subnormal
American Heritage Dictionary:
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sub·nor·mal
(sŭb-nôr'məl) 
adj.
Less than normal; below the average.
n.
One who is regarded as subnormal in some respect, such as in intelligence or coordination.
subnormality sub'nor·mal'i·ty (-nôr-măl'ĭ-tē) n.
adj.
Less than normal; below the average.
n.
One who is regarded as subnormal in some respect, such as in intelligence or coordination.
subnormality sub'nor·mal'i·ty (-nôr-măl'ĭ-tē) n.
Oxford Companion to the Mind:
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subnormality
Subnormality and severe subnormality are legal terms which were defined in the UK Mental Health Act of 1959. In the Mental Health Act of 1983 they have been replaced by the words 'mental impairment' and 'severe mental impairment' which are defined as follows. Mental impairment means a state of arrested or incomplete development of mind (not amounting to severe impairment) which includes significant impairment of intelligence and social functioning, and is associated with abnormally aggressive or seriously irresponsible conduct. Severe mental impairment means a state of arrested or incomplete development of mind which includes severe impairment of intelligence and social functioning and is associated with abnormally aggressive or seriously irresponsible conduct.
Incompleteness of the development of the mind has been observed for a very long time, and has been recognized in English law since 1325, whereas subnormality of intelligence is a concept which depends on the meaning given to the word intelligence by Alfred Binet, in 1909, i.e. ability to learn. Thus the inclusion of the concept of a minimum level of intelligence in the Act of 1959 was meant to complement and limit the definition of subnormality according to social incompetence. Before 1959 social incompetence was the prime definition of subnormality. In addition, in medieval times the legal definition included the idea of incurability, and was distinguished from mental illness insofar as the 'natural fool' was supposed to be incurable, whereas the lunatic was recognized as a person who might perhaps recover from his illness. These legal definitions were of course related to the protection of the property of those involved. They were also the basis for decisions made on the criminal responsibility of persons accused of serious offences.
Subnormality today is regarded as a condition which, when associated with very low intelligence — for example, below IQ 55 or IQ 50 — will have a relatively permanent character, whereas when associated with a level of intelligence between 55 and 70 will less frequently be combined with permanent social incompetence. In fact some authors have claimed that in mild subnormality of this kind IQ levels can be considerably increased by early and continuous educational attention. Whether this can be said with certainty or not, a great deal of research has shown that above IQ 55 ability to survive in the community is not very closely related to intelligence. Below this IQ level a relatively small proportion of people will be found to be socially independent, possibly between 10 and 20 per cent.
The prevalence of subnormality
If we turn our attention to the prevalence of the subnormal as distinct from the severely subnormal we find that, between IQ 70 and 55, 21.4 persons per 1,000 would be predicted on the basis of the normal curve of IQ, which for England and Wales would give an estimate of approximately 1,027,000 cases. In point of fact, the estimates for the mildly subnormal in England have ranged from 1.39 per 1,000 to 6.73 per 1,000. An intervening figure, that obtained by Kushlick in 1961 in Salford, was for an estimate of 2.60 per 1,000. This figure yields a prevalence rate for England and Wales of 124,000 cases. In this instance the discrepancy is in the opposite direction and is easily explained by the fact that the mildly subnormal very often survive in the community despite their relatively low intelligence. As a result they do not attract the attention of the available services, and the actual prevalence rate is found to be much below that which might be expected on the basis of intelligence alone. In this particular group, as was initially pointed out by Penrose (1949), the prevalence is most marked during school years because of the special scholastic demands made at that time. A number of studies since W. R. Baller's initial research in 1936 have shown that, on follow-up, the mildly subnormal are frequently shown to have succeeded very well in social and occupational situations. They often marry and conduct their own businesses, show stability in their job experience, and in normally favourable social circumstances do not fall foul of the law in a serious way or come to represent a social problem in their later years. A variety of theories possibly explaining the relative success of the adult subnormal has been reviewed by Clarke and Clarke (1974).
