[Mlir-commits] [mlir] 2ff43ce - Restore #91137 (#92003)

llvmlistbot at llvm.org llvmlistbot at llvm.org
Tue May 14 09:45:43 PDT 2024


Author: Jeremy Kun
Date: 2024-05-14T09:45:39-07:00
New Revision: 2ff43ce87e66d9324370e35ea6743ef57400c76e

URL: https://github.com/llvm/llvm-project/commit/2ff43ce87e66d9324370e35ea6743ef57400c76e
DIFF: https://github.com/llvm/llvm-project/commit/2ff43ce87e66d9324370e35ea6743ef57400c76e.diff

LOG: Restore #91137 (#92003)

#91137 reverted in #92001

A build error fix added in 28d5ece8ca93ef04fee9b0258b70b750b66c05ca

---------

Co-authored-by: Jeremy Kun <j2kun at users.noreply.github.com>

Added: 
    

Modified: 
    mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.h
    mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.td
    mlir/lib/Dialect/Polynomial/IR/Polynomial.cpp
    mlir/lib/Dialect/Polynomial/IR/PolynomialAttributes.cpp
    mlir/test/Dialect/Polynomial/attributes.mlir
    mlir/test/Dialect/Polynomial/ops.mlir
    mlir/test/Dialect/Polynomial/ops_errors.mlir
    mlir/test/Dialect/Polynomial/types.mlir

Removed: 
    


################################################################################
diff  --git a/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.h b/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.h
index 3325a6fa3f9fc..7f44c29a98707 100644
--- a/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.h
+++ b/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.h
@@ -11,10 +11,13 @@
 
 #include "mlir/Support/LLVM.h"
 #include "mlir/Support/LogicalResult.h"
+#include "llvm/ADT/APFloat.h"
 #include "llvm/ADT/APInt.h"
 #include "llvm/ADT/ArrayRef.h"
 #include "llvm/ADT/Hashing.h"
-#include "llvm/ADT/SmallVector.h"
+#include "llvm/ADT/SmallString.h"
+#include "llvm/ADT/Twine.h"
+#include "llvm/Support/raw_ostream.h"
 
 namespace mlir {
 
@@ -27,98 +30,202 @@ namespace polynomial {
 /// would want to specify 128-bit polynomials statically in the source code.
 constexpr unsigned apintBitWidth = 64;
 
-/// A class representing a monomial of a single-variable polynomial with integer
-/// coefficients.
-class Monomial {
+template <typename CoefficientType>
+class MonomialBase {
 public:
-  Monomial(int64_t coeff, uint64_t expo)
-      : coefficient(apintBitWidth, coeff), exponent(apintBitWidth, expo) {}
-
-  Monomial(const APInt &coeff, const APInt &expo)
+  MonomialBase(const CoefficientType &coeff, const APInt &expo)
       : coefficient(coeff), exponent(expo) {}
+  virtual ~MonomialBase() = default;
 
-  Monomial() : coefficient(apintBitWidth, 0), exponent(apintBitWidth, 0) {}
+  const CoefficientType &getCoefficient() const { return coefficient; }
+  CoefficientType &getMutableCoefficient() { return coefficient; }
+  const APInt &getExponent() const { return exponent; }
+  void setCoefficient(const CoefficientType &coeff) { coefficient = coeff; }
+  void setExponent(const APInt &exp) { exponent = exp; }
 
-  bool operator==(const Monomial &other) const {
+  bool operator==(const MonomialBase &other) const {
     return other.coefficient == coefficient && other.exponent == exponent;
   }
-  bool operator!=(const Monomial &other) const {
+  bool operator!=(const MonomialBase &other) const {
     return other.coefficient != coefficient || other.exponent != exponent;
   }
 
   /// Monomials are ordered by exponent.
-  bool operator<(const Monomial &other) const {
+  bool operator<(const MonomialBase &other) const {
     return (exponent.ult(other.exponent));
   }
 
-  friend ::llvm::hash_code hash_value(const Monomial &arg);
+  virtual bool isMonic() const = 0;
+  virtual void
+  coefficientToString(llvm::SmallString<16> &coeffString) const = 0;
 
-public:
-  APInt coefficient;
+  template <typename T>
+  friend ::llvm::hash_code hash_value(const MonomialBase<T> &arg);
 
-  // Always unsigned
+protected:
+  CoefficientType coefficient;
   APInt exponent;
 };
 
-/// A single-variable polynomial with integer coefficients.
-///
-/// Eg: x^1024 + x + 1
-///
-/// The symbols used as the polynomial's indeterminate don't matter, so long as
-/// it is used consistently throughout the polynomial.
-class Polynomial {
+/// A class representing a monomial of a single-variable polynomial with integer
+/// coefficients.
+class IntMonomial : public MonomialBase<APInt> {
 public:
-  Polynomial() = delete;
+  IntMonomial(int64_t coeff, uint64_t expo)
+      : MonomialBase(APInt(apintBitWidth, coeff), APInt(apintBitWidth, expo)) {}
 
-  explicit Polynomial(ArrayRef<Monomial> terms) : terms(terms){};
+  IntMonomial()
+      : MonomialBase(APInt(apintBitWidth, 0), APInt(apintBitWidth, 0)) {}
 
-  // Returns a Polynomial from a list of monomials.
-  // Fails if two monomials have the same exponent.
-  static FailureOr<Polynomial> fromMonomials(ArrayRef<Monomial> monomials);
+  ~IntMonomial() = default;
 
-  /// Returns a polynomial with coefficients given by `coeffs`. The value
-  /// coeffs[i] is converted to a monomial with exponent i.
-  static Polynomial fromCoefficients(ArrayRef<int64_t> coeffs);
+  bool isMonic() const override { return coefficient == 1; }
+
+  void coefficientToString(llvm::SmallString<16> &coeffString) const override {
+    coefficient.toStringSigned(coeffString);
+  }
+};
+
+/// A class representing a monomial of a single-variable polynomial with integer
+/// coefficients.
+class FloatMonomial : public MonomialBase<APFloat> {
+public:
+  FloatMonomial(double coeff, uint64_t expo)
+      : MonomialBase(APFloat(coeff), APInt(apintBitWidth, expo)) {}
+
+  FloatMonomial() : MonomialBase(APFloat((double)0), APInt(apintBitWidth, 0)) {}
+
+  ~FloatMonomial() = default;
+
+  bool isMonic() const override { return coefficient == APFloat(1.0); }
+
+  void coefficientToString(llvm::SmallString<16> &coeffString) const override {
+    coefficient.toString(coeffString);
+  }
+};
+
+template <typename Monomial>
+class PolynomialBase {
+public:
+  PolynomialBase() = delete;
+
+  explicit PolynomialBase(ArrayRef<Monomial> terms) : terms(terms) {};
 
   explicit operator bool() const { return !terms.empty(); }
-  bool operator==(const Polynomial &other) const {
+  bool operator==(const PolynomialBase &other) const {
     return other.terms == terms;
   }
-  bool operator!=(const Polynomial &other) const {
+  bool operator!=(const PolynomialBase &other) const {
     return !(other.terms == terms);
   }
 
-  // Prints polynomial to 'os'.
-  void print(raw_ostream &os) const;
   void print(raw_ostream &os, ::llvm::StringRef separator,
-             ::llvm::StringRef exponentiation) const;
+             ::llvm::StringRef exponentiation) const {
+    bool first = true;
+    for (const Monomial &term : getTerms()) {
+      if (first) {
+        first = false;
+      } else {
+        os << separator;
+      }
+      std::string coeffToPrint;
+      if (term.isMonic() && term.getExponent().uge(1)) {
+        coeffToPrint = "";
+      } else {
+        llvm::SmallString<16> coeffString;
+        term.coefficientToString(coeffString);
+        coeffToPrint = coeffString.str();
+      }
+
+      if (term.getExponent() == 0) {
+        os << coeffToPrint;
+      } else if (term.getExponent() == 1) {
+        os << coeffToPrint << "x";
+      } else {
+        llvm::SmallString<16> expString;
+        term.getExponent().toStringSigned(expString);
+        os << coeffToPrint << "x" << exponentiation << expString;
+      }
+    }
+  }
+
+  // Prints polynomial to 'os'.
+  void print(raw_ostream &os) const { print(os, " + ", "**"); }
+
   void dump() const;
 
