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//! Functions and data from the RPI Bootrom.
//!
//! From the [RP2040 datasheet](https://datasheets.raspberrypi.org/rp2040/rp2040-datasheet.pdf), Section 2.8.3.1:
//!
//! > The Bootrom contains a number of public functions that provide useful
//! > RP2040 functionality that might be needed in the absence of any other code
//! > on the device, as well as highly optimized versions of certain key
//! > functionality that would otherwise have to take up space in most user
//! > binaries.
/// A bootrom function table code.
pub type RomFnTableCode = [u8; 2];
/// This function searches for (table)
type RomTableLookupFn<T> = unsafe extern "C" fn(*const u16, u32) -> T;
/// The following addresses are described at `2.8.2. Bootrom Contents`
/// Pointer to the lookup table function supplied by the rom.
const ROM_TABLE_LOOKUP_PTR: *const u16 = 0x0000_0018 as _;
/// Pointer to helper functions lookup table.
const FUNC_TABLE: *const u16 = 0x0000_0014 as _;
/// Pointer to the public data lookup table.
const DATA_TABLE: *const u16 = 0x0000_0016 as _;
/// Address of the version number of the ROM.
const VERSION_NUMBER: *const u8 = 0x0000_0013 as _;
/// Retrieve rom content from a table using a code.
fn rom_table_lookup<T>(table: *const u16, tag: RomFnTableCode) -> T {
unsafe {
let rom_table_lookup_ptr: *const u32 = rom_hword_as_ptr(ROM_TABLE_LOOKUP_PTR);
let rom_table_lookup: RomTableLookupFn<T> = core::mem::transmute(rom_table_lookup_ptr);
rom_table_lookup(
rom_hword_as_ptr(table) as *const u16,
u16::from_le_bytes(tag) as u32,
)
}
}
/// To save space, the ROM likes to store memory pointers (which are 32-bit on
/// the Cortex-M0+) using only the bottom 16-bits. The assumption is that the
/// values they point at live in the first 64 KiB of ROM, and the ROM is mapped
/// to address `0x0000_0000` and so 16-bits are always sufficient.
///
/// This functions grabs a 16-bit value from ROM and expands it out to a full 32-bit pointer.
unsafe fn rom_hword_as_ptr(rom_address: *const u16) -> *const u32 {
let ptr: u16 = *rom_address;
ptr as *const u32
}
macro_rules! declare_rom_function {
(
$(#[$outer:meta])*
fn $name:ident( $($argname:ident: $ty:ty),* ) -> $ret:ty
$lookup:block
) => {
#[doc = r"Additional access for the `"]
#[doc = stringify!($name)]
#[doc = r"` ROM function."]
pub mod $name {
/// Retrieve a function pointer.
#[cfg(not(feature = "rom-func-cache"))]
pub fn ptr() -> extern "C" fn( $($argname: $ty),* ) -> $ret {
let p: *const u32 = $lookup;
unsafe {
let func : extern "C" fn( $($argname: $ty),* ) -> $ret = core::mem::transmute(p);
func
}
}
/// Retrieve a function pointer.
#[cfg(feature = "rom-func-cache")]
pub fn ptr() -> extern "C" fn( $($argname: $ty),* ) -> $ret {
use core::sync::atomic::{AtomicU16, Ordering};
// All pointers in the ROM fit in 16 bits, so we don't need a
// full width word to store the cached value.
static CACHED_PTR: AtomicU16 = AtomicU16::new(0);
// This is safe because the lookup will always resolve
// to the same value. So even if an interrupt or another
// core starts at the same time, it just repeats some
// work and eventually writes back the correct value.
let p: *const u32 = match CACHED_PTR.load(Ordering::Relaxed) {
0 => {
let raw: *const u32 = $lookup;
CACHED_PTR.store(raw as u16, Ordering::Relaxed);
raw
},
val => val as *const u32,
};
unsafe {
let func : extern "C" fn( $($argname: $ty),* ) -> $ret = core::mem::transmute(p);
func
}
}
}
$(#[$outer])*
pub extern "C" fn $name( $($argname: $ty),* ) -> $ret {
$name::ptr()($($argname),*)
}
};
(
$(#[$outer:meta])*
unsafe fn $name:ident( $($argname:ident: $ty:ty),* ) -> $ret:ty
$lookup:block
) => {
#[doc = r"Additional access for the `"]
#[doc = stringify!($name)]
#[doc = r"` ROM function."]
pub mod $name {
/// Retrieve a function pointer.
