OXIESEC PANEL
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opt
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golang
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1.19.4
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src
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runtime
Server IP: 2a02:4780:11:1084:0:327f:3464:10
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Name
Size
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📁
..
-
12/01/2022 06:13:58 PM
rwxr-xr-x
📄
HACKING.md
15.29 KB
12/01/2022 06:12:59 PM
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📄
Makefile
178 bytes
12/01/2022 06:12:59 PM
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abi_test.go
2.83 KB
12/01/2022 06:12:59 PM
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alg.go
9.45 KB
12/01/2022 06:12:59 PM
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align_runtime_test.go
2.73 KB
12/01/2022 06:12:59 PM
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align_test.go
5.26 KB
12/01/2022 06:12:59 PM
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📁
asan
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12/01/2022 06:13:56 PM
rwxr-xr-x
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asan.go
1.55 KB
12/01/2022 06:12:59 PM
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asan0.go
761 bytes
12/01/2022 06:12:59 PM
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asan_amd64.s
2.46 KB
12/01/2022 06:12:59 PM
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asan_arm64.s
2.15 KB
12/01/2022 06:12:59 PM
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asan_riscv64.s
1.92 KB
12/01/2022 06:12:59 PM
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asm.s
278 bytes
12/01/2022 06:12:59 PM
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asm_386.s
40.43 KB
12/01/2022 06:12:59 PM
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asm_amd64.h
411 bytes
12/01/2022 06:12:59 PM
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asm_amd64.s
57.44 KB
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asm_arm.s
30.2 KB
12/01/2022 06:12:59 PM
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asm_arm64.s
41.41 KB
12/01/2022 06:12:59 PM
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asm_loong64.s
21.79 KB
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asm_mips64x.s
22.43 KB
12/01/2022 06:12:59 PM
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asm_mipsx.s
24.41 KB
12/01/2022 06:12:59 PM
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asm_ppc64x.h
1023 bytes
12/01/2022 06:12:59 PM
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asm_ppc64x.s
35.21 KB
12/01/2022 06:12:59 PM
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asm_riscv64.s
26.43 KB
12/01/2022 06:12:59 PM
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asm_s390x.s
26.08 KB
12/01/2022 06:12:59 PM
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asm_wasm.s
9.38 KB
12/01/2022 06:12:59 PM
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atomic_arm64.s
259 bytes
12/01/2022 06:12:59 PM
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atomic_loong64.s
245 bytes
12/01/2022 06:12:59 PM
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atomic_mips64x.s
300 bytes
12/01/2022 06:12:59 PM
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atomic_mipsx.s
262 bytes
12/01/2022 06:12:59 PM
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atomic_pointer.go
2.62 KB
12/01/2022 06:12:59 PM
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atomic_ppc64x.s
437 bytes
12/01/2022 06:12:59 PM
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atomic_riscv64.s
275 bytes
12/01/2022 06:12:59 PM
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auxv_none.go
298 bytes
12/01/2022 06:12:59 PM
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callers_test.go
8.44 KB
12/01/2022 06:12:59 PM
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cgo
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12/01/2022 06:13:56 PM
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cgo.go
2 KB
12/01/2022 06:12:59 PM
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cgo_mmap.go
2.4 KB
12/01/2022 06:12:59 PM
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cgo_ppc64x.go
418 bytes
12/01/2022 06:12:59 PM
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cgo_sigaction.go
3.28 KB
12/01/2022 06:12:59 PM
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cgocall.go
19.12 KB
12/01/2022 06:12:59 PM
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cgocallback.go
317 bytes
12/01/2022 06:12:59 PM
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cgocheck.go
6.86 KB
12/01/2022 06:12:59 PM
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chan.go
23.73 KB
12/01/2022 06:12:59 PM
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chan_test.go
23.37 KB
12/01/2022 06:12:59 PM
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chanbarrier_test.go
1.4 KB
12/01/2022 06:12:59 PM
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checkptr.go
3.29 KB
12/01/2022 06:12:59 PM
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checkptr_test.go
2.73 KB
12/01/2022 06:12:59 PM
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closure_test.go
937 bytes
12/01/2022 06:12:59 PM
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compiler.go
410 bytes
12/01/2022 06:12:59 PM
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complex.go
1.59 KB
12/01/2022 06:12:59 PM
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complex_test.go
1.05 KB
12/01/2022 06:12:59 PM
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conv_wasm_test.go
2.96 KB
12/01/2022 06:12:59 PM
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cpuflags.go
810 bytes
12/01/2022 06:12:59 PM
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cpuflags_amd64.go
533 bytes
12/01/2022 06:12:59 PM
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cpuflags_arm64.go
334 bytes
12/01/2022 06:12:59 PM
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cpuprof.go
7.78 KB
12/01/2022 06:12:59 PM
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cputicks.go
449 bytes
12/01/2022 06:12:59 PM
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crash_cgo_test.go
18.14 KB
12/01/2022 06:12:59 PM
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crash_test.go
21.77 KB
12/01/2022 06:12:59 PM
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crash_unix_test.go
8.39 KB
12/01/2022 06:12:59 PM
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debug
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12/01/2022 06:13:56 PM
rwxr-xr-x
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debug.go
3.23 KB
12/01/2022 06:12:59 PM
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debug_test.go
7.98 KB
12/01/2022 06:12:59 PM
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debugcall.go
6.19 KB
12/01/2022 06:12:59 PM
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debuglog.go
17.87 KB
12/01/2022 06:12:59 PM
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debuglog_off.go
357 bytes
12/01/2022 06:12:59 PM
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debuglog_on.go
1.09 KB
12/01/2022 06:12:59 PM
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debuglog_test.go
4.56 KB
12/01/2022 06:12:59 PM
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defer_test.go
11.56 KB
12/01/2022 06:12:59 PM