   // Prints polynomial so that it can be used as a valid identifier
-  std::string toIdentifier() const;
+  std::string toIdentifier() const {
+    std::string result;
+    llvm::raw_string_ostream os(result);
+    print(os, "_", "");
+    return os.str();
+  }
 
-  unsigned getDegree() const;
+  unsigned getDegree() const {
+    return terms.back().getExponent().getZExtValue();
+  }
 
   ArrayRef<Monomial> getTerms() const { return terms; }
 
-  friend ::llvm::hash_code hash_value(const Polynomial &arg);
+  template <typename T>
+  friend ::llvm::hash_code hash_value(const PolynomialBase<T> &arg);
 
 private:
   // The monomial terms for this polynomial.
   SmallVector<Monomial> terms;
 };
 
-// Make Polynomial hashable.
-inline ::llvm::hash_code hash_value(const Polynomial &arg) {
+/// A single-variable polynomial with integer coefficients.
+///
+/// Eg: x^1024 + x + 1
+class IntPolynomial : public PolynomialBase<IntMonomial> {
+public:
+  explicit IntPolynomial(ArrayRef<IntMonomial> terms) : PolynomialBase(terms) {}
+
+  // Returns a Polynomial from a list of monomials.
+  // Fails if two monomials have the same exponent.
+  static FailureOr<IntPolynomial>
+  fromMonomials(ArrayRef<IntMonomial> monomials);
+
+  /// Returns a polynomial with coefficients given by `coeffs`. The value
+  /// coeffs[i] is converted to a monomial with exponent i.
+  static IntPolynomial fromCoefficients(ArrayRef<int64_t> coeffs);
+};
+
+/// A single-variable polynomial with double coefficients.
+///
+/// Eg: 1.0 x^1024 + 3.5 x + 1e-05
+class FloatPolynomial : public PolynomialBase<FloatMonomial> {
+public:
+  explicit FloatPolynomial(ArrayRef<FloatMonomial> terms)
+      : PolynomialBase(terms) {}
+
+  // Returns a Polynomial from a list of monomials.
+  // Fails if two monomials have the same exponent.
+  static FailureOr<FloatPolynomial>
+  fromMonomials(ArrayRef<FloatMonomial> monomials);
+
+  /// Returns a polynomial with coefficients given by `coeffs`. The value
+  /// coeffs[i] is converted to a monomial with exponent i.
+  static FloatPolynomial fromCoefficients(ArrayRef<double> coeffs);
+};
+
+// Make Polynomials hashable.
+template <typename T>
+inline ::llvm::hash_code hash_value(const PolynomialBase<T> &arg) {
   return ::llvm::hash_combine_range(arg.terms.begin(), arg.terms.end());
 }
 
-inline ::llvm::hash_code hash_value(const Monomial &arg) {
+template <typename T>
+inline ::llvm::hash_code hash_value(const MonomialBase<T> &arg) {
   return llvm::hash_combine(::llvm::hash_value(arg.coefficient),
                             ::llvm::hash_value(arg.exponent));
 }
 
-inline raw_ostream &operator<<(raw_ostream &os, const Polynomial &polynomial) {
+template <typename T>
+inline raw_ostream &operator<<(raw_ostream &os,
+                               const PolynomialBase<T> &polynomial) {
   polynomial.print(os);
   return os;
 }

diff  --git a/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.td b/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.td
index ed1f4ce8b7e59..ae8484501a50d 100644
--- a/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.td
+++ b/mlir/include/mlir/Dialect/Polynomial/IR/Polynomial.td
@@ -39,14 +39,14 @@ def Polynomial_Dialect : Dialect {
     %a = polynomial.constant <1 + x**2 - 3x**3> : polynomial.polynomial<#ring>
 
     // A constant polynomial in a ring with i32 coefficients, modulo (x^1024 + 1)
-    #modulus = #polynomial.polynomial<1 + x**1024>
+    #modulus = #polynomial.int_polynomial<1 + x**1024>
     #ring = #polynomial.ring<coefficientType=i32, polynomialModulus=#modulus>
     %a = polynomial.constant <1 + x**2 - 3x**3> : polynomial.polynomial<#ring>
 
     // A constant polynomial in a ring with i32 coefficients, with a polynomial
     // modulus of (x^1024 + 1) and a coefficient modulus of 17.
-    #modulus = #polynomial.polynomial<1 + x**1024>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=17, polynomialModulus=#modulus>
+    #modulus = #polynomial.int_polynomial<1 + x**1024>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=17:i32, polynomialModulus=#modulus>
     %a = polynomial.constant <1 + x**2 - 3x**3> : polynomial.polynomial<#ring>
     ```
   }];
@@ -60,12 +60,12 @@ class Polynomial_Attr<string name, string attrMnemonic, list<Trait> traits = []>
   let mnemonic = attrMnemonic;
 }
 
-def Polynomial_PolynomialAttr : Polynomial_Attr<"Polynomial", "polynomial"> {
-  let summary = "An attribute containing a single-variable polynomial.";
+def Polynomial_IntPolynomialAttr : Polynomial_Attr<"IntPolynomial", "int_polynomial"> {
+  let summary = "An attribute containing a single-variable polynomial with integer coefficients.";
   let description = [{
-    A polynomial attribute represents a single-variable polynomial, which
-    is used to define the modulus of a `RingAttr`, as well as to define constants
-    and perform constant folding for `polynomial` ops.
+    A polynomial attribute represents a single-variable polynomial with integer
+    coefficients, which is used to define the modulus of a `RingAttr`, as well
+    as to define constants and perform constant folding for `polynomial` ops.
 
     The polynomial must be expressed as a list of monomial terms, with addition
     or subtraction between them. The choice of variable name is arbitrary, but
@@ -76,10 +76,32 @@ def Polynomial_PolynomialAttr : Polynomial_Attr<"Polynomial", "polynomial"> {
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 + 1>
+    #poly = #polynomial.int_polynomial<x**1024 + 1>
     ```
   }];
-  let parameters = (ins "::mlir::polynomial::Polynomial":$polynomial);
+  let parameters = (ins "::mlir::polynomial::IntPolynomial":$polynomial);
+  let hasCustomAssemblyFormat = 1;
+}
+
+def Polynomial_FloatPolynomialAttr : Polynomial_Attr<"FloatPolynomial", "float_polynomial"> {
+  let summary = "An attribute containing a single-variable polynomial with double precision floating point coefficients.";
+  let description = [{
+    A polynomial attribute represents a single-variable polynomial with double
+    precision floating point coefficients.
+
+    The polynomial must be expressed as a list of monomial terms, with addition
+    or subtraction between them. The choice of variable name is arbitrary, but
+    must be consistent across all the monomials used to define a single
+    attribute. The order of monomial terms is arbitrary, each monomial degree
+    must occur at most once.
+
+    Example:
+
+    ```mlir
+    #poly = #polynomial.float_polynomial<0.5 x**7 + 1.5>
+    ```
+  }];
+  let parameters = (ins "FloatPolynomial":$polynomial);
   let hasCustomAssemblyFormat = 1;
 }
 
@@ -104,9 +126,9 @@ def Polynomial_RingAttr : Polynomial_Attr<"Ring", "ring"> {
     `x**1024 - 1`.
 
