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Copy pathinstructions.rs
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1279 lines (1145 loc) · 54 KB
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// spell-checker: disable
use super::{JitCompileError, JitSig, JitType};
use cranelift::codegen::ir::FuncRef;
use cranelift::prelude::*;
use num_traits::cast::ToPrimitive;
use rustpython_compiler_core::bytecode::{
self, BinaryOperator, BorrowedConstant, CodeObject, ComparisonOperator, Instruction, Label,
OpArg, OpArgState, UnaryOperator,
};
use std::collections::HashMap;
#[repr(u16)]
enum CustomTrapCode {
/// Raised when shifting by a negative number
NegativeShiftCount = 1,
}
#[derive(Clone)]
struct Local {
var: Variable,
ty: JitType,
}
#[derive(Debug)]
enum JitValue {
Int(Value),
Float(Value),
Bool(Value),
None,
Tuple(Vec<JitValue>),
FuncRef(FuncRef),
}
impl JitValue {
fn from_type_and_value(ty: JitType, val: Value) -> JitValue {
match ty {
JitType::Int => JitValue::Int(val),
JitType::Float => JitValue::Float(val),
JitType::Bool => JitValue::Bool(val),
}
}
fn to_jit_type(&self) -> Option<JitType> {
match self {
JitValue::Int(_) => Some(JitType::Int),
JitValue::Float(_) => Some(JitType::Float),
JitValue::Bool(_) => Some(JitType::Bool),
JitValue::None | JitValue::Tuple(_) | JitValue::FuncRef(_) => None,
}
}
fn into_value(self) -> Option<Value> {
match self {
JitValue::Int(val) | JitValue::Float(val) | JitValue::Bool(val) => Some(val),
JitValue::None | JitValue::Tuple(_) | JitValue::FuncRef(_) => None,
}
}
}
#[derive(Clone)]
struct DDValue {
hi: Value,
lo: Value,
}
pub struct FunctionCompiler<'a, 'b> {
builder: &'a mut FunctionBuilder<'b>,
stack: Vec<JitValue>,
variables: Box<[Option<Local>]>,
label_to_block: HashMap<Label, Block>,
pub(crate) sig: JitSig,
}
impl<'a, 'b> FunctionCompiler<'a, 'b> {
pub fn new(
builder: &'a mut FunctionBuilder<'b>,
num_variables: usize,
arg_types: &[JitType],
ret_type: Option<JitType>,
entry_block: Block,
) -> FunctionCompiler<'a, 'b> {
let mut compiler = FunctionCompiler {
builder,
stack: Vec::new(),
variables: vec![None; num_variables].into_boxed_slice(),
label_to_block: HashMap::new(),
sig: JitSig {
args: arg_types.to_vec(),
ret: ret_type,
},
};
let params = compiler.builder.func.dfg.block_params(entry_block).to_vec();
for (i, (ty, val)) in arg_types.iter().zip(params).enumerate() {
compiler
.store_variable(i as u32, JitValue::from_type_and_value(ty.clone(), val))
.unwrap();
}
compiler
}
fn pop_multiple(&mut self, count: usize) -> Vec<JitValue> {
let stack_len = self.stack.len();
self.stack.drain(stack_len - count..).collect()
}
fn store_variable(
&mut self,
idx: bytecode::NameIdx,
val: JitValue,
) -> Result<(), JitCompileError> {
let builder = &mut self.builder;
let ty = val.to_jit_type().ok_or(JitCompileError::NotSupported)?;
let local = self.variables[idx as usize].get_or_insert_with(|| {
let var = Variable::new(idx as usize);
let local = Local {
var,
ty: ty.clone(),
};
builder.declare_var(var, ty.to_cranelift());
local
});
if ty != local.ty {
Err(JitCompileError::NotSupported)
} else {
self.builder.def_var(local.var, val.into_value().unwrap());
Ok(())
}
}
fn boolean_val(&mut self, val: JitValue) -> Result<Value, JitCompileError> {
match val {
JitValue::Float(val) => {
let zero = self.builder.ins().f64const(0.0);
let val = self.builder.ins().fcmp(FloatCC::NotEqual, val, zero);
Ok(val)
}
JitValue::Int(val) => {
let zero = self.builder.ins().iconst(types::I64, 0);
let val = self.builder.ins().icmp(IntCC::NotEqual, val, zero);
Ok(val)
}
JitValue::Bool(val) => Ok(val),
JitValue::None => Ok(self.builder.ins().iconst(types::I8, 0)),
JitValue::Tuple(_) | JitValue::FuncRef(_) => Err(JitCompileError::NotSupported),
}
}
fn get_or_create_block(&mut self, label: Label) -> Block {
let builder = &mut self.builder;
*self
.label_to_block
.entry(label)
.or_insert_with(|| builder.create_block())
}
pub fn compile<C: bytecode::Constant>(
&mut self,
func_ref: FuncRef,
bytecode: &CodeObject<C>,
) -> Result<(), JitCompileError> {
let label_targets = bytecode.label_targets();
let mut arg_state = OpArgState::default();
// Track whether we have "returned" in the current block
let mut in_unreachable_code = false;
for (offset, &raw_instr) in bytecode.instructions.iter().enumerate() {
let label = Label(offset as u32);
let (instruction, arg) = arg_state.get(raw_instr);
// If this is a label that some earlier jump can target,
// treat it as the start of a new reachable block:
if label_targets.contains(&label) {
// Create or get the block for this label:
let target_block = self.get_or_create_block(label);
// If the current block isn't terminated, jump:
if let Some(cur) = self.builder.current_block() {
if cur != target_block && self.builder.func.layout.last_inst(cur).is_none() {
self.builder.ins().jump(target_block, &[]);
}
}
// Switch to the target block
if self.builder.current_block() != Some(target_block) {
self.builder.switch_to_block(target_block);
}
// We are definitely reachable again at this label
in_unreachable_code = false;
}
// If we're in unreachable code, skip this instruction unless the label re-entered above.
