To compile code performing an arithmetic operation.

§1. This section provides a single function to compile Inter code to perform an arithmetic operation. It implements the {-arithmetic-operation:X:Y} bracing when used in inline invocations, and is also needed for equation solving; see Compile Solutions to Equations. Because of that, the function is called either with X and Y set to values, or with EX and EY set to equation nodes, but not both. eqn is set only for the equations case; but in both cases KX and KY are the kinds of the arithmetic operands, and op is the operation number.

For unary operations, Y, EY and KY will all be NULL.

What happens is straightforward enough, but we provide a fair range of different operations, and we have to manage scaling factors and whether the underlying arithmetic is integer or floating-point.

void CompileArithmetic::perform_arithmetic_emit?Usage of CompileArithmetic::perform_arithmetic_emit:
Compile Invocations Inline - §6.6.9
Compile Solutions to Equations - §4.1(int op, equation *eqn,
    parse_node *X, equation_node *EX, kind *KX,
    parse_node *Y, equation_node *EY, kind *KY) {
    int binary = TRUE;
    if (Kinds::Dimensions::arithmetic_op_is_unary(op)) binary = FALSE;
    int use_fp = FALSE, promote_X = FALSE, promote_Y = FALSE, demote_result = FALSE;
    kind *KR = Kinds::Dimensions::arithmetic_on_kinds(KX, KY, op);
    if ((KX) && (KY)) {
        if (((Kinds::FloatingPoint::uses_floating_point(KX)) ||
                (Kinds::FloatingPoint::uses_floating_point(KY)))
            && (Kinds::FloatingPoint::uses_floating_point(KR) == FALSE)
            && ((op == TIMES_OPERATION) || (op == DIVIDE_OPERATION)))
            demote_result = TRUE;
    }
    Choose which form of arithmetic and promotion1.1;
    Optimise promotions from number to real number1.2;

    if (demote_result) Kinds::FloatingPoint::begin_deflotation_emit(KR);
    operand_emission_data oed_X, oed_Y;
    Set up the operands1.3;
    Emit the code for the operation1.4;
    if (demote_result) Kinds::FloatingPoint::end_deflotation_emit(KR);
}

§1.1. For a binary operation, note that "pi plus pi", "pi plus 3", and "3 plus pi" must all use floating-point, whereas "3 plus 3" uses integer arithmetic: in other words, if either operand is real, then real arithmetic must be used. "Promotion" means converting an integer to a real number (I'm not quite sure why that is traditionally thought of as being better) — in "pi plus 3", the integer 3 is promoted to real.

Choose which form of arithmetic and promotion1.1 =

    if (binary) {
        if (Kinds::FloatingPoint::uses_floating_point(KX)) {
            if (Kinds::FloatingPoint::uses_floating_point(KY)) {
                use_fp = TRUE; promote_X = FALSE; promote_Y = FALSE;
            } else {
                use_fp = TRUE; promote_X = FALSE; promote_Y = TRUE;
            }
        } else {
            if (Kinds::FloatingPoint::uses_floating_point(KY)) {
                use_fp = TRUE; promote_X = TRUE; promote_Y = FALSE;
            } else {
                use_fp = FALSE; promote_X = FALSE; promote_Y = FALSE;
            }
        }
    } else {
        if (Kinds::FloatingPoint::uses_floating_point(KX)) {
            use_fp = TRUE; promote_X = FALSE; promote_Y = FALSE;
        } else {
            use_fp = FALSE; promote_X = FALSE; promote_Y = FALSE;
        }
    }

• This code is used in §1.

§1.2. Making this optimisation ensures that if X or Y are literal K_number values then they will be converted to literal K_real_number values at compile time rather than at runtime, saving a function call in cases like

    let the magic value be 4 + pi;

where there is no need to convert 4 to 4.0 at runtime; we can simply reinterpret it as a real.

Optimise promotions from number to real number1.2 =

    if ((promote_X) && (Kinds::eq(KX, K_number))) { promote_X = FALSE; KX = K_real_number; }
    if ((promote_Y) && (Kinds::eq(KY, K_number))) { promote_Y = FALSE; KY = K_real_number; }

• This code is used in §1.

§1.3. Set up the operands1.3 =

    oed_X = CompileArithmetic::operand_data(X, EX, KX, promote_X, eqn);
    oed_Y = CompileArithmetic::operand_data(Y, EY, KY, promote_Y, eqn);
    if (use_fp == FALSE) {
        switch (op) {
            case TIMES_OPERATION:    oed_X.rescale_multiply_K = KY; break;
            case DIVIDE_OPERATION:   oed_X.rescale_divide_K = KY; break;
            case ROOT_OPERATION:     oed_X.rescale_root = 2; break;
            case CUBEROOT_OPERATION: oed_X.rescale_root = 3; break;
        }
    }

• This code is used in §1.

