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Libraries and Floating Point Support Guide

Preface The ARM C and C++ Libraries The ARM C Micro-library Floating-point Support About floating-point support The software floating-point library, fplib Calling fplib routines fplib arithmetic on numbers in a particular format fplib conversions between floats, long longs, doub fplib comparisons between floats and doubles fplib C99 functions Controlling the ARM floating-point environment Floating-point functions for compatibility with Mi C99-compatible functions for controlling the ARM f C99 rounding mode and floating-point exception mac Exception flag handling Functions for handling rounding modes Functions for saving and restoring the whole float Functions for temporarily disabling exceptions ARM floating-point compiler extensions to the C99 Writing a custom exception trap handler Example of a custom exception handler Exception trap handling by signals mathlib double and single-precision floating-point IEEE 754 arithmetic Basic data types for IEEE 754 arithmetic Single precision data type for IEEE 754 arithmetic Double precision data type for IEEE 754 arithmetic Sample single precision floating-point values for Sample double precision floating-point values for IEEE 754 arithmetic and rounding Exceptions arising from IEEE 754 floating-point ar Exception types recognized by the ARM floating-poi Using the Vector Floating-Point (VFP) support libr The C and C++ Library Functions reference Floating-point Support Functions Reference

Sample double precision floating-point values for IEEE 754 arithmetic

3.5.5 Sample double precision floating-point values for IEEE 754 arithmetic

Sample double bit patterns, together with their mathematical values.

Table 3-10 Sample double-precision floating-point values

Double value S Exp Frac Mathematical value
0x3FF0000000000000 0 0x3FF 000...000 1.0
0xBFF0000000000000 1 0x3FF 000...000 -1.0
0x3FF0000000000001a 0 0x3FF 000...001 1.000 000 000 000 000 222
0x3FE8000000000000 0 0x3FE 100...000 0.75
0x0010000000000000b 0 0x001 000...000 2.23*10-308
0x0000000000000001c 0 0x000 000...001 4.94*10-324
0x7FEFFFFFFFFFFFFFd 0 0x7FE 111...111 1.80*10308
0x7FF0000000000000 0 0x7FF 000...000 Plus infinity
0xFFF0000000000000 1 0x7FF 000...000 Minus infinity
0x0000000000000000e 0 0x000 000...000 0.0
0x7FF0000000000001 0 0x7FF 000...001 Signaling NaN
0x7FF8000000000000f 0 0x7FF 100...000 Quiet NaN
a
The smallest representable number that can be seen to be greater than 1.0. The amount that it differs from 1.0 is known as the machine epsilon. This is 0.000 000 119 in float, and 0.000 000 000 000 000 222 in double. The machine epsilon gives a rough idea of the number of significant figures the format can keep track of. float can do six or seven places. double can do fifteen or sixteen.
b
The smallest value that can be represented as a normalized number in each format. Numbers smaller than this can be stored as denormals, but are not held with as much precision.
c
The smallest positive number that can be distinguished from zero. This is the absolute lower limit of the format.
d
The largest finite number that can be stored. Attempting to increase this number by addition or multiplication causes overflow and generates infinity (in general).
e
Zero. Strictly speaking, they show plus zero. Zero with a sign bit of 1, minus zero, is treated differently by some operations, although the comparison operations (for example == and !=) report that the two types of zero are equal.
f 
There are two types of NaNs, signaling NaNs and quiet NaNs. Quiet NaNs have a 1 in the first bit of Frac, and signaling NaNs have a zero there. The difference is that signaling NaNs cause an exception when used, whereas quiet NaNs do not.
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