int64x64-cairo.cc

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/*
 * Copyright (c) 2006 INRIA
 *
 * SPDX-License-Identifier: GPL-2.0-only
 *
 * Author: Mathieu Lacage <mathieu.lacage@sophia.inria.fr>
 */
#include "int64x64-cairo.h"
 
#include "abort.h"
#include "assert.h"
#include "log.h"
#include "test.h"
 
#include <cmath>
#include <iostream>
 
#if defined(INT64X64_USE_CAIRO) && !defined(PYTHON_SCAN)
 
// Include directly to allow optimizations within this compilation unit.
extern "C"
{
#include "cairo-wideint.c"
}
 
/**
 * @file
 * @ingroup highprec
 * Implementation of the ns3::int64x64_t type using the Cairo implementation.
 */
 
namespace ns3
{
 
// Note:  Logging in this file is largely avoided due to the
// number of calls that are made to these functions and the possibility
// of causing recursions leading to stack overflow
NS_LOG_COMPONENT_DEFINE("int64x64-cairo");
 
/**
 * @ingroup highprec
 * Compute the sign of the result of multiplying or dividing
 * Q64.64 fixed precision operands.
 *
 * @param [in]  sa The signed value of the first operand.
 * @param [in]  sb The signed value of the second operand.
 * @param [out] ua The unsigned magnitude of the first operand.
 * @param [out] ub The unsigned magnitude of the second operand.
 * @returns True if the result will be negative.
 */
static inline bool
output_sign(const cairo_int128_t sa,
            const cairo_int128_t sb,
            cairo_uint128_t& ua,
            cairo_uint128_t& ub)
{
    bool negA = _cairo_int128_negative(sa);
    bool negB = _cairo_int128_negative(sb);
    ua = _cairo_int128_to_uint128(sa);
    ub = _cairo_int128_to_uint128(sb);
    ua = negA ? _cairo_uint128_negate(ua) : ua;
    ub = negB ? _cairo_uint128_negate(ub) : ub;
    return (negA && !negB) || (!negA && negB);
}
 
void
int64x64_t::Mul(const int64x64_t& o)
{
    cairo_uint128_t a, b;
    bool sign = output_sign(_v, o._v, a, b);
    cairo_uint128_t result = Umul(a, b);
    _v = sign ? _cairo_uint128_negate(result) : result;
}
 
cairo_uint128_t
int64x64_t::Umul(const cairo_uint128_t a, const cairo_uint128_t b)
{
    cairo_uint128_t result;
    cairo_uint128_t hiPart, loPart, midPart;
    cairo_uint128_t res1, res2;
 
    // Multiplying (a.h 2^64 + a.l) x (b.h 2^64 + b.l) =
    //             2^128 a.h b.h + 2^64*(a.h b.l+b.h a.l) + a.l b.l
    // get the low part a.l b.l
    // multiply the fractional part
    loPart = _cairo_uint64x64_128_mul(a.lo, b.lo);
    // compute the middle part 2^64*(a.h b.l+b.h a.l)
    midPart = _cairo_uint128_add(_cairo_uint64x64_128_mul(a.lo, b.hi),
                                 _cairo_uint64x64_128_mul(a.hi, b.lo));
    // compute the high part 2^128 a.h b.h
    hiPart = _cairo_uint64x64_128_mul(a.hi, b.hi);
    // if the high part is not zero, put a warning
    NS_ABORT_MSG_IF(hiPart.hi != 0,
                    "High precision 128 bits multiplication error: multiplication overflow.");
 
    // Adding 64-bit terms to get 128-bit results, with carries
    res1 = _cairo_uint64_to_uint128(loPart.hi);
    res2 = _cairo_uint64_to_uint128(midPart.lo);
    result = _cairo_uint128_add(res1, res2);
 
    res1 = _cairo_uint64_to_uint128(midPart.hi);
    res2 = _cairo_uint64_to_uint128(hiPart.lo);
    res1 = _cairo_uint128_add(res1, res2);
    res1 = _cairo_uint128_lsl(res1, 64);
 
    result = _cairo_uint128_add(result, res1);
 
    return result;
}
 
void
int64x64_t::Div(const int64x64_t& o)
{
    cairo_uint128_t a, b;
    bool sign = output_sign(_v, o._v, a, b);
    cairo_uint128_t result = Udiv(a, b);
    _v = sign ? _cairo_uint128_negate(result) : result;
}
 
cairo_uint128_t
int64x64_t::Udiv(const cairo_uint128_t a, const cairo_uint128_t b)
{
    cairo_uint128_t den = b;
    cairo_uquorem128_t qr = _cairo_uint128_divrem(a, b);
    cairo_uint128_t result = qr.quo;
    cairo_uint128_t rem = qr.rem;
 
