Fixed point representation

Heimdali can write pixel values to HDF5 and Inrimage file using their floating point representation or using a fixed point representation.

The conversion is explained by the formulaes:

\[\text{pixel_value} = \text{fixed_point_factor} \times \frac {2^\text{fixed_point_exponent}} {2^\text{fixed_point_nbits} - 1}\]
\[\text{fixed_point_factor} = round \left( \text{pixel_value} \times \frac {2^\text{fixed_point_nbits} - 1} {2^\text{fixed_point_exponent}} \right)\]

where:

  • pixel_value is a float.

  • fixed_point_exponent is a char of values in \([-100, 100]\) It is a global value for the image.

  • fixed_point_factor is of type fixed_point_type, and is defined on all pixel.

  • fixed_point_nbits is the number of bits of fixed_point_type (so number of bytes times 8). As all pixel are of the same type, it is a global value for the image.

  • fixed_point_type can be:
    • char (1 byte).
    • unsigned char (1 byte).
    • short (2 bytes).
    • unsigned short (2 bytes).
    • int (4 bytes).
    • unsigned int (4 bytes).

  • round convert a floating point to the nearest lower integer.

A file stores the fixed_point_exponent (one value), and an array of fixed_point_factor of type T. When the file is read or written, these values are converted to an array of float back and forth, and computation are performed using float.

Examples (fixed_point_exponent is 0)
pixel value fixed_point_type 2^pixed_point_nbits -1 fixed_point_factor
0.11 [unsigned] char 2^8 - 1 = 255 28
0.22 [unsigned] char 2^8 - 1 = 255 56
0.33 [unsigned] char 2^8 - 1 = 255 84
0.11 [unsigned] short 2^16 - 1 = 65534 7209
0.22 [unsigned] short 2^16 - 1 = 65534 14417
0.33 [unsigned] short 2^16 - 1 = 65534 21626
0.11 [unsigned] int 2^32 - 1 = 4294967294 472446400
0.22 [unsigned] int 2^32 - 1 = 4294967294 944892800
0.33 [unsigned] int 2^32 - 1 = 4294967294 1417339264