§1.4. Emit the code for the operation1.4 =

    switch (op) {
        case EQUALS_OPERATION: Emit set-equals1.4.1; break;
        case POWER_OPERATION: Emit a power of the left operand1.4.2; break;
        case IMPLICIT_APPLICATION_OPERATION: Emit implicit application1.4.3; break;
        case PLUS_OPERATION:
        case MINUS_OPERATION:
        case TIMES_OPERATION:
        case DIVIDE_OPERATION:
        case REMAINDER_OPERATION:
        case APPROXIMATE_OPERATION:
        case ROOT_OPERATION:
        case CUBEROOT_OPERATION:
        case NEGATE_OPERATION:
            CompileArithmetic::compile_by_schema(op, &oed_X, &oed_Y);
            break;
        case REALROOT_OPERATION:
            CompileArithmetic::compile_by_schema(ROOT_OPERATION, &oed_X, &oed_Y);
            break;
        default:
            StandardProblems::sentence_problem(Task::syntax_tree(), _p_(BelievedImpossible),
                "this doesn't seem to be an arithmetic operation",
                "suggesting a problem with some inline definition.");
            break;
    }

• This code is used in §1.

§1.4.1. Emit set-equals1.4.1 =

    EmitCode::inv(STORE_BIP);
    EmitCode::down();
        EmitCode::reference();
        EmitCode::down();
            CompileArithmetic::compile_operand(&oed_X);
        EmitCode::up();
        CompileArithmetic::compile_operand(&oed_Y);
    EmitCode::up();

• This code is used in §1.4.

§1.4.2. We accomplish integer powers by repeated multiplication. This is partly because Inter has no "to the power of" opcode, partly because the powers involved will always be small, partly because of the need for scaling to come out right.

Emit a power of the left operand1.4.2 =

    if (use_fp) {
        CompileArithmetic::compile_by_schema(op, &oed_X, &oed_Y);
    } else {
        int p = 0;
        if (Y) p = Rvalues::to_int(Y);
        else p = Rvalues::to_int(EY->leaf_constant);
        if (p <= 0) EquationSolver::issue_problem_on_root(eqn, EY);
        else if (p == 1) CompileArithmetic::compile_operand(&oed_X);
        else {
            for (int i=1; i<p; i++) {
                Kinds::Scalings::rescale_multiplication_emit_op(KX, KX);
                EmitCode::inv(TIMES_BIP);
                EmitCode::down();
                    CompileArithmetic::compile_operand(&oed_X);
            }
            CompileArithmetic::compile_operand(&oed_X);
            for (int i=1; i<p; i++) {
                EmitCode::up();
                Kinds::Scalings::rescale_multiplication_emit_factor(KX, KX);
            }
        }
    }

• This code is used in §1.4.

§1.4.3. This is used in equation solving only; here we are evaluating a mathematical function like log pi, where X is the function (in this case log) and Y the value (in this case pi). Clearly a function cannot be promoted.

Emit implicit application1.4.3 =

    oed_X.promote_me = FALSE;
    EmitCode::inv(INDIRECT1_BIP);
    EmitCode::down();
        CompileArithmetic::compile_operand(&oed_X);
        CompileArithmetic::compile_operand(&oed_Y);
    EmitCode::up();

• This code is used in §1.4.

§2.

typedef struct operand_emission_data {
    struct parse_node *X;
    struct equation_node *EX;
    struct kind *KX;
    struct equation *eqn;
    int promote_me;
    struct kind *rescale_divide_K;
    struct kind *rescale_multiply_K;
    int rescale_root;
} operand_emission_data;

operand_emission_data CompileArithmetic::operand_data?Usage of CompileArithmetic::operand_data:
§1.3(parse_node *X, equation_node *EX,
    kind *KX, int promote_me, equation *eqn) {
    operand_emission_data oed;
    oed.X = X; oed.EX = EX; oed.KX = KX; oed.promote_me = promote_me; oed.eqn = eqn;
    oed.rescale_divide_K = NULL; oed.rescale_multiply_K = NULL; oed.rescale_root = 0;
    return oed;
}

