It turns out that you DO need to turn on the FPU:
4.6.6 Enabling the FPU
The FPU is disabled from reset. You must enable it before you can use any floating-point instructions. Example 4-1shows an example code sequence for enabling the FPU in both privileged and user modes. The processor must be in privileged mode to read from and write to the CPACR.
Example 4-1 Enabling the FPU; CPACR is located at address 0xE000ED88
LDR.W R0, =0xE000ED88
; Read CPACR
LDR R1, [R0]
; Set bits 20-23 to enable CP10 and CP11 coprocessors
ORR R1, R1, #(0xF << 20)
; Write back the modified value to the CPACR
STR R1, [R0]; wait for store to complete
DSB
;reset pipeline now the FPU is enabled
ISB
In effect, the FPU is counted as coprocessor 10 and 11. Cortex-M doesn't fully support the concept of coprocessors, but it does in this context. We allow full unpriveleged access to coprocessors 10 and 11.
I don't know about waiting for the store to complete and resetting the pipeline. I just put some C++ code to do this long before the FPU is used, and let a bunch of other work instructions flush the pipeline.
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