8338529: Initial iteration of numerics modeling interfaces

src/java.base/share/classes/java/lang/Integral.java

@@ -0,0 +1,110 @@
+/*
+ * Copyright (c) 2024, 2026, Oracle and/or its affiliates. All rights reserved.
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * This code is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 2 only, as
+ * published by the Free Software Foundation.  Oracle designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Oracle in the LICENSE file that accompanied this code.
+ *
+ * This code is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * version 2 for more details (a copy is included in the LICENSE file that
+ * accompanied this code).
+ *
+ * You should have received a copy of the GNU General Public License version
+ * 2 along with this work; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+ * or visit www.oracle.com if you need additional information or have any
+ * questions.
+ */
+
+package java.lang;
+
+/**
+ * Indicates an integral type that supports:
+ * <ul>
+ * <li>{@linkplain Numerical arithmetic operations} ({@code +}, {@code
+ * -}, {@code*}, {@code /}, {@code %}) and so on.
+ *
+ * <li>{@linkplain Orderable ordered comparison operators}
+ * ({@code <}, {@code <=}, {@code >}, {@code >=})
+ *
+ * <li>integer-related bit-wise operators ({@code &}, {@code |},
+ * {@code ^}, {@code ~})
+ *
+ * <li>shifts ({@code * <<}, {@code >>}, {@code >>>})
+ *
+ * </ul>
+ *
+ * and participates in operator overloading of all those operators.
+ *
+ * @param <IT> The integral type
+ */
+public interface Integral<IT>
+    extends Numerical<IT>, Orderable<IT> {
+
+    /**
+     * {@return the AND of the two operands, binary operator "{@code &}"}
+     *
+     * @param op1 the first operand
+     * @param op2 the second operand
+     */
+    IT and(IT op1, IT op2);
+
+    /**
+     * {@return the OR of the two operands, binary operator "{@code |}"}
+     *
+     * @param op1 the first operand
+     * @param op2 the second operand
+     */
+    IT or(IT op1, IT op2);
+
+    /**
+     * {@return the XOR of the two operands, binary operator "{@code ^}"}
+     *
+     * @param op1 the first operand
+     * @param op2 the second operand
+     */
+    IT xor(IT op1, IT op2);
+
+    /**
+     * {@return the complement of the operand, unary operator "{@code ~}"}
+     *
+     * @param op1 the operand
+     * @throws UnsupportedOperationException if complement is not supposed
+     */
+    IT complement(IT op1);
+
+    /**
+     * {@return the first operand left shifted by the distance
+     * indicated by the second operand, binary operator "{@code <<"}}
+     *
+     * @param x the operand to be shifted
+     * @param shiftDistance the shift distance
+     */
+    IT shiftLeft(IT x, int shiftDistance);
+
+    /**
+     * {@return the first operand right shifted by the distance
+     * indicated by the second operand, operator "{@code >>}"}
+     *
+     * @param x the operand to be shifted
+     * @param shiftDistance the shift distance
+     */
+    IT shiftRight(IT x, int shiftDistance);
+
+    /**
+     * {@return the first operand right shifted, unsigned, by the
+     * distance indicated by the second operand, operator "{@code >>>}"}
+     *
+     * @param x the operand to be shifted
+     * @param shiftDistance the shift distance
+     * @throws UnsupportedOperationException if unsigned right shift is not supposed
+     */
+    IT shiftRightUnsigned(IT x, int shiftDistance);
+}

