Binary representation of integers and floating point numbers: is there a monotonically increasing one-to-one correspondence? -


dealing legacy system in need store integers using function accepts doubles input, came accross following problem. given binary number, example:

00111111 11000000 00000000 00000000

if represent integer number 1069547520. if represent ieee 754 floating point number 1.5. easy see there one-to-one correspondence between integers , ieee 754 floating point numbers. question following. given 2 integers , b, , corresponding ieee 754 floating point counterparts , b, > b imply > b?

i guess answer yes, lack strong arguments supporting it. hint?

positive ieee 754 binary32 numbers map increasing integers.

however:

  • the ieee 754 representation sign-magnitude, negative binary32 numbers map decreasing integers. if mapped unsigned int32s, negative floating-point numbers map above positive floating-point numbers (and if going bit-twiddle floating-point numbers, may map them unsigned int32s).

  • ieee 754 has +0.0 , -0.0, equal floating-point definition of “equal” map different integers (respectively 0 and, if mapping signed 32-bit int type, int_min).

  • ieee 754 has several representations of nan, map different integers.

  • this assumes floating-point , integer representations have same endianness. there many advantages in giving them same endianness, arm, cite example, has historically been doing strange things endianness, should point out.


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