     ```mlir
-    #poly_mod = #polynomial.polynomial<-1 + x**1024>
+    #poly_mod = #polynomial.int_polynomial<-1 + x**1024>
     #ring = #polynomial.ring<coefficientType=i32,
-                             coefficientModulus=4294967291,
+                             coefficientModulus=4294967291:i32,
                              polynomialModulus=#poly_mod>
 
     %0 = ... : polynomial.polynomial<#ring>
@@ -123,19 +145,24 @@ def Polynomial_RingAttr : Polynomial_Attr<"Ring", "ring"> {
   let parameters = (ins
     "Type": $coefficientType,
     OptionalParameter<"::mlir::IntegerAttr">: $coefficientModulus,
-    OptionalParameter<"::mlir::polynomial::PolynomialAttr">: $polynomialModulus,
+    OptionalParameter<"::mlir::polynomial::IntPolynomialAttr">: $polynomialModulus,
     OptionalParameter<"::mlir::IntegerAttr">: $primitiveRoot
   );
-
+  let assemblyFormat = "`<` struct(params) `>`";
   let builders = [
-    AttrBuilder<
+    AttrBuilderWithInferredContext<
         (ins "::mlir::Type":$coefficientTy,
-             "::mlir::IntegerAttr":$coefficientModulusAttr,
-             "::mlir::polynomial::PolynomialAttr":$polynomialModulusAttr), [{
-      return $_get($_ctxt, coefficientTy, coefficientModulusAttr, polynomialModulusAttr, nullptr);
-    }]>
+              CArg<"::mlir::IntegerAttr", "nullptr"> :$coefficientModulusAttr,
+              CArg<"::mlir::polynomial::IntPolynomialAttr", "nullptr"> :$polynomialModulusAttr,
+              CArg<"::mlir::IntegerAttr", "nullptr"> :$primitiveRootAttr), [{
+      return $_get(
+        coefficientTy.getContext(),
+        coefficientTy,
+        coefficientModulusAttr,
+        polynomialModulusAttr,
+        primitiveRootAttr);
+    }]>,
   ];
-  let hasCustomAssemblyFormat = 1;
 }
 
 class Polynomial_Type<string name, string typeMnemonic>
@@ -149,7 +176,7 @@ def Polynomial_PolynomialType : Polynomial_Type<"Polynomial", "polynomial"> {
     A type for polynomials in a polynomial quotient ring.
   }];
   let parameters = (ins Polynomial_RingAttr:$ring);
-  let assemblyFormat = "`<` $ring `>`";
+  let assemblyFormat = "`<` struct(params) `>`";
 }
 
 def PolynomialLike: TypeOrContainer<Polynomial_PolynomialType, "polynomial-like">;
@@ -187,10 +214,10 @@ def Polynomial_AddOp : Polynomial_BinaryOp<"add", [Commutative]> {
 
     ```mlir
     // add two polynomials modulo x^1024 - 1
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
-    %1 = polynomial.constant #polynomial.polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    %1 = polynomial.constant #polynomial.int_polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
     %2 = polynomial.add %0, %1 : !polynomial.polynomial<#ring>
     ```
   }];
@@ -211,10 +238,10 @@ def Polynomial_SubOp : Polynomial_BinaryOp<"sub"> {
 
     ```mlir
     // subtract two polynomials modulo x^1024 - 1
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
-    %1 = polynomial.constant #polynomial.polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    %1 = polynomial.constant #polynomial.int_polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
     %2 = polynomial.sub %0, %1 : !polynomial.polynomial<#ring>
     ```
   }];
@@ -235,10 +262,10 @@ def Polynomial_MulOp : Polynomial_BinaryOp<"mul", [Commutative]> {
 
     ```mlir
     // multiply two polynomials modulo x^1024 - 1
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
-    %1 = polynomial.constant #polynomial.polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    %1 = polynomial.constant #polynomial.int_polynomial<x**5 - x + 1> : !polynomial.polynomial<#ring>
     %2 = polynomial.mul %0, %1 : !polynomial.polynomial<#ring>
     ```
   }];
@@ -260,9 +287,9 @@ def Polynomial_MulScalarOp : Polynomial_Op<"mul_scalar", [
 
     ```mlir
     // multiply two polynomials modulo x^1024 - 1
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
     %1 = arith.constant 3 : i32
     %2 = polynomial.mul_scalar %0, %1 : !polynomial.polynomial<#ring>, i32
     ```
@@ -291,9 +318,9 @@ def Polynomial_LeadingTermOp: Polynomial_Op<"leading_term"> {
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
     %1, %2 = polynomial.leading_term %0 : !polynomial.polynomial<#ring> -> (index, i32)
     ```
   }];
@@ -314,8 +341,8 @@ def Polynomial_MonomialOp: Polynomial_Op<"monomial"> {
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
     %deg = arith.constant 1023 : index
     %five = arith.constant 5 : i32
     %0 = polynomial.monomial %five, %deg : (i32, index) -> !polynomial.polynomial<#ring>
@@ -354,8 +381,8 @@ def Polynomial_FromTensorOp : Polynomial_Op<"from_tensor", [Pure]> {
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
     %two = arith.constant 2 : i32
     %five = arith.constant 5 : i32
     %coeffs = tensor.from_elements %two, %two, %five : tensor<3xi32>
@@ -393,8 +420,8 @@ def Polynomial_ToTensorOp : Polynomial_Op<"to_tensor", [Pure]> {
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
     %two = arith.constant 2 : i32
     %five = arith.constant 5 : i32
     %coeffs = tensor.from_elements %two, %two, %five : tensor<3xi32>
@@ -405,24 +432,32 @@ def Polynomial_ToTensorOp : Polynomial_Op<"to_tensor", [Pure]> {
   let arguments = (ins Polynomial_PolynomialType:$input);
   let results = (outs RankedTensorOf<[AnyInteger]>:$output);
   let assemblyFormat = "$input attr-dict `:` type($input) `->` type($output)";
-
   let hasVerifier = 1;
 }
 
-def Polynomial_ConstantOp : Polynomial_Op<"constant", [Pure]> {
+def Polynomial_AnyPolynomialAttr : AnyAttrOf<[
+  Polynomial_FloatPolynomialAttr,
+  Polynomial_IntPolynomialAttr
+]>;
+
+// Not deriving from Polynomial_Op due to need for custom assembly format
+def Polynomial_ConstantOp : Op<Polynomial_Dialect, "constant", [Pure]> {
   let summary = "Define a constant polynomial via an attribute.";
   let description = [{
     Example:
 
     ```mlir
-    #poly = #polynomial.polynomial<x**1024 - 1>
-    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536, polynomialModulus=#poly>
-    %0 = polynomial.constant #polynomial.polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+    #poly = #polynomial.int_polynomial<x**1024 - 1>
+    #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=65536:i32, polynomialModulus=#poly>
+    %0 = polynomial.constant #polynomial.int_polynomial<1 + x**2> : !polynomial.polynomial<#ring>
+
+    #float_ring = #polynomial.ring<coefficientType=f32>
+    %0 = polynomial.constant #polynomial.float_polynomial<0.5 + 1.3e06 x**2> : !polynomial.polynomial<#float_ring>
     ```
   }];
-  let arguments = (ins Polynomial_PolynomialAttr:$input);
+  let arguments = (ins Polynomial_AnyPolynomialAttr:$value);
   let results = (outs Polynomial_PolynomialType:$output);
-  let assemblyFormat = "$input attr-dict `:` type($output)";
+  let assemblyFormat = "attr-dict `:` type($output)";
 }
 
 def Polynomial_NTTOp : Polynomial_Op<"ntt", [Pure]> {

diff  --git a/mlir/lib/Dialect/Polynomial/IR/Polynomial.cpp b/mlir/lib/Dialect/Polynomial/IR/Polynomial.cpp
index 5916ffba78e24..e85bced3cca7c 100644
--- a/mlir/lib/Dialect/Polynomial/IR/Polynomial.cpp
+++ b/mlir/lib/Dialect/Polynomial/IR/Polynomial.cpp
@@ -9,87 +9,60 @@
 #include "mlir/Dialect/Polynomial/IR/Polynomial.h"
 
