¡¾ÈéÏÙ°©¡¿¹Ø°®Å®ÐÔ½¡¿µ·ÀÈéÏÙ°©²»¿É²»ÖªµÄ5¼þÊÂ - Ç§ê¶Í¤ÐÂÎÅÍø

IEEE 754-2008 errata 2025-08-07

The current version of the IEEE Standard for Floating-Point Arithmetic (IEEE 754) was published in August 2008, and is available from the IEEE Xplore website. It is also an approved international standard: ISO/IEC/IEEE 60559:2011.

Since the standard was published, some minor problems have been noticed; this page lists those that the Editor of the standard is aware of, with suggested corrections. Please note that these have not been through any standardization process and hence are not ‘official’ or part of the standard, although most have been discussed on the IEEE 754 working group mailing list. Many thanks to everyone who contributed to those discussions.

New problems are best reported and discussed in the working group mailing list. Any corrections for or comments on this errata page should be sent to the Editor, Mike Cowlishaw (mfc@speleotrove.com).

Subclause 4.2
page 15 Problem: There is a missing cross-reference at the end of the third paragraph.
Correction: The paragraph should end: “... via the operations in 9.3.1 and 9.3.2.”
Reported by Fred J. Tydeman 2009.02.10.

Subclause 4.3.1
page 16 Problem: The rule for roundTiesToEven cannot apply when the precision p is 1 for numbers with the infinitely precise numerical value (b−½)×b^k (where b is the base, which is even, and k is an integer) because in this case the two nearest floating-point numbers bracketing this value are (b−1)×b^k (whose precision-1 significand is b−1, an odd number) and 1×b^k+1 (whose precision-1 significand is 1, also an odd number).
Correction: Add to the rule for roundTiesToEven: “; if that is not possible, the one larger in magnitude shall be delivered (this can happen for one-digit precision, possible with convertToDecimalCharacter for example)”
Note that this delivers the same numerical value result, b×b^k, as at higher settings of p.

Reported by Vincent Lefèvre 2009.03.24; clarification text suggested by Michel Hack.

Subclause 5.3.1
page 19 Problem: The term “signalingNaN” used here is inconsistent with other usage.
Correction: Add a space between “signaling” and “NaN” (in two places).
Reported by Fred J. Tydeman 2009.11.29.

Subclause 5.3.3
page 20
Subclause 5.4.1
page 21
Problem: In the NOTE in 5.3.3, and also in the description of the squareRoot operation in 5.4.1, the function floor() is used. However, it is never defined.
Correction: The function floor(x) computes the largest integer or integral value not greater than x.
This could be added in 5.3.3 and in 5.4.1. The floor function could also be added to the list of recommended functions.

Reported by Fred J. Tydeman 2009.02.06.

Subclause 6.2.1
page 34
Subclause 6.2.2
page 35
Problem: The headings on these subclauses imply that NaNs are encoded as specified here for all formats, however these rules only apply to interchange formats.
Correction: Change the headings 6.2.1 and 6.2.2 to read “NaN encodings in binary interchange formats” and “NaN encodings in decimal interchange formats” respectively.
Reported by Vincent Lefèvre 2009.03.24.

Subclause 9.1
page 41 Problem: The term “preferred quantum” is used in this subclause but nowhere else, and is not defined.
Correction: Change “preferred quantum” to “preferred exponent” (in two places).
Reported by Fred J. Tydeman 2008.08.29.

Subclause 9.2
page 43 Problem: The functions asinPi and acosPi are listed in the third paragraph following Table 9.1, but they do not appear in that table (and do not have special values defined in subclause 9.2.1).
Correction: Delete the functions asinPi and acosPi from the list. (A future revision might consider the addition of asinPi, acosPi, and tanPi to the list of recommended functions.)
Reported by James W Thomas 2013.11.06.

Subclause 9.2.1
pages 44 & 45 Problem: The term “exact expression” is used in this subclause but nowhere else, and is not defined.
Correction: Change “from the following exact expressions” to “from the exact results of the following expressions” (in two places).
Reported by James W Thomas 2013.11.07.

