IEEE Floating Point Standard

IEEE Floating Point Standard

(standard, mathematics)
(IEEE 754) "IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985)" or IEC 559: "Binary floating-point arithmetic for microprocessor systems". A standard, used by many CPUs and FPUs, which defines formats for representing floating-point numbers; representations of special values (e.g. infinity, very small values, NaN); five exceptions, when they occur, and what happens when they do occur; four rounding modes; and a set of floating-point operations that will work identically on any conforming system.

IEEE 754 specifies formats for representing floating-point values: single-precision (32-bit) is required, double-precision (64-bit) is optional. The standard also mentions that some implementations may include single-extended precision (80-bit) and double-extended precision (128-bit) formats.

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which is element-wise backward stable since under the IEEE floating point standard, we have that the computed roots satisfy
which is also element-wise backward stable since under the IEEE floating point standard, we have that the computed roots satisfy the element-wise bounds
According to the IEEE floating point standard, we have that the computed values [[?

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