 #include "mlir/Support/LogicalResult.h"
-#include "llvm/ADT/APInt.h"
-#include "llvm/ADT/SmallString.h"
 #include "llvm/ADT/SmallVector.h"
-#include "llvm/ADT/Twine.h"
-#include "llvm/Support/raw_ostream.h"
 
 namespace mlir {
 namespace polynomial {
 
-FailureOr<Polynomial> Polynomial::fromMonomials(ArrayRef<Monomial> monomials) {
+template <typename PolyT, typename MonomialT>
+FailureOr<PolyT> fromMonomialsImpl(ArrayRef<MonomialT> monomials) {
   // A polynomial's terms are canonically stored in order of increasing degree.
-  auto monomialsCopy = llvm::SmallVector<Monomial>(monomials);
+  auto monomialsCopy = llvm::SmallVector<MonomialT>(monomials);
   std::sort(monomialsCopy.begin(), monomialsCopy.end());
 
   // Ensure non-unique exponents are not present. Since we sorted the list by
   // exponent, a linear scan of adjancent monomials suffices.
   if (std::adjacent_find(monomialsCopy.begin(), monomialsCopy.end(),
-                         [](const Monomial &lhs, const Monomial &rhs) {
-                           return lhs.exponent == rhs.exponent;
+                         [](const MonomialT &lhs, const MonomialT &rhs) {
+                           return lhs.getExponent() == rhs.getExponent();
                          }) != monomialsCopy.end()) {
     return failure();
   }
 
-  return Polynomial(monomialsCopy);
+  return PolyT(monomialsCopy);
 }
 
-Polynomial Polynomial::fromCoefficients(ArrayRef<int64_t> coeffs) {
-  llvm::SmallVector<Monomial> monomials;
+FailureOr<IntPolynomial>
+IntPolynomial::fromMonomials(ArrayRef<IntMonomial> monomials) {
+  return fromMonomialsImpl<IntPolynomial, IntMonomial>(monomials);
+}
+
+FailureOr<FloatPolynomial>
+FloatPolynomial::fromMonomials(ArrayRef<FloatMonomial> monomials) {
+  return fromMonomialsImpl<FloatPolynomial, FloatMonomial>(monomials);
+}
+
+template <typename PolyT, typename MonomialT, typename CoeffT>
+PolyT fromCoefficientsImpl(ArrayRef<CoeffT> coeffs) {
+  llvm::SmallVector<MonomialT> monomials;
   auto size = coeffs.size();
   monomials.reserve(size);
   for (size_t i = 0; i < size; i++) {
     monomials.emplace_back(coeffs[i], i);
   }
-  auto result = Polynomial::fromMonomials(monomials);
+  auto result = PolyT::fromMonomials(monomials);
   // Construction guarantees unique exponents, so the failure mode of
   // fromMonomials can be bypassed.
   assert(succeeded(result));
   return result.value();
 }
 
-void Polynomial::print(raw_ostream &os, ::llvm::StringRef separator,
-                       ::llvm::StringRef exponentiation) const {
-  bool first = true;
-  for (const Monomial &term : terms) {
-    if (first) {
-      first = false;
-    } else {
-      os << separator;
-    }
-    std::string coeffToPrint;
-    if (term.coefficient == 1 && term.exponent.uge(1)) {
-      coeffToPrint = "";
-    } else {
-      llvm::SmallString<16> coeffString;
-      term.coefficient.toStringSigned(coeffString);
-      coeffToPrint = coeffString.str();
-    }
-
-    if (term.exponent == 0) {
-      os << coeffToPrint;
-    } else if (term.exponent == 1) {
-      os << coeffToPrint << "x";
-    } else {
-      llvm::SmallString<16> expString;
-      term.exponent.toStringSigned(expString);
-      os << coeffToPrint << "x" << exponentiation << expString;
-    }
-  }
-}
-
-void Polynomial::print(raw_ostream &os) const { print(os, " + ", "**"); }
-
-std::string Polynomial::toIdentifier() const {
-  std::string result;
-  llvm::raw_string_ostream os(result);
-  print(os, "_", "");
-  return os.str();
+IntPolynomial IntPolynomial::fromCoefficients(ArrayRef<int64_t> coeffs) {
+  return fromCoefficientsImpl<IntPolynomial, IntMonomial, int64_t>(coeffs);
 }
 
-unsigned Polynomial::getDegree() const {
-  return terms.back().exponent.getZExtValue();
+FloatPolynomial FloatPolynomial::fromCoefficients(ArrayRef<double> coeffs) {
+  return fromCoefficientsImpl<FloatPolynomial, FloatMonomial, double>(coeffs);
 }
 
 } // namespace polynomial

diff  --git a/mlir/lib/Dialect/Polynomial/IR/PolynomialAttributes.cpp b/mlir/lib/Dialect/Polynomial/IR/PolynomialAttributes.cpp
index 236bb78966352..890ce5226c30f 100644
--- a/mlir/lib/Dialect/Polynomial/IR/PolynomialAttributes.cpp
+++ b/mlir/lib/Dialect/Polynomial/IR/PolynomialAttributes.cpp
@@ -10,6 +10,7 @@
 #include "mlir/Dialect/Polynomial/IR/Polynomial.h"
 #include "mlir/Support/LLVM.h"
 #include "mlir/Support/LogicalResult.h"
+#include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/StringExtras.h"
 #include "llvm/ADT/StringRef.h"
 #include "llvm/ADT/StringSet.h"
@@ -17,22 +18,31 @@
 namespace mlir {
 namespace polynomial {
 
-void PolynomialAttr::print(AsmPrinter &p) const {
-  p << '<';
-  p << getPolynomial();
-  p << '>';
+void IntPolynomialAttr::print(AsmPrinter &p) const {
+  p << '<' << getPolynomial() << '>';
 }
 
+void FloatPolynomialAttr::print(AsmPrinter &p) const {
+  p << '<' << getPolynomial() << '>';
+}
+
+/// A callable that parses the coefficient using the appropriate method for the
+/// given monomial type, and stores the parsed coefficient value on the
+/// monomial.
+template <typename MonomialType>
+using ParseCoefficientFn = std::function<OptionalParseResult(MonomialType &)>;
+
 /// Try to parse a monomial. If successful, populate the fields of the outparam
 /// `monomial` with the results, and the `variable` outparam with the parsed
 /// variable name. Sets shouldParseMore to true if the monomial is followed by
 /// a '+'.
-ParseResult parseMonomial(AsmParser &parser, Monomial &monomial,
-                          llvm::StringRef &variable, bool &isConstantTerm,
-                          bool &shouldParseMore) {
-  APInt parsedCoeff(apintBitWidth, 1);
-  auto parsedCoeffResult = parser.parseOptionalInteger(parsedCoeff);
-  monomial.coefficient = parsedCoeff;
+///
+template <typename Monomial>
+ParseResult
+parseMonomial(AsmParser &parser, Monomial &monomial, llvm::StringRef &variable,
+              bool &isConstantTerm, bool &shouldParseMore,
+              ParseCoefficientFn<Monomial> parseAndStoreCoefficient) {
+  OptionalParseResult parsedCoeffResult = parseAndStoreCoefficient(monomial);
 
   isConstantTerm = false;
   shouldParseMore = false;
@@ -44,7 +54,7 @@ ParseResult parseMonomial(AsmParser &parser, Monomial &monomial,
     if (!parsedCoeffResult.has_value()) {
       return failure();
     }
-    monomial.exponent = APInt(apintBitWidth, 0);
+    monomial.setExponent(APInt(apintBitWidth, 0));
     isConstantTerm = true;
     shouldParseMore = true;
     return success();
@@ -58,7 +68,7 @@ ParseResult parseMonomial(AsmParser &parser, Monomial &monomial,
       return failure();
     }
 
