I and writing a PCIE driver for my custom FPGA base board, where bar0 and bar2 are adopted for io. However, after I insert this board to Openwrt router board, I find that the region size information given by /sys/devices/pci0000:00/0000:00:00.0/resource and /proc/iomem is conflict.

Content of /sys/devices/pci0000:00/0000:00:00.0/resource is (for bar0 and bar2):

0x0000000010008000 0x0000000010009000 0x0000000000040200
0x0000000010000000 0x0000000010008000 0x0000000000040200

While content of /proc/iomem is (for bar0 and bar2):

10000000-13ffffff : mem_base
10000000-13ffffff : PCI memory space
10000000-10007fff : 0000:00:00.0
10008000-10008fff : 0000:00:00.0

Obviously, the region size given by the former one is 4097, while the region size given by the latter one is 4096. According to the PCIE protocol, the region size should always be power of two, isn't it?

So what is the reason that cause this problem and how to fix it?

Welcome to LQ.

As one of the few hardware heads about here, let me have a go at this.
Am I correct in assuming the relevant figures are highlighted? That, indeed gives some dubious multiple of 4096 on a calculator, but in fact 4097 in hardware- my calculator is very odd. This one The first of those gives 0x7fff of a difference, the second 0x0fff, or 4095; when you look at that from a hardware perspective, it's 4096, remembering the days of limited address lines, number ranges go from 0x00-0xFF for 256 addressable bits with 8 lines. 0x00 is a valid address, 255 is the top address, giving 256 bits

Applying this logic to your figures, the output of /sys/devices/pci0000:00/0000:00:00.0/resource is suspect. You notice the address 0x0000000010008000 is assigned to both blocks? I suspect it shouldn't be. That looks like a kernel bug or system bug to me.
For your purposes, treat it as 0x0000 - 7FFF & 8000 - 8fff, and report the bug. There's a time penalty in doing that, but pay it.

I must say in passing, that I expected to be fingering your code, and not the kernel.

Also: the number of inclusive values in any range is hi - lo + 1 ... The number of values in the inclusive range [000...fff] is 4,096.