Scientific notation is the common way to express a number with an explicit order of magnitude. First a nonzero digit, then a radix point, then a fractional part, and the exponent. In binary, there is only one possible nonzero digit.
Floating-point math involves an implicit first digit equal to one, then the mantissa bits "follow the radix point."
So why does frexp() put the radix point to the left of the implicit bit, and return a number in [0.5, 1) instead of scientific-notation-like [1, 2)? Is there some overflow to beware of?
Effectively it subtracts one more than the bias value specified by IEEE 754/ISO 60559. In hardware, this potentially trades an addition for an XOR. Alone, that seems like a pretty weak argument, considering that in many cases getting back to normal will require another floating-point operation.
The rationale says:
4.5.4.2 The frexp function
The functions frexp, ldexp, and modf are primitives used by the remainder of the library. There was some sentiment for dropping them for the same reasons that ecvt, fcvt, and gcvt were dropped, but their adherents rescued them for general use. Their use is problematic: on nonbinary architectures ldexp may lose precision, and frexp may be inefficient.
One can speculate that the “remainder of the library” was more convenient to write with frexp's convention, or was already traditionally written against this interface although it did not provide any benefit.
I know that this does not fully answer the question, but it did not quite fit inside a comment.
I should also point out that some of the choices made in the design of the C language predate IEEE 754. Perhaps the format returned by frexp made sense with the PDP-11's floating-point format(s), or any other architecture on which a function frexp was first introduced. EDIT: See also page 155 of the manual for one PDP-11 model.
来源：https://stackoverflow.com/questions/24928833/why-does-frexp-not-yield-scientific-notation