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defs1_linux.go
845 bytes
12/01/2022 06:12:59 PM
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defs1_netbsd_386.go
2.83 KB
12/01/2022 06:12:59 PM
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defs1_netbsd_amd64.go
3.06 KB
12/01/2022 06:12:59 PM
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defs1_netbsd_arm.go
2.94 KB
12/01/2022 06:12:59 PM
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defs1_netbsd_arm64.go
3.17 KB
12/01/2022 06:12:59 PM
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defs1_solaris_amd64.go
4 KB
12/01/2022 06:12:59 PM
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defs2_linux.go
3.51 KB
12/01/2022 06:12:59 PM
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defs3_linux.go
1.09 KB
12/01/2022 06:12:59 PM
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defs_aix.go
4.16 KB
12/01/2022 06:12:59 PM
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defs_aix_ppc64.go
3.61 KB
12/01/2022 06:12:59 PM
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defs_arm_linux.go
2.67 KB
12/01/2022 06:12:59 PM
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defs_darwin.go
3.78 KB
12/01/2022 06:12:59 PM
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defs_darwin_amd64.go
6.07 KB
12/01/2022 06:12:59 PM
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defs_darwin_arm64.go
3.89 KB
12/01/2022 06:12:59 PM
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defs_dragonfly.go
2.59 KB
12/01/2022 06:12:59 PM
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defs_dragonfly_amd64.go
3.29 KB
12/01/2022 06:12:59 PM
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defs_freebsd.go
3.82 KB
12/01/2022 06:12:59 PM
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defs_freebsd_386.go
4.36 KB
12/01/2022 06:12:59 PM
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defs_freebsd_amd64.go
4.63 KB
12/01/2022 06:12:59 PM
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defs_freebsd_arm.go
3.69 KB
12/01/2022 06:12:59 PM
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defs_freebsd_arm64.go
4.01 KB
12/01/2022 06:12:59 PM
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defs_illumos_amd64.go
285 bytes
12/01/2022 06:12:59 PM
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defs_linux.go
3.25 KB
12/01/2022 06:12:59 PM
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defs_linux_386.go
4.42 KB
12/01/2022 06:12:59 PM
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defs_linux_amd64.go
4.93 KB
12/01/2022 06:12:59 PM
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defs_linux_arm.go
4.11 KB
12/01/2022 06:12:59 PM
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defs_linux_arm64.go
3.86 KB
12/01/2022 06:12:59 PM
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defs_linux_loong64.go
3.68 KB
12/01/2022 06:12:59 PM
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defs_linux_mips64x.go
3.85 KB
12/01/2022 06:12:59 PM
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defs_linux_mipsx.go
3.83 KB
12/01/2022 06:12:59 PM
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defs_linux_ppc64.go
3.93 KB
12/01/2022 06:12:59 PM
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defs_linux_ppc64le.go
3.93 KB
12/01/2022 06:12:59 PM
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defs_linux_riscv64.go
4.06 KB
12/01/2022 06:12:59 PM
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defs_linux_s390x.go
3.41 KB
12/01/2022 06:12:59 PM
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defs_netbsd.go
2.72 KB
12/01/2022 06:12:59 PM
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defs_netbsd_386.go
855 bytes
12/01/2022 06:12:59 PM
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defs_netbsd_amd64.go
1.01 KB
12/01/2022 06:12:59 PM
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defs_netbsd_arm.go
764 bytes
12/01/2022 06:12:59 PM
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defs_openbsd.go
3.09 KB
12/01/2022 06:12:59 PM
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defs_openbsd_386.go
2.87 KB
12/01/2022 06:12:59 PM
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defs_openbsd_amd64.go
3.07 KB
12/01/2022 06:12:59 PM
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defs_openbsd_arm.go
2.99 KB
12/01/2022 06:12:59 PM
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defs_openbsd_arm64.go
2.74 KB
12/01/2022 06:12:59 PM
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defs_openbsd_mips64.go
2.64 KB
12/01/2022 06:12:59 PM
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defs_plan9_386.go
1.63 KB
12/01/2022 06:12:59 PM
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defs_plan9_amd64.go
1.82 KB
12/01/2022 06:12:59 PM
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defs_plan9_arm.go
1.73 KB
12/01/2022 06:12:59 PM
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defs_solaris.go
3.31 KB
12/01/2022 06:12:59 PM
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defs_solaris_amd64.go
1004 bytes
12/01/2022 06:12:59 PM
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defs_windows.go
2.09 KB
12/01/2022 06:12:59 PM
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defs_windows_386.go
1.98 KB
12/01/2022 06:12:59 PM
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defs_windows_amd64.go
2.71 KB
12/01/2022 06:12:59 PM
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defs_windows_arm.go
2.11 KB
12/01/2022 06:12:59 PM
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defs_windows_arm64.go
2.63 KB
12/01/2022 06:12:59 PM
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duff_386.s
8.24 KB
12/01/2022 06:12:59 PM
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duff_amd64.s
5.62 KB
12/01/2022 06:12:59 PM
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duff_arm.s
7.11 KB
12/01/2022 06:12:59 PM
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duff_arm64.s
5.27 KB
12/01/2022 06:12:59 PM
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duff_loong64.s
12 KB
12/01/2022 06:12:59 PM
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duff_mips64x.s
11.28 KB
12/01/2022 06:12:59 PM
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duff_ppc64x.s
7.06 KB
12/01/2022 06:12:59 PM
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duff_riscv64.s
11.4 KB
12/01/2022 06:12:59 PM
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duff_s390x.s
507 bytes
12/01/2022 06:12:59 PM
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env_plan9.go
3 KB
12/01/2022 06:12:59 PM
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env_posix.go
1.79 KB
12/01/2022 06:12:59 PM
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env_test.go
1.16 KB
12/01/2022 06:12:59 PM
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error.go
9.21 KB
12/01/2022 06:12:59 PM
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example_test.go
1.55 KB
12/01/2022 06:12:59 PM
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export_aix_test.go
234 bytes
12/01/2022 06:12:59 PM
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export_arm_test.go
226 bytes
12/01/2022 06:12:59 PM
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export_darwin_test.go
382 bytes
12/01/2022 06:12:59 PM
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export_debug_amd64_test.go
3.6 KB
12/01/2022 06:12:59 PM
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export_debug_arm64_test.go
3.49 KB
12/01/2022 06:12:59 PM
