2.15 The Q flag

The Q flag indicates overflow or saturation. It is one of the program status flags held in the APSR.

In ARMv5TE, ARMv6 and later, the Q flag is set to 1 when saturation has occurred in saturating arithmetic instructions, or when overflow has occurred in certain multiply instructions.
The Q flag is a sticky flag. Although the saturating and certain multiply instructions can set the flag, they cannot clear it. You can execute a series of such instructions, and then test the flag to find out whether saturation or overflow occurred at any point in the series, without having to check the flag after each instruction.
To clear the Q flag, use an MSR instruction to read-modify-write the APSR:
    MRS r5, APSR
    BIC r5, r5, #(1<<27)
    MSR APSR_nzcvq, r5
The state of the Q flag cannot be tested directly by the condition codes. To read the state of the Q flag, use an MRS instruction.
    MRS r6, APSR
    TST r6, #(1<<27); Z is clear if Q flag was set
Related concepts
4.19 The Read-Modify-Write operation
Related reference
10.60 MRS (PSR to general-purpose register)
10.63 MSR (general-purpose register to PSR)
10.74 QADD
10.121 SMULxy
10.123 SMULWy
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