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.