Texas Instruments TMS320C67X/C67X+ DSP manual SPRU733

Overview of IEEE Standard Single- and Double-Precision Formats

3.3 Overview of IEEE Standard Single- and Double-Precision Formats

Floating-point operands are classified as single-precision (SP) and double- precision (DP). Single-precision floating-point values are 32-bit values stored in a single register. Double-precision floating-point values are 64-bit values stored in a register pair. The register pair consists of consecutive even and odd registers from the same register file. The 32 least-significant-bits are loaded into the even register; the 32 most-significant-bits containing the sign bit and exponent are loaded into the next register (that is always the odd register). The register pair syntax places the odd register first, followed by a colon, then the even register (that is, A1:A0, B1:B0, A3:A2, B3:B2, etc.).

Instructions that use DP sources fall in two categories: instructions that read the upper and lower 32-bit words on separate cycles, and instructions that read both 32-bit words on the same cycle. All instructions that produce a double-precision result write the low 32-bit word one cycle before writing the high 32-bit word. If an instruction that writes a DP result is followed by an instruction that uses the result as its DP source and it reads the upper and low- er words on separate cycles, then the second instruction can be scheduled on the same cycle that the high 32-bit word of the result is written. The lower result is written on the previous cycle. This is because the second instruction reads the low word of the DP source one cycle before the high word of the DP source.

IEEE floating-point numbers consist of normal numbers, denormalized numbers, NaNs (not a number), and infinity numbers. Denormalized numbers are nonzero numbers that are smaller than the smallest nonzero normal number. Infinity is a value that represents an infinite floating-point number. NaN values represent results for invalid operations, such as (+infinity + (−infinity)).

Normal single-precision values are always accurate to at least six decimal places, sometimes up to nine decimal places. Normal double-precision values are always accurate to at least 15 decimal places, sometimes up to 17 decimal places.

Table 3−3 shows notations used in discussing floating-point numbers.

SPRU733 Instruction Set 3-9