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export_debug_test.go
5.05 KB
12/01/2022 06:12:59 PM
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export_debuglog_test.go
1.24 KB
12/01/2022 06:12:59 PM
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export_linux_test.go
550 bytes
12/01/2022 06:12:59 PM
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export_mmap_test.go
429 bytes
12/01/2022 06:12:59 PM
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export_pipe2_test.go
310 bytes
12/01/2022 06:12:59 PM
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export_pipe_test.go
219 bytes
12/01/2022 06:12:59 PM
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export_solaris_test.go
282 bytes
12/01/2022 06:12:59 PM
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export_test.go
38.87 KB
12/01/2022 06:12:59 PM
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export_unix_test.go
2.18 KB
12/01/2022 06:12:59 PM
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export_windows_test.go
677 bytes
12/01/2022 06:12:59 PM
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extern.go
13.62 KB
12/01/2022 06:12:59 PM
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fastlog2.go
1.22 KB
12/01/2022 06:12:59 PM
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fastlog2_test.go
784 bytes
12/01/2022 06:12:59 PM
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fastlog2table.go
904 bytes
12/01/2022 06:12:59 PM
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float.go
1.35 KB
12/01/2022 06:12:59 PM
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float_test.go
699 bytes
12/01/2022 06:12:59 PM
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funcdata.h
2.55 KB
12/01/2022 06:12:59 PM
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gc_test.go
20.04 KB
12/01/2022 06:12:59 PM
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gcinfo_test.go
5.59 KB
12/01/2022 06:12:59 PM
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go_tls.h
366 bytes
12/01/2022 06:12:59 PM
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hash32.go
1.58 KB
12/01/2022 06:12:59 PM
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hash64.go
1.95 KB
12/01/2022 06:12:59 PM
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hash_test.go
16.77 KB
12/01/2022 06:12:59 PM
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heapdump.go
17.65 KB
12/01/2022 06:12:59 PM
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histogram.go
6.19 KB
12/01/2022 06:12:59 PM
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histogram_test.go
3.42 KB
12/01/2022 06:12:59 PM
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iface.go
15.66 KB
12/01/2022 06:12:59 PM
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iface_test.go
7.45 KB
12/01/2022 06:12:59 PM
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internal
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12/01/2022 06:13:56 PM
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lfstack.go
1.77 KB
12/01/2022 06:12:59 PM
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lfstack_32bit.go
532 bytes
12/01/2022 06:12:59 PM
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lfstack_64bit.go
2.18 KB
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lfstack_test.go
2.77 KB
12/01/2022 06:12:59 PM
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libfuzzer.go
6.5 KB
12/01/2022 06:12:59 PM
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libfuzzer_amd64.s
5.01 KB
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libfuzzer_arm64.s
3.15 KB
12/01/2022 06:12:59 PM
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lock_futex.go
5.19 KB
12/01/2022 06:12:59 PM
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lock_js.go
6.14 KB
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lock_sema.go
6.74 KB
12/01/2022 06:12:59 PM
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lockrank.go
13.26 KB
12/01/2022 06:12:59 PM
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lockrank_off.go
1.14 KB
12/01/2022 06:12:59 PM
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lockrank_on.go
9.83 KB
12/01/2022 06:12:59 PM
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lockrank_test.go
1.15 KB
12/01/2022 06:12:59 PM
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malloc.go
51.01 KB
12/01/2022 06:12:59 PM
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malloc_test.go
10.78 KB
12/01/2022 06:12:59 PM
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map.go
43.52 KB
12/01/2022 06:12:59 PM
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map_benchmark_test.go
10.48 KB
12/01/2022 06:12:59 PM
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map_fast32.go
12.72 KB
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map_fast64.go
12.91 KB
12/01/2022 06:12:59 PM
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map_faststr.go
14.3 KB
12/01/2022 06:12:59 PM
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map_test.go
27.44 KB
12/01/2022 06:12:59 PM
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mbarrier.go
12.43 KB
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metrics
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msan
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msan.go
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norace_test.go
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os_linux_mipsx.go
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os_netbsd_386.go
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os_netbsd_arm64.go
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os_only_solaris.go
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os_openbsd_libc.go
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os_openbsd_syscall1.go
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os_plan9.go
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os_plan9_arm.go
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os_solaris.go
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os_windows.go
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os_windows_arm64.go
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panic.go
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panic32.go
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panic_test.go
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plugin.go
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pprof
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preempt.go
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preempt_386.s
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preempt_nonwindows.go
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preempt_ppc64x.s
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print.go
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proc.go
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proflabel.go
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race
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race.go
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race0.go
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signal_windows_test.go
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sigqueue.go
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sigqueue_note.go
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sizeclasses.go
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sizeof_test.go