While the tendency during the early years of the 20th century was to consider that the prevalence of mental subnormality was increasing, N. Goodman and J. Tizard have argued, on the basis of their survey and by comparison with Lewis's earlier survey, that perhaps it is declining so far as the severely subnormal are concerned. The argument rests on two opposite trends, one being the decrease in infant mortality in England and Wales between 1900 and 1959 and the resulting possibility of a decrease in birth injuries, and the other being the likelihood that better birth conditions might lead not only to increasing survival of the fit but also to increasing survival of the unfit. Goodman and Tizard argue that, since many of the severely subnormal, perhaps as many as 25 per cent, suffer from Down's syndrome (mongolism), and since this group now survive longer than hitherto, an increasing number of the severely subnormal might be Down's syndrome cases. Down's syndrome is of genetic origin and perhaps little influenced by external factors except maternal age. If this were so, then it is possible that the number of the severely subnormal who were not Down's syndrome cases either remained the same or declined slightly between the Lewis survey in 1929 and the Goodman and Tizard survey in 1962.
Obviously, so far as the initial fears that gave rise to the UK Mental Deficiency Act of 1913 are concerned, a decline in national intelligence is no longer thought probable by those who are well informed about the prevalence of mental deficiency. This does not mean, of course, that there is no genetic element contributing to prevalence of subnormality. Perhaps today fewer severely subnormal children are being born, and fewer mildly subnormal adults need care, but of course those severely subnormal children who are born tend to live longer. B. W. Richards found that from 1949 there had been a steady trend towards ageing in the population in a mental deficiency hospital in Surrey. There was an especially great increase in the number and mean age of residents with Down's syndrome, even though the mean age of the Down's syndrome patients was lower than that of their comparable non-Down's syndrome fellow patients. B. Kirman (in Kirman and Bicknell 1975: 57) presented a table showing the trend of ages in National Health Service hospitals between 1954 and 1969. The main feature of this table is the relative increase in the number of patients aged over 55 as compared with those aged below 14. There is, however, some evidence that Down's syndrome cases continue to die somewhat earlier than non-Down's syndrome cases of the same IQ level. It is interesting to note that practically all Down's syndrome patients over 35 years of age show the same pathological changes in their brains as are seen in the brains of subjects who develop the clinical features of senile dementia of the Alzheimer type.
Clearly, therefore, the tendency is for fewer severely subnormal children to be born but for more of those who are born to survive over longer periods, and for fewer of the mildly subnormal to come to the notice of social aid services. These trends are probably matched by similar trends in the normal population, and it might be said that the subnormal, like the normal, are profiting from the general increase in the standard of living as well as from the improvement in medical care, especially in relation to birth conditions, since the beginning of the century.
For discussion of the causes of subnormality, and the care of mentally handicapped adults and children, see mental handicap.
(Published 1987)
Incompleteness of the development of the mind has been observed for a very long time, and has been recognized in English law since 1325, whereas subnormality of intelligence is a concept which depends on the meaning given to the word intelligence by Alfred Binet, in 1909, i.e. ability to learn. Thus the inclusion of the concept of a minimum level of intelligence in the Act of 1959 was meant to complement and limit the definition of subnormality according to social incompetence. Before 1959 social incompetence was the prime definition of subnormality. In addition, in medieval times the legal definition included the idea of incurability, and was distinguished from mental illness insofar as the 'natural fool' was supposed to be incurable, whereas the lunatic was recognized as a person who might perhaps recover from his illness. These legal definitions were of course related to the protection of the property of those involved. They were also the basis for decisions made on the criminal responsibility of persons accused of serious offences.
Subnormality today is regarded as a condition which, when associated with very low intelligence — for example, below IQ 55 or IQ 50 — will have a relatively permanent character, whereas when associated with a level of intelligence between 55 and 70 will less frequently be combined with permanent social incompetence. In fact some authors have claimed that in mild subnormality of this kind IQ levels can be considerably increased by early and continuous educational attention. Whether this can be said with certainty or not, a great deal of research has shown that above IQ 55 ability to survive in the community is not very closely related to intelligence. Below this IQ level a relatively small proportion of people will be found to be socially independent, possibly between 10 and 20 per cent.