if in_unreachable_code {
continue;
}
// Actually compile this instruction:
self.add_instruction(func_ref, bytecode, instruction, arg)?;
// If that was a return instruction, mark future instructions unreachable
match instruction {
Instruction::ReturnValue | Instruction::ReturnConst { .. } => {
in_unreachable_code = true;
}
_ => {}
}
}
// After processing, if the current block is unterminated, insert a trap or fallthrough
if let Some(cur) = self.builder.current_block() {
if self.builder.func.layout.last_inst(cur).is_none() {
self.builder.ins().trap(TrapCode::user(0).unwrap());
}
}
Ok(())
}
fn prepare_const<C: bytecode::Constant>(
&mut self,
constant: BorrowedConstant<'_, C>,
) -> Result<JitValue, JitCompileError> {
let value = match constant {
BorrowedConstant::Integer { value } => {
let val = self.builder.ins().iconst(
types::I64,
value.to_i64().ok_or(JitCompileError::NotSupported)?,
);
JitValue::Int(val)
}
BorrowedConstant::Float { value } => {
let val = self.builder.ins().f64const(value);
JitValue::Float(val)
}
BorrowedConstant::Boolean { value } => {
let val = self.builder.ins().iconst(types::I8, value as i64);
JitValue::Bool(val)
}
BorrowedConstant::None => JitValue::None,
_ => return Err(JitCompileError::NotSupported),
};
Ok(value)
}
fn return_value(&mut self, val: JitValue) -> Result<(), JitCompileError> {
if let Some(ref ty) = self.sig.ret {
// If the signature has a return type, enforce it
if val.to_jit_type().as_ref() != Some(ty) {
return Err(JitCompileError::NotSupported);
}
} else {
// First time we see a return, define it in the signature
let ty = val.to_jit_type().ok_or(JitCompileError::NotSupported)?;
self.sig.ret = Some(ty.clone());
self.builder
.func
.signature
.returns
.push(AbiParam::new(ty.to_cranelift()));
}
// If this is e.g. an Int, Float, or Bool we have a Cranelift `Value`.
// If we have JitValue::None or .Tuple(...) but can't handle that, error out (or handle differently).
