Decoding a time format

Question

I'm reverse engineering a hardware device which stores time a strange format:

32-bit word	H:MM:SS (rounded)
0x03200000	0:00:00
0x09700000	0:00:00
0x0A1B0000	0:00:01
0x0A160000	0:00:01
0x0B098000	0:00:02
0x0F376600	0:00:46
0x0F347800	0:00:46
0x10038B00	0:01:07
0x10040800	0:01:07
0x1056A600	0:01:49
0x10573C00	0:01:50
0x10589A00	0:01:50
0x1058B300	0:01:50
0x13173240	0:10:19
0x13173880	0:10:19

I believe the time is recorded in some internal high-frequency timer ticks, but I don't see any linear correspondence between the words and time values. Any tips?

UPD. I found out that it's Texas Instruments's custom floating-point format for TMS320 DSPs. Described here.

Answer 1

The values appear to be a floating point format similar to single-precision floating-point format.

If I interpret the first byte as an unbiased exponent and interpret the other bytes (excluding the highest bit) as a fraction, then the value (1 + fraction) × 2^exponent appears to be the number of milliseconds:

Equivalently, in the following textual table, the first byte e is the exponent, the other bytes n form the numerator of the fraction, and the denominator of the fraction is 2²³. The value (1 + n/2²³) × 2^e is the number of milliseconds:

e	n	e	n	(1 + n/223) × 2e
03	200000	3	2097152	10
09	700000	9	7340032	960
0A	1B0000	10	1769472	1240
0A	160000	10	1441792	1200
0B	098000	11	622592	2200
0F	376600	15	3630592	46950
0F	347800	15	3438592	46200
10	038B00	16	232192	67350
10	040800	16	264192	67600
10	56A600	16	5678592	109900
10	573C00	16	5716992	110200
10	589A00	16	5806592	110900
10	58B300	16	5812992	110950
13	173240	19	1520192	619300
13	173880	19	1521792	619400