Annex A
page 53 Problem: In citation [B17] the surname of the third author is misspelled.
Correction: It should be: “Runyon”.
Reported by Mark Erle 2008.09.26.

Annex B.3
page 55 Problem: The phrase “in an status flag” is ungrammatical.
Correction: Change “an” to “a”.
Reported by Fred J. Tydeman 2009.11.29.

This page was last updated on 2025-08-07.

°ÐÏòÒ©ÎïÊÇÊ²Ã´ ¶Ç×ÓÉÏ³¤Ã«ÊÇÊ²Ã´ÔÒò È®ÎÁÊÇÊ²Ã´ÔÒòÒýÆðµÄ ÓûÉúÓûËÀÊÇÊ²Ã´ÒâË¼ Ð¡Ã¨²ÈÄÌÊÇÊ²Ã´ÒâË¼

ÄÐÈËÊ±¼ä¶ÌÊ²Ã´ÔÒò ´óÔËÕý¹ÙÊÇÊ²Ã´ÒâË¼ ºÈ¾ÆÉËÊ²Ã´Æ÷¹Ù ÈËÈÞÃ«Ä¤´ÙÐÔÏÙ¼¤ËØÊÇ²éÊ²Ã´µÄ ´óÄ´Ö¸·¢¶¶ÊÇÊ²Ã´ÔÒò

¼Ù»¨·ÅÔÚ¼ÒÀïÓÐÊ²Ã´¼É»ä 97ÄêÎåÐÐÊôÊ²Ã´ ÃæÅºÊÇÊ²Ã´×öµÄ ËÄÎïÌÀÊ²Ã´Ê±ºòºÈ Ò½ÉúÎåÐÐÊôÊ²Ã´

ÍíµÄ·´Òå´ÊÊÇÊ²Ã´ 7ÔÂÒ»ÈÕÊÇÊ²Ã´½ÚÈÕ ðåÕî³ÔÊ²Ã´Ò©ºÃ 1ÔÂ2ÈÕÊ²Ã´ÐÇ×ù òÚò¼³ÔÊ²Ã´

³¤ÆÚÊ§Ãß³ÔÊ²Ã´Ò©hcv9jop8ns2r.cn Ð¡º¢ÑÛÊº¶àÊÇÊ²Ã´ÔÒòÒýÆðµÄhcv9jop0ns7r.cn ¿ÍÖ®ðëÊÇÊ²Ã´ÒâË¼xianpinbao.com Ò»Ê²Ã´ÈË¼Òhcv9jop5ns9r.cn ÁÜ°Í½áÖ×´óÊÇÊ²Ã´ÔÒòhebeidezhi.com

ØºÍèÍ´¹ÒÊ²Ã´¿Æhcv8jop7ns6r.cn ¸ÐÃ°Á÷±ÇÌé³ÔÊ²Ã´Ò©ºÃµÃ¿ìhcv9jop6ns5r.cn Ò»ÇÐ¾¡ÔÚ²»ÑÔÖÐÊÇÊ²Ã´ÒâË¼hcv8jop1ns7r.cn º®í×ÊÇÊ²Ã´ÒâË¼hcv7jop6ns7r.cn ÃÎ¼û½ø¼àÓüÊÇÊ²Ã´Õ×Í·hcv8jop2ns7r.cn

¼Ç³Ô²»¼Ç´òµÄÏÂÒ»¾äÊÇÊ²Ã´hcv7jop4ns8r.cn ÖÎ×ÖÎåÐÐÊôÊ²Ã´jiuxinfghf.com ÄÐÐÔ¸ÐÈ¾Ö§ÔÌåÓÐÊ²Ã´Ö¢×´hcv8jop2ns1r.cn ¼¡Ëá¼¤Ã¸Ê²Ã´ÒâË¼kuyehao.com ·´ò¢ÊÇÊ²Ã´ÒâË¼hebeidezhi.com