let cr_val = val.into_value().ok_or(JitCompileError::NotSupported)?;
self.builder.ins().return_(&[cr_val]);
Ok(())
}
pub fn add_instruction<C: bytecode::Constant>(
&mut self,
func_ref: FuncRef,
bytecode: &CodeObject<C>,
instruction: Instruction,
arg: OpArg,
) -> Result<(), JitCompileError> {
match instruction {
Instruction::ExtendedArg => Ok(()),
Instruction::JumpIfFalse { target } => {
let cond = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let val = self.boolean_val(cond)?;
let then_block = self.get_or_create_block(target.get(arg));
let else_block = self.builder.create_block();
self.builder
.ins()
.brif(val, else_block, &[], then_block, &[]);
self.builder.switch_to_block(else_block);
Ok(())
}
Instruction::JumpIfTrue { target } => {
let cond = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let val = self.boolean_val(cond)?;
let then_block = self.get_or_create_block(target.get(arg));
let else_block = self.builder.create_block();
self.builder
.ins()
.brif(val, then_block, &[], else_block, &[]);
self.builder.switch_to_block(else_block);
Ok(())
}
Instruction::Jump { target } => {
let target_block = self.get_or_create_block(target.get(arg));
self.builder.ins().jump(target_block, &[]);
Ok(())
}
Instruction::LoadFast(idx) => {
let local = self.variables[idx.get(arg) as usize]
.as_ref()
.ok_or(JitCompileError::BadBytecode)?;
self.stack.push(JitValue::from_type_and_value(
local.ty.clone(),
self.builder.use_var(local.var),
));
Ok(())
}
Instruction::StoreFast(idx) => {
let val = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
self.store_variable(idx.get(arg), val)
}
Instruction::LoadConst { idx } => {
let val = self
.prepare_const(bytecode.constants[idx.get(arg) as usize].borrow_constant())?;
self.stack.push(val);
Ok(())
}
Instruction::BuildTuple { size } => {
let elements = self.pop_multiple(size.get(arg) as usize);
self.stack.push(JitValue::Tuple(elements));
Ok(())
}
Instruction::UnpackSequence { size } => {
let val = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let elements = match val {
JitValue::Tuple(elements) => elements,
_ => return Err(JitCompileError::NotSupported),
};
if elements.len() != size.get(arg) as usize {
return Err(JitCompileError::NotSupported);
}
self.stack.extend(elements.into_iter().rev());
Ok(())
}
Instruction::ReturnValue => {
let val = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
self.return_value(val)
}
Instruction::ReturnConst { idx } => {
let val = self
.prepare_const(bytecode.constants[idx.get(arg) as usize].borrow_constant())?;
self.return_value(val)
}
Instruction::CompareOperation { op, .. } => {
let op = op.get(arg);
// the rhs is popped off first
let b = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let a = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let a_type: Option<JitType> = a.to_jit_type();
let b_type: Option<JitType> = b.to_jit_type();
match (a, b) {
(JitValue::Int(a), JitValue::Int(b))
| (JitValue::Bool(a), JitValue::Bool(b))
| (JitValue::Bool(a), JitValue::Int(b))
| (JitValue::Int(a), JitValue::Bool(b)) => {
let operand_one = match a_type.unwrap() {
JitType::Bool => self.builder.ins().uextend(types::I64, a),
_ => a,
};
let operand_two = match b_type.unwrap() {
JitType::Bool => self.builder.ins().uextend(types::I64, b),
_ => b,
};
let cond = match op {
ComparisonOperator::Equal => IntCC::Equal,
ComparisonOperator::NotEqual => IntCC::NotEqual,
ComparisonOperator::Less => IntCC::SignedLessThan,
ComparisonOperator::LessOrEqual => IntCC::SignedLessThanOrEqual,
ComparisonOperator::Greater => IntCC::SignedGreaterThan,
ComparisonOperator::GreaterOrEqual => IntCC::SignedGreaterThanOrEqual,
};
let val = self.builder.ins().icmp(cond, operand_one, operand_two);
self.stack.push(JitValue::Bool(val));
Ok(())
}
(JitValue::Float(a), JitValue::Float(b)) => {
let cond = match op {
ComparisonOperator::Equal => FloatCC::Equal,
ComparisonOperator::NotEqual => FloatCC::NotEqual,
ComparisonOperator::Less => FloatCC::LessThan,
ComparisonOperator::LessOrEqual => FloatCC::LessThanOrEqual,
ComparisonOperator::Greater => FloatCC::GreaterThan,
ComparisonOperator::GreaterOrEqual => FloatCC::GreaterThanOrEqual,
};
let val = self.builder.ins().fcmp(cond, a, b);
self.stack.push(JitValue::Bool(val));
Ok(())
}
_ => Err(JitCompileError::NotSupported),
}
}
Instruction::UnaryOperation { op, .. } => {
let op = op.get(arg);
let a = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
match (op, a) {
(UnaryOperator::Minus, JitValue::Int(val)) => {
// Compile minus as 0 - a.
