What is claimed is:1. A processor-based device, comprising:a processor device comprising:an exception stack; anda plurality of dedicated stack panic fault exception state registers;the processor device configured to:detect a first exception while executing a software process;responsive to detecting the first exception, transfer program control to an exception handler corresponding to the first exception;execute a store operation within the exception handler to store state data in the exception stack;detect a second exception while executing the store operation;determine that the second exception should be handled as a stack panic fault exception; andresponsive to determining that the second exception should be handled as a stack panic fault exception:save stack panic fault exception state data in the plurality of dedicated stack panic fault exception state registers; andtransfer program control to a stack panic fault exception handler corresponding to the stack panic fault exception.2. The processor-based device of claim 1, wherein the processor device is configured to determine that the second exception should be handled as a stack panic fault exception by being configured to determine that the store operation is performed by a store instruction that comprises a custom opcode indicating that the store instruction raises a stack panic fault exception.3. The processor-based device of claim 1, wherein the processor device is configured to determine that the second exception should be handled as a stack panic fault exception by being configured to determine that the store operation is performed by a store instruction that comprises a custom bit indicator indicating that the store instruction raises a stack panic fault exception.4. The processor-based device of claim 1, wherein the processor device is configured to determine that the second exception should be handled as a stack panic fault exception by being configured to determine that the store operation is performed by a store instruction that comprises a custom operand indicating that the store instruction raises a stack panic fault exception.5. The processor-based device of claim 1, wherein the processor device is configured to determine that the second exception should be handled as a stack panic fault exception by being configured to determine that the store operation is performed by a store instruction that is among a first N store instructions within the exception handler, where N is a positive integer.6. The processor-based device of claim 1, wherein:the processor device further comprises a stack panic indicator;the processor device is configured to determine that the second exception should be handled as a stack panic fault exception by being configured to determine that the stack panic indicator is set; andthe processor device is further configured to:further responsive to detecting the first exception, set the stack panic indicator;transfer program control back to the exception handler once the stack panic fault exception handler completes execution; andclear the stack panic indicator once the exception handler completes execution.7. The processor-based device of claim 1, wherein the processor device is further configured to transfer program control to the stack panic fault exception handler corresponding to the stack panic fault exception based on a stack panic fault exception vector of the processor device.8. A method for providing exception stack management using stack panic fault exceptions, comprising:detecting, by a processor device of a processor-based device, a first exception while executing a software process;responsive to detecting the first exception, transferring program control to an exception handler corresponding to the first exception;executing a store operation within the exception handler to store state data in an exception stack of the processor device;detecting a second exception while executing the store operation;determining that the second exception should be handled as a stack panic fault exception; andresponsive to determining that the second exception should be handled as a stack panic fault exception:saving stack panic fault exception state data in a plurality of dedicated stack panic fault exception state registers; andtransferring program control to a stack panic fault exception handler corresponding to the stack panic fault exception.9. The method of claim 8, wherein determining that the second exception should be handled as a stack panic fault exception comprises determining that the store operation is performed by a store instruction that comprises a custom opcode indicating that the store instruction raises a stack panic fault exception.10. The method of claim 8, wherein determining that the second exception should be handled as a stack panic fault exception comprises determining that the store operation is performed by a store instruction that comprises a custom bit indicator indicating that the store instruction raises a stack panic fault exception.11. The method of claim 8, wherein determining that the second exception should be handled as a stack panic fault exception comprises determining that the store operation is performed by a store instruction that comprises a custom operand indicating that the store instruction raises a stack panic fault exception.12. The method of claim 8, wherein determining that the second exception should be handled as a stack panic fault exception comprises determining that the store operation is performed by a store instruction that is among a first N store instructions within the exception handler, where N is a positive integer.13. The method of claim 8, wherein:determining that the second exception should be handled as a stack panic fault exception comprises determining that the stack panic indicator is set; andthe method further comprises:further responsive to detecting the first exception, setting the stack panic indicator;transferring program control back to the exception handler once the stack panic fault exception handler completes execution; andclearing the stack panic indicator once the exception handler completes execution.14. The method of claim 8, further comprising transferring program control to a stack panic fault exception handler corresponding to the stack panic fault exception based on a stack panic fault exception vector of the processor device.15. A non-transitory computer-readable medium having stored thereon computer-executable instructions which, when executed by a processor, cause the processor to:detect a first exception while executing a software process;responsive to detecting the first exception, transfer program control to an exception handler corresponding to the first exception;execute a store operation within the exception handler to store state data in an exception stack;detect a second exception while executing the store operation;determine that the second exception should be handled as a stack panic fault exception; andresponsive to determining that the second exception should be handled as a stack panic fault exception:save stack panic fault exception state data in a plurality of dedicated stack panic fault exception state registers of the processor; andtransfer program control to a stack panic fault exception handler corresponding to the stack panic fault exception.16. The non-transitory computer-readable medium of claim 15, wherein the computer-executable instructions cause the processor to determine that the second exception should be handled as a stack panic fault exception by causing the processor to determine that the store operation is performed by a store instruction that comprises a custom opcode indicating that the store instruction raises a stack panic fault exception.17. The non-transitory computer-readable medium of claim 15, wherein the computer-executable instructions cause the processor to determine that the second exception should be handled as a stack panic fault exception by causing the processor to determine that the store operation is performed by a store instruction that comprises a custom bit indicator indicating that the store instruction raises a stack panic fault exception.18. The non-transitory computer-readable medium of claim 15, wherein the computer-executable instructions cause the processor to determine that the second exception should be handled as a stack panic fault exception by causing the processor to determine that the store operation is performed by a store instruction that comprises a custom operand indicating that the store instruction raises a stack panic fault exception.19. The non-transitory computer-readable medium of claim 15, wherein the computer-executable instructions cause the processor to determine that the second exception should be handled as a stack panic fault exception by causing the processor to determine that the store operation is performed by a store instruction that is among a first N store instructions within the exception handler, where N is a positive integer.20. The non-transitory computer-readable medium of claim 15, wherein:the computer-executable instructions cause the processor to determine that the second exception should be handled as a stack panic fault exception by causing the processor to determine that the stack panic indicator is set; andthe computer-executable instructions further cause the processor to:further responsive to detecting the first exception, set the stack panic indicator;transfer program control back to the exception handler once the stack panic fault exception handler completes execution; andclear the stack panic indicator once the exception handler completes execution.