#[cfg(not(feature = "rom-func-cache"))]
pub fn ptr() -> unsafe extern "C" fn( $($argname: $ty),* ) -> $ret {
let p: *const u32 = $lookup;
unsafe {
let func : unsafe extern "C" fn( $($argname: $ty),* ) -> $ret = core::mem::transmute(p);
func
}
}
/// Retrieve a function pointer.
#[cfg(feature = "rom-func-cache")]
pub fn ptr() -> unsafe extern "C" fn( $($argname: $ty),* ) -> $ret {
use core::sync::atomic::{AtomicU16, Ordering};
// All pointers in the ROM fit in 16 bits, so we don't need a
// full width word to store the cached value.
static CACHED_PTR: AtomicU16 = AtomicU16::new(0);
// This is safe because the lookup will always resolve
// to the same value. So even if an interrupt or another
// core starts at the same time, it just repeats some
// work and eventually writes back the correct value.
let p: *const u32 = match CACHED_PTR.load(Ordering::Relaxed) {
0 => {
let raw: *const u32 = $lookup;
CACHED_PTR.store(raw as u16, Ordering::Relaxed);
raw
},
val => val as *const u32,
};
unsafe {
let func : unsafe extern "C" fn( $($argname: $ty),* ) -> $ret = core::mem::transmute(p);
func
}
}
}
$(#[$outer])*
/// # Safety
///
/// This is a low-level C function. It may be difficult to call safely from
/// Rust. If in doubt, check the RP2040 datasheet for details and do your own
/// safety evaluation.
pub unsafe extern "C" fn $name( $($argname: $ty),* ) -> $ret {
$name::ptr()($($argname),*)
}
};
}
macro_rules! rom_functions {
() => {};
(
$(#[$outer:meta])*
$c:literal fn $name:ident( $($argname:ident: $ty:ty),* ) -> $ret:ty;
$($rest:tt)*
) => {
declare_rom_function! {
$(#[$outer])*
fn $name( $($argname: $ty),* ) -> $ret {
$crate::rom_data::rom_table_lookup($crate::rom_data::FUNC_TABLE, *$c)
}
}
rom_functions!($($rest)*);
};
(
$(#[$outer:meta])*
$c:literal unsafe fn $name:ident( $($argname:ident: $ty:ty),* ) -> $ret:ty;
$($rest:tt)*
) => {
declare_rom_function! {
$(#[$outer])*
unsafe fn $name( $($argname: $ty),* ) -> $ret {
$crate::rom_data::rom_table_lookup($crate::rom_data::FUNC_TABLE, *$c)
}
}
rom_functions!($($rest)*);
};
}
rom_functions! {
/// Return a count of the number of 1 bits in value.
b"P3" fn popcount32(value: u32) -> u32;
/// Return the bits of value in the reverse order.
b"R3" fn reverse32(value: u32) -> u32;
/// Return the number of consecutive high order 0 bits of value. If value is zero, returns 32.
b"L3" fn clz32(value: u32) -> u32;
/// Return the number of consecutive low order 0 bits of value. If value is zero, returns 32.
b"T3" fn ctz32(value: u32) -> u32;
/// Resets the RP2040 and uses the watchdog facility to re-start in BOOTSEL mode:
/// * gpio_activity_pin_mask is provided to enable an 'activity light' via GPIO attached LED
/// for the USB Mass Storage Device:
/// * 0 No pins are used as per cold boot.
/// * Otherwise a single bit set indicating which GPIO pin should be set to output and
/// raised whenever there is mass storage activity from the host.
/// * disable_interface_mask may be used to control the exposed USB interfaces:
/// * 0 To enable both interfaces (as per cold boot).
/// * 1 To disable the USB Mass Storage Interface.
/// * 2 to Disable the USB PICOBOOT Interface.
b"UB" fn reset_to_usb_boot(gpio_activity_pin_mask: u32, disable_interface_mask: u32) -> ();
/// Sets n bytes start at ptr to the value c and returns ptr
b"MS" unsafe fn memset(ptr: *mut u8, c: u8, n: u32) -> *mut u8;
/// Sets n bytes start at ptr to the value c and returns ptr.