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slice.go
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slice_test.go
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stack.go
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stack_test.go
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string.go
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string_test.go
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symtab.go
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symtab_test.go
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sys_aix_ppc64.s
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sys_arm.go
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sys_darwin.go
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sys_darwin_amd64.s
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sys_darwin_arm64.go
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sys_dragonfly_amd64.s
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Editing: mpagealloc.go
Close
// Copyright 2019 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // Page allocator. // // The page allocator manages mapped pages (defined by pageSize, NOT // physPageSize) for allocation and re-use. It is embedded into mheap. // // Pages are managed using a bitmap that is sharded into chunks. // In the bitmap, 1 means in-use, and 0 means free. The bitmap spans the // process's address space. Chunks are managed in a sparse-array-style structure // similar to mheap.arenas, since the bitmap may be large on some systems. // // The bitmap is efficiently searched by using a radix tree in combination // with fast bit-wise intrinsics. Allocation is performed using an address-ordered // first-fit approach. // // Each entry in the radix tree is a summary that describes three properties of // a particular region of the address space: the number of contiguous free pages // at the start and end of the region it represents, and the maximum number of // contiguous free pages found anywhere in that region. // // Each level of the radix tree is stored as one contiguous array, which represents // a different granularity of subdivision of the processes' address space. Thus, this // radix tree is actually implicit in these large arrays, as opposed to having explicit // dynamically-allocated pointer-based node structures. Naturally, these arrays may be // quite large for system with large address spaces, so in these cases they are mapped // into memory as needed. The leaf summaries of the tree correspond to a bitmap chunk. // // The root level (referred to as L0 and index 0 in pageAlloc.summary) has each // summary represent the largest section of address space (16 GiB on 64-bit systems), // with each subsequent level representing successively smaller subsections until we // reach the finest granularity at the leaves, a chunk. // // More specifically, each summary in each level (except for leaf summaries) // represents some number of entries in the following level. For example, each // summary in the root level may represent a 16 GiB region of address space, // and in the next level there could be 8 corresponding entries which represent 2 // GiB subsections of that 16 GiB region, each of which could correspond to 8 // entries in the next level which each represent 256 MiB regions, and so on. // // Thus, this design only scales to heaps so large, but can always be extended to // larger heaps by simply adding levels to the radix tree, which mostly costs // additional virtual address space. The choice of managing large arrays also means // that a large amount of virtual address space may be reserved by the runtime. package runtime import ( "runtime/internal/atomic" "unsafe" ) const ( // The size of a bitmap chunk, i.e. the amount of bits (that is, pages) to consider // in the bitmap at once. pallocChunkPages = 1 << logPallocChunkPages pallocChunkBytes = pallocChunkPages * pageSize logPallocChunkPages = 9 logPallocChunkBytes = logPallocChunkPages + pageShift // The number of radix bits for each level. // // The value of 3 is chosen such that the block of summaries we need to scan at // each level fits in 64 bytes (2^3 summaries * 8 bytes per summary), which is // close to the L1 cache line width on many systems. Also, a value of 3 fits 4 tree // levels perfectly into the 21-bit pallocBits summary field at the root level. // // The following equation explains how each of the constants relate: // summaryL0Bits + (summaryLevels-1)*summaryLevelBits + logPallocChunkBytes = heapAddrBits // // summaryLevels is an architecture-dependent value defined in mpagealloc_*.go. summaryLevelBits = 3 summaryL0Bits = heapAddrBits - logPallocChunkBytes - (summaryLevels-1)*summaryLevelBits // pallocChunksL2Bits is the number of bits of the chunk index number // covered by the second level of the chunks map. // // See (*pageAlloc).chunks for more details. Update the documentation // there should this change. pallocChunksL2Bits = heapAddrBits - logPallocChunkBytes - pallocChunksL1Bits pallocChunksL1Shift = pallocChunksL2Bits ) // maxSearchAddr returns the maximum searchAddr value, which indicates // that the heap has no free space. // // This function exists just to make it clear that this is the maximum address // for the page allocator's search space. See maxOffAddr for details. // // It's a function (rather than a variable) because it needs to be // usable before package runtime's dynamic initialization is complete. // See #51913 for details. func maxSearchAddr() offAddr { return maxOffAddr } // Global chunk index. // // Represents an index into the leaf level of the radix tree. // Similar to arenaIndex, except instead of arenas, it divides the address // space into chunks. type chunkIdx uint // chunkIndex returns the global index of the palloc chunk containing the // pointer p. func chunkIndex(p uintptr) chunkIdx { return chunkIdx((p - arenaBaseOffset) / pallocChunkBytes) } // chunkIndex returns the base address of the palloc chunk at index ci. func chunkBase(ci chunkIdx) uintptr { return uintptr(ci)*pallocChunkBytes + arenaBaseOffset } // chunkPageIndex computes the index of the page that contains p, // relative to the chunk which contains p. func chunkPageIndex(p uintptr) uint { return uint(p % pallocChunkBytes / pageSize) } // l1 returns the index into the first level of (*pageAlloc).chunks. func (i chunkIdx) l1() uint { if pallocChunksL1Bits == 0 { // Let the compiler optimize this away if there's no // L1 map. return 0 } else { return uint(i) >> pallocChunksL1Shift } } // l2 returns the index into the second level of (*pageAlloc).chunks. func (i chunkIdx) l2() uint { if pallocChunksL1Bits == 0 { return uint(i) } else { return uint(i) & (1<<pallocChunksL2Bits - 1) } } // offAddrToLevelIndex converts an address in the offset address space // to the index into summary[level] containing addr. func offAddrToLevelIndex(level int, addr offAddr) int { return int((addr.a - arenaBaseOffset) >> levelShift[level]) } // levelIndexToOffAddr converts an index into summary[level] into // the corresponding address in the offset address space. func levelIndexToOffAddr(level, idx int) offAddr { return offAddr{(uintptr(idx) << levelShift[level]) + arenaBaseOffset} } // addrsToSummaryRange converts base and limit pointers into a range // of entries for the given summary level. // // The returned range is inclusive on the lower bound and exclusive on // the upper bound. func