void CompileArithmetic::compile_by_schema?Usage of CompileArithmetic::compile_by_schema:
§1.4, §1.4.2(int op,
    operand_emission_data *oed_X, operand_emission_data *oed_Y) {
    if (oed_X->rescale_multiply_K)
        Kinds::Scalings::rescale_multiplication_emit_op(oed_X->KX, oed_Y->KX);
    TEMPORARY_TEXT(prototype)
    CompileArithmetic::schema(prototype, oed_X->KX, oed_Y->KX, op, I"*1", I"*2");
    i6_schema *sch = Calculus::Schemas::new("%S;", prototype);
    CompileSchemas::with_callbacks_in_val_context(sch, oed_X, oed_Y,
        &CompileArithmetic::compile_operand);
    DISCARD_TEXT(prototype)
    if (oed_X->rescale_multiply_K)
        Kinds::Scalings::rescale_multiplication_emit_factor(oed_X->KX, oed_Y->KX);
}

void CompileArithmetic::compile_operand?Usage of CompileArithmetic::compile_operand:
§1.4.1, §1.4.2, §1.4.3(void *oed_v) {
    operand_emission_data *oed = (operand_emission_data *) oed_v;
    if (Kinds::Behaviour::uses_block_values(oed->KX)) {
        EmitCode::call(Hierarchy::find(COPYPV_HL));
        EmitCode::down();
            Frames::emit_new_local_value(oed->KX);
    }
    if (oed->promote_me) Kinds::FloatingPoint::begin_flotation_emit(oed->KX);

    if (oed->rescale_divide_K) Kinds::Scalings::rescale_division_emit_op(oed->KX, oed->rescale_divide_K);
    else if (oed->rescale_root) Kinds::Scalings::rescale_root_emit_op(oed->KX, oed->rescale_root);

    if (oed->X) CompileValues::to_code_val_of_kind(oed->X, oed->KX);
    else EquationSolver::compile_enode(oed->eqn, oed->EX);

    if (oed->rescale_divide_K) Kinds::Scalings::rescale_division_emit_factor(oed->KX, oed->rescale_divide_K);
    else if (oed->rescale_root) Kinds::Scalings::rescale_root_emit_factor(oed->KX, oed->rescale_root);

    if (oed->promote_me) Kinds::FloatingPoint::end_flotation_emit(oed->KX);
    if (Kinds::Behaviour::uses_block_values(oed->KX)) {
        EmitCode::up();
    }
}

• The structure operand_emission_data is private to this section.

§3.

void CompileArithmetic::schema?Usage of CompileArithmetic::schema:
§2
Compile Lvalues - §5(OUTPUT_STREAM, kind *KX, kind *KY,
    int operation, text_stream *X, text_stream *Y) {
    int reducing_modulo_1440 = FALSE;
    #ifdef IF_MODULE
    kind *KT = TimesOfDay::kind();
    if ((KT) && (Kinds::eq(KX, KT))) reducing_modulo_1440 = TRUE;
    #endif
    int modulus = Kinds::Behaviour::get_arithmetic_modulus(KX);
    if (modulus > 0) WRITE("CongruenceClass(");

    text_stream *defn = Kinds::Behaviour::get_arithmetic_schema(operation, KX, KY);
    if (Str::eq(defn, I"none")) Throw problem message and return3.1;
    if (Str::len(defn) == 0) {
        if (Kinds::FloatingPoint::uses_floating_point(KX))
            defn = Kinds::Behaviour::get_arithmetic_schema(operation, K_real_number, K_real_number);
        else
            defn = Kinds::Behaviour::get_arithmetic_schema(operation, K_number, K_number);
    }
    if ((Str::len(defn) == 0) || (Str::eq(defn, I"none")))
        Throw problem message and return3.1;
    WRITE("%S", defn);
    if (modulus > 0) WRITE(", %d)", modulus);
}

§3.1. Throw problem message and return3.1 =

    WRITE("0");
    Problems::quote_source(1, current_sentence);
    Problems::quote_kind(2, KX);
    Problems::quote_kind(3, KY);
    StandardProblems::handmade_problem(Task::syntax_tree(),
        _p_(PM_ArithmeticImpossible));
    switch (operation) {
        case PLUS_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't add %2 and %3.");
            break;
        case MINUS_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't subtract %2 from %3.");
            break;
        case TIMES_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't multiply %2 and %3.");
            break;
        case DIVIDE_OPERATION:
        case REMAINDER_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't divide %2 by %3.");
            break;
        case APPROXIMATE_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't approximate %2 to %3.");
            break;
        case ROOT_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't take a square root of %2.");
            break;
        case CUBEROOT_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't take a cube root of %2.");
            break;
        case NEGATE_OPERATION:
            Problems::issue_problem_segment(
                "In '%1', I can't negate %2.");
            break;
        default:
            Problems::issue_problem_segment(
                "In '%1', I can't perform this arithmetic operation on %2 and %3.");
            break;
    }
    Problems::issue_problem_end();
    return;

• This code is used in §3 (twice).