///
/// Note this is a slightly more efficient variant of _memset that may only
/// be used if ptr is word aligned.
// Note the datasheet does not match the actual ROM for the code here, see
// https://github.com/raspberrypi/pico-feedback/issues/217
b"S4" unsafe fn memset4(ptr: *mut u32, c: u8, n: u32) -> *mut u32;
/// Copies n bytes starting at src to dest and returns dest. The results are undefined if the
/// regions overlap.
b"MC" unsafe fn memcpy(dest: *mut u8, src: *const u8, n: u32) -> *mut u8;
/// Copies n bytes starting at src to dest and returns dest. The results are undefined if the
/// regions overlap.
///
/// Note this is a slightly more efficient variant of _memcpy that may only be
/// used if dest and src are word aligned.
b"C4" unsafe fn memcpy44(dest: *mut u32, src: *const u32, n: u32) -> *mut u8;
/// Restore all QSPI pad controls to their default state, and connect the SSI to the QSPI pads.
b"IF" unsafe fn connect_internal_flash() -> ();
/// First set up the SSI for serial-mode operations, then issue the fixed XIP exit sequence.
///
/// Note that the bootrom code uses the IO forcing logic to drive the CS pin, which must be
/// cleared before returning the SSI to XIP mode (e.g. by a call to _flash_flush_cache). This
/// function configures the SSI with a fixed SCK clock divisor of /6.
b"EX" unsafe fn flash_exit_xip() -> ();
/// Erase a count bytes, starting at addr (offset from start of flash). Optionally, pass a
/// block erase command e.g. D8h block erase, and the size of the block erased by this
/// command — this function will use the larger block erase where possible, for much higher
/// erase speed. addr must be aligned to a 4096-byte sector, and count must be a multiple of
/// 4096 bytes.
b"RE" unsafe fn flash_range_erase(addr: u32, count: usize, block_size: u32, block_cmd: u8) -> ();
/// Program data to a range of flash addresses starting at `addr` (and
/// offset from the start of flash) and `count` bytes in size. The value
/// `addr` must be aligned to a 256-byte boundary, and `count` must be a
/// multiple of 256.
b"RP" unsafe fn flash_range_program(addr: u32, data: *const u8, count: usize) -> ();
/// Flush and enable the XIP cache. Also clears the IO forcing on QSPI CSn, so that the SSI can
/// drive the flashchip select as normal.
b"FC" unsafe fn flash_flush_cache() -> ();
/// Configure the SSI to generate a standard 03h serial read command, with 24 address bits,
/// upon each XIP access. This is a very slow XIP configuration, but is very widely supported.
/// The debugger calls this function after performing a flash erase/programming operation, so
/// that the freshly-programmed code and data is visible to the debug host, without having to
/// know exactly what kind of flash device is connected.
b"CX" unsafe fn flash_enter_cmd_xip() -> ();
/// This is the method that is entered by core 1 on reset to wait to be launched by core 0.
/// There are few cases where you should call this method (resetting core 1 is much better).
/// This method does not return and should only ever be called on core 1.
b"WV" unsafe fn wait_for_vector() -> !;
}
// Various C intrinsics in the ROM
intrinsics! {
#[alias = __popcountdi2]
extern "C" fn __popcountsi2(x: u32) -> u32 {
popcount32(x)
}
#[alias = __clzdi2]
extern "C" fn __clzsi2(x: u32) -> u32 {
clz32(x)
}
#[alias = __ctzdi2]
extern "C" fn __ctzsi2(x: u32) -> u32 {
ctz32(x)
}
// __rbit is only unofficial, but it show up in the ARM documentation,
// so may as well hook it up.