let zero = self.builder.ins().iconst(types::I64, 0);
let out = self.compile_sub(zero, val);
self.stack.push(JitValue::Int(out));
Ok(())
}
(UnaryOperator::Plus, JitValue::Int(val)) => {
// Nothing to do
self.stack.push(JitValue::Int(val));
Ok(())
}
(UnaryOperator::Not, a) => {
let boolean = self.boolean_val(a)?;
let not_boolean = self.builder.ins().bxor_imm(boolean, 1);
self.stack.push(JitValue::Bool(not_boolean));
Ok(())
}
_ => Err(JitCompileError::NotSupported),
}
}
Instruction::BinaryOperation { op } | Instruction::BinaryOperationInplace { op } => {
let op = op.get(arg);
// the rhs is popped off first
let b = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let a = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
let a_type = a.to_jit_type();
let b_type = b.to_jit_type();
let val = match (op, a, b) {
(BinaryOperator::Add, JitValue::Int(a), JitValue::Int(b)) => {
let (out, carry) = self.builder.ins().sadd_overflow(a, b);
self.builder.ins().trapnz(carry, TrapCode::INTEGER_OVERFLOW);
JitValue::Int(out)
}
(BinaryOperator::Subtract, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.compile_sub(a, b))
}
(BinaryOperator::FloorDivide, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().sdiv(a, b))
}
(BinaryOperator::Divide, JitValue::Int(a), JitValue::Int(b)) => {
// Check if b == 0, If so trap with a division by zero error
self.builder
.ins()
.trapz(b, TrapCode::INTEGER_DIVISION_BY_ZERO);
// Else convert to float and divide
let a_float = self.builder.ins().fcvt_from_sint(types::F64, a);
let b_float = self.builder.ins().fcvt_from_sint(types::F64, b);
JitValue::Float(self.builder.ins().fdiv(a_float, b_float))
}
(BinaryOperator::Multiply, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().imul(a, b))
}
(BinaryOperator::Modulo, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().srem(a, b))
}
(BinaryOperator::Power, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.compile_ipow(a, b))
}
(
BinaryOperator::Lshift | BinaryOperator::Rshift,
JitValue::Int(a),
JitValue::Int(b),
) => {
// Shifts throw an exception if we have a negative shift count
// Remove all bits except the sign bit, and trap if its 1 (i.e. negative).
let sign = self.builder.ins().ushr_imm(b, 63);
self.builder.ins().trapnz(
sign,
TrapCode::user(CustomTrapCode::NegativeShiftCount as u8).unwrap(),
);
let out = if op == BinaryOperator::Lshift {
self.builder.ins().ishl(a, b)
} else {
self.builder.ins().sshr(a, b)
};
JitValue::Int(out)
}
(BinaryOperator::And, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().band(a, b))
}
(BinaryOperator::Or, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().bor(a, b))
}
(BinaryOperator::Xor, JitValue::Int(a), JitValue::Int(b)) => {
JitValue::Int(self.builder.ins().bxor(a, b))
}
// Floats
(BinaryOperator::Add, JitValue::Float(a), JitValue::Float(b)) => {
JitValue::Float(self.builder.ins().fadd(a, b))
}
(BinaryOperator::Subtract, JitValue::Float(a), JitValue::Float(b)) => {
JitValue::Float(self.builder.ins().fsub(a, b))
}
(BinaryOperator::Multiply, JitValue::Float(a), JitValue::Float(b)) => {
JitValue::Float(self.builder.ins().fmul(a, b))
}
(BinaryOperator::Divide, JitValue::Float(a), JitValue::Float(b)) => {
JitValue::Float(self.builder.ins().fdiv(a, b))
}
(BinaryOperator::Power, JitValue::Float(a), JitValue::Float(b)) => {
JitValue::Float(self.compile_fpow(a, b))
}
// Floats and Integers
(_, JitValue::Int(a), JitValue::Float(b))
| (_, JitValue::Float(a), JitValue::Int(b)) => {
let operand_one = match a_type.unwrap() {
JitType::Int => self.builder.ins().fcvt_from_sint(types::F64, a),
_ => a,
};
let operand_two = match b_type.unwrap() {
JitType::Int => self.builder.ins().fcvt_from_sint(types::F64, b),
_ => b,
};
match op {
BinaryOperator::Add => {
JitValue::Float(self.builder.ins().fadd(operand_one, operand_two))
}
BinaryOperator::Subtract => {
JitValue::Float(self.builder.ins().fsub(operand_one, operand_two))
}
BinaryOperator::Multiply => {
JitValue::Float(self.builder.ins().fmul(operand_one, operand_two))
}
BinaryOperator::Divide => {
JitValue::Float(self.builder.ins().fdiv(operand_one, operand_two))
}
BinaryOperator::Power => {
JitValue::Float(self.compile_fpow(operand_one, operand_two))
}
_ => return Err(JitCompileError::NotSupported),
}
}