    // Now, manage the remainder
    const uint64_t DIGITS = 64; // Number of fraction digits (bits) we need
    const cairo_uint128_t ZERO = _cairo_uint32_to_uint128((uint32_t)0);
 
    NS_ASSERT_MSG(_cairo_uint128_lt(rem, den), "Remainder not less than divisor");
 
    uint64_t digis = 0; // Number of digits we have already
    uint64_t shift = 0; // Number we are going to get this round
 
    // Skip trailing zeros in divisor
    while ((shift < DIGITS) && !(den.lo & 0x1))
    {
        ++shift;
        den = _cairo_uint128_rsl(den, 1);
    }
 
    while ((digis < DIGITS) && !(_cairo_uint128_eq(rem, ZERO)))
    {
        // Skip leading zeros in remainder
        while ((digis + shift < DIGITS) && !(rem.hi & HPCAIRO_MASK_HI_BIT))
        {
            ++shift;
            rem = _cairo_int128_lsl(rem, 1);
        }
 
        // Cast off denominator bits if:
        //   Need more digits and
        //     LSB is zero or
        //     rem < den
        while ((digis + shift < DIGITS) && (!(den.lo & 0x1) || _cairo_uint128_lt(rem, den)))
        {
            ++shift;
            den = _cairo_uint128_rsl(den, 1);
        }
 
        // Do the division
        qr = _cairo_uint128_divrem(rem, den);
 
        // Add in the quotient as shift bits of the fraction
        result = _cairo_uint128_lsl(result, static_cast<int>(shift));
        result = _cairo_uint128_add(result, qr.quo);
        rem = qr.rem;
        digis += shift;
        shift = 0;
    }
    // Did we run out of remainder?
    if (digis < DIGITS)
    {
        shift = DIGITS - digis;
        result = _cairo_uint128_lsl(result, static_cast<int>(shift));
    }
 
    return result;
}
 
void
int64x64_t::MulByInvert(const int64x64_t& o)
{
    bool sign = _cairo_int128_negative(_v);
    cairo_uint128_t a = sign ? _cairo_int128_negate(_v) : _v;
    cairo_uint128_t result = UmulByInvert(a, o._v);
 
    _v = sign ? _cairo_int128_negate(result) : result;
}
 
cairo_uint128_t
int64x64_t::UmulByInvert(const cairo_uint128_t a, const cairo_uint128_t b)
{
    cairo_uint128_t result;
    cairo_uint128_t hi, mid;
    hi = _cairo_uint64x64_128_mul(a.hi, b.hi);
    mid = _cairo_uint128_add(_cairo_uint64x64_128_mul(a.hi, b.lo),
                             _cairo_uint64x64_128_mul(a.lo, b.hi));
    mid.lo = mid.hi;
    mid.hi = 0;
    result = _cairo_uint128_add(hi, mid);
    return result;
}
 
int64x64_t
int64x64_t::Invert(const uint64_t v)
{
    NS_ASSERT(v > 1);
    cairo_uint128_t a, factor;
    a.hi = 1;
    a.lo = 0;
    factor.hi = 0;
    factor.lo = v;
    int64x64_t result;
    result._v = Udiv(a, factor);
    int64x64_t tmp = int64x64_t(v, 0);
    tmp.MulByInvert(result);
    if (tmp.GetHigh() != 1)
    {
        cairo_uint128_t one = {1, 0};
        result._v = _cairo_uint128_add(result._v, one);
    }
    return result;
}
 
} // namespace ns3
 
#endif /* INT64X64_CAIRO_H */