#[alias = __rbitl]
extern "C" fn __rbit(x: u32) -> u32 {
reverse32(x)
}
unsafe extern "aapcs" fn __aeabi_memset(dest: *mut u8, n: usize, c: i32) -> () {
// Different argument order
memset(dest, c as u8, n as u32);
}
#[alias = __aeabi_memset8]
unsafe extern "aapcs" fn __aeabi_memset4(dest: *mut u8, n: usize, c: i32) -> () {
// Different argument order
memset4(dest as *mut u32, c as u8, n as u32);
}
unsafe extern "aapcs" fn __aeabi_memclr(dest: *mut u8, n: usize) -> () {
memset(dest, 0, n as u32);
}
#[alias = __aeabi_memclr8]
unsafe extern "aapcs" fn __aeabi_memclr4(dest: *mut u8, n: usize) -> () {
memset4(dest as *mut u32, 0, n as u32);
}
unsafe extern "aapcs" fn __aeabi_memcpy(dest: *mut u8, src: *const u8, n: usize) -> () {
memcpy(dest, src, n as u32);
}
#[alias = __aeabi_memcpy8]
unsafe extern "aapcs" fn __aeabi_memcpy4(dest: *mut u8, src: *const u8, n: usize) -> () {
memcpy44(dest as *mut u32, src as *const u32, n as u32);
}
}
unsafe fn convert_str(s: *const u8) -> &'static str {
let mut end = s;
while *end != 0 {
end = end.add(1);
}
let s = core::slice::from_raw_parts(s, end.offset_from(s) as usize);
core::str::from_utf8_unchecked(s)
}
/// The version number of the rom.
pub fn rom_version_number() -> u8 {
unsafe { *VERSION_NUMBER }
}
/// The Raspberry Pi Trading Ltd copyright string.
pub fn copyright_string() -> &'static str {
let s: *const u8 = rom_table_lookup(DATA_TABLE, *b"CR");
unsafe { convert_str(s) }
}
/// The 8 most significant hex digits of the Bootrom git revision.
pub fn git_revision() -> u32 {
let s: *const u32 = rom_table_lookup(DATA_TABLE, *b"GR");
unsafe { *s }
}
/// The start address of the floating point library code and data.
///
/// This and fplib_end along with the individual function pointers in
/// soft_float_table can be used to copy the floating point implementation into
/// RAM if desired.
pub fn fplib_start() -> *const u8 {
rom_table_lookup(DATA_TABLE, *b"FS")
}
/// See Table 180 in the RP2040 datasheet for the contents of this table.
pub fn soft_float_table() -> *const usize {
rom_table_lookup(DATA_TABLE, *b"SF")
}
/// The end address of the floating point library code and data.
pub fn fplib_end() -> *const u8 {
rom_table_lookup(DATA_TABLE, *b"FE")
}
/// This entry is only present in the V2 bootrom. See Table 182 in the RP2040 datasheet for the contents of this table.
pub fn soft_double_table() -> *const usize {
if rom_version_number() < 2 {
panic!(
"Double precision operations require V2 bootrom (found: V{})",
rom_version_number()
);
}
rom_table_lookup(DATA_TABLE, *b"SD")
}
/// ROM functions using single-precision arithmetic (i.e. 'f32' in Rust terms)
pub mod float_funcs {
macro_rules! make_functions {
(
$(
$(#[$outer:meta])*
$offset:literal $name:ident (
$( $aname:ident : $aty:ty ),*
) -> $ret:ty;
)*
) => {
$(
declare_rom_function! {
$(#[$outer])*
fn $name( $( $aname : $aty ),* ) -> $ret {
let table: *const usize = $crate::rom_data::soft_float_table();
unsafe {
// This is the entry in the table. Our offset is given as a
// byte offset, but we want the table index (each pointer in
// the table is 4 bytes long)
let entry: *const usize = table.offset($offset / 4);
// Read the pointer from the table
core::ptr::read(entry) as *const u32
}
}
}
)*
}
}
make_functions! {
/// Calculates `a + b`
0x00 fadd(a: f32, b: f32) -> f32;
/// Calculates `a - b`
0x04 fsub(a: f32, b: f32) -> f32;
/// Calculates `a * b`
0x08 fmul(a: f32, b: f32) -> f32;
/// Calculates `a / b`
0x0c fdiv(a: f32, b: f32) -> f32;
// 0x10 and 0x14 are deprecated
/// Calculates `sqrt(v)` (or return -Infinity if v is negative)
0x18 fsqrt(v: f32) -> f32;
/// Converts an f32 to a signed integer,
/// rounding towards -Infinity, and clamping the result to lie within the
/// range `-0x80000000` to `0x7FFFFFFF`
0x1c float_to_int(v: f32) -> i32;
/// Converts an f32 to an signed fixed point
/// integer representation where n specifies the position of the binary
/// point in the resulting fixed point representation, e.g.
