̾??

math - ???إ饤?֥????ؿ???Ƴ??

????

???δؿ??ϡ?C ?ο??إ饤?֥??? libm ?????????ޤ??????󥯥??ǥ????ϡ?“-lm” ???ץ????󤬻??ꤵ?????ȡ????Υ饤?֥????򸡺????ޤ??????δؿ??? ?????ϡ????󥯥롼?ɥե????? ???????Ǥ??ޤ???

?ؿ??ꥹ??

?ʲ??Τ??줾????????????ư?????????ؿ??ϡ?ñ???ٴؿ????ФˤʤäƤ??ꡢ ̾???? f ?ǽ??????ؿ???ñ??????ư?????????򰷤??ޤ??????Ȥ??? acos(double x) ?ϡ???ư?????򰷤? acosf(float x) ???ФˤʤäƤ??ޤ???

̾??	?ڡ???	????	???顼??« (ULP)

acos	sin.3m	?ջ??Ѵؿ?	3
acosh	asinh.3m	???ж????ؿ?	3
asin	sin.3m	?ջ??Ѵؿ?	3
asinh	asinh.3m	???ж????ؿ?	3
atan	sin.3m	?ջ??Ѵؿ?	1
atanh	asinh.3m	???ж????ؿ?	3
atan2	sin.3m	?ջ??Ѵؿ?	2
cabs	hypot.3m	ʣ????????	1
cbrt	sqrt.3m	Ω????	1
ceil	floor.3m	?ʾ???????	0
copysign	ieee.3m	?????ӥåȤΥ??ԡ?	0
cos	sin.3m	???Ѵؿ?	1
cosh	sinh.3m	?ж????ؿ?	3
erf	erf.3m	?????ؿ?	???
erfc	erf.3m	???????ؿ?	???
exp	exp.3m	?ؿ?	1
expm1	exp.3m	exp(x)-1	1
fabs	floor.3m	??????	0
floor	floor.3m	?ʲ???????	0
hypot	hypot.3m	?桼?????åɵ?Υ	1
ilogb	ieee.3m	?ؿ?????	0
j0	j0.3m	?٥å????ؿ?	???
j1	j0.3m	?٥å????ؿ?	???
jn	j0.3m	?٥å????ؿ?	???
lgamma	lgamma.3m	?п??????޴ؿ?(?? gamma.3m)
log	exp.3m	?????п?	1
log10	exp.3m	?줬10???п?	3
log1p	exp.3m	log(1+x)	1
pow	exp.3m	?ؿ? x**y	60-500
remainder	ieee.3m	;??	0
rint	floor.3m	?Ǥ??ᤤ?????˴ݤ???	0
scalbn	ieee.3m	?ؿ?Ĵ??	0
sin	sin.3m	???Ѵؿ?	1
sinh	sinh.3m	?ж????ؿ?	3
sqrt	sqrt.3m	ʿ????	1
tan	sin.3m	???Ѵؿ?	3
tanh	sinh.3m	?ж????ؿ?	3
y0	j0.3m	?٥å????ؿ?	???
y1	j0.3m	?٥å????ؿ?	???
yn	j0.3m	?٥å????ؿ?	???

??

?????ե????˥????ؤ??? 1985 ǯ???????ۤ??줿 4.3 BSD ?Ǥϡ??嵭?δؿ??? 2 ?ĤΥС??????????Ѱդ????Ƥ??ޤ???1 ?Ĥ? DEC VAX-11 ?ե??ߥ??? ?????ԥ塼?????????? "D" ?ե????ޥåȤǡ??⤦ 1 ?Ĥ? IEEE 754 ɸ???? ?Х??ʥ???ư?????????黻?˽??򤷤??????ٱ黻?Ǥ??? UNIX ???????????Ȥ??Τ??Τ????⡢¾?Υץ??????ब???ΤǴ????ˤʤä????? ????ͽ?ۤǤ????褦?ˡ????? 2 ?ĤΥС????????⡢?????˻????褦?? ??ư?򼨤??ޤ??????Ȥ??С????????Υץ????????ϡ?????ɽ?? ulps ?? ???????????ΤǤ???ulp ?ϡ??ǽ?????ñ?̤Ǥ??????????Υץ????????ϡ? ???ĤƤο??إ饤?֥??? libm ??ȯ?????Ƥ????۾????֤????????ޤ????? ???ΰ۾????֤?ȯ???????ȡ??ʲ??Τ褦?ʷ??̤????????Ƥ??ޤ?????

