Determining s390x CPU for C++ compilation with -march

I had some trouble compiling with -march=native as that is not supported on s390x. So I tried to determine the type of CPU, i.e. z10, z14, etc. To save others the problem this is the output from cat /proc/cpuinfo and lscpu:

vendor_id       : IBM/S390
# processors    : 4
bogomips per cpu: 3241.00
max thread id   : 0
features	: esan3 zarch stfle msa ldisp eimm dfp edat etf3eh highgprs te vx vxd vxe gs vxe2 vxp sort dflt 
facilities      : 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 32 33 34 35 36 37 38 40 41 42 43 44 45 47 48 49 50 51 52 53 54 57 58 59 60 61 64 69 71 73 74 75 76 77 78 80 81 82 129 130 131 133 134 135 138 139 146 147 148 150 151 152 155 156
cache0          : level=1 type=Data scope=Private size=128K line_size=256 associativity=8
cache1          : level=1 type=Instruction scope=Private size=128K line_size=256 associativity=8
cache2          : level=2 type=Data scope=Private size=4096K line_size=256 associativity=8
cache3          : level=2 type=Instruction scope=Private size=4096K line_size=256 associativity=8
cache4          : level=3 type=Unified scope=Shared size=262144K line_size=256 associativity=32
cache5          : level=4 type=Unified scope=Shared size=983040K line_size=256 associativity=60
processor 0: version = FF,  identification = 0618E8,  machine = 8561
processor 1: version = FF,  identification = 0618E8,  machine = 8561
processor 2: version = FF,  identification = 0618E8,  machine = 8561
processor 3: version = FF,  identification = 0618E8,  machine = 8561

cpu number      : 0
cpu MHz dynamic : 5200
cpu MHz static  : 5200
cpu number      : 1
cpu MHz dynamic : 5200
cpu MHz static  : 5200
cpu number      : 2
cpu MHz dynamic : 5200
cpu MHz static  : 5200
cpu number      : 3
cpu MHz dynamic : 5200
cpu MHz static  : 5200
Architecture:          s390x
CPU op-mode(s):        32-bit, 64-bit
Byte Order:            Big Endian
CPU(s):                4
On-line CPU(s) list:   0-3
Thread(s) per core:    1
Core(s) per socket:    1
Socket(s) per book:    1
Book(s):               4
NUMA node(s):          1
Vendor ID:             IBM/S390
BogoMIPS:              3241.00
Hypervisor:            KVM/Linux
Hypervisor vendor:     KVM
Virtualization type:   full
Dispatching mode:      horizontal
L1d cache:             128K
L1i cache:             128K
L2d cache:             4096K
L2i cache:             4096K
NUMA node0 CPU(s):     0-3
Flags:                 esan3 zarch stfle msa ldisp eimm dfp edat etf3eh highgprs te vx vxd vxe gs vxe2 vxp sort dflt

I believe that machine = 8561 indicates that this is a z15 but I might be mistaken. Anyway I read a few things and it seems that compiling with -march=z10 is a good compromise if you want to produce forward and backward compatible binaries.

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