/// `f(0.5f, 16) == 0x8000`. This method rounds towards -Infinity,
/// and clamps the resulting integer to lie within the range `0x00000000` to
/// `0xFFFFFFFF`
0x20 float_to_fix(v: f32, n: i32) -> i32;
/// Converts an f32 to an unsigned integer,
/// rounding towards -Infinity, and clamping the result to lie within the
/// range `0x00000000` to `0xFFFFFFFF`
0x24 float_to_uint(v: f32) -> u32;
/// Converts an f32 to an unsigned fixed point
/// integer representation where n specifies the position of the binary
/// point in the resulting fixed point representation, e.g.
/// `f(0.5f, 16) == 0x8000`. This method rounds towards -Infinity,
/// and clamps the resulting integer to lie within the range `0x00000000` to
/// `0xFFFFFFFF`
0x28 float_to_ufix(v: f32, n: i32) -> u32;
/// Converts a signed integer to the nearest
/// f32 value, rounding to even on tie
0x2c int_to_float(v: i32) -> f32;
/// Converts a signed fixed point integer
/// representation to the nearest f32 value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so `f =
/// nearest(v/(2^n))`
0x30 fix_to_float(v: i32, n: i32) -> f32;
/// Converts an unsigned integer to the nearest
/// f32 value, rounding to even on tie
0x34 uint_to_float(v: u32) -> f32;
/// Converts an unsigned fixed point integer
/// representation to the nearest f32 value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so `f =
/// nearest(v/(2^n))`
0x38 ufix_to_float(v: u32, n: i32) -> f32;
/// Calculates the cosine of `angle`. The value
/// of `angle` is in radians, and must be in the range `-128` to `128`
0x3c fcos(angle: f32) -> f32;
/// Calculates the sine of `angle`. The value of
/// `angle` is in radians, and must be in the range `-128` to `128`
0x40 fsin(angle: f32) -> f32;
/// Calculates the tangent of `angle`. The value
/// of `angle` is in radians, and must be in the range `-128` to `128`
0x44 ftan(angle: f32) -> f32;
// 0x48 is deprecated
/// Calculates the exponential value of `v`,
/// i.e. `e ** v`
0x4c fexp(v: f32) -> f32;
/// Calculates the natural logarithm of `v`. If `v <= 0` return -Infinity
0x50 fln(v: f32) -> f32;
}
macro_rules! make_functions_v2 {
(
$(
$(#[$outer:meta])*
$offset:literal $name:ident (
$( $aname:ident : $aty:ty ),*
) -> $ret:ty;
)*
) => {
$(
declare_rom_function! {
$(#[$outer])*
fn $name( $( $aname : $aty ),* ) -> $ret {
if $crate::rom_data::rom_version_number() < 2 {
panic!(
"Floating point function requires V2 bootrom (found: V{})",
$crate::rom_data::rom_version_number()
);
}
let table: *const usize = $crate::rom_data::soft_float_table();
unsafe {
// This is the entry in the table. Our offset is given as a
// byte offset, but we want the table index (each pointer in
// the table is 4 bytes long)
let entry: *const usize = table.offset($offset / 4);
// Read the pointer from the table
core::ptr::read(entry) as *const u32
}
}
}
)*
}
}
// These are only on BootROM v2 or higher
make_functions_v2! {
/// Compares two floating point numbers, returning:
/// • 0 if a == b
/// • -1 if a < b
/// • 1 if a > b
0x54 fcmp(a: f32, b: f32) -> i32;
/// Computes the arc tangent of `y/x` using the
/// signs of arguments to determine the correct quadrant
0x58 fatan2(y: f32, x: f32) -> f32;
/// Converts a signed 64-bit integer to the
/// nearest f32 value, rounding to even on tie
0x5c int64_to_float(v: i64) -> f32;
/// Converts a signed fixed point 64-bit integer
/// representation to the nearest f32 value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so `f =
/// nearest(v/(2^n))`
0x60 fix64_to_float(v: i64, n: i32) -> f32;
/// Converts an unsigned 64-bit integer to the
/// nearest f32 value, rounding to even on tie