The prevalence of subnormality
The prevalence of subnormality
At the beginning of the 20th century, the prevalence of subnormality was thought to be increasing, because the views of Francis Galton (Hereditary Genius, 1869) and Karl Pearson were uncritically applied to the concept of intelligence. It was supposed, therefore, that because of differential fertility more children would be born to those with less intellectual endowment and that, as a result, the average level of intelligence would decline. Few authorities, with the exception of L. S. Penrose, disagreed with this view, though today few would agree with it. As a result of later studies, the prevalence of severe subnormality is now better understood and we know more about the intelligence level of the children of the mildly subnormal. If we were to define the prevalence of subnormality solely in terms of the level of intelligence, and if all below IQ 70 were assumed to be subnormal, then, further assuming distribution according to Karl Pearson's 'normal' curve, 2.28 per cent of the population would be expected to be subnormal. The great majority of these cases would be between IQs 70 and 55, say 2.14 per cent of the total population. The remaining 0.14 per cent (67,200 in England and Wales) would have IQs in the range of severe subnormality, i.e. lower than IQ 55. When investigations were made, however, fairly firm figures began to emerge for the severely subnormal. These figures were 3.88 per 1,000 (E. O. Lewis), 3.45 per 1,000 (N. Goodman and J. Tizard), for age ranges 7–14 years, and 3.75 per 1,000 (A. Kushlick) for the 15–19 age range. Obviously the actual findings, which for a population of 48 million people would yield a total prevalence of approximately 180,000 severely subnormal cases on the basis of Kushlick's figures, very much exceed the number which would be expected if the definition were based on intelligence level and the normal curve. The difference was accounted for long ago by Pearson and G. A. Jaederholm (On the Continuity of Mental Defect, 1914), the excess of severely subnormal subjects being assumed to be due to the pathological conditions so frequently found at this IQ level.If we turn our attention to the prevalence of the subnormal as distinct from the severely subnormal we find that, between IQ 70 and 55, 21.4 persons per 1,000 would be predicted on the basis of the normal curve of IQ, which for England and Wales would give an estimate of approximately 1,027,000 cases. In point of fact, the estimates for the mildly subnormal in England have ranged from 1.39 per 1,000 to 6.73 per 1,000. An intervening figure, that obtained by Kushlick in 1961 in Salford, was for an estimate of 2.60 per 1,000. This figure yields a prevalence rate for England and Wales of 124,000 cases. In this instance the discrepancy is in the opposite direction and is easily explained by the fact that the mildly subnormal very often survive in the community despite their relatively low intelligence. As a result they do not attract the attention of the available services, and the actual prevalence rate is found to be much below that which might be expected on the basis of intelligence alone. In this particular group, as was initially pointed out by Penrose (1949), the prevalence is most marked during school years because of the special scholastic demands made at that time. A number of studies since W. R. Baller's initial research in 1936 have shown that, on follow-up, the mildly subnormal are frequently shown to have succeeded very well in social and occupational situations. They often marry and conduct their own businesses, show stability in their job experience, and in normally favourable social circumstances do not fall foul of the law in a serious way or come to represent a social problem in their later years. A variety of theories possibly explaining the relative success of the adult subnormal has been reviewed by Clarke and Clarke (1974).
While the tendency during the early years of the 20th century was to consider that the prevalence of mental subnormality was increasing, N. Goodman and J. Tizard have argued, on the basis of their survey and by comparison with Lewis's earlier survey, that perhaps it is declining so far as the severely subnormal are concerned. The argument rests on two opposite trends, one being the decrease in infant mortality in England and Wales between 1900 and 1959 and the resulting possibility of a decrease in birth injuries, and the other being the likelihood that better birth conditions might lead not only to increasing survival of the fit but also to increasing survival of the unfit. Goodman and Tizard argue that, since many of the severely subnormal, perhaps as many as 25 per cent, suffer from Down's syndrome (mongolism), and since this group now survive longer than hitherto, an increasing number of the severely subnormal might be Down's syndrome cases. Down's syndrome is of genetic origin and perhaps little influenced by external factors except maternal age. If this were so, then it is possible that the number of the severely subnormal who were not Down's syndrome cases either remained the same or declined slightly between the Lewis survey in 1929 and the Goodman and Tizard survey in 1962.
Obviously, so far as the initial fears that gave rise to the UK Mental Deficiency Act of 1913 are concerned, a decline in national intelligence is no longer thought probable by those who are well informed about the prevalence of mental deficiency. This does not mean, of course, that there is no genetic element contributing to prevalence of subnormality. Perhaps today fewer severely subnormal children are being born, and fewer mildly subnormal adults need care, but of course those severely subnormal children who are born tend to live longer. B. W. Richards found that from 1949 there had been a steady trend towards ageing in the population in a mental deficiency hospital in Surrey. There was an especially great increase in the number and mean age of residents with Down's syndrome, even though the mean age of the Down's syndrome patients was lower than that of their comparable non-Down's syndrome fellow patients. B. Kirman (in Kirman and Bicknell 1975: 57) presented a table showing the trend of ages in National Health Service hospitals between 1954 and 1969. The main feature of this table is the relative increase in the number of patients aged over 55 as compared with those aged below 14. There is, however, some evidence that Down's syndrome cases continue to die somewhat earlier than non-Down's syndrome cases of the same IQ level. It is interesting to note that practically all Down's syndrome patients over 35 years of age show the same pathological changes in their brains as are seen in the brains of subjects who develop the clinical features of senile dementia of the Alzheimer type.
