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//! Algebraic simplification for the lowered IR.
//!
//! Applies constant folding and algebraic identities to [`LoweredOp`] trees.
//! Also provides canonical pattern recognition (e.g. `sin(x)/cos(x) → tan(x)`).
use crate::lower::LoweredOp;
/// Compute a u64 structural hash of a `LoweredOp` node using `DefaultHasher`.
///
/// Used internally for structural-equality checks in the simplifier's
/// canonical pattern recognisers (e.g. `sin(x)/cos(x) → tan(x)`).
pub(crate) fn ops_struct_hash(op: &LoweredOp) -> u64 {
use std::collections::hash_map::DefaultHasher;
use std::hash::Hasher;
let mut h = DefaultHasher::new();
op.structural_hash(&mut h);
h.finish()
}
impl LoweredOp {
/// Simplify the lowered operation tree.
///
/// Applies constant folding and algebraic simplifications.
pub fn simplify(&self) -> Self {
match self {
Self::Add(a, b) => {
let a_s = a.simplify();
let b_s = b.simplify();
// 0 + x = x
if let Self::Const(c) = &a_s {
if c.abs() < 1e-15 {
return b_s;
}
}
// x + 0 = x
if let Self::Const(c) = &b_s {
if c.abs() < 1e-15 {
return a_s;
}
}
// const + const
if let (Self::Const(a_c), Self::Const(b_c)) = (&a_s, &b_s) {
return Self::Const(a_c + b_c);
}
// a + (-b) = a - b
if let Self::Neg(inner) = &b_s {
return Self::Sub(Box::new(a_s), inner.clone());
}
Self::Add(Box::new(a_s), Box::new(b_s))
}
Self::Sub(a, b) => {
let a_s = a.simplify();
let b_s = b.simplify();
// x - 0 = x
if let Self::Const(c) = &b_s {
if c.abs() < 1e-15 {
return a_s;
}
}
// 0 - x = -x
if let Self::Const(c) = &a_s {
if c.abs() < 1e-15 {
return Self::Neg(Box::new(b_s));
}
}
if let (Self::Const(a_c), Self::Const(b_c)) = (&a_s, &b_s) {
return Self::Const(a_c - b_c);
}
// a - (-b) = a + b
if let Self::Neg(inner) = &b_s {
return Self::Add(Box::new(a_s), inner.clone());
}
Self::Sub(Box::new(a_s), Box::new(b_s))
}
Self::Mul(a, b) => {
let a_s = a.simplify();
let b_s = b.simplify();
// 0 * x = 0
if let Self::Const(c) = &a_s {
if c.abs() < 1e-15 {
return Self::Const(0.0);
}
}
if let Self::Const(c) = &b_s {
if c.abs() < 1e-15 {
return Self::Const(0.0);
}
}
// 1 * x = x
if let Self::Const(c) = &a_s {
if (*c - 1.0).abs() < 1e-15 {
return b_s;
}
}
if let Self::Const(c) = &b_s {
if (*c - 1.0).abs() < 1e-15 {
return a_s;
}
}
if let (Self::Const(a_c), Self::Const(b_c)) = (&a_s, &b_s) {
return Self::Const(a_c * b_c);
}
// -1 * x = -x
if let Self::Const(c) = &a_s {
if (*c + 1.0).abs() < 1e-15 {
return Self::Neg(Box::new(b_s));
}
}
// x * -1 = -x
if let Self::Const(c) = &b_s {
if (*c + 1.0).abs() < 1e-15 {
return Self::Neg(Box::new(a_s));
}
}
Self::Mul(Box::new(a_s), Box::new(b_s))
}
Self::Div(a, b) => {
let a_s = a.simplify();
let b_s = b.simplify();
// x / 1 = x
if let Self::Const(c) = &b_s {
if (*c - 1.0).abs() < 1e-15 {
return a_s;
}
}
// Canonical pattern recognizer: sin(x) / cos(x) -> tan(x)
if let (Self::Sin(sa), Self::Cos(ca)) = (&a_s, &b_s) {
if ops_struct_hash(sa) == ops_struct_hash(ca) {
return Self::Tan(sa.clone());
}
}
// Canonical pattern recognizer: sinh(x) / cosh(x) -> tanh(x)
if let (Self::Sinh(sa), Self::Cosh(ca)) = (&a_s, &b_s) {
if ops_struct_hash(sa) == ops_struct_hash(ca) {
return Self::Tanh(sa.clone());
}
}
// Canonical pattern recognizer: (exp(x) - exp(-x)) / 2 -> sinh(x)
// a_s must be Sub(Exp(x), Exp(Neg(x))) and b_s must be Const(2.0)
if let Self::Const(d) = &b_s {
if (*d - 2.0).abs() < 1e-15 {
if let Self::Sub(sub_a, sub_b) = &a_s {
if let (Self::Exp(ea), Self::Exp(eb)) = (sub_a.as_ref(), sub_b.as_ref())
{
if let Self::Neg(neg_inner) = eb.as_ref() {
if ops_struct_hash(ea) == ops_struct_hash(neg_inner) {
return Self::Sinh(ea.clone());
}
}
}
}
}
}
// Canonical pattern recognizer: (exp(x) + exp(-x)) / 2 -> cosh(x)
// a_s must be Add(Exp(x), Exp(Neg(x))) and b_s must be Const(2.0)
