tan" , tanl, 1 .96349540849362069750 E0L, -2 .41421508789062500000 E0L,1 .52551752942854759743 E-6 L, 6 .82842712474619262118 E0L, TOL},"tan" , tanl, 2 .35619449019234483700 E0L, -1 .00001525878906250000 E0L,1 .52587890623163029801 E-5 L, 2 .00000000000000036739 E0L, TOL},"tan" , tanl, 2 .74889357189106897650 E0L, -4 .14215087890625000000 E-1 L,1 .52551752982565655126 E-6 L, 1 .17157287525381000640 E0L, TOL},"atan" , atanl, 4 .14213562373094923430 E-1 L, 3 .92684936523437500000 E-1 L,1 .41451752865477964149 E-5 L, 8 .53553390593273837869 E-1 L, TOL},"atan" , atanl, 1 .0 L, 7 .85385131835937500000 E-1 L,1 .30315615108096156608 E-5 L, 0 .5 L, TOL},"atan" , atanl, 2 .41421356237309492343 E0L, 1 .17808532714843750000 E0L,1 .19179477349460632350 E-5 L, 1 .46446609406726250782 E-1 L, TOL},"atan" , atanl, -2 .41421356237309514547 E0L, -1 .17810058593750000000 E0L,3 .34084132752141908545 E-6 L, 1 .46446609406726227789 E-1 L, TOL},"atan" , atanl, -1 .0 L, -7 .85400390625000000000 E-1 L,2 .22722755169038433915 E-6 L, 0 .5 L, TOL},"atan" , atanl, -4 .14213562373095145475 E-1 L, -3 .92700195312500000000 E-1 L,1 .11361377576267665972 E-6 L, 8 .53553390593273703853 E-1 L, TOL},"asin" , asinl, 3 .82683432365089615246 E-1 L, 3 .92684936523437500000 E-1 L,1 .41451752864854321970 E-5 L, 1 .08239220029239389286 E0L, TOL},"asin" , asinl, 0 .5 L, 5 .23590087890625000000 E-1 L,8 .68770767387307710723 E-6 L, 1 .15470053837925152902 E0L, TOL},"asin" , asinl, 7 .07106781186547461715 E-1 L, 7 .85385131835937500000 E-1 L,1 .30315615107209645016 E-5 L, 1 .41421356237309492343 E0L, TOL},"asin" , asinl, 9 .23879532511286738483 E-1 L, 1 .17808532714843750000 E0L,1 .19179477349183147612 E-5 L, 2 .61312592975275276483 E0L, TOL},"asin" , asinl, -0 .5 L, -5 .23605346679687500000 E-1 L,6 .57108138862692289277 E-6 L, 1 .15470053837925152902 E0L, TOL},"asin" , asinl, 1 .16415321826934814453125 e-10 L,1 .16415321826934814453125 e-10 L, 2 .629536350736706018055 e-31 L,1 .0000000000000000000067762 L, TOL},"asin" , asinl, 1 .0000000000000000000183779 E-10 L,9 .9999999979890480394928431 E-11 L, 2 .0109519607076028264987890 E-20 L,1 .0 L, TOL},"asin" , asinl, 1 .0000000000000000000007074 E-8 L,9 .9999999999948220585910263 E-9 L, 5 .1781080827147808155022014 E-21 L,1 .0 L, TOL},"asin" , asinl, 0 .97499847412109375 L, 1 .346710205078125 L,3 .969526822009922560999 e-6 L, 4 .500216008585875735254 L, TOL},"acos" , acosl, 1 .95090322016128192573 E-1 L, 1 .37443542480468750000 E0L,1 .13611408471185777914 E-5 L, -1 .01959115820831832232 E0L, TOL},"acos" , acosl, 3 .82683432365089615246 E-1 L, 1 .17808532714843750000 E0L,1 .19179477351337991247 E-5 L, -1 .08239220029239389286 E0L, TOL},"acos" , acosl, 0 .5 L, 1 .04719543457031250000 E0L,2 .11662628524615421446 E-6 L, -1 .15470053837925152902 E0L, TOL},"acos" , acosl, 7 .07106781186547461715 E-1 L, 7 .85385131835937500000 E-1 L,1 .30315615108982668201 E-5 L, -1 .41421356237309492343 E0L, TOL},"acos" , acosl, 9 .23879532511286738483 E-1 L, 3 .92684936523437500000 E-1 L,1 .41451752867009165605 