Clearly, therefore, the tendency is for fewer severely subnormal children to be born but for more of those who are born to survive over longer periods, and for fewer of the mildly subnormal to come to the notice of social aid services. These trends are probably matched by similar trends in the normal population, and it might be said that the subnormal, like the normal, are profiting from the general increase in the standard of living as well as from the improvement in medical care, especially in relation to birth conditions, since the beginning of the century.
For discussion of the causes of subnormality, and the care of mentally handicapped adults and children, see mental handicap.
(Published 1987)
— Neil O'Connor
- Bibliography
- Clarke, A. M., and Clarke, A. D. B. (eds.) (1974). Mental Deficiency: The Changing Outlook.
- Kirman, B., and Bicknell, J. (1975). Mental Handicap.
- Penrose, L. S. (1949). The Biology of Mental Defect.
Saunders Veterinary Dictionary:
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subnormality
A state less than normal or that usually encountered.
Random House Word Menu:
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categories related to 'subnormality'
- Defects and Disabilities - subnormality: state of arrested or incomplete mental development due to congenital defect, injury, or gross environmental deprivation
Wikipedia on Answers.com:
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Denormal number
In computer science, denormal numbers or denormalized numbers (now often called subnormal numbers) fill the underflow gap around zero in floating point arithmetic: any non-zero number which is smaller than the smallest normal number is 'sub-normal'.
In a normal floating point value there are no leading zeros in the significand, instead leading zeros are moved to the exponent. So 0.0123 would be written as 1.23 * 10-2. Denormal numbers are numbers where this representation would result in an exponent that is too small (the exponent usually having a limited range). Such numbers are represented using leading zeros in the significand.
The significand (or mantissa) of an IEEE number is the part of a floating point number that represents the significant digits. For a positive normalised number it can be represented as m0.m1m2m3...mp-2mp-1 (where m represents a significant digit and p is the precision, and m0 is non-zero). Notice that for a binary radix, the leading binary digit is one. In a denormal number, since the exponent is the least that it can be, zero is the lead significand digit (0.m1m2m3...mp-2mp-1) in order to represent numbers closer to zero than the smallest normal number.
By filling the underflow gap like this, significant digits are lost, but not to the extent as when doing flush to zero on underflow (losing all significant digits all through the underflow gap). Hence the production of a denormal number is sometimes called gradual underflow because it allows a calculation to lose precision slowly when the result is small.
In IEEE 754-2008, denormal numbers are renamed subnormal numbers, and are supported in both binary and decimal formats. In binary interchange formats, subnormal numbers are encoded with a biased exponent of 0, but are interpreted with the value of the smallest allowed exponent, which is one greater (i.e., as if it were encoded as a 1). In decimal interchange formats they require no special encoding because the format supports unnormalized numbers directly.
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Background
Denormal numbers provide the guarantee that addition and subtraction of floating-point numbers never underflows; two nearby floating-point numbers always have a representable non-zero difference. Without gradual underflow, the subtraction a−b can underflow and produce zero even though the values are not equal. This can, in turn, lead to division by zero errors that cannot occur when gradual underflow is used.
Denormal numbers were implemented in the Intel 8087 while the IEEE 754 standard was being written. They were by far the most controversial feature in the K-C-S format proposal that was eventually adopted,[1] but this implementation demonstrated that denormals could be supported in a practical implementation. Some implementations of floating point units do not directly support denormal numbers in hardware, but rather trap to some kind of software support. While this may be transparent to the user, it can result in calculations which produce or consume denormal numbers being much slower than similar calculations on normal numbers.