·¢¸£ÁËÊÇÊ²Ã´ÒâË¼hcv8jop9ns0r.cn ÐØÄ¤Ñ×³ÔÊ²Ã´ÏûÑ×Ò©hcv8jop2ns7r.cn »áÑáÑ×ÊÇÊ²Ã´²¡hcv9jop5ns2r.cn Ê²Ã´ÊÇ·øÉähcv8jop9ns8r.cn ´óÒÌÂèÆÚ¼ä¿ÉÒÔ³ÔÊ²Ã´Ë®¹ûhcv8jop5ns2r.cn

°Ù¶È

Subclause 4.2 page 15	Problem: There is a missing cross-reference at the end of the third paragraph.
	Correction: The paragraph should end: “... via the operations in 9.3.1 and 9.3.2.”
	Reported by Fred J. Tydeman 2009.02.10.

Subclause 4.3.1 page 16	Problem: The rule for roundTiesToEven cannot apply when the precision p is 1 for numbers with the infinitely precise numerical value (b−½)×b^k (where b is the base, which is even, and k is an integer) because in this case the two nearest floating-point numbers bracketing this value are (b−1)×b^k (whose precision-1 significand is b−1, an odd number) and 1×b^k+1 (whose precision-1 significand is 1, also an odd number).
	Correction: Add to the rule for roundTiesToEven: “; if that is not possible, the one larger in magnitude shall be delivered (this can happen for one-digit precision, possible with convertToDecimalCharacter for example)” Note that this delivers the same numerical value result, b×b^k, as at higher settings of p.
	Reported by Vincent Lefèvre 2009.03.24; clarification text suggested by Michel Hack.

Subclause 5.3.1 page 19	Problem: The term “signalingNaN” used here is inconsistent with other usage.
	Correction: Add a space between “signaling” and “NaN” (in two places).
	Reported by Fred J. Tydeman 2009.11.29.

Subclause 5.3.3 page 20 Subclause 5.4.1 page 21	Problem: In the NOTE in 5.3.3, and also in the description of the squareRoot operation in 5.4.1, the function floor() is used. However, it is never defined.
	Correction: The function floor(x) computes the largest integer or integral value not greater than x. This could be added in 5.3.3 and in 5.4.1. The floor function could also be added to the list of recommended functions.
	Reported by Fred J. Tydeman 2009.02.06.

Subclause 6.2.1 page 34 Subclause 6.2.2 page 35	Problem: The headings on these subclauses imply that NaNs are encoded as specified here for all formats, however these rules only apply to interchange formats.
	Correction: Change the headings 6.2.1 and 6.2.2 to read “NaN encodings in binary interchange formats” and “NaN encodings in decimal interchange formats” respectively.
	Reported by Vincent Lefèvre 2009.03.24.

Subclause 9.1 page 41	Problem: The term “preferred quantum” is used in this subclause but nowhere else, and is not defined.
	Correction: Change “preferred quantum” to “preferred exponent” (in two places).
	Reported by Fred J. Tydeman 2008.08.29.

Subclause 9.2 page 43	Problem: The functions asinPi and acosPi are listed in the third paragraph following Table 9.1, but they do not appear in that table (and do not have special values defined in subclause 9.2.1).
	Correction: Delete the functions asinPi and acosPi from the list. (A future revision might consider the addition of asinPi, acosPi, and tanPi to the list of recommended functions.)
	Reported by James W Thomas 2013.11.06.

Subclause 9.2.1 pages 44 & 45	Problem: The term “exact expression” is used in this subclause but nowhere else, and is not defined.
	Correction: Change “from the following exact expressions” to “from the exact results of the following expressions” (in two places).
	Reported by James W Thomas 2013.11.07.

Annex A page 53	Problem: In citation [B17] the surname of the third author is misspelled.
	Correction: It should be: “Runyon”.
	Reported by Mark Erle 2008.09.26.

Annex B.3 page 55	Problem: The phrase “in an status flag” is ungrammatical.
	Correction: Change “an” to “a”.
	Reported by Fred J. Tydeman 2009.11.29.