sqrt(-1.0) = 0.0 ?Ǥ??? log(-1.0)= -1.7e38
cos(1.0e-11) > cos(0.0) > 1.0
x = 2.0, 3.0, 4.0, ..., 9.0 ?ΤȤ??ˡ?pow(x,1.0) != x
pow(-1.0,1.0e10) ???????????Хե????㳰?򵯤????Ƥ??? sqrt(1.0e30) ?? sqrt(1.0e-30) ?η׻??????????٤??ä?

?????????? 2 ?ĤΥС????????ˤϡ????????ʤ????Фʤ??ʤ? ?㤤???????ޤ????ʲ??????դ??Ƥ?????????

DEC VAX-11 D_floating-point:

?????ϡ????ꥸ?ʥ??ο??إ饤?֥??? libm ????ȯ???줿?ե????ޥå? ?Ǥ??ꡢ???Υޥ˥奢?뤬??§Ū?˰ͤä?Ω?ĥե????ޥåȤǤ????????ϡ? PDP-11 ?????ӽ????? VAX-11 ?ޥ??????????٥ե????ޥåȤǤ??? 1983 ǯ?ʹߤ? VAX-11 ?ϡ?IEEE ?????٥ե????ޥåȤˤ????ᤤ?? ???ץ??????? "G" ?ե????ޥåȤ??????Ƥ??ޤ????????? DEC MiroVAX ?ˤ? D ?ե????ޥåȤ??ʤ???G ?????٤Τߤ? ?????äƤ??ޤ???

D_floating-point ?Υץ??ѥƥ?:

??ɥ?????: 64 ?ӥåȡ?8 ?Х??ȡ?????: ?Х??ʥꡣ
????: 56 ?ӥåȡ?10 ?ʿ????? 17 ?塣

x ?? x' ??Ϣ³???????? D_floating-point ??ư???????? (1 ulp ???İۤʤ?) ?Ǥ????????ϡ?
1.3e-17 < 0.5**56 < (x'-x)/x ≤ 0.5**55 < 2.8e-17
?Ȥʤ롣

?ϰ?:	?????Хե???????????	= 2.0**127	= 1.7e38
	???????ե???????????	= 0.5**128	= 2.9e-39
	????: ?????ϰϤ?????Ū?˶????ʤäƤ??ޤ???

?????Хե?????ȯ???????ȡ??׻??Ͼ??????Ǥ????ޤ???
???????ե?????ȯ???????ȡ?0 ?ˤʤ??ޤ???
?ٹ?:

???????ե????ˤ??ꡢx != y ?? x-y = 0 ?Ȥʤ???ǽ?????????ޤ???Ʊ???褦?ˡ? x > y > 0 ?Ǥ??äƤ⡢x∗y = 0 ?⤷???? y/x = 0 ?Ȥ??????Ȥ??ٹ??ʤ???ȯ?????Ƥ??ޤ??ޤ???

0 ??ۣ????ɽ???????ޤ???

?ϡ??ɥ??????Ǥϡ?2**55 ?̤??? 0 ??ɽ???????????ޤ????? ?????????????Τ????餫??ɽ???????Ǥ??? VAX ?ˤ? -0 ???????ޤ?????

VAX ???????ƥ??????ˤ?̵?? ( Infinity ) ?⤢???ޤ?????
ͽ?󥪥ڥ?????:

?ϡ??ɥ??????? 2**55 ?̤???ǧ?????ޤ??????????????????Τ? 1 ?Ĥ????Ǥ??? ͽ?󥪥ڥ????ɤ??Ф?????ư?????黻?ϡ?MOVF ?? MOVD ?Ǥ????׻??????Ǥ??? ?Τǡ????ޤ????Ѥ????ޤ?????

?㳰:

0 ?????ȥ????Хե??????륪?ڥ졼?????????????ʥ??ڥ졼???????ǡ? ?׻??????Ǥ????ޤ????Ť??ޥ????Ǥ?ͽ?󥪥ڥ????ɤ????????졢 ?׻??????Ǥ????ޤ???