_ => return Err(JitCompileError::NotSupported),
};
self.stack.push(val);
Ok(())
}
Instruction::SetupLoop => {
let loop_head = self.builder.create_block();
self.builder.ins().jump(loop_head, &[]);
self.builder.switch_to_block(loop_head);
Ok(())
}
Instruction::PopBlock => {
// TODO: block support
Ok(())
}
Instruction::LoadGlobal(idx) => {
let name = &bytecode.names[idx.get(arg) as usize];
if name.as_ref() != bytecode.obj_name.as_ref() {
Err(JitCompileError::NotSupported)
} else {
self.stack.push(JitValue::FuncRef(func_ref));
Ok(())
}
}
Instruction::CallFunctionPositional { nargs } => {
let nargs = nargs.get(arg);
let mut args = Vec::new();
for _ in 0..nargs {
let arg = self.stack.pop().ok_or(JitCompileError::BadBytecode)?;
args.push(arg.into_value().unwrap());
}
match self.stack.pop().ok_or(JitCompileError::BadBytecode)? {
JitValue::FuncRef(reference) => {
let call = self.builder.ins().call(reference, &args);
let returns = self.builder.inst_results(call);
self.stack.push(JitValue::Int(returns[0]));
Ok(())
}
_ => Err(JitCompileError::BadBytecode),
}
}
Instruction::Nop => Ok(()),
Instruction::Swap { index } => {
let len = self.stack.len();
let i = len - 1;
let j = len - 1 - index.get(arg) as usize;
self.stack.swap(i, j);
Ok(())
}
Instruction::Pop => {
self.stack.pop();
Ok(())
}
Instruction::Resume { arg: _resume_arg } => {
// TODO: Implement the resume instruction
Ok(())
}
_ => Err(JitCompileError::NotSupported),
}
}
fn compile_sub(&mut self, a: Value, b: Value) -> Value {
let (out, carry) = self.builder.ins().ssub_overflow(a, b);
self.builder.ins().trapnz(carry, TrapCode::INTEGER_OVERFLOW);
out
}
/// Creates a double–double (DDValue) from a regular f64 constant.
/// The high part is set to x and the low part is set to 0.0.
fn dd_from_f64(&mut self, x: f64) -> DDValue {
DDValue {
hi: self.builder.ins().f64const(x),
lo: self.builder.ins().f64const(0.0),
}
}
/// Creates a DDValue from a Value (assumed to represent an f64).
/// This function initializes the high part with x and the low part to 0.0.
fn dd_from_value(&mut self, x: Value) -> DDValue {
DDValue {
hi: x,
lo: self.builder.ins().f64const(0.0),
}
}
/// Creates a DDValue from two f64 parts.
/// The 'hi' parameter sets the high part and 'lo' sets the low part.
fn dd_from_parts(&mut self, hi: f64, lo: f64) -> DDValue {
DDValue {
hi: self.builder.ins().f64const(hi),
lo: self.builder.ins().f64const(lo),
}
}
/// Converts a DDValue back to a single f64 value by adding the high and low parts.
fn dd_to_f64(&mut self, dd: DDValue) -> Value {
self.builder.ins().fadd(dd.hi, dd.lo)
}
/// Computes the negation of a DDValue.
/// It subtracts both the high and low parts from zero.
fn dd_neg(&mut self, dd: DDValue) -> DDValue {
let zero = self.builder.ins().f64const(0.0);
DDValue {
hi: self.builder.ins().fsub(zero, dd.hi),
lo: self.builder.ins().fsub(zero, dd.lo),
}
}
/// Adds two DDValue numbers using error-free transformations to maintain extra precision.
/// It carefully adds the high parts, computes the rounding error, adds the low parts along with the error,
/// and then normalizes the result.
fn dd_add(&mut self, a: DDValue, b: DDValue) -> DDValue {
// Compute the sum of the high parts.
let s = self.builder.ins().fadd(a.hi, b.hi);
// Compute t = s - a.hi to capture part of the rounding error.
let t = self.builder.ins().fsub(s, a.hi);
// Compute the error e from the high part additions.
let s_minus_t = self.builder.ins().fsub(s, t);
let part1 = self.builder.ins().fsub(a.hi, s_minus_t);
let part2 = self.builder.ins().fsub(b.hi, t);
let e = self.builder.ins().fadd(part1, part2);
// Sum the low parts along with the error.
let lo = self.builder.ins().fadd(a.lo, b.lo);
let lo_sum = self.builder.ins().fadd(lo, e);
// Renormalize: add the low sum to s and compute a new low component.
let hi_new = self.builder.ins().fadd(s, lo_sum);
let hi_new_minus_s = self.builder.ins().fsub(hi_new, s);
let lo_new = self.builder.ins().fsub(lo_sum, hi_new_minus_s);
DDValue {
hi: hi_new,
lo: lo_new,
}
}
/// Subtracts DDValue b from DDValue a by negating b and then using the addition function.
fn dd_sub(&mut self, a: DDValue, b: DDValue) -> DDValue {
let neg_b = self.dd_neg(b);
self.dd_add(a, neg_b)
}
/// Multiplies two DDValue numbers using double–double arithmetic.