addrsToSummaryRange(level int, base, limit uintptr) (lo int, hi int) { // This is slightly more nuanced than just a shift for the exclusive // upper-bound. Note that the exclusive upper bound may be within a // summary at this level, meaning if we just do the obvious computation // hi will end up being an inclusive upper bound. Unfortunately, just // adding 1 to that is too broad since we might be on the very edge // of a summary's max page count boundary for this level // (1 << levelLogPages[level]). So, make limit an inclusive upper bound // then shift, then add 1, so we get an exclusive upper bound at the end. lo = int((base - arenaBaseOffset) >> levelShift[level]) hi = int(((limit-1)-arenaBaseOffset)>>levelShift[level]) + 1 return } // blockAlignSummaryRange aligns indices into the given level to that // level's block width (1 << levelBits[level]). It assumes lo is inclusive // and hi is exclusive, and so aligns them down and up respectively. func blockAlignSummaryRange(level int, lo, hi int) (int, int) { e := uintptr(1) << levelBits[level] return int(alignDown(uintptr(lo), e)), int(alignUp(uintptr(hi), e)) } type pageAlloc struct { // Radix tree of summaries. // // Each slice's cap represents the whole memory reservation. // Each slice's len reflects the allocator's maximum known // mapped heap address for that level. // // The backing store of each summary level is reserved in init // and may or may not be committed in grow (small address spaces // may commit all the memory in init). // // The purpose of keeping len <= cap is to enforce bounds checks // on the top end of the slice so that instead of an unknown // runtime segmentation fault, we get a much friendlier out-of-bounds // error. // // To iterate over a summary level, use inUse to determine which ranges // are currently available. Otherwise one might try to access // memory which is only Reserved which may result in a hard fault. // // We may still get segmentation faults < len since some of that // memory may not be committed yet. summary [summaryLevels][]pallocSum // chunks is a slice of bitmap chunks. // // The total size of chunks is quite large on most 64-bit platforms // (O(GiB) or more) if flattened, so rather than making one large mapping // (which has problems on some platforms, even when PROT_NONE) we use a // two-level sparse array approach similar to the arena index in mheap. // // To find the chunk containing a memory address `a`, do: // chunkOf(chunkIndex(a)) // // Below is a table describing the configuration for chunks for various // heapAddrBits supported by the runtime. // // heapAddrBits | L1 Bits | L2 Bits | L2 Entry Size // ------------------------------------------------ // 32 | 0 | 10 | 128 KiB // 33 (iOS) | 0 | 11 | 256 KiB // 48 | 13 | 13 | 1 MiB // // There's no reason to use the L1 part of chunks on 32-bit, the // address space is small so the L2 is small. For platforms with a // 48-bit address space, we pick the L1 such that the L2 is 1 MiB // in size, which is a good balance between low granularity without // making the impact on BSS too high (note the L1 is stored directly // in pageAlloc). // // To iterate over the bitmap, use inUse to determine which ranges // are currently available. Otherwise one might iterate over unused // ranges. // // Protected by mheapLock. // // TODO(mknyszek): Consider changing the definition of the bitmap // such that 1 means free and 0 means in-use so that summaries and // the bitmaps align better on zero-values. chunks [1 << pallocChunksL1Bits]*[1 << pallocChunksL2Bits]pallocData // The address to start an allocation search with. It must never // point to any memory that is not contained in inUse, i.e. // inUse.contains(searchAddr.addr()) must always be true. The one // exception to this rule is that it may take on the value of // maxOffAddr to indicate that the heap is exhausted. // // We guarantee that all valid heap addresses below this value // are allocated and not worth searching. searchAddr offAddr // start and end represent the chunk indices // which pageAlloc knows about. It assumes // chunks in the range [start, end) are // currently ready to use. start, end chunkIdx // inUse is a slice of ranges of address space which are // known by the page allocator to be currently in-use (passed // to grow). // // This field is currently unused on 32-bit architectures but // is harmless to track. We care much more about having a // contiguous heap in these cases and take additional measures // to ensure that, so in nearly all cases this should have just // 1 element. // // All access is protected by the mheapLock. inUse addrRanges _ uint32 // Align scav so it's easier to reason about alignment within scav. // scav stores the scavenger state. scav struct { // index is an efficient index of chunks that have pages available to // scavenge. index scavengeIndex // released is the amount of memory released this generation. // // Updated atomically. released uintptr _ uint32 // Align assistTime for atomics on 32-bit platforms. // scavengeAssistTime is the time spent scavenging in the last GC cycle. // // This is reset once a GC cycle ends. assistTime atomic.Int64 } // mheap_.lock. This level of indirection makes it possible // to test pageAlloc indepedently of the runtime allocator. mheapLock *mutex // sysStat is the runtime memstat to update when new system // memory is committed by the pageAlloc for allocation metadata. sysStat *sysMemStat // summaryMappedReady is the number of bytes mapped in the Ready state // in the summary structure. Used only for testing currently. // // Protected by mheapLock. summaryMappedReady uintptr // Whether or not this struct is being used in tests. test bool } func (p *pageAlloc) init(mheapLock *mutex, sysStat *sysMemStat) { if levelLogPages[0] > logMaxPackedValue { // We can't represent 1<<levelLogPages[0] pages, the maximum number // of pages we need to represent at the root level, in a summary, which // is a big problem. Throw. print("runtime: root level max pages = ", 1<<levelLogPages[0], "\n") print("runtime: summary max pages = ", maxPackedValue, "\n") throw("root level max pages doesn't fit in summary") } p.sysStat = sysStat // Initialize p.inUse. p.inUse.init(sysStat) // System-dependent initialization. p.sysInit() // Start with the searchAddr in a state indicating there's no free memory. p.searchAddr = maxSearchAddr() // Set the mheapLock. p.mheapLock = mheapLock } // tryChunkOf returns the bitmap data for the given chunk. // // Returns nil if the chunk data has not been mapped. func (p *pageAlloc) tryChunkOf(ci chunkIdx) *pallocData { l2 := p.chunks[ci.l1()] if l2 == nil { return nil } return &l2[ci.l2()] } // chunkOf returns the chunk at the given chunk index. // // The chunk index must be valid or this method may throw. func (p *pageAlloc) chunkOf(ci chunkIdx) *pallocData { return &p.chunks[ci.l1()][ci.l2()] } // grow sets up the metadata for the address range [base, base+size). // It may allocate metadata, in which case *p.sysStat will be updated. // // p.mheapLock must be held. func (p *pageAlloc) grow(base, size uintptr) { assertLockHeld(p.mheapLock) // Round up to chunks, since we can't deal with increments smaller // than chunks. Also, sysGrow expects aligned values. limit := alignUp(base+size, pallocChunkBytes) base = alignDown(base, pallocChunkBytes) // Grow the summary levels in a system-dependent manner. // We just update a bunch of additional metadata