compiler-rt/lib/builtins/fp_trunc_impl.inc

//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file implements a fairly generic conversion from a wider to a narrower
// IEEE-754 floating-point type in the default (round to nearest, ties to even)
// rounding mode.  The constants and types defined following the includes below
// parameterize the conversion.
//
// This routine can be trivially adapted to support conversions to
// half-precision or from quad-precision. It does not support types that don't
// use the usual IEEE-754 interchange formats; specifically, some work would be
// needed to adapt it to (for example) the Intel 80-bit format or PowerPC
// double-double format.
//
// Note please, however, that this implementation is only intended to support
// *narrowing* operations; if you need to convert to a *wider* floating-point
// type (e.g. float -> double), then this routine will not do what you want it
// to.
//
// It also requires that integer types at least as large as both formats
// are available on the target platform; this may pose a problem when trying
// to add support for quad on some 32-bit systems, for example.
//
// Finally, the following assumptions are made:
//
// 1. Floating-point types and integer types have the same endianness on the
//    target platform.
//
// 2. Quiet NaNs, if supported, are indicated by the leading bit of the
//    significand field being set.
//
//===----------------------------------------------------------------------===//

#include "fp_trunc.h"

static __inline dst_t __truncXfYf2__(src_t a) {
  // Various constants whose values follow from the type parameters.
  // Any reasonable optimizer will fold and propagate all of these.
  const int srcBits = sizeof(src_t) * CHAR_BIT;
  const int srcExpBits = srcBits - srcSigBits - 1;
  const int srcInfExp = (1 << srcExpBits) - 1;
  const int srcExpBias = srcInfExp >> 1;

  const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
  const src_rep_t srcSignificandMask = srcMinNormal - 1;
  const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
  const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
  const src_rep_t srcAbsMask = srcSignMask - 1;
  const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
  const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
  const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigBits - 1);
  const src_rep_t srcNaNCode = srcQNaN - 1;

  const int dstBits = sizeof(dst_t) * CHAR_BIT;
  const int dstExpBits = dstBits - dstSigBits - 1;
  const int dstInfExp = (1 << dstExpBits) - 1;
  const int dstExpBias = dstInfExp >> 1;

  const int underflowExponent = srcExpBias + 1 - dstExpBias;
  const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
  const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
  const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;

  const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
  const dst_rep_t dstNaNCode = dstQNaN - 1;

  // Break a into a sign and representation of the absolute value.
  const src_rep_t aRep = srcToRep(a);
  const src_rep_t aAbs = aRep & srcAbsMask;
  const src_rep_t sign = aRep & srcSignMask;
  dst_rep_t absResult;

  if (aAbs - underflow < aAbs - overflow) {
    // The exponent of a is within the range of normal numbers in the
    // destination format.  We can convert by simply right-shifting with
    // rounding and adjusting the exponent.
    absResult = aAbs >> (srcSigBits - dstSigBits);
    absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;

    const src_rep_t roundBits = aAbs & roundMask;
    // Round to nearest.
    if (roundBits > halfway)
      absResult++;
    // Tie to even.
    else if (roundBits == halfway)
      absResult += absResult & 1;
  } else if (aAbs > srcInfinity) {
    // a is NaN.
    // Conjure the result by beginning with infinity, setting the qNaN
    // bit and inserting the (truncated) trailing NaN field.
    absResult = (dst_rep_t)dstInfExp << dstSigBits;
    absResult |= dstQNaN;
    absResult |=
        ((aAbs & srcNaNCode) >> (srcSigBits - dstSigBits)) & dstNaNCode;
  } else if (aAbs >= overflow) {
    // a overflows to infinity.
    absResult = (dst_rep_t)dstInfExp << dstSigBits;
  } else {
    // a underflows on conversion to the destination type or is an exact
    // zero.  The result may be a denormal or zero.  Extract the exponent
    // to get the shift amount for the denormalization.
    const int aExp = aAbs >> srcSigBits;
    const int shift = srcExpBias - dstExpBias - aExp + 1;

    const src_rep_t significand = (aRep & srcSignificandMask) | srcMinNormal;

    // Right shift by the denormalization amount with sticky.
    if (shift > srcSigBits) {
      absResult = 0;
    } else {
      const bool sticky = (significand << (srcBits - shift)) != 0;
      src_rep_t denormalizedSignificand = significand >> shift | sticky;
      absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
      const src_rep_t roundBits = denormalizedSignificand & roundMask;
      // Round to nearest
      if (roundBits > halfway)
        absResult++;
      // Ties to even
      else if (roundBits == halfway)
        absResult += absResult & 1;
    }
  }

  // Apply the signbit to the absolute value.
  const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
  return dstFromRep(result);
}