src/java.base/share/classes/java/lang/Numerical.java

@@ -0,0 +1,193 @@
+/*
+ * Copyright (c) 2024, 2026, Oracle and/or its affiliates. All rights reserved.
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * This code is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 2 only, as
+ * published by the Free Software Foundation.  Oracle designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Oracle in the LICENSE file that accompanied this code.
+ *
+ * This code is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * version 2 for more details (a copy is included in the LICENSE file that
+ * accompanied this code).
+ *
+ * You should have received a copy of the GNU General Public License version
+ * 2 along with this work; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+ * or visit www.oracle.com if you need additional information or have any
+ * questions.
+ */
+
+package java.lang;
+
+/**
+ * Indicates a type supports the basic binary arithmetic operations of
+ * addition, subtraction, multiplication, (optionally) division, and
+ * (optionally) remainder, ({@code +}, {@code -}, {@code *}, {@code
+ * /}, {@code %}, respectively), as well as (optionally) negation (unary
+ * {@code -}), and participates in operator overloading of those
+ * operators.
+ *
+ * <p>The intention of this interface is to enable types that
+ * customarily support numerical notions of addition, subtraction,
+ * multiplication and division to enjoy operator overloading syntax
+ * even if the underlying algebraic properties do not hold because of
+ * limitations in approximation. This includes <dfn>algebraic
+ * fields</dfn> and field-like numbers as well as <dfn>algebraic
+ * rings</dfn> and ring-links numbers.
+ *
+ * <p>For example, mathematical integers form a ring and, including
+ * Euclidean division support, integers support the operations in
+ * this interface. Fields also support the operations in
+ * question. Commonly used fields include rational numbers, real
+ * numbers, and complex numbers.  A field has a set of values and
+ * operations on those values. The operations have various properties
+ * known as the <dfn>field axioms</dfn>. These include associativity
+ * of addition and multiplication, commutativity of addition and
+ * multiplication, and multiplication distributing over
+ * addition. Fields can be {@linkplain Orderable ordered} (rational
+ * numbers, real numbers) or unordered (complex numbers).
+ *
+ * <p>Types used to approximate a field, such as a floating-point type
+ * used to approximate real numbers, will both approximate the set of
+ * values of the field and the set of properties over the supported
+ * operations. In particular, properties like associativity of
+ * addition are <em>not</em> expected to hold for a floating-point
+ * type.
+ *
+ * @apiNote
+ * A particular numerical type may support returning a number of that
+ * type for all arguments to add, subtract, multiply, and (possibly)
+ * divide. An operation having that property is said to be
+ * <dfn>closed</dfn> over that operation. For example, built-in {@code
+ * int} arithmetic is closed over add, subtract, and multiply, but is
+ * <em>not</em> closed under divide since an {@code
+ * ArithmeticException} is thrown on a zero divisor. Built-in
+ * arithmetic on {@code float} and {@code double} is closed under all
+ * of add, subtract, multiply, and divide, with infinities and NaN
+ * (not-a-number) being returned for cases that would otherwise be
+ * exceptional.
+ *
+ * <p>A given numerical type implementing this interface may or may
+ * not be closed under any particular operation. If it is <em>not</em>
+ * closed, the conditions where an exception is thrown should be
+ * documented with the expected outcome being throwing an {@code
+ * ArithmeticException} rather than returning a value.
+ *
+ * <p>Future work: consider interactions with / support from {@link
+ * java.util.Formatter} and numerical types.
+ *
+ * @param <NT> The numerical type
+ * @see Orderable
+ */
+public interface Numerical<NT> {
+    /**
+     * Addition operation, binary operator "{@code +}".
+     *
+     * @param addend the first operand
+     * @param augend the second operand
+     * @return the sum of the operands
+     * @throws ArithmeticException if the numerical type does not
+     * allow adding the operands in question
+     */
+     NT add(NT addend, NT augend);
+
+    /**
+     * Subtraction operation, binary operator "{@code -}".
+     *
+     * @implSpec
+     * The default implementation returns the sum of the first
+     * operand with the negation of the second operand.
+     *
+     * @param minuend the first operand
+     * @param  subtrahend the second operand
+     * @return the difference of the operands
+     * @throws ArithmeticException if the numerical type does not
+     * allow subtracting the operands in question
+     */
+    default NT subtract(NT minuend, NT subtrahend) {
+        return this.add(minuend, this.negate(subtrahend));
+    }
+
+    /**
+     * Multiplication operation, binary operator "{@code *}".
+     *
+     * @param multiplier the first operand
+     * @param multiplicand the second operand
+     * @return the product of the operands
+     * @throws ArithmeticException if the numerical type does not
+     * allow multiplying the operands in question
+     */
+     NT multiply(NT multiplier, NT multiplicand);
+
+    /**
+     * Division operation, binary operator "{@code /}".
+     *
+     * @apiNote
+     * Numerical types can have different policies regarding how
+     * divisors equal to zero are handled. Many types will throw an
+     * {@code ArithmeticException} in those cases. However, other
+     * types like {@linkplain StandardFloatingPoint floating-point
+     * types} can return a special value like NaN (not-a-number).
+     *
+     * @throws ArithmeticException if the divisor is zero and zero
+     * divisors are not allowed
+     * @throws UnsupportedOperationException if division is not supported
+     * @param dividend the first operand
+     * @param divisor the second operand
+     * @return the quotient of the operands
+     */
+     NT divide(NT dividend, NT divisor);
+
+    /**
+     * Remainder operation, binary operator "{@code %}".
+     *
+     * @apiNote
+     * Numerical types can have different policies regarding how
+     * divisors equal to zero are handled. Many types will throw an
+     * {@code ArithmeticException} in those cases. However, other
+     * types like {@linkplain StandardFloatingPoint floating-point
+     * types} can return a special value like NaN (not-a-number).
+     *
+     * @throws ArithmeticException if the divisor is zero and zero
+     * divisors are not allowed
+     * @throws UnsupportedOperationException if remainder is not supported
+     * @param dividend the first operand
+     * @param divisor the second operand
+     * @return the quotient of the operands
+     */
+     NT remainder(NT dividend, NT divisor);
+
+    /**
+     * Unary plus operation, unary operator "{@code +}".
+     *
+     * @apiNote
+     * It this needed? Default to returning this/operand? Or just to
+     * be be no-op not recognized for overloading?
+     *
+     * @implSpec
+     * The default implementation returns the operand.
+     *
+     * @param operand the operand
+     * @return unary plus of the operand
+     */
+     default NT plus(NT operand) {
+         return operand;
+     }
+
+    /**
+     * Negation operation, unary operator "{@code -}".
+     *
+     * @throws UnsupportedOperationException if negation is not supported
+     * @param operand the operand
+     * @return the negation of the operand
+     * @throws ArithmeticException if the numerical type does not
+     * allow negating the operand in question
+     */
+     NT negate(NT operand);
+}