We are compiling an embedded C++ application that is deployed in a shielded device in an environment bombarded with ionizing radiation. We are using GCC and cross-compiling
Writing code for radioactive environments is not really any different than writing code for any mission-critical application.
In addition to what has already been mentioned, here are some miscellaneous tips:
Use everyday "bread & butter" safety measures that should be present on any semi-professional embedded system: internal watchdog, internal low-voltage detect, internal clock monitor. These things shouldn't even need to be mentioned in the year 2016 and they are standard on pretty much every modern microcontroller.
If you have a safety and/or automotive-oriented MCU, it will have certain watchdog features, such as a given time window, inside which you need to refresh the watchdog. This is preferred if you have a mission-critical real-time system.
In general, use a MCU suitable for these kind of systems, and not some generic mainstream fluff you received in a packet of corn flakes. Almost every MCU manufacturer nowadays have specialized MCUs designed for safety applications (TI, Freescale, Renesas, ST, Infineon etc etc). These have lots of built-in safety features, including lock-step cores: meaning that there are 2 CPU cores executing the same code, and they must agree with each other.
IMPORTANT: You must ensure the integrity of internal MCU registers. All control & status registers of hardware peripherals that are writeable may be located in RAM memory, and are therefore vulnerable.
To protect yourself against register corruptions, preferably pick a microcontroller with built-in "write-once" features of registers. In addition, you need to store default values of all hardware registers in NVM and copy-down those values to your registers at regular intervals. You can ensure the integrity of important variables in the same manner.
Note: always use defensive programming. Meaning that you have to setup all registers in the MCU and not just the ones used by the application. You don't want some random hardware peripheral to suddenly wake up.
There are all kinds of methods to check for errors in RAM or NVM: checksums, "walking patterns", software ECC etc etc. The best solution nowadays is to not use any of these, but to use a MCU with built-in ECC and similar checks. Because doing this in software is complex, and the error check in itself could therefore introduce bugs and unexpected problems.
Use redundancy. You could store both volatile and non-volatile memory in two identical "mirror" segments, that must always be equivalent. Each segment could have a CRC checksum attached.
Avoid using external memories outside the MCU.
Implement a default interrupt service routine / default exception handler for all possible interrupts/exceptions. Even the ones you are not using. The default routine should do nothing except shutting off its own interrupt source.
Understand and embrace the concept of defensive programming. This means that your program needs to handle all possible cases, even those that cannot occur in theory. Examples.
High quality mission-critical firmware detects as many errors as possible, and then handles or ignores them in a safe manner.
Never write programs that rely on poorly-specified behavior. It is likely that such behavior might change drastically with unexpected hardware changes caused by radiation or EMI. The best way to ensure that your program is free from such crap is to use a coding standard like MISRA, together with a static analyser tool. This will also help with defensive programming and with weeding out bugs (why would you not want to detect bugs in any kind of application?).
IMPORTANT: Don't implement any reliance of the default values of static storage duration variables. That is, don't trust the default contents of the .data or .bss. There could be any amount of time between the point of initialization to the point where the variable is actually used, there could have been plenty of time for the RAM to get corrupted. Instead, write the program so that all such variables are set from NVM in run-time, just before the time when such a variable is used for the first time.
In practice this means that if a variable is declared at file scope or as static, you should never use = to initialize it (or you could, but it is pointless, because you cannot rely on the value anyhow). Always set it in run-time, just before use. If it is possible to repeatedly update such variables from NVM, then do so.
Similarly in C++, don't rely on constructors for static storage duration variables. Have the constructor(s) call a public "set-up" routine, which you can also call later on in run-time, straight from the caller application.
If possible, remove the "copy-down" start-up code that initializes .data and .bss (and calls C++ constructors) entirely, so that you get linker errors if you write code relying on such. Many compilers have the option to skip this, usually called "minimal/fast start-up" or similar.
This means that any external libraries have to be checked so that they don't contain any such reliance.
Implement and define a safe state for the program, to where you will revert in case of critical errors.
Implementing an error report/error log system is always helpful.