?ݤ?:

(PDP-11 ?Ǥ?ɬ?????⤽???Ȥϸ????ޤ?????) VAX?ǤΤ??٤Ƥ?ͭ?????黻 (+, -, ∗, /) ?ϡ??????Хե????????????ե?????0 ?????? ȯ?????ʤ????硢ulp ??Ⱦʬ?????˴ݤ??????ޤ????ݤ??????? ulp ?Τ??礦??Ⱦʬ?Ǥ??????硢?ݤ??? 0 ????Υ???ޤ???

?ϰϤ????????Ȥ??̤ˤ????ȡ?D_floating-point ?ϡ?1960 ǯ?????߷פ??줿 ???ΤȤ??Ƥ?ͥ?줿?????ԥ塼?????ѱ黻?ΤҤȤĤǤ??? D_floating-point ?Υץ??ѥƥ??ϡ?4.3 BSD ?????ۤ??줿 VAX ?? ????Ū?ʴؿ??????¤?ȿ?Ǥ????Ƥ??ޤ????????Хե????? ???????ե?????ȯ???????Τϡ????̤??ϰϳ??ˤʤ뤫?ϰϳ????????˶ᤤ ?????Τߤǡ????ξ????ϥ????Хե????䥢?????ե????򵯤???ͭ?????? ???ڥ졼????????Ʊ???褦??ư???򤷤ޤ???Ʊ???褦?ˡ?log(0) ?? atanh(1) ?Τ褦?ʼ??? 1/0 ?Τ褦??ư???sqrt(-3) ?? acos(3) ?? 0/0 ?Τ褦??ư??ޤ??????????Ϥ??٤?ͽ?󥪥ڥ????ɤ????????? ?׻??????Ǥ????ޤ??????ξ????ˤĤ??Ƥϡ? ???줾???Υޥ˥奢???ڡ????Ǿܤ??????????ޤ???

???Υ쥹?ݥ󥹤ϸ????᤮???Τǡ????٤Ƥ???ư?????黻???㳰??Ŭ?ڤ? ?????????褦?˳?ȯ???줿???????????줵?줿?????????Ƕᤤ?????? ?֤???????????ͽ???Ǥ???

UNIX ?? 4.3 BSD ?ο????? libm ?δؿ??? DEC ?? VAX/VMS ?饤?֥????? ???Ӥ????ȡ??????? VMS ?ؿ???¿??®??????????¿?????٤??⤯???????? ???ʤ??㳰?˸??????ʤä?(pow(0.0,0.0) ?? atan2(0.0,0.0) ?ʤ?)???ꡢ ?ۤȤ??ɤϡ?libm ??????¿???Υ??????????Ѥ??ޤ??? VMS ?????ɤϡ??礭???ơ??֥??????֤???®???????٤?ã?????Ƥ??ޤ??? libm ?????ɤϡ??????Ϥ??٤Ƥ? ROM ?˼??ޤꤽ???ʤۤ? ?????????????פ??Ť餷?????????Ѥ??Ƥ??ޤ???

???????????פʤ??Ȥϡ?DEC ?? VMS ?????ɤ??õ??Ȥߤʤ??????Ĥʤ? ???Ѥ??뤳?Ȥ򸷤????ؤ??Ƥ????Τ??Ф???4.3 BSD ?? libm ?????ɤ? public domain ???տޤ??Ƥ????Ȥ??????ȤǤ????Ĥޤꡢ ?н??????????餫?ˤ??ơ??桼?????????ɤ????Ѥ??????ۤ????𤷤? ?????ɤκ??Ԥθ????˶??Ϥ????¤??ˤ????ơ?libm ?????ɤϼ? ͳ?˥??ԡ??Ǥ??ޤ????????椨?????ѽ????? VAX D_floating-point ?˻??Ƥ????ޥ????? UNIX ?桼???Ǥ??äƤ⡢?????? libm ?????? ???????Τ????Ѥ???ɬ?פ??ʤ??Ȥ??????ȤǤ???