-    monomial.exponent = APInt(apintBitWidth, 0);
+    monomial.setExponent(APInt(apintBitWidth, 0));
     isConstantTerm = true;
     return success();
   }
@@ -80,9 +90,9 @@ ParseResult parseMonomial(AsmParser &parser, Monomial &monomial,
       return failure();
     }
 
-    monomial.exponent = parsedExponent;
+    monomial.setExponent(parsedExponent);
   } else {
-    monomial.exponent = APInt(apintBitWidth, 1);
+    monomial.setExponent(APInt(apintBitWidth, 1));
   }
 
   if (succeeded(parser.parseOptionalPlus())) {
@@ -91,22 +101,21 @@ ParseResult parseMonomial(AsmParser &parser, Monomial &monomial,
   return success();
 }
 
-Attribute PolynomialAttr::parse(AsmParser &parser, Type type) {
-  if (failed(parser.parseLess()))
-    return {};
-
-  llvm::SmallVector<Monomial> monomials;
-  llvm::StringSet<> variables;
-
+template <typename PolynoimalAttrTy, typename Monomial>
+LogicalResult
+parsePolynomialAttr(AsmParser &parser, llvm::SmallVector<Monomial> &monomials,
+                    llvm::StringSet<> &variables,
+                    ParseCoefficientFn<Monomial> parseAndStoreCoefficient) {
   while (true) {
     Monomial parsedMonomial;
     llvm::StringRef parsedVariableRef;
     bool isConstantTerm;
     bool shouldParseMore;
-    if (failed(parseMonomial(parser, parsedMonomial, parsedVariableRef,
-                             isConstantTerm, shouldParseMore))) {
+    if (failed(parseMonomial<Monomial>(
+            parser, parsedMonomial, parsedVariableRef, isConstantTerm,
+            shouldParseMore, parseAndStoreCoefficient))) {
       parser.emitError(parser.getCurrentLocation(), "expected a monomial");
-      return {};
+      return failure();
     }
 
     if (!isConstantTerm) {
@@ -124,7 +133,7 @@ Attribute PolynomialAttr::parse(AsmParser &parser, Type type) {
     parser.emitError(
         parser.getCurrentLocation(),
         "expected + and more monomials, or > to end polynomial attribute");
-    return {};
+    return failure();
   }
 
   if (variables.size() > 1) {
@@ -133,96 +142,67 @@ Attribute PolynomialAttr::parse(AsmParser &parser, Type type) {
         parser.getCurrentLocation(),
         "polynomials must have one indeterminate, but there were multiple: " +
             vars);
+    return failure();
   }
 
-  auto result = Polynomial::fromMonomials(monomials);
-  if (failed(result)) {
-    parser.emitError(parser.getCurrentLocation())
-        << "parsed polynomial must have unique exponents among monomials";
-    return {};
-  }
-  return PolynomialAttr::get(parser.getContext(), result.value());
-}
-
-void RingAttr::print(AsmPrinter &p) const {
-  p << "#polynomial.ring<coefficientType=" << getCoefficientType()
-    << ", coefficientModulus=" << getCoefficientModulus()
-    << ", polynomialModulus=" << getPolynomialModulus() << '>';
+  return success();
 }
 
-Attribute RingAttr::parse(AsmParser &parser, Type type) {
+Attribute IntPolynomialAttr::parse(AsmParser &parser, Type type) {
   if (failed(parser.parseLess()))
     return {};
 
-  if (failed(parser.parseKeyword("coefficientType")))
-    return {};
+  llvm::SmallVector<IntMonomial> monomials;
+  llvm::StringSet<> variables;
 
-  if (failed(parser.parseEqual()))
+  if (failed(parsePolynomialAttr<IntPolynomialAttr, IntMonomial>(
+          parser, monomials, variables,
+          [&](IntMonomial &monomial) -> OptionalParseResult {
+            APInt parsedCoeff(apintBitWidth, 1);
+            OptionalParseResult result =
+                parser.parseOptionalInteger(parsedCoeff);
+            monomial.setCoefficient(parsedCoeff);
+            return result;
+          }))) {
     return {};
+  }
 
-  Type ty;
-  if (failed(parser.parseType(ty)))
+  auto result = IntPolynomial::fromMonomials(monomials);
+  if (failed(result)) {
+    parser.emitError(parser.getCurrentLocation())
+        << "parsed polynomial must have unique exponents among monomials";
     return {};
+  }
+  return IntPolynomialAttr::get(parser.getContext(), result.value());
+}
 
-  if (failed(parser.parseComma()))
+Attribute FloatPolynomialAttr::parse(AsmParser &parser, Type type) {
+  if (failed(parser.parseLess()))
     return {};
 
-  IntegerAttr coefficientModulusAttr = nullptr;
-  if (succeeded(parser.parseKeyword("coefficientModulus"))) {
-    if (failed(parser.parseEqual()))
-      return {};
-
-    IntegerType iType = mlir::dyn_cast<IntegerType>(ty);
-    if (!iType) {
-      parser.emitError(parser.getCurrentLocation(),
-                       "coefficientType must specify an integer type");
-      return {};
-    }
-    APInt coefficientModulus(iType.getWidth(), 0);
-    auto result = parser.parseInteger(coefficientModulus);
-    if (failed(result)) {
-      parser.emitError(parser.getCurrentLocation(),
-                       "invalid coefficient modulus");
-      return {};
-    }
-    coefficientModulusAttr = IntegerAttr::get(iType, coefficientModulus);
-
-    if (failed(parser.parseComma()))
-      return {};
-  }
-
-  PolynomialAttr polyAttr = nullptr;
-  if (succeeded(parser.parseKeyword("polynomialModulus"))) {
-    if (failed(parser.parseEqual()))
-      return {};
+  llvm::SmallVector<FloatMonomial> monomials;
+  llvm::StringSet<> variables;
 
-    PolynomialAttr attr;
-    if (failed(parser.parseAttribute<PolynomialAttr>(attr)))
-      return {};
-    polyAttr = attr;
-  }
+  ParseCoefficientFn<FloatMonomial> parseAndStoreCoefficient =
+      [&](FloatMonomial &monomial) -> OptionalParseResult {
+    double coeffValue = 1.0;
+    ParseResult result = parser.parseFloat(coeffValue);
+    monomial.setCoefficient(APFloat(coeffValue));
+    return OptionalParseResult(result);
+  };
 
-  Polynomial poly = polyAttr.getPolynomial();
-  APInt root(coefficientModulusAttr.getValue().getBitWidth(), 0);
-  IntegerAttr rootAttr = nullptr;
-  if (succeeded(parser.parseOptionalComma())) {
-    if (failed(parser.parseKeyword("primitiveRoot")) ||
-        failed(parser.parseEqual()))
-      return {};
-
-    ParseResult result = parser.parseInteger(root);
-    if (failed(result)) {
-      parser.emitError(parser.getCurrentLocation(), "invalid primitiveRoot");
-      return {};
-    }
-    rootAttr = IntegerAttr::get(coefficientModulusAttr.getType(), root);
+  if (failed(parsePolynomialAttr<FloatPolynomialAttr, FloatMonomial>(
+          parser, monomials, variables, parseAndStoreCoefficient))) {
+    return {};
   }
 
-  if (failed(parser.parseGreater()))
+  auto result = FloatPolynomial::fromMonomials(monomials);
+  if (failed(result)) {
+    parser.emitError(parser.getCurrentLocation())
+        << "parsed polynomial must have unique exponents among monomials";
     return {};
-
-  return RingAttr::get(parser.getContext(), ty, coefficientModulusAttr,
-                       polyAttr, rootAttr);
+  }
+  return FloatPolynomialAttr::get(parser.getContext(), result.value());
 }
 