/// It calculates the high product, uses a fused multiply–add (FMA) to capture rounding error,
/// computes the cross products, and then normalizes the result.
fn dd_mul(&mut self, a: DDValue, b: DDValue) -> DDValue {
// p = a.hi * b.hi (primary product)
let p = self.builder.ins().fmul(a.hi, b.hi);
// err = fma(a.hi, b.hi, -p) recovers the rounding error.
let zero = self.builder.ins().f64const(0.0);
let neg_p = self.builder.ins().fsub(zero, p);
let err = self.builder.ins().fma(a.hi, b.hi, neg_p);
// Compute cross terms: a.hi*b.lo + a.lo*b.hi.
let a_hi_b_lo = self.builder.ins().fmul(a.hi, b.lo);
let a_lo_b_hi = self.builder.ins().fmul(a.lo, b.hi);
let cross = self.builder.ins().fadd(a_hi_b_lo, a_lo_b_hi);
// Sum p and the cross terms.
let s = self.builder.ins().fadd(p, cross);
// Isolate rounding error from the addition.
let t = self.builder.ins().fsub(s, p);
let s_minus_t = self.builder.ins().fsub(s, t);
let part1 = self.builder.ins().fsub(p, s_minus_t);
let part2 = self.builder.ins().fsub(cross, t);
let e = self.builder.ins().fadd(part1, part2);
// Include the error from the low parts multiplication.
let a_lo_b_lo = self.builder.ins().fmul(a.lo, b.lo);
let err_plus_e = self.builder.ins().fadd(err, e);
let lo_sum = self.builder.ins().fadd(err_plus_e, a_lo_b_lo);
// Renormalize the sum.
let hi_new = self.builder.ins().fadd(s, lo_sum);
let hi_new_minus_s = self.builder.ins().fsub(hi_new, s);
let lo_new = self.builder.ins().fsub(lo_sum, hi_new_minus_s);
DDValue {
hi: hi_new,
lo: lo_new,
}
}
/// Multiplies a DDValue by a regular f64 (Value) using similar techniques as dd_mul.
/// It multiplies both the high and low parts by b, computes the rounding error,
/// and then renormalizes the result.
fn dd_mul_f64(&mut self, a: DDValue, b: Value) -> DDValue {
// p = a.hi * b (primary product)
let p = self.builder.ins().fmul(a.hi, b);
// Compute the rounding error using fma.
let zero = self.builder.ins().f64const(0.0);
let neg_p = self.builder.ins().fsub(zero, p);
let err = self.builder.ins().fma(a.hi, b, neg_p);
// Multiply the low part.
let cross = self.builder.ins().fmul(a.lo, b);
// Sum the primary product and the low multiplication.
let s = self.builder.ins().fadd(p, cross);
// Capture rounding error from addition.
let t = self.builder.ins().fsub(s, p);
let s_minus_t = self.builder.ins().fsub(s, t);
let part1 = self.builder.ins().fsub(p, s_minus_t);
let part2 = self.builder.ins().fsub(cross, t);
let e = self.builder.ins().fadd(part1, part2);
// Combine the error components.
let lo_sum = self.builder.ins().fadd(err, e);
// Renormalize to form the final double–double number.
let hi_new = self.builder.ins().fadd(s, lo_sum);
let hi_new_minus_s = self.builder.ins().fsub(hi_new, s);
let lo_new = self.builder.ins().fsub(lo_sum, hi_new_minus_s);
DDValue {
hi: hi_new,
lo: lo_new,
}
}
/// Scales a DDValue by multiplying both its high and low parts by the given factor.
fn dd_scale(&mut self, dd: DDValue, factor: Value) -> DDValue {
DDValue {
hi: self.builder.ins().fmul(dd.hi, factor),
lo: self.builder.ins().fmul(dd.lo, factor),
}
}
/// Approximates ln(1+f) using its Taylor series expansion in double–double arithmetic.
/// It computes the series ∑ (-1)^(i-1) * f^i / i from i = 1 to 1000 for high precision.
fn dd_ln_1p_series(&mut self, f: Value) -> DDValue {
// Convert f to a DDValue and initialize the sum and term.
let f_dd = self.dd_from_value(f);
let mut sum = f_dd.clone();
let mut term = f_dd;
// Alternating sign starts at -1 for the second term.
let mut sign = -1.0_f64;
let range = 1000;
// Loop over terms from i = 2 to 1000.
for i in 2..=range {
// Compute f^i by multiplying the previous term by f.
term = self.dd_mul_f64(term, f);
// Divide the term by i.
let inv_i = 1.0 / (i as f64);
let c_inv_i = self.builder.ins().f64const(inv_i);
let term_div = self.dd_mul_f64(term.clone(), c_inv_i);
// Multiply by the alternating sign.
let dd_sign = self.dd_from_f64(sign);
let to_add = self.dd_mul(dd_sign, term_div);
// Add the term to the cumulative sum.
sum = self.dd_add(sum, to_add);
// Flip the sign for the next term.
sign = -sign;
}
sum
}
/// Computes the natural logarithm ln(x) in double–double arithmetic.