IEEE STANDARD 754 ??ư???????????ѱ黻:

????ɸ???ϡ?¾?Υ????ԥ塼?????ѱ黻?????????⹭?? ???Ѥ????Ƥ??Ƥ??ޤ????ʲ??Τ褦??¿???Υ᡼??????????ɸ???ΰ????? ?С????????˽??򤷤? VLSI ???åפ???¤???Ƥ??ޤ???

	Intel i8087, i80287	National Semiconductor  32081
	Motorola 68881	Weitek WTL-1032, ... , -1165
	Zilog Z8070	Western Electric (AT&T) WE32106.

????¾?ˤ⡢???եȥ??????ˤ??????? (Apple Macintosh ?ϴ????ˤ???) ???顢 Hewlett-Packard 9000 ???꡼???? VLSI ?ˤ????????䡢?̤Ƥ? ECL ?? ???Ȥ???3 Megaflop ??ã?????? ELXSI 6400 ?ޤǶˤ??ƹ????????????? ?ؤ??ޤ???¾?δ??Ȥ????ˤϡ??ݤᡢ?????Хե????????????ե??? ?ʤɤ??㳰?ν????Ǥ???ɸ??????ˡ?˽??鷺?ˡ?IEEE 754 ?Υե????ޥå? ?????????Ѥ??Ƥ??ޤ??? DEC VAX G_floating-point ?ե????ޥåȤϡ?IEEE 754 Double ?ե????ޥåȤ??????˻??Ƥ????Τǡ????˵󤲤??ۤȤ??ɤν????ؿ??? IEEE ?С????????? C ?ץ????????ϡ?MicroVAX ?Ǽ¹Ԥ????褦?˴?ñ?? ?Ѵ??Ǥ??ޤ??????虜?虜?Ѵ????Ƥ??????Ȥ????ͤϤ??ʤ??褦?Ǥ???

4.3 BSD libm ?Υ????ɤΤ?????IEEE 754 ?????ޥ????ѤΤ??Τϡ? National Semi. 32081 ?? WTL 1164/65 ?ѤˤʤäƤ??ޤ??? Intel ???åפ? Zilog ???åס??ޤ??? Apple Macintosh ?? ELXSI 6400 ?Ǥ??Υ????ɤ????Ѥ????????ϡ????????δ??Ȥ??󶡤????????褤?????? (̵???ˤʤ??Ȼפ?????) ???????Υ????ɤκ??Ԥ??߷פ??? ?????ɤ????Ѥ??뤳?Ȥˤʤ??ޤ??? atan, cabs, cbrt, erf, erfc, hypot, j0-jn, lgamma, pow, y0-yn ???????С? Motorola 68881 ?? libm ?Τ??٤Ƥδؿ??????åפ????ܤ??? ??????????®?????ΤˤʤäƤ??ޤ??? Motorola, Apple, i8087, z8070, WE32106 ?Ǥϡ? ͭ?????? 64 ?ӥåȤ????Ѥ??Ƥ??ޤ???4.3 BSD ?? libm ?????ɤˤϡ? public domain ???տޤ??Ƥ????Ȥ???Ĺ?꤬?????ޤ??? ?н??????????餫?ˤ????桼?????????ɤ????Ѥ??????ۤ????𤷤? ???Ԥθ????˶??Ϥ????С?libm ?????ɤϼ?ͳ?˥??ԡ??Ǥ??ޤ??? ???ѱ黻?? IEEE 754 ?˻??Ƥ????ޥ????? UNIX ?桼???ϡ??????? libm ?????????Τ????Ѥ???ɬ?פ??ʤ??Ȥ??????ȤǤ???

IEEE 754 Double-Precision ?Υץ??ѥƥ?:

??ɥ?????: 64 ?ӥåȡ?8 ?Х??ȡ?????: ?Х??ʥ?
????: 53 ?ӥåȡ?(10 ?ʿ???) ?? 16 ?塣

x ?? x' ??Ϣ³????????????????ư?????????Ǥ??? (1 ulp ???İۤʤ?) ?????ϡ?
1.1e-16 < 0.5**53 < (x'-x)/x ≤ 0.5**52 < 2.3e-16 ?Ȥʤ롣

?ϰ?:	?????Хե???????????	= 2.0**1024	= 1.8e308
	???????ե???????????	= 0.5**1022	= 2.2e-308

?????Хե?????ȯ???????ȡ??ǥե????Ȥ??????դ???̵?¤ˤʤ??ޤ??? ???????ե????? 0.5**1074 = 4.9e-324 ???ܿ????????Τ????Ǥ? ?ᤤ???Τ??ʳ?Ū?˴ݤ??????ޤ???