 } // namespace polynomial

diff  --git a/mlir/test/Dialect/Polynomial/attributes.mlir b/mlir/test/Dialect/Polynomial/attributes.mlir
index 3973ae3944335..4bdfd44fd4d15 100644
--- a/mlir/test/Dialect/Polynomial/attributes.mlir
+++ b/mlir/test/Dialect/Polynomial/attributes.mlir
@@ -1,6 +1,6 @@
 // RUN: mlir-opt %s --split-input-file --verify-diagnostics
 
-#my_poly = #polynomial.polynomial<y + x**1024>
+#my_poly = #polynomial.int_polynomial<y + x**1024>
 // expected-error at below {{polynomials must have one indeterminate, but there were multiple: x, y}}
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
 
@@ -9,37 +9,31 @@
 // expected-error at below {{expected integer value}}
 // expected-error at below {{expected a monomial}}
 // expected-error at below {{found invalid integer exponent}}
-#my_poly = #polynomial.polynomial<5 + x**f>
+#my_poly = #polynomial.int_polynomial<5 + x**f>
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
 
 // -----
 
-#my_poly = #polynomial.polynomial<5 + x**2 + 3x**2>
+#my_poly = #polynomial.int_polynomial<5 + x**2 + 3x**2>
 // expected-error at below {{parsed polynomial must have unique exponents among monomials}}
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
 
 // -----
 
 // expected-error at below {{expected + and more monomials, or > to end polynomial attribute}}
-#my_poly = #polynomial.polynomial<5 + x**2 7>
+#my_poly = #polynomial.int_polynomial<5 + x**2 7>
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
 
 // -----
 
 // expected-error at below {{expected a monomial}}
-#my_poly = #polynomial.polynomial<5 + x**2 +>
+#my_poly = #polynomial.int_polynomial<5 + x**2 +>
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
 
 
 // -----
 
-#my_poly = #polynomial.polynomial<5 + x**2>
-// expected-error at below {{coefficientType must specify an integer type}}
-#ring1 = #polynomial.ring<coefficientType=f64, coefficientModulus=2837465, polynomialModulus=#my_poly>
-
-// -----
-
-#my_poly = #polynomial.polynomial<5 + x**2>
-// expected-error at below {{expected integer value}}
-// expected-error at below {{invalid coefficient modulus}}
+#my_poly = #polynomial.int_polynomial<5 + x**2>
+// expected-error at below {{failed to parse Polynomial_RingAttr parameter 'coefficientModulus' which is to be a `::mlir::IntegerAttr`}}
+// expected-error at below {{expected attribute value}}
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=x, polynomialModulus=#my_poly>

diff  --git a/mlir/test/Dialect/Polynomial/ops.mlir b/mlir/test/Dialect/Polynomial/ops.mlir
index a29cfc2e9cc54..ff709960c50e9 100644
--- a/mlir/test/Dialect/Polynomial/ops.mlir
+++ b/mlir/test/Dialect/Polynomial/ops.mlir
@@ -2,85 +2,87 @@
 
 // This simply tests for syntax.
 
-#my_poly = #polynomial.polynomial<1 + x**1024>
-#my_poly_2 = #polynomial.polynomial<2>
-#my_poly_3 = #polynomial.polynomial<3x>
-#my_poly_4 = #polynomial.polynomial<t**3 + 4t + 2>
+#my_poly = #polynomial.int_polynomial<1 + x**1024>
+#my_poly_2 = #polynomial.int_polynomial<2>
+#my_poly_3 = #polynomial.int_polynomial<3x>
+#my_poly_4 = #polynomial.int_polynomial<t**3 + 4t + 2>
 #ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
-#one_plus_x_squared = #polynomial.polynomial<1 + x**2>
+#ring2 = #polynomial.ring<coefficientType=f32>
+#one_plus_x_squared = #polynomial.int_polynomial<1 + x**2>
 
-#ideal = #polynomial.polynomial<-1 + x**1024>
+#ideal = #polynomial.int_polynomial<-1 + x**1024>
 #ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256, polynomialModulus=#ideal, primitiveRoot=193>
-!poly_ty = !polynomial.polynomial<#ring>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
-#ntt_poly = #polynomial.polynomial<-1 + x**8>
+#ntt_poly = #polynomial.int_polynomial<-1 + x**8>
 #ntt_ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256, polynomialModulus=#ntt_poly, primitiveRoot=31>
-!ntt_poly_ty = !polynomial.polynomial<#ntt_ring>
+!ntt_poly_ty = !polynomial.polynomial<ring=#ntt_ring>
 
 module {
-  func.func @test_multiply() -> !polynomial.polynomial<#ring1> {
+  func.func @test_multiply() -> !polynomial.polynomial<ring=#ring1> {
     %c0 = arith.constant 0 : index
     %two = arith.constant 2 : i16
     %five = arith.constant 5 : i16
     %coeffs1 = tensor.from_elements %two, %two, %five : tensor<3xi16>
     %coeffs2 = tensor.from_elements %five, %five, %two : tensor<3xi16>
 
-    %poly1 = polynomial.from_tensor %coeffs1 : tensor<3xi16> -> !polynomial.polynomial<#ring1>
-    %poly2 = polynomial.from_tensor %coeffs2 : tensor<3xi16> -> !polynomial.polynomial<#ring1>
+    %poly1 = polynomial.from_tensor %coeffs1 : tensor<3xi16> -> !polynomial.polynomial<ring=#ring1>
+    %poly2 = polynomial.from_tensor %coeffs2 : tensor<3xi16> -> !polynomial.polynomial<ring=#ring1>
 
-    %3 = polynomial.mul %poly1, %poly2 : !polynomial.polynomial<#ring1>
+    %3 = polynomial.mul %poly1, %poly2 : !polynomial.polynomial<ring=#ring1>
 
-    return %3 : !polynomial.polynomial<#ring1>
+    return %3 : !polynomial.polynomial<ring=#ring1>
   }
 
-  func.func @test_elementwise(%p0 : !polynomial.polynomial<#ring1>, %p1: !polynomial.polynomial<#ring1>) {
-    %tp0 = tensor.from_elements %p0, %p1 : tensor<2x!polynomial.polynomial<#ring1>>
-    %tp1 = tensor.from_elements %p1, %p0 : tensor<2x!polynomial.polynomial<#ring1>>
+  func.func @test_elementwise(%p0 : !polynomial.polynomial<ring=#ring1>, %p1: !polynomial.polynomial<ring=#ring1>) {
+    %tp0 = tensor.from_elements %p0, %p1 : tensor<2x!polynomial.polynomial<ring=#ring1>>
+    %tp1 = tensor.from_elements %p1, %p0 : tensor<2x!polynomial.polynomial<ring=#ring1>>
 
     %c = arith.constant 2 : i32
-    %mul_const_sclr = polynomial.mul_scalar %tp0, %c : tensor<2x!polynomial.polynomial<#ring1>>, i32
+    %mul_const_sclr = polynomial.mul_scalar %tp0, %c : tensor<2x!polynomial.polynomial<ring=#ring1>>, i32
 