if let Self::Const(d) = &b_s {
if (*d - 2.0).abs() < 1e-15 {
if let Self::Add(add_a, add_b) = &a_s {
if let (Self::Exp(ea), Self::Exp(eb)) = (add_a.as_ref(), add_b.as_ref())
{
if let Self::Neg(neg_inner) = eb.as_ref() {
if ops_struct_hash(ea) == ops_struct_hash(neg_inner) {
return Self::Cosh(ea.clone());
}
}
}
}
}
}
// Constant folding (propagates NaN/Inf)
if let (Self::Const(a_c), Self::Const(b_c)) = (&a_s, &b_s) {
return Self::Const(a_c / b_c);
}
Self::Div(Box::new(a_s), Box::new(b_s))
}
Self::Exp(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
if c.abs() < 1e-15 {
return Self::Const(1.0); // exp(0) = 1
}
// General const fold: exp(c), propagates NaN/Inf as-is
return Self::Const(c.exp());
}
// exp(ln(x)) = x
if let Self::Ln(inner) = &a_s {
return *inner.clone();
}
Self::Exp(Box::new(a_s))
}
Self::Ln(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
if (*c - 1.0).abs() < 1e-15 {
return Self::Const(0.0); // ln(1) = 0
}
// General const fold: ln(c), propagates NaN for c <= 0
return Self::Const(c.ln());
}
// ln(exp(x)) = x
if let Self::Exp(inner) = &a_s {
return *inner.clone();
}
Self::Ln(Box::new(a_s))
}
Self::Neg(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(-c);
}
// neg(neg(x)) = x
if let Self::Neg(inner) = &a_s {
return *inner.clone();
}
// -(a - b) = b - a
if let Self::Sub(lhs, rhs) = &a_s {
return Self::Sub(rhs.clone(), lhs.clone());
}
Self::Neg(Box::new(a_s))
}
Self::Pow(a, b) => {
let a_s = a.simplify();
let b_s = b.simplify();
// x^0 = 1
if let Self::Const(c) = &b_s {
if c.abs() < 1e-15 {
return Self::Const(1.0);
}
// x^1 = x
if (*c - 1.0).abs() < 1e-15 {
return a_s;
}
}
// Constant folding: propagates NaN/Inf as-is
if let (Self::Const(a_c), Self::Const(b_c)) = (&a_s, &b_s) {
return Self::Const(a_c.powf(*b_c));
}
Self::Pow(Box::new(a_s), Box::new(b_s))
}
Self::Sin(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.sin());
}
// sin(arcsin(x)) -> x
if let Self::Arcsin(inner) = &a_s {
return *inner.clone();
}
Self::Sin(Box::new(a_s))
}
Self::Cos(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.cos());
}
// Canonical pattern recognizer: cos(arccos(x)) -> x
if let Self::Arccos(inner) = &a_s {
return *inner.clone();
}
Self::Cos(Box::new(a_s))
}
Self::Tan(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.tan());
}
// tan(arctan(x)) -> x
if let Self::Arctan(inner) = &a_s {
return *inner.clone();
}
Self::Tan(Box::new(a_s))
}
Self::Sinh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.sinh());
}
// sinh(arcsinh(x)) -> x
if let Self::Arcsinh(inner) = &a_s {
return *inner.clone();
}
Self::Sinh(Box::new(a_s))
}
Self::Cosh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.cosh());
}
// cosh(arccosh(x)) -> x
if let Self::Arccosh(inner) = &a_s {
return *inner.clone();
}
Self::Cosh(Box::new(a_s))
}
Self::Tanh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.tanh());
}
// tanh(arctanh(x)) -> x
if let Self::Arctanh(inner) = &a_s {
return *inner.clone();
}
Self::Tanh(Box::new(a_s))
}
Self::Arcsin(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.asin());
}
Self::Arcsin(Box::new(a_s))
}
Self::Arccos(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.acos());
}
Self::Arccos(Box::new(a_s))
}
Self::Arctan(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.atan());
}
Self::Arctan(Box::new(a_s))
}
Self::Arcsinh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.asinh());
}
Self::Arcsinh(Box::new(a_s))
}
Self::Arccosh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.acosh());
}
Self::Arccosh(Box::new(a_s))
}
Self::Arctanh(a) => {
let a_s = a.simplify();
if let Self::Const(c) = &a_s {
return Self::Const(c.atanh());
}
Self::Arctanh(Box::new(a_s))
}
Self::Const(_) | Self::Var(_) | Self::NamedConst(_) => self.clone(),
}
}
}