root/src/Lerp.cpp

DEFINITIONS

1. lower_lerp

#include <cmath>
#include <algorithm>

#include "Lerp.h"
#include "IROperator.h"
#include "Simplify.h"

namespace Halide {
namespace Internal {

Expr lower_lerp(Expr zero_val, Expr one_val, Expr weight) {

    Expr result;

    internal_assert(zero_val.type() == one_val.type());
    internal_assert(weight.type().is_uint() || weight.type().is_float());

    Type result_type = zero_val.type();

    Expr bias_value = make_zero(result_type);
    Type computation_type = result_type;

    if (zero_val.type().is_int()) {
        computation_type = UInt(zero_val.type().bits(), zero_val.type().lanes());
        // We must take care to do the addition and subtraction of the
        // bias while in the unsigned computation type, where overflow
        // is well-defined.
        bias_value = cast(computation_type, result_type.min());
    }

    // For signed integer types, just convert everything to unsigned
    // and then back at the end to ensure proper rounding, etc.
    // There is likely a better way to handle this.
    if (result_type != computation_type) {
        zero_val = Cast::make(computation_type, zero_val) - bias_value;
        one_val =  Cast::make(computation_type, one_val)  - bias_value;
    }

    if (result_type.is_bool()) {
        Expr half_weight;
        if (weight.type().is_float())
            half_weight = 0.5f;
        else {
            half_weight = weight.type().max() / 2;
        }

        result = select(weight > half_weight, one_val, zero_val);
    } else {
        Expr typed_weight;
        Expr inverse_typed_weight;

        if (weight.type().is_float()) {
            typed_weight = weight;
            if (computation_type.is_uint()) {
                // TODO: Verify this reduces to efficient code or
                // figure out a better way to express a multiply
                // of unsigned 2^32-1 by a double promoted weight
                if (computation_type.bits() == 32) {
                    typed_weight =
                        Cast::make(computation_type,
                                   cast<double>(Expr(65535.0f)) * cast<double>(Expr(65537.0f)) *
                                   Cast::make(Float(64, typed_weight.type().lanes()), typed_weight));
                } else {
                    typed_weight =
                        Cast::make(computation_type,
                                   computation_type.max() * typed_weight);
                }
                inverse_typed_weight = computation_type.max() - typed_weight;
            } else {
                inverse_typed_weight = 1.0f - typed_weight;
            }

        } else {
            if (computation_type.is_float()) {
                int weight_bits = weight.type().bits();
                if (weight_bits == 32) {
                    // Should use ldexp, but can't make Expr from result
                    // that is double
                    typed_weight =
                        Cast::make(computation_type,
                                   cast<double>(weight) / (pow(cast<double>(2), 32) - 1));
                } else {
                    typed_weight =
                        Cast::make(computation_type,
                                   weight / ((float)ldexp(1.0f, weight_bits) - 1));
                }
                inverse_typed_weight = 1.0f - typed_weight;
            } else {
                // This code rescales integer weights to the right number of bits.
                // It takes advantage of (2^n - 1) == (2^(n/2) - 1)(2^(n/2) + 1)
                // e.g. 65535 = 255 * 257. (Ditto for the 32-bit equivalent.)
                // To recale a weight of m bits to be n bits, we need to do:
                //     scaled_weight = (weight / (2^m - 1)) * (2^n - 1)
                // which power of two values for m and n, results in a series like
                // so:
                //     (2^(m/2) + 1) * (2^(m/4) + 1) ... (2^(n*2) + 1)
                // The loop below computes a scaling constant and either multiples
                // or divides by the constant and relies on lowering and llvm to
                // generate efficient code for the operation.
                int bit_size_difference = weight.type().bits() - computation_type.bits();
                if (bit_size_difference == 0) {
                    typed_weight = weight;
                } else {
                    typed_weight = Cast::make(computation_type, weight);

                    int bits_left = ::abs(bit_size_difference);
                    int shift_amount = std::min(computation_type.bits(), weight.type().bits());
                    uint64_t scaling_factor = 1;
                    while (bits_left != 0) {
                        internal_assert(bits_left > 0);
                        scaling_factor = scaling_factor + (scaling_factor << shift_amount);
                        bits_left -= shift_amount;
                        shift_amount *= 2;
                    }
                    if (bit_size_difference < 0) {
                        typed_weight =
                            Cast::make(computation_type, weight) *
                            cast(computation_type, (int32_t)scaling_factor);
                    } else {
                        typed_weight =
                            Cast::make(computation_type,
                                       weight / cast(weight.type(), (int32_t)scaling_factor));
                    }
                }
                inverse_typed_weight =
                    Cast::make(computation_type,
                               computation_type.max() - typed_weight);
            }
        }

        if (computation_type.is_float()) {
            result = zero_val * inverse_typed_weight +
                one_val * typed_weight;
        } else {
            int32_t bits = computation_type.bits();
            switch (bits) {
            case 1:
                result = select(typed_weight, one_val, zero_val);
                break;
            case 8:
            case 16:
            case 32: {
                Expr zero_expand = Cast::make(UInt(2 * bits, computation_type.lanes()),
                                              zero_val);
                Expr  one_expand = Cast::make(UInt(2 * bits, one_val.type().lanes()),
                                              one_val);

                Expr rounding = Cast::make(UInt(2 * bits), 1) << Cast::make(UInt(2 * bits), (bits - 1));
                Expr divisor  = Cast::make(UInt(2 * bits), 1) << Cast::make(UInt(2 * bits), bits);

                Expr prod_sum = zero_expand * inverse_typed_weight +
                    one_expand * typed_weight + rounding;
                Expr divided = ((prod_sum / divisor) + prod_sum) / divisor;

                result = Cast::make(UInt(bits, computation_type.lanes()), divided);
                break;
            }
            case 64:
                // TODO: 64-bit lerp is not supported as current approach
                // requires double-width multiply.
                // There is an informative error message in IROperator.h.
                internal_error << "Can't do a 64-bit lerp.\n";
                break;
            default:
                break;
            }
        }

        if (!is_zero(bias_value)) {
            result = Cast::make(result_type, result + bias_value);
        }
    }

    return simplify(result);
}

}
}