0x64 uint64_to_float(v: u64) -> f32;
/// Converts an unsigned fixed point 64-bit
/// integer representation to the nearest f32 value, rounding to even on
/// tie. `n` specifies the position of the binary point in fixed point, so
/// `f = nearest(v/(2^n))`
0x68 ufix64_to_float(v: u64, n: i32) -> f32;
/// Convert an f32 to a signed 64-bit integer, rounding towards -Infinity,
/// and clamping the result to lie within the range `-0x8000000000000000` to
/// `0x7FFFFFFFFFFFFFFF`
0x6c float_to_int64(v: f32) -> i64;
/// Converts an f32 to a signed fixed point
/// 64-bit integer representation where n specifies the position of the
/// binary point in the resulting fixed point representation - e.g. `f(0.5f,
/// 16) == 0x8000`. This method rounds towards -Infinity, and clamps the
/// resulting integer to lie within the range `-0x8000000000000000` to
/// `0x7FFFFFFFFFFFFFFF`
0x70 float_to_fix64(v: f32, n: i32) -> i64;
/// Converts an f32 to an unsigned 64-bit
/// integer, rounding towards -Infinity, and clamping the result to lie
/// within the range `0x0000000000000000` to `0xFFFFFFFFFFFFFFFF`
0x74 float_to_uint64(v: f32) -> u64;
/// Converts an f32 to an unsigned fixed point
/// 64-bit integer representation where n specifies the position of the
/// binary point in the resulting fixed point representation, e.g. `f(0.5f,
/// 16) == 0x8000`. This method rounds towards -Infinity, and clamps the
/// resulting integer to lie within the range `0x0000000000000000` to
/// `0xFFFFFFFFFFFFFFFF`
0x78 float_to_ufix64(v: f32, n: i32) -> u64;
/// Converts an f32 to an f64.
0x7c float_to_double(v: f32) -> f64;
}
}
/// Functions using double-precision arithmetic (i.e. 'f64' in Rust terms)
pub mod double_funcs {
macro_rules! make_double_funcs {
(
$(
$(#[$outer:meta])*
$offset:literal $name:ident (
$( $aname:ident : $aty:ty ),*
) -> $ret:ty;
)*
) => {
$(
declare_rom_function! {
$(#[$outer])*
fn $name( $( $aname : $aty ),* ) -> $ret {
let table: *const usize = $crate::rom_data::soft_double_table();
unsafe {
// This is the entry in the table. Our offset is given as a
// byte offset, but we want the table index (each pointer in
// the table is 4 bytes long)
let entry: *const usize = table.offset($offset / 4);
// Read the pointer from the table
core::ptr::read(entry) as *const u32
}
}
}
)*
}
}
make_double_funcs! {
/// Calculates `a + b`
0x00 dadd(a: f64, b: f64) -> f64;
/// Calculates `a - b`
0x04 dsub(a: f64, b: f64) -> f64;
/// Calculates `a * b`
0x08 dmul(a: f64, b: f64) -> f64;
/// Calculates `a / b`
0x0c ddiv(a: f64, b: f64) -> f64;
// 0x10 and 0x14 are deprecated
/// Calculates `sqrt(v)` (or return -Infinity if v is negative)
0x18 dsqrt(v: f64) -> f64;
/// Converts an f64 to a signed integer,
/// rounding towards -Infinity, and clamping the result to lie within the
/// range `-0x80000000` to `0x7FFFFFFF`
0x1c double_to_int(v: f64) -> i32;
/// Converts an f64 to an signed fixed point
/// integer representation where n specifies the position of the binary
/// point in the resulting fixed point representation, e.g.
/// `f(0.5f, 16) == 0x8000`. This method rounds towards -Infinity,
/// and clamps the resulting integer to lie within the range `0x00000000` to
/// `0xFFFFFFFF`
0x20 double_to_fix(v: f64, n: i32) -> i32;
/// Converts an f64 to an unsigned integer,
/// rounding towards -Infinity, and clamping the result to lie within the
/// range `0x00000000` to `0xFFFFFFFF`
0x24 double_to_uint(v: f64) -> u32;
/// Converts an f64 to an unsigned fixed point
/// integer representation where n specifies the position of the binary
/// point in the resulting fixed point representation, e.g.