here. p.sysGrow(base, limit) // Update p.start and p.end. // If no growth happened yet, start == 0. This is generally // safe since the zero page is unmapped. firstGrowth := p.start == 0 start, end := chunkIndex(base), chunkIndex(limit) if firstGrowth || start < p.start { p.start = start } if end > p.end { p.end = end } // Note that [base, limit) will never overlap with any existing // range inUse because grow only ever adds never-used memory // regions to the page allocator. p.inUse.add(makeAddrRange(base, limit)) // A grow operation is a lot like a free operation, so if our // chunk ends up below p.searchAddr, update p.searchAddr to the // new address, just like in free. if b := (offAddr{base}); b.lessThan(p.searchAddr) { p.searchAddr = b } // Add entries into chunks, which is sparse, if needed. Then, // initialize the bitmap. // // Newly-grown memory is always considered scavenged. // Set all the bits in the scavenged bitmaps high. for c := chunkIndex(base); c < chunkIndex(limit); c++ { if p.chunks[c.l1()] == nil { // Create the necessary l2 entry. // // Store it atomically to avoid races with readers which // don't acquire the heap lock. r := sysAlloc(unsafe.Sizeof(*p.chunks[0]), p.sysStat) if r == nil { throw("pageAlloc: out of memory") } atomic.StorepNoWB(unsafe.Pointer(&p.chunks[c.l1()]), r) } p.chunkOf(c).scavenged.setRange(0, pallocChunkPages) } // Update summaries accordingly. The grow acts like a free, so // we need to ensure this newly-free memory is visible in the // summaries. p.update(base, size/pageSize, true, false) } // update updates heap metadata. It must be called each time the bitmap // is updated. // // If contig is true, update does some optimizations assuming that there was // a contiguous allocation or free between addr and addr+npages. alloc indicates // whether the operation performed was an allocation or a free. // // p.mheapLock must be held. func (p *pageAlloc) update(base, npages uintptr, contig, alloc bool) { assertLockHeld(p.mheapLock) // base, limit, start, and end are inclusive. limit := base + npages*pageSize - 1 sc, ec := chunkIndex(base), chunkIndex(limit) // Handle updating the lowest level first. if sc == ec { // Fast path: the allocation doesn't span more than one chunk, // so update this one and if the summary didn't change, return. x := p.summary[len(p.summary)-1][sc] y := p.chunkOf(sc).summarize() if x == y { return } p.summary[len(p.summary)-1][sc] = y } else if contig { // Slow contiguous path: the allocation spans more than one chunk // and at least one summary is guaranteed to change. summary := p.summary[len(p.summary)-1] // Update the summary for chunk sc. summary[sc] = p.chunkOf(sc).summarize() // Update the summaries for chunks in between, which are // either totally allocated or freed. whole := p.summary[len(p.summary)-1][sc+1 : ec] if alloc { // Should optimize into a memclr. for i := range whole { whole[i] = 0 } } else { for i := range whole { whole[i] = freeChunkSum } } // Update the summary for chunk ec. summary[ec] = p.chunkOf(ec).summarize() } else { // Slow general path: the allocation spans more than one chunk // and at least one summary is guaranteed to change. // // We can't assume a contiguous allocation happened, so walk over // every chunk in the range and manually recompute the summary. summary := p.summary[len(p.summary)-1] for c := sc; c <= ec; c++ { summary[c] = p.chunkOf(c).summarize() } } // Walk up the radix tree and update the summaries appropriately. changed := true for l := len(p.summary) - 2; l >= 0 && changed; l-- { // Update summaries at level l from summaries at level l+1. changed = false // "Constants" for the previous level which we // need to compute the summary from that level. logEntriesPerBlock := levelBits[l+1] logMaxPages := levelLogPages[l+1] // lo and hi describe all the parts of the level we need to look at. lo, hi := addrsToSummaryRange(l, base, limit+1) // Iterate over each block, updating the corresponding summary in the less-granular level. for i := lo; i < hi; i++ { children := p.summary[l+1][i<<logEntriesPerBlock : (i+1)<<logEntriesPerBlock] sum := mergeSummaries(children, logMaxPages) old := p.summary[l][i] if old != sum { changed = true p.summary[l][i] = sum } } } } // allocRange marks the range of memory [base, base+npages*pageSize) as // allocated. It also updates the summaries to reflect the newly-updated // bitmap. // // Returns the amount of scavenged memory in bytes present in the // allocated range. // // p.mheapLock must be held. func (p *pageAlloc) allocRange(base, npages uintptr) uintptr { assertLockHeld(p.mheapLock) limit := base + npages*pageSize - 1 sc, ec := chunkIndex(base), chunkIndex(limit) si, ei := chunkPageIndex(base), chunkPageIndex(limit) scav := uint(0) if sc == ec { // The range doesn't cross any chunk boundaries. chunk := p.chunkOf(sc) scav += chunk.scavenged.popcntRange(si, ei+1-si) chunk.allocRange(si, ei+1-si) } else { // The range crosses at least one chunk boundary. chunk := p.chunkOf(sc) scav += chunk.scavenged.popcntRange(si, pallocChunkPages-si) chunk.allocRange(si, pallocChunkPages-si) for c := sc + 1; c < ec; c++ { chunk := p.chunkOf(c) scav += chunk.scavenged.popcntRange(0, pallocChunkPages) chunk.allocAll() } chunk = p.chunkOf(ec) scav += chunk.scavenged.popcntRange(0, ei+1) chunk.allocRange(0, ei+1) } p.update(base, npages, true, true) return uintptr(scav) * pageSize } // findMappedAddr returns the smallest mapped offAddr that is // >= addr. That is, if addr refers to mapped memory, then it is // returned. If addr is higher than any mapped region, then // it returns maxOffAddr. // // p.mheapLock must be held. func (p *pageAlloc) findMappedAddr(addr offAddr) offAddr { assertLockHeld(p.mheapLock) // If we're not in a test, validate first by checking mheap_.arenas. // This is a fast path which is only safe to use outside of testing. ai := arenaIndex(addr.addr()) if p.test || mheap_.arenas[ai.l1()] == nil || mheap_.arenas[ai.l1()][ai.l2()] == nil { vAddr, ok := p.inUse.findAddrGreaterEqual(addr.addr()) if ok { return offAddr{vAddr} } else { // The candidate search address is greater than any // known address, which means we definitely have no // free memory left. return maxOffAddr } } return addr } // find searches for the first (address-ordered) contiguous free region of // npages in size and returns a base address for that region. // // It uses p.searchAddr to prune its search and assumes that no palloc chunks // below chunkIndex(p.searchAddr) contain any free memory at all. // // find also computes and returns a candidate p.searchAddr, which may or // may not prune more of the address space than p.searchAddr already does. // This candidate is always a valid p.searchAddr. // // find represents the slow path and the full radix tree search. // // Returns a base address of 0 on failure, in which case the candidate // searchAddr returned is invalid and must be ignored. // // p.mheapLock must be held. func (p *pageAlloc) find(npages uintptr) (uintptr, offAddr) { assertLockHeld(p.mheapLock) // Search algorithm. // // This algorithm walks each level l of the radix tree from the root level // to the leaf level. It iterates over at most 1 << levelBits[l] of entries // in a given level in the radix tree, and uses the summary information to // find either: // 1) That a given subtree contains a large enough contiguous region, at // which point it continues iterating on the next level, or // 2) That