stdlib/rand: replace weak LCG with xorshift32 PRNG

[Zepp-Hanzj]

Summary

The existing first-order LCG (seed = 470001 * seed % 999563) has several quality problems:

• Output range limited to [1, 999562] (~20 bits) instead of full 32-bit
• Lower bits have very short periods (8-bit period = 1, 16-bit = 105)
• Overall period only ~1M, far too short for many applications
• Causes mbedtls_rsa_gen_key to loop forever when rand() consumption aligns with the cycle length ([BUG] rand()'s cycle seems too short #16760)

Replace the entire order-based LCG implementation (CONFIG_LIBC_RAND_ORDER 0-3) with Marsaglia's xorshift32:

• Full 32-bit output range
• Period 2^32 - 1 (~4.29 billion)
• Fast: just three XOR/shift operations
• No floating-point math needed
• No CONFIG_LIBC_RAND_ORDER configuration required

Remove the CONFIG_LIBC_RAND_ORDER Kconfig option and clean up all defconfig references (12 boards) and related comments.

Verification

Built and tested on sim:nsh. Replaced hello_main.c with a test program that checks rand() quality, then restored it after testing.

Build command:

make distclean
tools/configure.sh sim:nsh
make -j$(nproc)

Run command:

printf 'hello\npoweroff\n' | timeout 30 ./nuttx 2>/dev/null

Test output (3 consecutive runs, all identical as expected for deterministic PRNG with same seed):

NuttShell (NSH) NuttX-13.0.0-RC0
nsh> hello
=== rand() quality test ===
Range after 10000 calls: [84907, 2147393180]
Expected: [0, 2147483647]
Full value repeat within 500k: NOT FOUND (period=0)
Expected: NOT FOUND (period should be ~4 billion)
srand(0) first call: 270369 (should be non-zero)
nrand(100) = 89 (should be 0-99)
=== test complete ===
nsh> poweroff

What each check means:

Range [84907, 2147393180] — max value close to INT_MAX (2147483647), old LCG only reached ~999562
Full value repeat: NOT FOUND — no repeat within 500k calls, old LCG repeated within ~1M
srand(0) non-zero — zero seed does not degenerate the generator
nrand(100) in [0,99] — range mapping works correctly

Also confirmed via nm that the NuttX xorshift32 is linked into the binary (not host GLIBC):

$ nm nuttx | grep xorshift32
000000004019d160 b __gcov0.xorshift32
00000000401740a0 d _gcov.xorshift32
00000000400c4052 t xorshift32

[github-actions]

MemBrowse Memory Report

qemu-armv8a

• Code: .rodata -16 B, .text.nrand -48 B (-0.0%, 315,310 B)

qemu-intel64

• Code: .text -117 B (-0.0%, 8,655,349 B)
• Data: .bss -16 B, .data +4 B (-0.0%, 120,423 B)
  No memory changes detected for:
• arduino-mega2560
• esp32-devkitc
• hifive1-revb
• mirtoo
• rx65n-rsk2mb
• s698pm-dkit
• stm32-nucleo-f103rb

[xiaoxiang781216]

@Zepp-Hanzj flash is too small:

====================================================================================
Configuration/Tool: stm32l0538-disco/nsh,CONFIG_ARM_TOOLCHAIN_GNU_EABI
2026-07-01 08:26:56
------------------------------------------------------------------------------------
  Cleaning...
  Configuring...
  Disabling CONFIG_ARM_TOOLCHAIN_GNU_EABI
  Enabling CONFIG_ARM_TOOLCHAIN_GNU_EABI
  Building NuttX...
arm-none-eabi-ld: /github/workspace/sources/nuttx/nuttx section `.data' will not fit in region `flash'
arm-none-eabi-ld: region `flash' overflowed by 20 bytes
make[1]: *** [Makefile:230: nuttx] Error 1
make: *** [tools/Unix.mk:569: nuttx] Error 2
make: Target 'all' not remade because of errors.

[michallenc]

@Zepp-Hanzj flash is too small:

====================================================================================
Configuration/Tool: stm32l0538-disco/nsh,CONFIG_ARM_TOOLCHAIN_GNU_EABI
2026-07-01 08:26:56
------------------------------------------------------------------------------------
  Cleaning...
  Configuring...
  Disabling CONFIG_ARM_TOOLCHAIN_GNU_EABI
  Enabling CONFIG_ARM_TOOLCHAIN_GNU_EABI
  Building NuttX...
arm-none-eabi-ld: /github/workspace/sources/nuttx/nuttx section `.data' will not fit in region `flash'
arm-none-eabi-ld: region `flash' overflowed by 20 bytes
make[1]: *** [Makefile:230: nuttx] Error 1
make: *** [tools/Unix.mk:569: nuttx] Error 2
make: Target 'all' not remade because of errors.

This seems like a mainline issue, happens across all new merge requests.

[xiaoxiang781216]

@Zepp-Hanzj please fix:

../nuttx/tools/checkpatch.sh -c -u -m -g  f0c94bb64acff1471d4ba5b23b1e0e5c8d57019c..HEAD
❌ Missing Signed-off-by
❌ Missing Signed-off-by
Used config files:
    1: .codespellrc
Some checks failed. For contributing guidelines, see:
  https://github.com/apache/nuttx/blob/master/CONTRIBUTING.md

[Zepp-Hanzj]

@xiaoxiang781216 Sorry for the noise. The two empty "ci: retrigger build" commits were added to retrigger CI after the stm32l0538-disco flash overflow issue was resolved on upstream master. They have been removed now — the PR contains only the single actual change commit. CI should pass cleanly this time.