-    %add = polynomial.add %tp0, %tp1 : tensor<2x!polynomial.polynomial<#ring1>>
-    %sub = polynomial.sub %tp0, %tp1 : tensor<2x!polynomial.polynomial<#ring1>>
-    %mul = polynomial.mul %tp0, %tp1 : tensor<2x!polynomial.polynomial<#ring1>>
+    %add = polynomial.add %tp0, %tp1 : tensor<2x!polynomial.polynomial<ring=#ring1>>
+    %sub = polynomial.sub %tp0, %tp1 : tensor<2x!polynomial.polynomial<ring=#ring1>>
+    %mul = polynomial.mul %tp0, %tp1 : tensor<2x!polynomial.polynomial<ring=#ring1>>
 
     return
   }
 
-  func.func @test_to_from_tensor(%p0 : !polynomial.polynomial<#ring1>) {
+  func.func @test_to_from_tensor(%p0 : !polynomial.polynomial<ring=#ring1>) {
     %c0 = arith.constant 0 : index
     %two = arith.constant 2 : i16
     %coeffs1 = tensor.from_elements %two, %two : tensor<2xi16>
     // CHECK: from_tensor
-    %poly = polynomial.from_tensor %coeffs1 : tensor<2xi16> -> !polynomial.polynomial<#ring1>
+    %poly = polynomial.from_tensor %coeffs1 : tensor<2xi16> -> !polynomial.polynomial<ring=#ring1>
     // CHECK: to_tensor
-    %tensor = polynomial.to_tensor %poly : !polynomial.polynomial<#ring1> -> tensor<1024xi16>
+    %tensor = polynomial.to_tensor %poly : !polynomial.polynomial<ring=#ring1> -> tensor<1024xi16>
 
     return
   }
 
-  func.func @test_degree(%p0 : !polynomial.polynomial<#ring1>) {
-    %0, %1 = polynomial.leading_term %p0 : !polynomial.polynomial<#ring1> -> (index, i32)
+  func.func @test_degree(%p0 : !polynomial.polynomial<ring=#ring1>) {
+    %0, %1 = polynomial.leading_term %p0 : !polynomial.polynomial<ring=#ring1> -> (index, i32)
     return
   }
 
   func.func @test_monomial() {
     %deg = arith.constant 1023 : index
     %five = arith.constant 5 : i16
-    %0 = polynomial.monomial %five, %deg : (i16, index) -> !polynomial.polynomial<#ring1>
+    %0 = polynomial.monomial %five, %deg : (i16, index) -> !polynomial.polynomial<ring=#ring1>
     return
   }
 
   func.func @test_monic_monomial_mul() {
     %five = arith.constant 5 : index
-    %0 = polynomial.constant #one_plus_x_squared : !polynomial.polynomial<#ring1>
-    %1 = polynomial.monic_monomial_mul %0, %five : (!polynomial.polynomial<#ring1>, index) -> !polynomial.polynomial<#ring1>
+    %0 = polynomial.constant {value=#one_plus_x_squared} : !polynomial.polynomial<ring=#ring1>
+    %1 = polynomial.monic_monomial_mul %0, %five : (!polynomial.polynomial<ring=#ring1>, index) -> !polynomial.polynomial<ring=#ring1>
     return
   }
 
   func.func @test_constant() {
-    %0 = polynomial.constant #one_plus_x_squared : !polynomial.polynomial<#ring1>
-    %1 = polynomial.constant <1 + x**2> : !polynomial.polynomial<#ring1>
+    %0 = polynomial.constant {value=#one_plus_x_squared} : !polynomial.polynomial<ring=#ring1>
+    %1 = polynomial.constant {value=#polynomial.int_polynomial<1 + x**2>} : !polynomial.polynomial<ring=#ring1>
+    %2 = polynomial.constant {value=#polynomial.float_polynomial<1.5 + 0.5 x**2>} : !polynomial.polynomial<ring=#ring2>
     return
   }
 

diff  --git a/mlir/test/Dialect/Polynomial/ops_errors.mlir b/mlir/test/Dialect/Polynomial/ops_errors.mlir
index 2c20e7bcbf1d6..af8e4aa5da862 100644
--- a/mlir/test/Dialect/Polynomial/ops_errors.mlir
+++ b/mlir/test/Dialect/Polynomial/ops_errors.mlir
@@ -1,8 +1,8 @@
 // RUN: mlir-opt --split-input-file --verify-diagnostics %s
 
-#my_poly = #polynomial.polynomial<1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly>
-!ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i32, polynomialModulus=#my_poly>
+!ty = !polynomial.polynomial<ring=#ring>
 
 func.func @test_from_tensor_too_large_coeffs() {
   %two = arith.constant 2 : i32
@@ -15,13 +15,13 @@ func.func @test_from_tensor_too_large_coeffs() {
 
 // -----
 
-#my_poly = #polynomial.polynomial<1 + x**4>
-#ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256, polynomialModulus=#my_poly>
-!ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<1 + x**4>
+#ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256:i32, polynomialModulus=#my_poly>
+!ty = !polynomial.polynomial<ring=#ring>
 func.func @test_from_tensor_wrong_tensor_type() {
   %two = arith.constant 2 : i32
   %coeffs1 = tensor.from_elements %two, %two, %two, %two, %two : tensor<5xi32>
-  // expected-error at below {{input type 'tensor<5xi32>' does not match output type '!polynomial.polynomial<#polynomial.ring<coefficientType=i32, coefficientModulus=256 : i32, polynomialModulus=#polynomial.polynomial<1 + x**4>>>'}}
+  // expected-error at below {{input type 'tensor<5xi32>' does not match output type '!polynomial.polynomial<ring = <coefficientType = i32, coefficientModulus = 256 : i32, polynomialModulus = <1 + x**4>>>'}}
   // expected-note at below {{at most the degree of the polynomialModulus of the output type's ring attribute}}
   %poly = polynomial.from_tensor %coeffs1 : tensor<5xi32> -> !ty
   return
@@ -29,11 +29,11 @@ func.func @test_from_tensor_wrong_tensor_type() {
 
 // -----
 
-#my_poly = #polynomial.polynomial<1 + x**4>
-#ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256, polynomialModulus=#my_poly>
-!ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<1 + x**4>
+#ring = #polynomial.ring<coefficientType=i32, coefficientModulus=256:i32, polynomialModulus=#my_poly>
+!ty = !polynomial.polynomial<ring=#ring>
 func.func @test_to_tensor_wrong_output_tensor_type(%arg0 : !ty) {
-  // expected-error at below {{input type '!polynomial.polynomial<#polynomial.ring<coefficientType=i32, coefficientModulus=256 : i32, polynomialModulus=#polynomial.polynomial<1 + x**4>>>' does not match output type 'tensor<5xi32>'}}
+  // expected-error at below {{input type '!polynomial.polynomial<ring = <coefficientType = i32, coefficientModulus = 256 : i32, polynomialModulus = <1 + x**4>>>' does not match output type 'tensor<5xi32>'}}
   // expected-note at below {{at most the degree of the polynomialModulus of the input type's ring attribute}}
   %tensor = polynomial.to_tensor %arg0 : !ty -> tensor<5xi32>
   return
@@ -41,9 +41,9 @@ func.func @test_to_tensor_wrong_output_tensor_type(%arg0 : !ty) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly>
-!ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i32, polynomialModulus=#my_poly>
+!ty = !polynomial.polynomial<ring=#ring>
 
 func.func @test_mul_scalar_wrong_type(%arg0: !ty) -> !ty {
   %scalar = arith.constant 2 : i32  // should be i16
@@ -54,9 +54,9 @@ func.func @test_mul_scalar_wrong_type(%arg0: !ty) -> !ty {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly, primitiveRoot=31>
-!poly_ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<-1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly, primitiveRoot=31:i16>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_ntt
 // CHECK-NOT: polynomial.ntt
@@ -68,9 +68,9 @@ func.func @test_invalid_ntt(%0 : !poly_ty) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly, primitiveRoot=31>
-!poly_ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<-1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly, primitiveRoot=31:i16>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_ntt
 // CHECK-NOT: polynomial.ntt
@@ -82,10 +82,10 @@ func.func @test_invalid_ntt(%0 : !poly_ty) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly>
-#ring1 = #polynomial.ring<coefficientType=i16, coefficientModulus=257, polynomialModulus=#my_poly, primitiveRoot=31>
-!poly_ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<-1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly>
+#ring1 = #polynomial.ring<coefficientType=i16, coefficientModulus=257:i16, polynomialModulus=#my_poly, primitiveRoot=31:i16>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_intt
 // CHECK-NOT: polynomial.intt
@@ -97,9 +97,9 @@ func.func @test_invalid_intt(%0 : tensor<1024xi32, #ring1>) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly, primitiveRoot=31>
-!poly_ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<-1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly, primitiveRoot=31:i16>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_intt
 // CHECK-NOT: polynomial.intt
@@ -112,9 +112,9 @@ func.func @test_invalid_intt(%0 : tensor<1025xi32, #ring>) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**1024>
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly>
-!poly_ty = !polynomial.polynomial<#ring>
+#my_poly = #polynomial.int_polynomial<-1 + x**1024>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_ntt
 // CHECK-NOT: polynomial.ntt
@@ -126,10 +126,10 @@ func.func @test_invalid_ntt(%0 : !poly_ty) {
 
