Implementation notes: amd64, bolero, crypto_aead/ascon128abi32v12

Computer: bolero
Microarchitecture: amd64; Broadwell+AES (406f1)
Architecture: amd64
CPU ID: GenuineIntel-000406f1-1fc9cbf5
SUPERCOP version: 20240808
Operation: crypto_aead
Primitive: ascon128abi32v12

Time	Object size	Test size	Implementation	Compiler	Benchmark date	SUPERCOP version
90696	8665 0 0	22052 816 856	`bi32`	`clang_-march=native_-O_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
90928	28335 0 0	44998 776 928	`ref`	`gcc_-march=native_-mtune=native_-O3_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
91416	18064 0 0	34948 816 872	`ref`	`clang_-march=native_-O2_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
91596	18064 0 0	35260 816 872	`ref`	`clang_-march=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
92380	8638 0 0	22726 808 920	`bi32`	`clang_-march=native_-Os_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
92432	8407 0 0	24308 816 856	`bi32`	`clang_-mcpu=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
92632	8683 0 0	25908 816 872	`bi32`	`clang_-march=native_-O2_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
92720	10601 0 0	26540 816 856	`ref`	`clang_-mcpu=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
92856	8692 0 0	26220 816 872	`bi32`	`clang_-march=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
95840	10470 0 0	24990 776 928	`bi32`	`gcc_-march=native_-mtune=native_-O2_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
96144	13639 0 0	27534 808 920	`ref`	`clang_-march=native_-Os_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
96652	10443 0 0	23345 752 896	`bi32`	`gcc_-march=native_-mtune=native_-Os_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
98200	4276 0 0	21892 816 872	`bi32_lowreg`	`clang_-march=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
98252	4276 0 0	21580 816 872	`bi32_lowreg`	`clang_-march=native_-O2_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
98440	4155 0 0	18358 808 920	`bi32_lowreg`	`clang_-march=native_-Os_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
100880	13763 0 0	27909 768 928	`bi32`	`gcc_-march=native_-mtune=native_-O_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
102968	10168 0 0	23604 816 856	`ref`	`clang_-march=native_-O_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
103272	5548 0 0	20158 776 928	`bi32_lowreg`	`gcc_-march=native_-mtune=native_-O2_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
104148	1777 0 0	15902 808 920	`bi32_lowsize`	`clang_-march=native_-Os_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
104292	2015 0 0	19572 816 872	`bi32_lowsize`	`clang_-march=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
104588	1785 0 0	19036 816 872	`bi32_lowsize`	`clang_-march=native_-O2_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
105864	4299 0 0	20300 816 856	`bi32_lowreg`	`clang_-mcpu=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
109872	2317 0 0	16885 784 928	`bi32_lowsize`	`gcc_-march=native_-mtune=native_-O2_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
110188	1984 0 0	17932 816 856	`bi32_lowsize`	`clang_-mcpu=native_-O3_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
110384	11708 0 0	28278 776 928	`bi32`	`gcc_-march=native_-mtune=native_-O3_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
116140	4279 0 0	17772 816 856	`bi32_lowreg`	`clang_-march=native_-O_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
116244	1663 0 0	15084 816 856	`bi32_lowsize`	`clang_-march=native_-O_-fwrapv_-Qunused-arguments_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
117180	5972 0 0	22614 776 928	`bi32_lowreg`	`gcc_-march=native_-mtune=native_-O3_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
118488	5478 0 0	20102 776 928	`ref`	`gcc_-march=native_-mtune=native_-O2_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
118732	5524 0 0	19773 768 928	`ref`	`gcc_-march=native_-mtune=native_-O_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
119364	5395 0 0	18369 752 896	`bi32_lowreg`	`gcc_-march=native_-mtune=native_-Os_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
121672	2740 0 0	19349 784 928	`bi32_lowsize`	`gcc_-march=native_-mtune=native_-O3_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
121944	7973 0 0	22213 768 928	`bi32_lowreg`	`gcc_-march=native_-mtune=native_-O_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
122096	2149 0 0	15064 760 896	`bi32_lowsize`	`gcc_-march=native_-mtune=native_-Os_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
126424	2923 0 0	15977 752 896	`ref`	`gcc_-march=native_-mtune=native_-Os_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808
128088	3388 0 0	17556 776 928	`bi32_lowsize`	`gcc_-march=native_-mtune=native_-O_-fwrapv_-fPIC_-fPIE_-gdwarf-4_-Wall`	20240809	20240808