Performance issues
Some systems handle denormal values in hardware, in the same way as normal values. Others leave the handling of denormal values to system software, only handling normal values and zero in hardware. Handling denormal values in software always leads to a significant decrease in performance. But even when denormal values are entirely computed in hardware, the speed of computation is significantly reduced on most modern processors; in extreme cases, instructions involving denormal operands may run as much as 100 times slower.[2][3]
Some applications need to contain code to avoid denormal numbers, either to maintain accuracy, or in order to avoid the performance penalty in some processors. For instance, in audio processing applications, denormal values usually represent a signal so quiet that it is out of the human hearing range. Because of this, a common measure to avoid denormals on processors where there would be a performance penalty is to cut the signal to zero once it reaches denormal levels or mix in an extremely quiet noise signal.[4] Since the SSE2 processor extension, Intel has provided such a functionality in CPU hardware, which rounds denormalized numbers to zero.[5]
References
- ^ An Interview with the Old Man of Floating-Point Reminiscences elicited from William Kahan by Charles Severance
- ^ Dooley, Isaac; Kale, Laxmikant (2006-09-12). "Quantifying the Interference Caused by Subnormal Floating-Point Values". http://charm.cs.uiuc.edu/papers/SubnormalOSIHPA06.pdf. Retrieved 2010-11-30.
- ^ Fog, Agner. "Instruction tables: Lists of instruction latencies, throughputs and microoperation breakdowns for Intel, AMD and VIA CPUs". http://www.agner.org/optimize/instruction_tables.pdf. Retrieved 2011-01-25.
- ^ Serris, John (2002-04-16). "Pentium 4 denormalization: CPU spikes in audio applications". http://phonophunk.com/articles/pentium4-denormalization.php. Retrieved 2010-09-03.
- ^ Casey, Shawn (2008-10-16). "x87 and SSE Floating Point Assists in IA-32: Flush-To-Zero (FTZ) and Denormals-Are-Zero (DAZ)". http://software.intel.com/en-us/articles/x87-and-sse-floating-point-assists-in-ia-32-flush-to-zero-ftz-and-denormals-are-zero-daz/. Retrieved 2010-09-03.
Further reading
- Eric Schwarz, Martin Schmookler and Son Dao Trong (June 2003). "Hardware Implementations of Denormalized Numbers". Proceedings 16th IEEE Symposium on Computer Arithmetic (Arith16). 16th IEEE Symposium on Computer Arithmetic. IEEE Computer Society. pp. 104–111. ISBN 0-7695-1894-X. http://www.ece.ucdavis.edu/acsel/arithmetic/arith16/papers/ARITH16_Schwarz.pdf.
See also various papers on William Kahan's web site [1] for examples of where denormal numbers help improve the results of calculations.
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
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Subnormal
Dansk (Danish)
adj. - under normalen
n. - nedfælde den vinkelrette på aksen
Nederlands (Dutch)
achterlijk, minder dan normaal
Français (French)
adj. - arriéré, au-dessous de la normale
n. - arriéré
Deutsch (German)
adj. - unterdurchschnittlich
n. - Minderbegabter
Ελληνική (Greek)
adj. - κάτω του φυσιολογικού ή του κανονικού
n. - (μαθημ.) υποκάθετος
Português (Portuguese)
adj. - subnormal
n. - subnormal (m)
Русский (Russian)
поднормальный, умственно неполноценный человек, дебил, меньше или ниже нормального, умственно отсталый, слабоумный
Español (Spanish)
adj. - subnormal, deficiente
n. - subnormal
Svenska (Swedish)
adj. - under det normala, utvecklingsmässigt under det normala, subnormal, undernormal
n. - det subnormala, det undernormala
中文（简体）(Chinese (Simplified))
正常以下的, 低能的, 普通以下的, 不及常人者, 弱智者
中文（繁體）(Chinese (Traditional))
adj. - 正常以下的, 低能的, 普通以下的
n. - 不及常人者, 弱智者
한국어 (Korean)
adj. - 정상에 못 미치는, 저능의
n. - 정상 이하의 사람, 저능자, 차법선
日本語 (Japanese)
adj. - 普通以下の, 知恵遅れの
العربيه (Arabic)
(صفه) دون المعدل الطبيعي (الاسم) متخلف عقليا
עברית (Hebrew)
adj. - תת-נורמלי (בעיקר מבחינת רמת המשכל)
n. - אדם תת-נורמלי
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American Heritage Dictionary
The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.
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Oxford Companion to the Mind
The Oxford Companion to the Mind. Second Edition. Copyright © Oxford University Press, 2004. All rights reserved.
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Saunders Veterinary Dictionary
Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.
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Random House Word Menu
© 2010 Write Brothers Inc. Word Menu is a registered trademark of the Estate of Stephen Glazier.
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Wikipedia on Answers.com
This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article Denormal number.
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