0 ?ϡ?+0 ?? -0 ?Τ褦?ˤ????ޤ???ɽ???????ޤ???

?????Ͼ軻???????????????Ѵ????졢?????դ? 0 ?βû??ǰݻ??????ޤ??? ?????? x ??ͭ?¤? ???硢x-x ?? +0 ?ˤʤ??ޤ???0 ?????椬 ?????ˤʤ??黻?ϡ?0 ?????? copysign(x,±0) ?ΤߤǤ??? ?Ȥ??????? (x > y, x ≥ y ?ʤ?) ?? 0 ?????椫?? ?ƶ????????ޤ??󤬡?ͭ?¤??? x = y ?Ǥ????????ϡ? Infinity = 1/(x-y) != -1/(y-x) = -Infinity ?ˤʤ??ޤ???

Infinity ???????դ??Ǥ???

Infinity ?򤽤켫?Ȥ?ͭ?¤ο??ͤ˲û????Ƥ? ̵?¤ϰݻ??????ޤ??? Infinity ???????Ͼ軻?Ƚ????????????Ѵ????졢 (ͭ????)/±Infinity = ±0 (?? 0 ??))/0 = ±Infinity ?ˤʤ??ޤ??????????? ̵??-̵??, ̵??∗0, ̵??/̵?? ?ϡ?0/0 ?? sqrt(-3) ??Ʊ?ͤ??????ʱ黻?Ǥ??ꡢNaN ???????????ޤ???

ͽ?󥪥ڥ?????:

2**53-2 ?̤???ͽ?󥪥ڥ????ɤ????ꡢ???٤? NaN (Not a Number) ?ȸƤФ??ޤ?????????ȯ?? NaN ?ȸƤФ졢???????Ф?????ư???????黻???¹Ԥ????ȥȥ??åפ?ȯ?????ޤ??? ?ͤη??̤?????????ޤ?????????¸?ߤ??ʤ????Ǥ??ޡ??????뤿???? ???Ѥ????ޤ???????¾??̵ȯ?? NaN ?ȸƤФ??ޤ????????? ?????黻?η??̤Υǥե??????ͤǡ??????ʸ??λ??ѱ黻?˱ƶ????ȵڤ??ޤ??? x != x ?Ǥ??????硢x ?? NaN ?Ǥ???????¾???٤Ƥ??????黻 (x > y, x = y, x < y ?ʤ?) ?ϡ?NaN ???ط??????????? ???ˤʤ??ޤ???
????: NaN ?ϻ?ʬˡ??˸?????ޤ???

NaN ???ط????????硢?????? (??) ???ͱ黻?ǤϤʤ? ?????դ????Ӥ?ȼ???????黻?? ???ˤʤ??????Ǥʤ????????黻?Ȥʤ??ޤ???

?ݤ?:

?ǥե????ȤǤϡ????٤Ƥ??????黻 (+, -, ∗, /, sqrt) ?ϡ?ulp ??Ⱦʬ?????˴ݤ??????ޤ????ݤ??????? ulp ?Τ??礦??Ⱦʬ?Ǥ??????硢?ݤ᤿?ͤκǲ???ͭ???ӥåȤ? 0 ?ˤʤ??ޤ??? ?̾??Ϥ??Τ褦?ʴݤ᤬??Ŭ?ǡ????Ȥ??? x = 1.0, 2.0, 3.0, 4.0, ..., 2.0**52 ?Ǥ??????硢?????Ѥ?ξ?????ݤ????????ˤ??ؤ??餺?? (x/3.0)∗3.0 == x, (x/10.0)∗10.0 == x, ... ?ˤʤ??ޤ??????Τ褦?ʷ??̤Ȥʤ??Τϡ?IEEE 754 ?Τ褦?ʴݤ??ΤߤǤ??? ?????? 1 ?Ĥδݤ᤬?ɤξ????Ǥ???Ŭ?Ǥ????Ȥϸ¤??ʤ????ᡢ IEEE 754 ?Ǥϡ?0 ?ؤδݤᡢ +Infinity ?ؤδݤᡢ -Infinity ?ؤδݤ????ץ??????ޤ??????Ǥ????褦?ˤʤäƤ??ޤ????????Ǥ? 1.0e-10 ???? 1.0e37 ???餤?ޤǤǤϡ? ?Х??ʥ??Ⱦ??????Ѵ???Ʊ???????δݤ????????Ǥ??ޤ???

