PIO_LET - Raspberry Pi Pico SDK project for PRNG on a state machine

---> pio_let.pio

; Rename to just pio_let.pio, the arrow is to get it first in a Gist

; (C) 2026 alwynallan@gmail.com MIT License

; pio_let is an efficient PRNG that runs on a RP2040 family state machine

; Prove me wrong - LFSR on a PIO state machine is impossible!

.program pio_let
                            ; pio_sm_exec()s load initial state in osr; zero isr and y
.wrap_target
    ;set pins, 1            ; LED for testing
    mov x, ::osr
next_2_bits:
    out y, 2
dec_x_until_y_zero:
    jmp x-- nowhere
nowhere:
    jmp y-- dec_x_until_y_zero
    in x, 2
    jmp !osre next_2_bits
    mov osr, ~isr           ; osr full
    mov isr, osr            ; for push
    ;set pins, 0
    push block              ; mean cycle time 0.88 us
                            ; at full rate, output will repeat every 63 minutes
.wrap                       ; CBC mode!

% c-sdk {
void pio_let_program_init(PIO pio, uint sm, uint offset, uint led_pin, uint initial) {
    pio_gpio_init(pio, led_pin);
    pio_sm_set_consecutive_pindirs(pio, sm, led_pin, 1, true);
    pio_sm_config c = pio_let_program_get_default_config(offset);
    sm_config_set_in_shift(&c, false, false, 32);
    sm_config_set_out_shift(&c, true, false, 32);
    sm_config_set_set_pins(&c, led_pin, 1);
    sm_config_set_fifo_join(&c, PIO_FIFO_JOIN_RX); // makes initialization tricky
    pio_sm_init(pio, sm, offset, &c);
    // set initial value in x without TX_FIFO
    for(int i=7; i>=0; i--) {
        pio_sm_exec(pio, sm, pio_encode_set(pio_x, (initial>>(i*4)) & 15));
        pio_sm_exec(pio, sm, pio_encode_in(pio_x, 4));
    }
    pio_sm_exec(pio, sm, pio_encode_mov(pio_osr, pio_isr));
    pio_sm_exec(pio, sm, pio_encode_set(pio_isr, 0)); // in case of restart
    pio_sm_exec(pio, sm, pio_encode_set(pio_y, 0)); // in case of restart
}
%}

CMakeLists.txt

# Generated Cmake Pico project file

cmake_minimum_required(VERSION 3.13)

set(CMAKE_C_STANDARD 11)
set(CMAKE_CXX_STANDARD 17)
set(CMAKE_EXPORT_COMPILE_COMMANDS ON)

# Initialise pico_sdk from installed location
# (note this can come from environment, CMake cache etc)

# == DO NOT EDIT THE FOLLOWING LINES for the Raspberry Pi Pico VS Code Extension to work ==
if(WIN32)
    set(USERHOME $ENV{USERPROFILE})
else()
    set(USERHOME $ENV{HOME})
endif()
set(sdkVersion 2.2.0)
set(toolchainVersion 14_2_Rel1)
set(picotoolVersion 2.2.0-a4)
set(picoVscode ${USERHOME}/.pico-sdk/cmake/pico-vscode.cmake)
if (EXISTS ${picoVscode})
    include(${picoVscode})
endif()
# ====================================================================================
set(PICO_BOARD adafruit_feather_rp2350 CACHE STRING "Board type")

# Pull in Raspberry Pi Pico SDK (must be before project)
include(pico_sdk_import.cmake)

project(pio_let_test C CXX ASM)

set(PICO_SYS_CLOCK 150000000)

# Initialise the Raspberry Pi Pico SDK
pico_sdk_init()

# Add executable. Default name is the project name, version 0.1

add_executable(pio_let_test pio_let_test.c )

pico_set_program_name(pio_let_test "pio_let_test")
pico_set_program_version(pio_let_test "0.1")

# Generate PIO header
pico_generate_pio_header(pio_let_test ${CMAKE_CURRENT_LIST_DIR}/pio_let.pio)

# Modify the below lines to enable/disable output over UART/USB
pico_enable_stdio_uart(pio_let_test 0)
pico_enable_stdio_usb(pio_let_test 1)

# Add the standard library to the build
target_link_libraries(pio_let_test
        pico_stdlib
        pico_rand)

# Add the standard include files to the build
target_include_directories(pio_let_test PRIVATE
        ${CMAKE_CURRENT_LIST_DIR}
)

# Add any user requested libraries
target_link_libraries(pio_let_test 
        hardware_pio
        )

pico_add_extra_outputs(pio_let_test)

pio_let_test.c

// (C) 2026 alwynallan@gmail.com MIT License

#include <stdio.h>
#include "pico/stdlib.h"
#include "pico/rand.h"
#include "hardware/pio.h"
#include "hardware/clocks.h"

#include "pio_let.pio.h"

#define ROR32(x, n)      (((x) >> (n)) | ((x) << (32 - (n))))

#define rev32(value) __builtin_arm_rbit(value)

#define PIO_LET(osr) { \
  uint32_t x = rev32(osr); \
  uint32_t isr = 0; \
  for(int i=0; i<16; i++) { \
    x -= (osr & 3) + 1; \
    osr = osr >> 2; \
    isr = (isr << 2) | (x & 3); \
  } \
  osr = ~isr; \
}

// https://www.reddit.com/r/RNG/comments/1sfsez6/comment/of1c837/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button
uint32_t inv(uint32_t isr) {
	uint32_t x0; // will be the initial x = rev32(osr);
	uint32_t osr = 0;
	isr = ~isr;
	for (int i = 0; i < 16; i++) {
		osr <<= 2;
		if (i != 15) {
			osr |= ((isr >> 2) - isr - 1) & 3;
		} else {
			osr |= ( x0        - isr - 1) & 3;
		}
		if (i == 0) {
			x0 = (osr >> 1) | ((osr & 1) << 1); // bit reverse
		}
		isr >>= 2;
	}
	return osr;
}

int main() {
  stdio_init_all();
  bool inv_correct = true;
  for(int i=0; i<1000; i++) {
    uint32_t a = get_rand_32();
    uint32_t b = a; PIO_LET(b);
    uint32_t c = inv(b);
    if(a != c) inv_correct = false;
  }
  while(!stdio_usb_connected()) sleep_ms(100); // wait for usb host
  if(!inv_correct) printf("Error case found in inv()\n");

  PIO pio = pio0;
  uint sm = 0;
  uint offset = pio_add_program(pio, &pio_let_program);
  printf("Loaded program at %d\n", offset);
  printf("System Clock: %u Hz\n", clock_get_hz(clk_sys));
  //uint in = 0;
  uint in = get_rand_32();
  pio_let_program_init(pio, sm, offset, PICO_DEFAULT_LED_PIN, in);
  pio_sm_set_enabled(pio, sm, true);

  uint exp = in, out, runs = 0;
  while (--runs) {
    uint t=time_us_32();
    for(int i=0; i<2097152; i++) {
      out = pio_sm_get_blocking(pio, sm);
      //printf("%08x\n", out); stdio_flush();
      PIO_LET(exp);
    }
    t = time_us_32() - t;
    printf("8MB in %u ms\n", t/1000); stdio_flush();
    if(out != exp) {
      printf("Error\n");
      stdio_flush();
    }
  }
  while(1); // keeps USB alive for BOOTSEL
}