Compiler output

aead.c: In file included from round.h:8,
aead.c:                  from permutations.h:11,
aead.c:                  from aead.c:4:
aead.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
aead.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
aead.c:       |           ^~~~~~~~~~~~~~~~~~~~~~
permutations.c: In file included from round.h:8,
permutations.c:                  from permutations.h:11,
permutations.c:                  from permutations.c:1:
permutations.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
permutations.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
permutations.c:       |           ^~~~~~~~~~~~~~~~~~~~~~

Number of similar (implementation,compiler) pairs: 8, namely:

Implementation	Compiler
`bi32`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`

Compiler output

aead.c: In file included from round.h:8,
aead.c:                  from permutations.h:11,
aead.c:                  from aead.c:3:
aead.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
aead.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
aead.c:       |           ^~~~~~~~~~~~~~~~~~~~~~
crypto_aead.c: In file included from round.h:8,
crypto_aead.c:                  from permutations.h:11,
crypto_aead.c:                  from crypto_aead.c:8:
crypto_aead.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
crypto_aead.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
crypto_aead.c:       |           ^~~~~~~~~~~~~~~~~~~~~~
permutations.c: In file included from round.h:8,
permutations.c:                  from permutations.h:11,
permutations.c:                  from permutations.c:1:
permutations.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
permutations.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
permutations.c:       |           ^~~~~~~~~~~~~~~~~~~~~~
update.c: In file included from round.h:8,
update.c:                  from permutations.h:11,
update.c:                  from update.c:3:
update.c: word.h:55:11: warning: 'crypto_int64_bitmod_01' is static but used in inline function 'NOTZERO' which is not static
update.c:    55 |   return (crypto_int64_bitmod_01(((int)(result & 0xff) - 1),8)) - 1;
update.c:       |           ^~~~~~~~~~~~~~~~~~~~~~

Number of similar (implementation,compiler) pairs: 4, namely:

Implementation	Compiler
`bi32_lowsize`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`

Namespace violations

constants.o constants R
permutations.o P12 T
permutations.o P8 T

Number of similar (implementation,compiler) pairs: 9, namely:

Implementation	Compiler
`bi32`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`

Namespace violations

aead.o ascon_adata T
aead.o ascon_decrypt T
aead.o ascon_encrypt T
aead.o ascon_final T
aead.o ascon_initaead T
aead.o ascon_loadkey T
constants.o constants R

Number of similar (implementation,compiler) pairs: 9, namely:

Implementation	Compiler
`bi32_lowreg`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`

Namespace violations

aead.o ascon_aead T
constants.o constants R
permutations.o P T
update.o ascon_update T

Number of similar (implementation,compiler) pairs: 9, namely:

Implementation	Compiler
`bi32_lowsize`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`

Passed TIMECOP

TIMECOP iterations: 10

Number of similar (implementation,compiler) pairs: 36, namely:

Implementation	Compiler
`bi32`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowreg`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`bi32_lowsize`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`ref`	`clang -march=native -O2 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`ref`	`clang -march=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`ref`	`clang -march=native -O -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`ref`	`clang -march=native -Os -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`ref`	`clang -mcpu=native -O3 -fwrapv -Qunused-arguments -fPIC -fPIE -gdwarf-4 -Wall (Ubuntu_Clang_14.0.0)`
`ref`	`gcc -march=native -mtune=native -O2 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`ref`	`gcc -march=native -mtune=native -O3 -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`ref`	`gcc -march=native -mtune=native -O -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`
`ref`	`gcc -march=native -mtune=native -Os -fwrapv -fPIC -fPIE -gdwarf-4 -Wall (11.4.0)`