?㳰:

IEEE 754 ?Ǥϡ?5 ????????ư?????㳰??ǧ???????ޤ??? ?ʲ??Ǥϡ????פʽ??ˤ??? 5 ???????󤲤ޤ???

?㳰	?ǥե????Ȥη???
?????黻	NaN, ?ޤ??ϵ?
?????Хե???	±̵??
0 ????	±̵?? 
???????ե???	?ʳ?Ū???????ե???
????̩	?ݤ᤿??

????: ?㳰?ϡ?Ŭ?ڤ˽??????????Х??顼?ǤϤ????ޤ????? ?㳰???㳰Ū?ʤ??Τˤ??Ƥ??ޤ??Τϡ????٤Ƥ??????????? ?ǥե????ȥ쥹?ݥ󥹤??ʤ??????Ǥ????դˡ??ǥե????ȥ쥹?ݥ󥹤? ?ۤȤ??ɤ??????????????硢?????Ǥ??????????ʤ??????? ?㳰??ȯ?????뤿?Ӥ˱黻?????Ǥ????Ȥ????????????????뤳?Ȥ? ?Ǥ??ޤ?????

IEEE 754 ?Ǥϡ????줾??????ư?????㳰?Τ????˥ե饰?? ?Ѱդ??Ƥ??ޤ??????Υե饰???㳰??ȯ?????뤿?Ӥ˾夬?ꡢ?ץ????????? ?ꥻ?åȤ????ޤǡ??夬?ä????֤ǻĤ??ޤ????ץ????????Ǥϡ??ե饰?Υƥ??ȡ? ??¸?????????Ǥ??ޤ??? IEEE 754 ?ˤϡ??ǥե????Ȥη??̤????ιԤ????ΤǤʤ? ?㳰?˥ץ??????????н褹????ˡ?Ȥ??ơ??ʲ??? 3 ?Ĥ??????ޤ???

1): ?????㳰?θ????Ȥʤ???ǽ???????????????ƥ??Ȥ??????? ?ƥ??ȷ??̤˽??äƽ??????Ѥ????㳰???򤱤롣
2): ?ե饰???ƥ??Ȥ????ץ????????ǺǸ??˥ե饰???ꥻ?å? ???Ƥ????㳰??ȯ?????????ɤ???????ǧ???롣
3): ???̤??ƥ??Ȥ???1 ?Ĥ??㳰?Τߤ?ȯ???????ͤǤ??뤫?ɤ???????ǧ???롣

?ٹ?: ???????ե?????ȯ?????????ɤ??????μ¤?ȯ???????ˤϡ? ?Ѥ侦?????????ե??????????ͤ??? 0 ?˶ᤤ???ɤ??????ƥ??? ???뤫?????????ե????ե饰???ƥ??Ȥ??뤷???????ޤ????? (IEEE 754 ?Ǥϡ??¤Ⱥ??????????ե????򵯤??????ȤϤ????ޤ????? x != y ?Ǥ??????硢x-y ?ϴ????????Τǡ??ͤ????????Ƥ? 0 ?ǤϤ????ޤ????? ) ?ʳ?Ū?˥??????ե????򵯤????ѤȾ??ϡ??????????٤򼺤äƤ? 0 ?ˤϤʤ??ʤ????ᡢ0 ?????Ӥ??Ƥ? (VAX ?Ǽ¹Ԥ?????ǽ????????)?? ?????????餫?ˤʤ??ޤ??????ʳ?Ū?˥??????ե????򵯤??????ͤ? ???????ե??????????ͤ????礭???ͤȲû????????硢?ʳ?Ū?? ???????ե????Ǽ????????????ڤ??ΤƤ??????ΤǼ??????ޤ????? ???Τ??ᡢ?̾??ξ??硢?ʳ?Ū?ʥ??????ե?????̵???Ǥ??뤳?Ȥ??????ޤ??? 0 ?˥ե??å??夵???륢?????ե????Ǥϡ?Ʊ?????Ȥ????????Ȥϸ¤??ޤ?????

