ID 683176
Date 9/24/2018
Public

## 3.3.1. Floating-Point versus Fixed-Point Representations

An FPGA contains a substantial amount of logic for implementing floating-point operations. However, you can increase the amount of hardware resources available by using a fixed-point representation of the data whenever possible. The hardware necessary to implement a fixed-point operation is typically smaller than the equivalent floating-point operation. As a result, you can fit more fixed-point operations into an FPGA than the floating-point equivalent.

The OpenCL® standard does not support fixed-point representation; you must implement fixed-point representations using integer data types. Hardware developers commonly achieve hardware savings by using fixed-point data representations and only retain a data resolution required for performing calculations. You must use an 8, 16, 32, or 64-bit scalar data type because the OpenCL standard supports only these data resolutions. However, you can incorporate the appropriate masking operations in your source code so that the hardware compilation tools can perform optimizations to conserve hardware resources.

For example, if an algorithm uses a fixed-point representation of 17-bit data, you must use a 32-bit data type to store the value. If you then direct the to add two 17-bit fixed-point values together, the offline compiler must create extra hardware to handle the addition of the excess upper 15 bits. To avoid having this additional hardware, you can use static bit masks to direct the hardware compilation tools to disregard the unnecessary bits during hardware compilation. The code below implements this masking operation:

__kernel fixed_point_add (__global const unsigned int * restrict a,
__global const unsigned int * restrict b,
__global unsigned int * restrict result)
{
size_t gid = get_global_id(0);

unsigned int temp;
temp = 0x3_FFFF & ((0x1_FFFF & a[gid]) + ((0x1_FFFF & b[gid]));

result[gid] = temp & 0x3_FFFF;
}

In this code example, the upper 15 bits of inputs a and b are masked away and added together. Because the result of adding two 17-bit values cannot exceed an 18-bit resolution, the offline compiler applies an additional mask to mask away the upper 14 bits of the result. The final hardware implementation is a 17-bit addition as opposed to a full 32-bit addition. The logic savings in this example are relatively minor compared to the sheer number of hardware resources available in the FPGA. However, these small savings, if applied often, can accumulate into a larger hardware saving across the entire FPGA.

Did you find the information on this page useful?

Characters remaining:

Feedback Message