°ÐÏòÒ©ÎïÊÇÊ²Ã´	¶Ç×ÓÉÏ³¤Ã«ÊÇÊ²Ã´ÔÒò	È®ÎÁÊÇÊ²Ã´ÔÒòÒýÆðµÄ	ÓûÉúÓûËÀÊÇÊ²Ã´ÒâË¼	Ð¡Ã¨²ÈÄÌÊÇÊ²Ã´ÒâË¼
ÄÐÈËÊ±¼ä¶ÌÊ²Ã´ÔÒò	´óÔËÕý¹ÙÊÇÊ²Ã´ÒâË¼	ºÈ¾ÆÉËÊ²Ã´Æ÷¹Ù	ÈËÈÞÃ«Ä¤´ÙÐÔÏÙ¼¤ËØÊÇ²éÊ²Ã´µÄ	´óÄ´Ö¸·¢¶¶ÊÇÊ²Ã´ÔÒò
¼Ù»¨·ÅÔÚ¼ÒÀïÓÐÊ²Ã´¼É»ä	97ÄêÎåÐÐÊôÊ²Ã´	ÃæÅºÊÇÊ²Ã´×öµÄ	ËÄÎïÌÀÊ²Ã´Ê±ºòºÈ	Ò½ÉúÎåÐÐÊôÊ²Ã´
ÍíµÄ·´Òå´ÊÊÇÊ²Ã´	7ÔÂÒ»ÈÕÊÇÊ²Ã´½ÚÈÕ	ðåÕî³ÔÊ²Ã´Ò©ºÃ	1ÔÂ2ÈÕÊ²Ã´ÐÇ×ù	òÚò¼³ÔÊ²Ã´

³¤ÆÚÊ§Ãß³ÔÊ²Ã´Ò©hcv9jop8ns2r.cn	Ð¡º¢ÑÛÊº¶àÊÇÊ²Ã´ÔÒòÒýÆðµÄhcv9jop0ns7r.cn	¿ÍÖ®ðëÊÇÊ²Ã´ÒâË¼xianpinbao.com	Ò»Ê²Ã´ÈË¼Òhcv9jop5ns9r.cn	ÁÜ°Í½áÖ×´óÊÇÊ²Ã´ÔÒòhebeidezhi.com
ØºÍèÍ´¹ÒÊ²Ã´¿Æhcv8jop7ns6r.cn	¸ÐÃ°Á÷±ÇÌé³ÔÊ²Ã´Ò©ºÃµÃ¿ìhcv9jop6ns5r.cn	Ò»ÇÐ¾¡ÔÚ²»ÑÔÖÐÊÇÊ²Ã´ÒâË¼hcv8jop1ns7r.cn	º®í×ÊÇÊ²Ã´ÒâË¼hcv7jop6ns7r.cn	ÃÎ¼û½ø¼àÓüÊÇÊ²Ã´Õ×Í·hcv8jop2ns7r.cn
¼Ç³Ô²»¼Ç´òµÄÏÂÒ»¾äÊÇÊ²Ã´hcv7jop4ns8r.cn	ÖÎ×ÖÎåÐÐÊôÊ²Ã´jiuxinfghf.com	ÄÐÐÔ¸ÐÈ¾Ö§ÔÌåÓÐÊ²Ã´Ö¢×´hcv8jop2ns1r.cn	¼¡Ëá¼¤Ã¸Ê²Ã´ÒâË¼kuyehao.com	·´ò¢ÊÇÊ²Ã´ÒâË¼hebeidezhi.com
·¢¸£ÁËÊÇÊ²Ã´ÒâË¼hcv8jop9ns0r.cn	ÐØÄ¤Ñ×³ÔÊ²Ã´ÏûÑ×Ò©hcv8jop2ns7r.cn	»áÑáÑ×ÊÇÊ²Ã´²¡hcv9jop5ns2r.cn	Ê²Ã´ÊÇ·øÉähcv8jop9ns8r.cn	´óÒÌÂèÆÚ¼ä¿ÉÒÔ³ÔÊ²Ã´Ë®¹ûhcv8jop5ns2r.cn