Pfthb

Given integers exp and 0<=sig<2^52, how can I create the float64 with exp as exponent and whose significand bits are the same as the binary representation of sig (in Go)?

The IEEE-754 standard defines the floating point arithmetics which Go uses for floating point numbers such as float32 and float64 (just like almost any other language).

Since your significand may be up to 52 bits, obviously it can only be represented using a float64 value.

The memory layout (bits) of a float64 value is described in Double-precision floating-point format.

Here's a picture of the bits of a float64 value (taken from Wikipedia):

You claim you have the exponent value and the significand (which is the fraction part).

You may use simple bitwise arithmetic to construct the 64-bit value of the floating point like this:

bits := exp<<52 | sig

(Note: exp and sig should be of type uint64. If not, use a type conversion.)

Once you have the bits, you may use the math.Float64frombits() function to get it as a float64 value:

f := math.Float64frombits(bits)

Note that the exponent value of the memory layout is not the "direct" number you have to use when calculating the value of the number, but:

The double-precision binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 1023; also known as exponent bias in the IEEE 754 standard.

So the number encoded in the above double-precision format is calculated like:

(-1)^sign x 2^e-1023 x 1.fraction