/// `f(0.5f, 16) == 0x8000`. This method rounds towards -Infinity,
/// and clamps the resulting integer to lie within the range `0x00000000` to
/// `0xFFFFFFFF`
0x28 double_to_ufix(v: f64, n: i32) -> u32;
/// Converts a signed integer to the nearest
/// double value, rounding to even on tie
0x2c int_to_double(v: i32) -> f64;
/// Converts a signed fixed point integer
/// representation to the nearest double value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so `f =
/// nearest(v/(2^n))`
0x30 fix_to_double(v: i32, n: i32) -> f64;
/// Converts an unsigned integer to the nearest
/// double value, rounding to even on tie
0x34 uint_to_double(v: u32) -> f64;
/// Converts an unsigned fixed point integer
/// representation to the nearest double value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so f =
/// nearest(v/(2^n))
0x38 ufix_to_double(v: u32, n: i32) -> f64;
/// Calculates the cosine of `angle`. The value
/// of `angle` is in radians, and must be in the range `-1024` to `1024`
0x3c dcos(angle: f64) -> f64;
/// Calculates the sine of `angle`. The value of
/// `angle` is in radians, and must be in the range `-1024` to `1024`
0x40 dsin(angle: f64) -> f64;
/// Calculates the tangent of `angle`. The value
/// of `angle` is in radians, and must be in the range `-1024` to `1024`
0x44 dtan(angle: f64) -> f64;
// 0x48 is deprecated
/// Calculates the exponential value of `v`,
/// i.e. `e ** v`
0x4c dexp(v: f64) -> f64;
/// Calculates the natural logarithm of v. If v <= 0 return -Infinity
0x50 dln(v: f64) -> f64;
// These are only on BootROM v2 or higher
/// Compares two floating point numbers, returning:
/// • 0 if a == b
/// • -1 if a < b
/// • 1 if a > b
0x54 dcmp(a: f64, b: f64) -> i32;
/// Computes the arc tangent of `y/x` using the
/// signs of arguments to determine the correct quadrant
0x58 datan2(y: f64, x: f64) -> f64;
/// Converts a signed 64-bit integer to the
/// nearest double value, rounding to even on tie
0x5c int64_to_double(v: i64) -> f64;
/// Converts a signed fixed point 64-bit integer
/// representation to the nearest double value, rounding to even on tie. `n`
/// specifies the position of the binary point in fixed point, so `f =
/// nearest(v/(2^n))`
0x60 fix64_to_double(v: i64, n: i32) -> f64;
/// Converts an unsigned 64-bit integer to the
/// nearest double value, rounding to even on tie
0x64 uint64_to_double(v: u64) -> f64;
/// Converts an unsigned fixed point 64-bit
/// integer representation to the nearest double value, rounding to even on
/// tie. `n` specifies the position of the binary point in fixed point, so
/// `f = nearest(v/(2^n))`
0x68 ufix64_to_double(v: u64, n: i32) -> f64;
/// Convert an f64 to a signed 64-bit integer, rounding towards -Infinity,
/// and clamping the result to lie within the range `-0x8000000000000000` to
/// `0x7FFFFFFFFFFFFFFF`
0x6c double_to_int64(v: f64) -> i64;
/// Converts an f64 to a signed fixed point
/// 64-bit integer representation where n specifies the position of the
/// binary point in the resulting fixed point representation - e.g. `f(0.5f,
/// 16) == 0x8000`. This method rounds towards -Infinity, and clamps the
/// resulting integer to lie within the range `-0x8000000000000000` to
/// `0x7FFFFFFFFFFFFFFF`
0x70 double_to_fix64(v: f64, n: i32) -> i64;
/// Converts an f64 to an unsigned 64-bit
/// integer, rounding towards -Infinity, and clamping the result to lie
/// within the range `0x0000000000000000` to `0xFFFFFFFFFFFFFFFF`
0x74 double_to_uint64(v: f64) -> u64;
/// Converts an f64 to an unsigned fixed point
/// 64-bit integer representation where n specifies the position of the
/// binary point in the resulting fixed point representation, e.g. `f(0.5f,
/// 16) == 0x8000`. This method rounds towards -Infinity, and clamps the
/// resulting integer to lie within the range `0x0000000000000000` to
/// `0xFFFFFFFFFFFFFFFF`
0x78 double_to_ufix64(v: f64, n: i32) -> u64;
/// Converts an f64 to an f32
0x7c double_to_float(v: f64) -> f32;
}
}