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.
Dictionary:
sub·nor·mal (sŭb-nôr'məl) ![]() |
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.| 5min Related Video: subnormal |
| World of the Mind: 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.— Neil O'Connor
| Wikipedia: Denormal number |
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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'.
For example, if the smallest positive 'normal' number is 1×β−n (where β is the base of the floating-point system, usually 2 or 10), then any smaller positive numbers that can be represented are denormal.
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 smallest 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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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.
Some processors handle denormal values in hardware, just as normal values are. Denormal values (as arguments or results) then pose no particular performance issue; they are handled at the same speed as normal values. But some processors leave the handling of denormal values to system software, only handling normal values (and zero) in hardware. In this case, computing with denormal values is significantly slower than computing with normal values.
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's out of the human hearing range. Because of this, common measures to avoid denormals (on processors where there would be a performance penalty) is to cut the signal to zero once it reaches denormal levels, mix an extremely quiet noise signal in, or simply add an extremely small (like 10−24) DC offset.[2]
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: 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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