 // -----
 
-#my_poly = #polynomial.polynomial<-1 + x**8>
+#my_poly = #polynomial.int_polynomial<-1 + x**8>
 // A valid root is 31
-#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256, polynomialModulus=#my_poly, primitiveRoot=32>
-!poly_ty = !polynomial.polynomial<#ring>
+#ring = #polynomial.ring<coefficientType=i16, coefficientModulus=256:i16, polynomialModulus=#my_poly, primitiveRoot=32:i16>
+!poly_ty = !polynomial.polynomial<ring=#ring>
 
 // CHECK-NOT: @test_invalid_intt
 // CHECK-NOT: polynomial.intt

diff  --git a/mlir/test/Dialect/Polynomial/types.mlir b/mlir/test/Dialect/Polynomial/types.mlir
index 00296a36e890f..dcc5663ceb84c 100644
--- a/mlir/test/Dialect/Polynomial/types.mlir
+++ b/mlir/test/Dialect/Polynomial/types.mlir
@@ -2,13 +2,13 @@
 
 // CHECK-LABEL: func @test_types
 // CHECK-SAME:  !polynomial.polynomial<
-// CHECK-SAME:    #polynomial.ring<
-// CHECK-SAME:       coefficientType=i32,
-// CHECK-SAME:       coefficientModulus=2837465 : i32,
-// CHECK-SAME:       polynomialModulus=#polynomial.polynomial<1 + x**1024>>>
-#my_poly = #polynomial.polynomial<1 + x**1024>
-#ring1 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly>
-!ty = !polynomial.polynomial<#ring1>
+// CHECK-SAME:    ring = <
+// CHECK-SAME:       coefficientType = i32,
+// CHECK-SAME:       coefficientModulus = 2837465 : i32,
+// CHECK-SAME:       polynomialModulus = <1 + x**1024>>>
+#my_poly = #polynomial.int_polynomial<1 + x**1024>
+#ring1 = #polynomial.ring<coefficientType = i32, coefficientModulus = 2837465 : i32, polynomialModulus=#my_poly>
+!ty = !polynomial.polynomial<ring=#ring1>
 func.func @test_types(%0: !ty) -> !ty {
   return %0 : !ty
 }
@@ -16,13 +16,13 @@ func.func @test_types(%0: !ty) -> !ty {
 
 // CHECK-LABEL: func @test_non_x_variable_64_bit
 // CHECK-SAME:  !polynomial.polynomial<
-// CHECK-SAME:    #polynomial.ring<
-// CHECK-SAME:       coefficientType=i64,
-// CHECK-SAME:       coefficientModulus=2837465 : i64,
-// CHECK-SAME:       polynomialModulus=#polynomial.polynomial<2 + 4x + x**3>>>
-#my_poly_2 = #polynomial.polynomial<t**3 + 4t + 2>
-#ring2 = #polynomial.ring<coefficientType=i64, coefficientModulus=2837465, polynomialModulus=#my_poly_2>
-!ty2 = !polynomial.polynomial<#ring2>
+// CHECK-SAME:    ring = <
+// CHECK-SAME:       coefficientType = i64,
+// CHECK-SAME:       coefficientModulus = 2837465 : i64,
+// CHECK-SAME:       polynomialModulus = <2 + 4x + x**3>>>
+#my_poly_2 = #polynomial.int_polynomial<t**3 + 4t + 2>
+#ring2 = #polynomial.ring<coefficientType = i64, coefficientModulus = 2837465 : i64, polynomialModulus=#my_poly_2>
+!ty2 = !polynomial.polynomial<ring=#ring2>
 func.func @test_non_x_variable_64_bit(%0: !ty2) -> !ty2 {
   return %0 : !ty2
 }
@@ -30,27 +30,36 @@ func.func @test_non_x_variable_64_bit(%0: !ty2) -> !ty2 {
 
 // CHECK-LABEL: func @test_linear_poly
 // CHECK-SAME:  !polynomial.polynomial<
-// CHECK-SAME:    #polynomial.ring<
-// CHECK-SAME:       coefficientType=i32,
-// CHECK-SAME:       coefficientModulus=12 : i32,
-// CHECK-SAME:       polynomialModulus=#polynomial.polynomial<4x>>
-#my_poly_3 = #polynomial.polynomial<4x>
-#ring3 = #polynomial.ring<coefficientType=i32, coefficientModulus=12, polynomialModulus=#my_poly_3>
-!ty3 = !polynomial.polynomial<#ring3>
+// CHECK-SAME:    ring = <
+// CHECK-SAME:       coefficientType = i32,
+// CHECK-SAME:       coefficientModulus = 12 : i32,
+// CHECK-SAME:       polynomialModulus = <4x>>
+#my_poly_3 = #polynomial.int_polynomial<4x>
+#ring3 = #polynomial.ring<coefficientType = i32, coefficientModulus=12 : i32, polynomialModulus=#my_poly_3>
+!ty3 = !polynomial.polynomial<ring=#ring3>
 func.func @test_linear_poly(%0: !ty3) -> !ty3 {
   return %0 : !ty3
 }
 
 // CHECK-LABEL: func @test_negative_leading_1
 // CHECK-SAME:  !polynomial.polynomial<
-// CHECK-SAME:    #polynomial.ring<
-// CHECK-SAME:       coefficientType=i32,
-// CHECK-SAME:       coefficientModulus=2837465 : i32,
-// CHECK-SAME:       polynomialModulus=#polynomial.polynomial<-1 + x**1024>>>
-#my_poly_4 = #polynomial.polynomial<-1 + x**1024>
-#ring4 = #polynomial.ring<coefficientType=i32, coefficientModulus=2837465, polynomialModulus=#my_poly_4>
-!ty4 = !polynomial.polynomial<#ring4>
+// CHECK-SAME:    ring = <
+// CHECK-SAME:       coefficientType = i32,
+// CHECK-SAME:       coefficientModulus = 2837465 : i32,
+// CHECK-SAME:       polynomialModulus = <-1 + x**1024>>>
+#my_poly_4 = #polynomial.int_polynomial<-1 + x**1024>
+#ring4 = #polynomial.ring<coefficientType = i32, coefficientModulus = 2837465 : i32, polynomialModulus=#my_poly_4>
+!ty4 = !polynomial.polynomial<ring=#ring4>
 func.func @test_negative_leading_1(%0: !ty4) -> !ty4 {
   return %0 : !ty4
 }
 
+// CHECK-LABEL: func @test_float_coefficients
+// CHECK-SAME:  !polynomial.polynomial<ring = <coefficientType = f32>>
+#my_poly_5 = #polynomial.float_polynomial<0.5 + 1.6e03 x**1024>
+#ring5 = #polynomial.ring<coefficientType=f32>
+!ty5 = !polynomial.polynomial<ring=#ring5>
+func.func @test_float_coefficients(%0: !ty5) -> !ty5 {
+  return %0 : !ty5
+}
+


        


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