IEEE 754 ?˽??򤹤륷???ƥ??Ǥϡ??ʲ??Τ褦????ˡ?Ǥ??㳰?? ?н??Ǥ??ޤ???

4): ?۾ｪλ (ABORT)?????Υᥫ?˥????Ǥϡ???ON ERROR GO TO?פΤ褦?? ???顼???????ơ??ȥ????Ȥ˴?Ϣ??????ˡ?ǽ??????????????Ȥ??ơ??㳰?? ?????ä?ʬ?ष?ޤ??????줬?ۤʤ??С????Υ??ơ??ȥ????Ȥη????? ?Ѥ????ޤ????????Τ褦?ʶ??̤?????ħ???????ޤ???
—: ?㳰?򵯤??????黻???̤??ͤ????Ѥ??????????椫???׻??? ?Ƴ???????ˡ???ʤ??ʤ??ޤ????㳰?η??̤??????????ޤ???
—: ???顼???????ơ??ȥ????Ȥ??ʤ????֥ץ????????Ǥϡ??ɤ? ?ץ??????ब?ƤӽФ??Ƥ⤽?Υ??֥ץ??????????㳰?Τ????˰۾ｪλ???? ???顼???????ơ??ȥ????Ȥ????Ĥ????ޤǥ??֥ץ??????ब?????˸Ƥ? ?Ф????뤫???????????Τ??۾ｪλ???ƥ??????Υ????פ????????ޤ???
5): ????(STOP)?????÷??ΥǥХå??Ķ???ɬ?פˤʤ뤳?Υᥫ?˥????ϡ? ?ץ????????ѤǤ??äƥץ????????????ǤϤ????ޤ??????㳰?ϥץ??????ޤ? ?ְ㤤???????Ȥ????????ä?ʬ?व???ޤ????㳰??ȯ???????ȡ??㳰?򵯤????? ???ڥ졼???????ζ᤯?Ǽ¹Ԥ????ߤ??????Τǡ??ץ??????ޤϡ??㳰???ɤΤ褦?? ȯ???????Τ?????ǧ?Ǥ??ޤ???¿???ξ????ϡ??ǽ??ο??Ĥ??㳰???礭?? ?????ǤϤʤ????ץ??????ޤϤ??줾?????㳰??ȯ?????뤿?Ӥˡ??¹Ԥ? ???ߤ????ʤ??ä????Τ褦?˼¹Ԥ??Ƴ??Ǥ??ޤ???
6): ... ????¾????ˡ?ˤĤ??Ƥϡ?????ʸ???Ǥ????????ޤ?????

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fpgetround(3), fpsetround(3), fpgetprec(3), fpsetprec(3), fpgetmask(3), fpsetmask(3), fpgetsticky(3), fpresetsticky(3) - IEEE ??ư???????󥿥ե?????

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IEEE 754 ?ȥ??????ƥ󥷥??? p854 ?ˤĤ??Ƥϡ? 1984 ǯ 8 ????ȯ?Ԥ??줿??IEEE ?λ?????MICRO?٤򻲾Ȥ??Ƥ????????? W. J. Cody ?餬??A Proposed Radix- and Word-length-independent Standard for Floating-point Arithmetic?פȤ????????????? ???????Ƥ??ޤ???Apple Macintosh ?? Pascal, C, BASIC ?Υޥ˥奢?? ?ˤϡ?IEEE 754 ?ε?ǽ?˴ؤ???ʬ?????䤹?????????????ޤ??? IEEE ?λ?????COMPUTER vol. 14 no. 3??(1981 ǯ 3 ??) ?? 1979 ǯ 10 ???? ??ACM SIGNUM Newsletter Special Issue?٤ε???????Ω???ޤ????????? ?????ϤΤ????ѹ????줿ɸ?????ͰƤ˴ط????Ƥ??ޤ???