/// It first checks for domain errors (x ≤ 0 or NaN), then extracts the exponent
/// and mantissa from the bit-level representation of x. It computes ln(mantissa) using
/// the ln(1+f) series and adds k*ln2 to obtain ln(x).
fn dd_ln(&mut self, x: Value) -> DDValue {
// (A) Prepare a DDValue representing NaN.
let dd_nan = self.dd_from_f64(f64::NAN);
// Build a zero constant for comparisons.
let zero_f64 = self.builder.ins().f64const(0.0);
// Check if x is less than or equal to 0 or is NaN.
let cmp_le = self
.builder
.ins()
.fcmp(FloatCC::LessThanOrEqual, x, zero_f64);
let cmp_nan = self.builder.ins().fcmp(FloatCC::Unordered, x, x);
let need_nan = self.builder.ins().bor(cmp_le, cmp_nan);
// (B) Reinterpret the bits of x as an integer.
let bits = self.builder.ins().bitcast(types::I64, MemFlags::new(), x);
// (C) Extract the exponent (top 11 bits) from the bit representation.
let shift_52 = self.builder.ins().ushr_imm(bits, 52);
let exponent_mask = self.builder.ins().iconst(types::I64, 0x7FF);
let exponent = self.builder.ins().band(shift_52, exponent_mask);
// k = exponent - 1023 (unbias the exponent).
let bias = self.builder.ins().iconst(types::I64, 1023);
let k_i64 = self.builder.ins().isub(exponent, bias);
// (D) Extract the fraction (mantissa) from the lower 52 bits.
let fraction_mask = self.builder.ins().iconst(types::I64, 0x000F_FFFF_FFFF_FFFF);
let fraction_part = self.builder.ins().band(bits, fraction_mask);
// (E) For normal numbers (exponent ≠ 0), add the implicit leading 1.
let implicit_one = self.builder.ins().iconst(types::I64, 1 << 52);
let zero_exp = self.builder.ins().icmp_imm(IntCC::Equal, exponent, 0);
let frac_one_bor = self.builder.ins().bor(fraction_part, implicit_one);
let fraction_with_leading_one = self.builder.ins().select(
zero_exp,
fraction_part, // For subnormals, do not add the implicit 1.
frac_one_bor,
);
// (F) Force the exponent bits to 1023, yielding a mantissa m in [1, 2).
let new_exp = self.builder.ins().iconst(types::I64, 0x3FF0_0000_0000_0000);
let fraction_bits = self.builder.ins().bor(fraction_with_leading_one, new_exp);
let m = self
.builder
.ins()
.bitcast(types::F64, MemFlags::new(), fraction_bits);
// (G) Compute ln(m) using the series ln(1+f) with f = m - 1.
let one_f64 = self.builder.ins().f64const(1.0);
let f_val = self.builder.ins().fsub(m, one_f64);
let dd_ln_m = self.dd_ln_1p_series(f_val);
// (H) Compute k*ln2 in double–double arithmetic.
let ln2_dd = self.dd_from_parts(
f64::from_bits(0x3fe62e42fefa39ef),
f64::from_bits(0x3c7abc9e3b39803f),
);
let k_f64 = self.builder.ins().fcvt_from_sint(types::F64, k_i64);
let dd_ln2_k = self.dd_mul_f64(ln2_dd, k_f64);
// Add ln(m) and k*ln2 to get the final ln(x).
let normal_result = self.dd_add(dd_ln_m, dd_ln2_k);
// (I) If x was nonpositive or NaN, return NaN; otherwise, return the computed result.
let final_hi = self
.builder
.ins()
.select(need_nan, dd_nan.hi, normal_result.hi);
let final_lo = self
.builder
.ins()
.select(need_nan, dd_nan.lo, normal_result.lo);
DDValue {
hi: final_hi,
lo: final_lo,
}
}
/// Computes the exponential function exp(x) in double–double arithmetic.