E-5 L, -2 .61312592975275276483 E0L, TOL},"acos" , acosl, 9 .80785280403230430579 E-1 L, 1 .96334838867187500000 E-1 L,1 .47019821746724723933 E-5 L, -5 .12583089548300990774 E0L, TOL},"acos" , acosl, -0 .5 L, 2 .09439086914062500000 E0L,4 .23325257049230842892 E-6 L, -1 .15470053837925152902 E0L, TOL},"sinh" , sinhl, 1 .0 L, 1 .17518615722656250000 E0L,1 .50364172389568823819 E-5 L, 1 .54308063481524377848 E0L, TOL},"sinh" , sinhl, 7 .09089565712818057364 E2L, 4 .49423283712885057274 E307L,1 .70878916528708958045 E289L, 4 .49423283712885057274 E307L, TOL},"sinh" , sinhl, 2 .22044604925031308085 E-16 L, 0 .00000000000000000000 E0L,2 .22044604925031308085 E-16 L, 1 .00000000000000000000 E0L, TOL},"sinh" , sinhl, 3 .7252902984619140625 e-9 L, 3 .7252902984619140625 e-9 L,8 .616464714094038285889380656847999229 E-27 L,1 .00000000000000000693889 L, TOL},"sinh" , sinhl, 2 .3283064365386962890625 e-10 L, 2 .3283064365386962890625 e-10 L,2 .103629080589364814436978072135626630 E-30 ,1 .000000000000000000027105 L, TOL},"cosh" , coshl, 7 .09089565712818057364 E2L, 4 .49423283712885057274 E307L,1 .70878916528708958045 E289L, 4 .49423283712885057274 E307L, TOL},"cosh" , coshl, 1 .0 L, 1 .54307556152343750000 E0L,5 .07329180627847790562 E-6 L, 1 .17520119364380145688 E0L, TOL},"cosh" , coshl, 0 .5 L, 1 .12762451171875000000 E0L,1 .45348763078522622516 E-6 L, 5 .21095305493747361622 E-1 L, TOL},"tanh" , tanhl, 0 .5 L, 4 .62112426757812500000 E-1 L,4 .73050219725850231848 E-6 L, 7 .86447732965927410150 E-1 L, TOL},"tanh" , tanhl, 5 .49306144334054780032 E-1 L, 4 .99984741210937500000 E-1 L,1 .52587890624507506378 E-5 L, 7 .50000000000000049249 E-1 L, TOL},"tanh" , tanhl, 0 .625 L, 5 .54595947265625000000 E-1 L,3 .77508375729399903910 E-6 L, 6 .92419147969988069631 E-1 L, TOL},"asinh" , asinhl, 0 .5 L, 4 .81201171875000000000 E-1 L,1 .06531846034474977589 E-5 L, 8 .94427190999915878564 E-1 L, TOL},"asinh" , asinhl, 1 .0 L, 8 .81362915039062500000 E-1 L,1 .06719804805252326093 E-5 L, 7 .07106781186547524401 E-1 L, TOL},"asinh" , asinhl, 2 .0 L, 1 .44363403320312500000 E0L,1 .44197568534249327674 E-6 L, 4 .47213595499957939282 E-1 L, TOL},"acosh" , acoshl, 2 .0 L, 1 .31695556640625000000 E0L,2 .33051856670862504635 E-6 L, 5 .77350269189625764509 E-1 L, TOL},"acosh" , acoshl, 1 .5 L, 9 .62417602539062500000 E-1 L,6 .04758014439499551783 E-6 L, 8 .94427190999915878564 E-1 L, TOL},"acosh" , acoshl, 1 .03125 L, 2 .49343872070312500000 E-1 L,9 .62177257298785143908 E-6 L, 3 .96911150685467059809 E0L, TOL},"atanh" , atanhl, 0 .5 L, 5 .49301147460937500000 E-1 L,4 .99687311734569762262 E-6 L, 1 .33333333333333333333 E0L, TOL},"j0" , j0l, 8 .0 L, 1 .71646118164062500000 E-1 L,4 .68897349140609086941 E-6 L, -2 .34636346853914624381 E-1 , -4 },"j0" , j0l, 4 .54541015625 L, -3 .09783935546875000000 E-1 L,7 .07472668157686463367 E-6 L, 2 .42993657373627558460 E-1 L, -4 },"j0" , j0l, 2 .85711669921875 L, -2 .07901000976562500000 E-1 L,1 .15237285263902751582 E-5 L, -3 .90402225324501311651 E-1 L, -4 },"j0" , j0l, 2 .0 L, 2 .23876953125000000000 E-1 L,1 .38260162356680518275 E-5 L, -5 .76724807756873387202 E-1 L, -4 },"j0" , j0l, 1 .16415321826934814453125 e-10 L, 9 .99984741210937500000 E-1 L,1 .52587890624999966119 E-5 L, 9 .99999999999999999997 E-1 L, -4 },"j0" , j0l, -2 .0 L, 2 .23876953125000000000 E-1 L,1 .38260162356680518275 E-5 L, 5 .76724807756873387202 E-1 L, -4 },"y0" , y0l, 8 .0 L, 2 .23510742187500000000 E-1 L,1 .07472000662205273234 E-5 L, 1 .58060461731247494256 E-1 L, -4 },"y0" , y0l, 4 .54541015625 L, -2 .08114624023437500000 E-1 L,1 .45018823856668874574 E-5 L, -2 .88887645307401250876 E-1 L, -4 },"y0" , y0l, 2 .85711669921875 L, 4 .20303344726562500000 E-1 L,1 .32781607563122276008 E-5 L, -2 .82488638474982469213 E-1 , -4 },"y0" , y0l, 2 .0 L, 5 .10360717773437500000 E-1 L,1 .49548763076195966066 E-5 L, 1 .07032431540937546888 E-1 L, -4 },"y0" , y0l, 1 .16415321826934814453125 e-10 L, -1 .46357574462890625000 E1L,3 .54110537011061127637 E-6 L, 5 .46852220461145271913 E9L, -4 },"j1" , j1l, 8 .0 L, 2 .34634399414062500000 E-1 L,1 .94743985212438127665 E-6 L,1 .42321263780814578043 E-1 , -4 },"j1" , j1l, 4 .54541015625 L, -2 .42996215820312500000 E-1 L,2 .55844668494153980076 E-6 L, -2 .56317734136211337012 E-1 , -4 },"j1" , j1l, 2 .85711669921875 L, 3 .90396118164062500000 E-1 L,6 .10716043881165077013 E-6 L, -3 .44531507106757980441 E-1 L, -4 },"j1" , j1l, 2 .0 L, 5 .76721191406250000000 E-1 L,3 .61635062338720244824 E-6 L, -6 .44716247372010255494 E-2 L, -4 },"j1" , j1l, 1 .16415321826934814453125 e-10 L,5 .820677273504770710133016109466552734375 e-11 L,8 .881784197001251337312921818461805735896 e-16 L,4 .99999999999999999997 E-1 L, -4 },"j1" , j1l, -2 .0 L, -5 .76721191406250000000 E-1 L,3 .61635062338720244824 E-6 L, -6 .44716247372010255494 E-2 L, -4 },"y1" , y1l, 8 .0 L, -1 .58065795898437500000 E-1 L,5 .33416719000574444473 E-6 L, 2 .43279047103972157309 E-1 L, -4 },"y1" , y1l, 4 .54541015625 L, 2 .88879394531250000000 E-1 L,8 .25077615125087585195 E-6 L, -2 .71656024771791736625 E-1 L, -4 },"y1" , y1l, 2 .85711669921875 L, 2 .82485961914062500000 E-1 ,2 .67656091996921314433 E-6 L, 3 .21444694221532719737 E-1 , -4 },"y1" , y1l, 2 .0 L, -1 .07040405273437500000 E-1 L,7 .97373249995311162923 E-6 L, 5 .63891888420213893041 E-1 , -4 },"y1" , y1l, 1 .16415321826934814453125 e-10 L, -5 .46852220500000000000 E9L, 3 .88547280871200700671 E-1 L, 4 .69742480525120196168 E19L, -4 },"gamma" , gammal, 1 .0 L, 1 .0 L,0 .0 L, -5 .772156649015328606 e-1 L, TOL},"gamma" , gammal, 2 .0 L, 1 .0 L,0 .0 L, 4 .2278433509846713939 e-1 L, TOL},"gamma" , gammal, 3 .0 L, 2 .0 L,0 .0 L, 1 .845568670196934279 L, TOL},"gamma" , gammal, 4 .0 L, 6 .0 L,0 .0 L, 7 .536706010590802836 L, TOL},"lgamma" , lgammal, 8 .0 L, 8 .525146484375 L,1 .48766904143001655310 E-5 , 2 .01564147795560999654 E0L, TOL},"lgamma" , lgammal, 8 .99993896484375 e-1 L, 6 .6375732421875 e-2 L,5 .11505711292524166220 E-6 L, -7 .54938684259372234258 E-1 , -TOL},"lgamma" , lgammal, 7 .31597900390625 e-1 L, 2 .2369384765625 e-1 L,5 .21506341809849792422 E-6 L,-1 .13355566660398608343 E0L, -TOL},"lgamma" , lgammal, 2 .31639862060546875 e-1 L, 1 .3686676025390625 L,1 .12609441752996145670 E-5 L, -4 .56670961813812679012 E0, -TOL},"lgamma" , lgammal, 1 .73162841796875 L, -8 .88214111328125 e-2 L,3 .36207740803753034508 E-6 L, 2 .33339034686200586920 E-1 L, -TOL},"lgamma" , lgammal, 1 .23162841796875 L,-9 .3902587890625 e-2 L,1 .28765089229009648104 E-5 L, -2 .49677345775751390414 E-1 L, -TOL},"lgamma" , lgammal, 7 .3786976294838206464 e19L, 3 .301798506038663053312 e21L,1 .656137564136932662487046269677 E5L, 4 .57477139169563904215 E1L, TOL},"lgamma" , lgammal, 1 .0 L, 0 .0 L,0 .0 L, -5 .77215664901532860607 E-1 L, -TOL},"lgamma" , lgammal, 2 .0 L, 0 .0 L,0 .0 L, 4 .22784335098467139393 E-1 L, -TOL},"lgamma" , lgammal, 1 .08420217248550443401 E-19 L,4 .36682586669921875 e1L,1 .37082843669932230418 E-5 L, -9 .22337203685477580858 E18L, TOL},"lgamma" , lgammal, -0 .5 L, 1 .2655029296875 L,9 .19379714539648894580 E-6 L, 3 .64899739785765205590 E-2 L, TOL},"lgamma" , lgammal, -1 .5 L, 8 .6004638671875 e-1 L,6 .28657731014510932682 E-7 L, 7 .03156640645243187226 E-1 L, TOL},"lgamma" , lgammal, -2 .5 L, -5 .6243896484375 E-2 L,1 .79986700949327405470 E-7 , 1 .10315664064524318723 E0L, -TOL},"lgamma" , lgammal, -3 .5 L, -1 .30902099609375 L,1 .43111007079536392848 E-5 L, 1 .38887092635952890151 E0L, TOL},"null" , NULL, 0 .0 L, 0 .0 L, 0 .0 L, 1 },/* These take care of extra-precise floating point register problems. */ volatile long double volat1;volatile long double volat2;/* Return the next nearest floating point value to X in the direction of UPDOWN ( + 1 or - 1 ) . long double long double x;int updown;long double m;int i;0 .25 L * MACHEPL * volat1 * updown;if (volat2 != volat1)"successor failed\n" );for (i = 2 ; i < 10 ; i++)if (volat1 != volat2)return volat2;"nextval failed\n" );return volat1;int long double (*fun1) (long double );int i, j, errs, tests, err_thresh;long double x, x0, dy, err;0 ;0 ;0 ;for (;;)/* Function call reference. */ if (fun1 == NULL)break ;/* Function argument. */ /* x0 is the given argument, x scans from slightly below to above x0. */ for (j = 0 ; j <= NPTS; j++)/* delta x */ /* delta y */ /* y + delta y */ /* Run the function under test. */ if (volat2 != volat1)/* Estimate difference between program result /* Compare difference with reporting threshold. */ if (err_thresh >= 0 )/* relative error */ else /* absolute error */ /* ...but relative error if function value > 1 */ if (fabsl(volat1) > 1 .0 L)if (fabsl (err) > (err_thresh * MACHEPL))"%d %s(%.19Le) = %.19Le, rel err = %.3Le\n" ,1 ;1 );1 ;1 );for (j = 1 ; j < NPTS; j++)if (volat2 != volat1)if (err_thresh >= 0 )/* relative error */ else if (fabsl(volat1) > 1 .0 L)if (fabsl (err) > (err_thresh * MACHEPL))"%d %s(%.19Le) = %.19Le, rel err = %.3Le\n" ,1 ;1 );1 ;1 ;"%d errors in %d tests\n" , errs, tests);exit (0 );
Messung V0.5 in Prozent C=94 H=96 G=94
¤ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet am 2026-06-14)
¤ *© Formatika GbR, Deutschland
