X64) - By MAGNiTUDE

limits.h includes definitions of the characteristics of common variable types. The values are implementation specific, but may not be of lower magnitude than certain specified values in a conforming C implementation.

x64) - by MAGNiTUDE

Download File

The "minimum-magnitude value" column is the minimum possible magnitude for this constant as specified by the standard. In particular, _MIN values represent the minimum magnitude representable in the rarely-used one's complement and sign-magnitude forms. Most implementations will have larger magnitudes for at least some of these numbers. For instance:

The two images are annotated snippets of the star field from a recent attempt to record the occultation of 2UCAC 33330361 by the asteroid (418) Alemannia , from my location in Gardnerville, NV. The star 2UCAC 33330361 is 12.5 magnitude and located in Pisces. The asteroid (418) Alemannia is approximately 40km in diameter with a visual magnitude of approx. 14. The occultation event was predicted for Sunday, December 1st at 05:53:14 (UT) +/- 7 seconds. My location was about 40 km south of the predicted shadow center-line, and just outside the predicted shadow. The snippets are recorded at a sense-up of X64, at approximately 20 minutes before and 20 minutes after the predicted occultation. The actual occultation recording was made at X8 to improve timing accuracy. Magnitude drop was predicted to be 1.9 to 2.2 mag.The path of the asteroid is from right to left in the images. Alemannia, at mag 14, can clearly be seen in the images as it approaches the predicted target star. Both the star and asteroid are also represented in the adjacent light intensity graphs from LiMovie.Although the visual path of the asteroid appears to be directly toward, and away, from the target star in these images, an occultation event was NOT recorded from my location. James Bean recorded the same event in Carson City, and was within the predicted shadow. He also, did NOT observe an occultation.

The difference between the value 8.388612 105 assigned to y and the value printed out is 0.000000125, which is seven decimal orders of magnitude smaller than y. The accuracy of representing y in IEEE single format is about 6 to 7 significant digits, or that y has about six significant digits if it is to be represented in IEEE single format.

Similarly, the difference between the value 1.3 assigned to z and the value printed out is 0.00000004768, which is eight decimal orders of magnitude smaller than z. The accuracy of representing z in IEEE single format is about 7 to 8 significant digits, or that z has about seven significant digits if it is to be represented in IEEE single format.

The IEEE standard requires correct rounding for typical numbers whose magnitudes range from 10-44 to 10+44 but permits slightly incorrect rounding for larger exponents. (See section 5.6 of IEEE Standard 754.) The libc table-driven algorithms round correctly throughout the entire range of single, double, and double extended formats.

The presence of subnormal numbers provides greater precision to floating-point calculations that involve small numbers, although the subnormal numbers themselves have fewer bits of precision than normal numbers. Producing subnormal numbers (rather than returning the answer zero) when the mathematically correct result has magnitude less than the smallest positive normal number is known as gradual underflow.

The smallest positive normal number that can be stored, then, has the negative exponent of greatest magnitude and a fraction of all zeros. Even smaller numbers can be accommodated by considering the leading bit to be zero rather than one. In the double-precision format, this effectively extends the minimum exponent from 10-308 to 10-324, because the fraction part is 52 bits long (roughly 16 decimal digits.) These are the subnormal numbers; returning a subnormal number (rather than flushing an underflowed result to zero) is gradual underflow.

Recall that only a finite set of numbers can be exactly represented in any computer arithmetic. As the magnitudes of numbers get smaller and approach zero, the gap between neighboring representable numbers narrows. Conversely, as the magnitude of numbers gets larger, the gap between neighboring representable numbers widens.

In the IEEE single format, the difference in magnitude between the two smallest positive subnormal numbers is approximately 10-45, whereas the difference in magnitude between the two largest finite numbers is approximately 1031!

The following example illustrates comparable specifications of the CUMPRINC and FINANCE functions to obtain the cumulative principle paid on a loan between two periods. The FINANCE function returns a value that is equal in magnitude but opposite in sign of the result returned by the CUMPRINC function.

I'm analyzing a fungal RNA-Seq data set with just 2 groups, 3 reps per group. The BCV is extremely low and the treatment effect is sufficiently large, such that 3/4 of the genes end up with FDR p 2ff7e9595c