/// It uses range reduction to write x = k*ln2 + r, computes exp(r) via a Taylor series,
/// scales the result by 2^k, and handles overflow by checking if k exceeds the maximum.
fn dd_exp(&mut self, dd: DDValue) -> DDValue {
// (A) Range reduction: Convert dd to a single f64 value.
let x = self.dd_to_f64(dd.clone());
let ln2_f64 = self
.builder
.ins()
.f64const(f64::from_bits(0x3fe62e42fefa39ef));
let div = self.builder.ins().fdiv(x, ln2_f64);
let half = self.builder.ins().f64const(0.5);
let div_plus_half = self.builder.ins().fadd(div, half);
// Rounding: floor(div + 0.5) gives the nearest integer k.
let k = self.builder.ins().fcvt_to_sint(types::I64, div_plus_half);
// --- OVERFLOW CHECK ---
// Check if k is greater than the maximum exponent for finite doubles (1023).
let max_k = self.builder.ins().iconst(types::I64, 1023);
let is_overflow = self.builder.ins().icmp(IntCC::SignedGreaterThan, k, max_k);
// Define infinity and zero for the overflow case.
let inf = self.builder.ins().f64const(f64::INFINITY);
let zero = self.builder.ins().f64const(0.0);
// (B) Compute exp(x) normally when not overflowing.
// Compute k*ln2 in double–double arithmetic and subtract it from x.
let ln2_dd = self.dd_from_parts(
f64::from_bits(0x3fe62e42fefa39ef),
f64::from_bits(0x3c7abc9e3b39803f),
);
let k_f64 = self.builder.ins().fcvt_from_sint(types::F64, k);
let k_ln2 = self.dd_mul_f64(ln2_dd, k_f64);
let r = self.dd_sub(dd, k_ln2);
// Compute exp(r) using a Taylor series.
let mut sum = self.dd_from_f64(1.0); // Initialize sum to 1.
let mut term = self.dd_from_f64(1.0); // Initialize the first term to 1.
let n_terms = 1000;
for i in 1..=n_terms {
term = self.dd_mul(term, r.clone());
let inv = 1.0 / (i as f64);
let inv_const = self.builder.ins().f64const(inv);
term = self.dd_mul_f64(term, inv_const);
sum = self.dd_add(sum, term.clone());
}
// Reconstruct the final result by scaling with 2^k.
let bias = self.builder.ins().iconst(types::I64, 1023);
let k_plus_bias = self.builder.ins().iadd(k, bias);
let shift_count = self.builder.ins().iconst(types::I64, 52);
let shifted = self.builder.ins().ishl(k_plus_bias, shift_count);
let two_to_k = self
.builder
.ins()
.bitcast(types::F64, MemFlags::new(), shifted);
let result = self.dd_scale(sum, two_to_k);
// (C) If overflow was detected, return infinity; otherwise, return the computed value.
let final_hi = self.builder.ins().select(is_overflow, inf, result.hi);
let final_lo = self.builder.ins().select(is_overflow, zero, result.lo);
DDValue {
hi: final_hi,
lo: final_lo,
}
}
/// Computes the power function a^b (f_pow) for f64 values using double–double arithmetic for high precision.
/// It handles different cases for the base 'a':
/// - For a > 0: Computes exp(b * ln(a)).
/// - For a == 0: Handles special cases for 0^b, including returning 0, 1, or a domain error.
/// - For a < 0: Allows only an integer exponent b and adjusts the sign if b is odd.
fn compile_fpow(&mut self, a: Value, b: Value) -> Value {
let f64_ty = types::F64;
let i64_ty = types::I64;
let zero_f = self.builder.ins().f64const(0.0);
let one_f = self.builder.ins().f64const(1.0);
let nan_f = self.builder.ins().f64const(f64::NAN);
let inf_f = self.builder.ins().f64const(f64::INFINITY);
let neg_inf_f = self.builder.ins().f64const(f64::NEG_INFINITY);
// Merge block for final result.
let merge_block = self.builder.create_block();
self.builder.append_block_param(merge_block, f64_ty);
// --- Edge Case 1: b == 0.0 → return 1.0
let cmp_b_zero = self.builder.ins().fcmp(FloatCC::Equal, b, zero_f);
let b_zero_block = self.builder.create_block();
let continue_block = self.builder.create_block();
self.builder
.ins()
.brif(cmp_b_zero, b_zero_block, &[], continue_block, &[]);
self.builder.switch_to_block(b_zero_block);
self.builder.ins().jump(merge_block, &[one_f]);
self.builder.switch_to_block(continue_block);
// --- Edge Case 2: b is NaN → return NaN
let cmp_b_nan = self.builder.ins().fcmp(FloatCC::Unordered, b, b);
let b_nan_block = self.builder.create_block();
let continue_block2 = self.builder.create_block();
self.builder
.ins()
.brif(cmp_b_nan, b_nan_block, &[], continue_block2, &[]);
self.builder.switch_to_block(b_nan_block);
self.builder.ins().jump(merge_block, &[nan_f]);
self.builder.switch_to_block(continue_block2);