there are enough contiguous boundary-crossing bits to satisfy // the allocation, at which point it knows exactly where to start // allocating from. // // i tracks the index into the current level l's structure for the // contiguous 1 << levelBits[l] entries we're actually interested in. // // NOTE: Technically this search could allocate a region which crosses // the arenaBaseOffset boundary, which when arenaBaseOffset != 0, is // a discontinuity. However, the only way this could happen is if the // page at the zero address is mapped, and this is impossible on // every system we support where arenaBaseOffset != 0. So, the // discontinuity is already encoded in the fact that the OS will never // map the zero page for us, and this function doesn't try to handle // this case in any way. // i is the beginning of the block of entries we're searching at the // current level. i := 0 // firstFree is the region of address space that we are certain to // find the first free page in the heap. base and bound are the inclusive // bounds of this window, and both are addresses in the linearized, contiguous // view of the address space (with arenaBaseOffset pre-added). At each level, // this window is narrowed as we find the memory region containing the // first free page of memory. To begin with, the range reflects the // full process address space. // // firstFree is updated by calling foundFree each time free space in the // heap is discovered. // // At the end of the search, base.addr() is the best new // searchAddr we could deduce in this search. firstFree := struct { base, bound offAddr }{ base: minOffAddr, bound: maxOffAddr, } // foundFree takes the given address range [addr, addr+size) and // updates firstFree if it is a narrower range. The input range must // either be fully contained within firstFree or not overlap with it // at all. // // This way, we'll record the first summary we find with any free // pages on the root level and narrow that down if we descend into // that summary. But as soon as we need to iterate beyond that summary // in a level to find a large enough range, we'll stop narrowing. foundFree := func(addr offAddr, size uintptr) { if firstFree.base.lessEqual(addr) && addr.add(size-1).lessEqual(firstFree.bound) { // This range fits within the current firstFree window, so narrow // down the firstFree window to the base and bound of this range. firstFree.base = addr firstFree.bound = addr.add(size - 1) } else if !(addr.add(size-1).lessThan(firstFree.base) || firstFree.bound.lessThan(addr)) { // This range only partially overlaps with the firstFree range, // so throw. print("runtime: addr = ", hex(addr.addr()), ", size = ", size, "\n") print("runtime: base = ", hex(firstFree.base.addr()), ", bound = ", hex(firstFree.bound.addr()), "\n") throw("range partially overlaps") } } // lastSum is the summary which we saw on the previous level that made us // move on to the next level. Used to print additional information in the // case of a catastrophic failure. // lastSumIdx is that summary's index in the previous level. lastSum := packPallocSum(0, 0, 0) lastSumIdx := -1 nextLevel: for l := 0; l < len(p.summary); l++ { // For the root level, entriesPerBlock is the whole level. entriesPerBlock := 1 << levelBits[l] logMaxPages := levelLogPages[l] // We've moved into a new level, so let's update i to our new // starting index. This is a no-op for level 0. i <<= levelBits[l] // Slice out the block of entries we care about. entries := p.summary[l][i : i+entriesPerBlock] // Determine j0, the first index we should start iterating from. // The searchAddr may help us eliminate iterations if we followed the // searchAddr on the previous level or we're on the root leve, in which // case the searchAddr should be the same as i after levelShift. j0 := 0 if searchIdx := offAddrToLevelIndex(l, p.searchAddr); searchIdx&^(entriesPerBlock-1) == i { j0 = searchIdx & (entriesPerBlock - 1) } // Run over the level entries looking for // a contiguous run of at least npages either // within an entry or across entries. // // base contains the page index (relative to // the first entry's first page) of the currently // considered run of consecutive pages. // // size contains the size of the currently considered // run of consecutive pages. var base, size uint for j := j0; j < len(entries); j++ { sum := entries[j] if sum == 0 { // A full entry means we broke any streak and // that we should skip it altogether. size = 0 continue } // We've encountered a non-zero summary which means // free memory, so update firstFree. foundFree(levelIndexToOffAddr(l, i+j), (uintptr(1)<<logMaxPages)*pageSize) s := sum.start() if size+s >= uint(npages) { // If size == 0 we don't have a run yet, // which means base isn't valid. So, set // base to the first page in this block. if size == 0 { base = uint(j) << logMaxPages } // We hit npages; we're done! size += s break } if sum.max() >= uint(npages) { // The entry itself contains npages contiguous // free pages, so continue on the next level // to find that run. i += j lastSumIdx = i lastSum = sum continue nextLevel } if size == 0 || s < 1<<logMaxPages { // We either don't have a current run started, or this entry // isn't totally free (meaning we can't continue the current // one), so try to begin a new run by setting size and base // based on sum.end. size = sum.end() base = uint(j+1)<<logMaxPages - size continue } // The entry is completely free, so continue the run. size += 1 << logMaxPages } if size >= uint(npages) { // We found a sufficiently large run of free pages straddling // some boundary, so compute the address and return it. addr := levelIndexToOffAddr(l, i).add(uintptr(base) * pageSize).addr() return addr, p.findMappedAddr(firstFree.base) } if l == 0 { // We're at level zero, so that means we've exhausted our search. return 0, maxSearchAddr() } // We're not at level zero, and we exhausted the level we were looking in. // This means that either our calculations were wrong or the level above // lied to us. In either case, dump some useful state and throw. print("runtime: summary[", l-1, "][", lastSumIdx, "] = ", lastSum.start(), ", ", lastSum.max(), ", ", lastSum.end(), "\n") print("runtime: level = ", l, ", npages = ", npages, ", j0 = ", j0, "\n") print("runtime: p.searchAddr = ", hex(p.searchAddr.addr()), ", i = ", i, "\n") print("runtime: levelShift[level] = ", levelShift[l], ", levelBits[level] = ", levelBits[l], "\n") for j := 0; j < len(entries); j++ { sum := entries[j] print("runtime: summary[", l, "][", i+j, "] = (", sum.start(), ", ", sum.max(), ", ", sum.end(), ")\n") } throw("bad summary data") } // Since we've gotten to this point, that means we haven't found a // sufficiently-sized free region straddling some boundary (chunk or larger). // This means the last summary we inspected must have had a large enough "max" // value, so look inside the chunk to find a suitable run. // // After iterating over all levels, i must contain a chunk index which // is what the final level represents. ci := chunkIdx(i) j, searchIdx := p.chunkOf(ci).find(npages, 0) if j == ^uint(0) { // We couldn't find any space in this chunk despite the summaries telling // us it should be there. There's likely a bug, so dump some state and throw. sum := p.summary[len(p.summary)-1][i] print("runtime: summary[", len(p.summary)-1, "][", i, "] = (", sum.start(), ", ", sum.max(), ", ", sum.end(), ")\n") print("runtime: npages = ", npages, "\n") throw("bad summary data") } // Compute the address at which the free space starts. addr := chunkBase(ci) + uintptr(j)*pageSize // Since we actually searched the chunk, we may have // found an even narrower free window. searchAddr := chunkBase(ci) + uintptr(searchIdx)*pageSize foundFree(offAddr{searchAddr}, chunkBase(ci+1)-searchAddr) return addr, p.findMappedAddr(firstFree.base) } // alloc allocates npages worth of memory from the page heap, returning the base // address for the allocation and the amount of scavenged memory in bytes // contained in the region [base address, base address + npages*pageSize). // // Returns a 0 base address on failure, in which case other returned values // should be ignored. // // p.mheapLock must be held. // // Must run on the system stack because p.mheapLock must be held. // //go:systemstack func (p *pageAlloc) alloc(npages uintptr) (addr uintptr, scav uintptr) { assertLockHeld(p.mheapLock) // If the searchAddr refers to a region which has a higher address than // any known chunk, then we know we're out of memory. if chunkIndex(p.searchAddr.addr()) >= p.end { return 0, 0 } // If npages has a chance of fitting in the chunk where the searchAddr is, // search it directly. searchAddr := minOffAddr if pallocChunkPages-chunkPageIndex(p.searchAddr.addr()) >= uint(npages) { // npages is guaranteed to be no greater than pallocChunkPages here. i := chunkIndex(p.searchAddr.addr()) if max := p.summary[len(p.summary)-1][i].max(); max >= uint(npages) { j, searchIdx := p.chunkOf(i).find(npages, chunkPageIndex(p.searchAddr.addr())) if j == ^uint(0) { print("runtime: max = ", max, ", npages = ", npages, "\n") print("runtime: searchIdx = ", chunkPageIndex(p.searchAddr.addr()), ", p.searchAddr = ", hex(p.searchAddr.addr()), "\n") throw("bad summary data") } addr = chunkBase(i) + uintptr(j)*pageSize searchAddr = offAddr{chunkBase(i) + uintptr(searchIdx)*pageSize} goto Found } } // We failed to use a searchAddr for one reason or another, so try // the slow path. addr, searchAddr = p.find(npages) if addr == 0 { if npages == 1 { // We failed to find a single free page, the smallest unit // of allocation. This means we know the heap is completely // exhausted. Otherwise, the heap still might have free // space in it, just not enough contiguous space to // accommodate npages. p.searchAddr = maxSearchAddr() } return 0, 0 } Found: // Go ahead and actually mark the bits now that we have an address. scav = p.allocRange(addr, npages) // If we found a higher searchAddr, we know that all the // heap memory before that searchAddr in an offset address space is // allocated, so bump p.searchAddr up to the new one. if p.searchAddr.lessThan(searchAddr) { p.searchAddr = searchAddr } return addr, scav } // free returns npages worth of memory starting at base back to the page heap. // // p.mheapLock must be held. // // Must run on the system stack because p.mheapLock must be held. // //go:systemstack func (p *pageAlloc) free(base, npages uintptr, scavenged bool) { assertLockHeld(p.mheapLock) // If we're freeing pages below the p.searchAddr, update searchAddr. if b := (offAddr{base}); b.lessThan(p.searchAddr) { p.searchAddr = b } limit := base + npages*pageSize - 1 if !scavenged { p.scav.index.mark(base, limit+1) } if npages == 1 { // Fast path: we're clearing a single bit, and we know exactly // where it is, so mark it directly. i := chunkIndex(base) p.chunkOf(i).free1(chunkPageIndex(base)) } else { // Slow path: we're clearing more bits so we may need to iterate. sc, ec := chunkIndex(base), chunkIndex(limit) si, ei := chunkPageIndex(base), chunkPageIndex(limit) if sc == ec { // The range doesn't cross any chunk boundaries. p.chunkOf(sc).free(si, ei+1-si) } else { // The range crosses at least one chunk boundary. p.chunkOf(sc).free(si, pallocChunkPages-si) for c := sc + 1; c < ec; c++ { p.chunkOf(c).freeAll() } p.chunkOf(ec).free(0, ei+1) } } p.update(base, npages, true, false) } const ( pallocSumBytes = unsafe.Sizeof(pallocSum(0)) // maxPackedValue is the maximum value that any of the three fields in // the pallocSum may take on. maxPackedValue = 1 << logMaxPackedValue logMaxPackedValue = logPallocChunkPages + (summaryLevels-1)*summaryLevelBits freeChunkSum = pallocSum(uint64(pallocChunkPages) | uint64(pallocChunkPages<<logMaxPackedValue) | uint64(pallocChunkPages<<(2*logMaxPackedValue))) ) // pallocSum is a packed summary type which packs three numbers: start, max, // and end into a single 8-byte value. Each of these values are a summary of // a bitmap and are thus counts, each of which may have a maximum value of // 2^21 - 1, or all three may be equal to 2^21. The latter case is represented // by just setting the 64th bit. type pallocSum uint64 // packPallocSum takes a start, max, and end value and produces a pallocSum. func packPallocSum(start, max, end uint) pallocSum { if max == maxPackedValue { return pallocSum(uint64(1 << 63)) } return pallocSum((uint64(start) & (maxPackedValue - 1)) | ((uint64(max) & (maxPackedValue - 1)) << logMaxPackedValue) | ((uint64(end) & (maxPackedValue - 1)) << (2 * logMaxPackedValue))) } // start extracts the start value from a packed sum. func (p pallocSum) start() uint { if uint64(p)&uint64(1<<63) != 0 { return maxPackedValue } return uint(uint64(p) & (maxPackedValue - 1)) } // max extracts the max value from a packed sum. func (p pallocSum) max() uint { if uint64(p)&uint64(1<<63) != 0 { return maxPackedValue } return uint((uint64(p) >> logMaxPackedValue) & (maxPackedValue - 1)) } // end extracts the end value from a packed sum. func (p pallocSum) end() uint { if uint64(p)&uint64(1<<63) != 0 { return maxPackedValue } return uint((uint64(p) >> (2 * logMaxPackedValue)) & (maxPackedValue - 1)) } // unpack unpacks all three values from the summary. func (p pallocSum) unpack() (uint, uint, uint) { if uint64(p)&uint64(1<<63) != 0 { return maxPackedValue, maxPackedValue, maxPackedValue } return uint(uint64(p) & (maxPackedValue - 1)), uint((uint64(p) >> logMaxPackedValue) & (maxPackedValue - 1)), uint((uint64(p) >> (2 * logMaxPackedValue)) & (maxPackedValue - 1)) } // mergeSummaries merges consecutive summaries which may each represent at // most 1 << logMaxPagesPerSum pages each together into one. func mergeSummaries(sums []pallocSum, logMaxPagesPerSum uint) pallocSum { // Merge the summaries in sums into one. // // We do this by keeping a running summary representing the merged // summaries of sums[:i] in start, max, and end. start, max, end := sums[0].unpack() for i := 1; i < len(sums); i++ { // Merge in sums[i]. si, mi, ei := sums[i].unpack() // Merge in sums[i].start only if the running summary is // completely free, otherwise this summary's start // plays no role in the combined sum. if start == uint(i)<<logMaxPagesPerSum { start += si } // Recompute the max value of the running sum by looking // across the boundary between the running sum and sums[i] // and at the max sums[i], taking the greatest of those two // and the max of the running sum. if end+si > max { max = end + si } if mi > max { max = mi } // Merge in end by checking if this new summary is totally // free. If it is, then we want to extend the running sum's // end by the new summary. If not, then we have some alloc'd // pages in there and we just want to take the end value in // sums[i]. if ei == 1<<logMaxPagesPerSum { end += 1 << logMaxPagesPerSum } else { end = ei } } return packPallocSum(start, max, end) }