1//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file implements a fairly generic conversion from a wider to a narrower
10// IEEE-754 floating-point type in the default (round to nearest, ties to even)
11// rounding mode.  The constants and types defined following the includes below
12// parameterize the conversion.
13//
14// This routine can be trivially adapted to support conversions to
15// half-precision or from quad-precision. It does not support types that don't
16// use the usual IEEE-754 interchange formats; specifically, some work would be
17// needed to adapt it to (for example) the Intel 80-bit format or PowerPC
18// double-double format.
19//
20// Note please, however, that this implementation is only intended to support
21// *narrowing* operations; if you need to convert to a *wider* floating-point
22// type (e.g. float -> double), then this routine will not do what you want it
23// to.
24//
25// It also requires that integer types at least as large as both formats
26// are available on the target platform; this may pose a problem when trying
27// to add support for quad on some 32-bit systems, for example.
28//
29// Finally, the following assumptions are made:
30//
31// 1. Floating-point types and integer types have the same endianness on the
32//    target platform.
33//
34// 2. Quiet NaNs, if supported, are indicated by the leading bit of the
35//    significand field being set.
36//
37//===----------------------------------------------------------------------===//
38
39#include "fp_trunc.h"
40
41static __inline dst_t __truncXfYf2__(src_t a) {
42  // Various constants whose values follow from the type parameters.
43  // Any reasonable optimizer will fold and propagate all of these.
44  const int srcBits = sizeof(src_t) * CHAR_BIT;
45  const int srcExpBits = srcBits - srcSigBits - 1;
46  const int srcInfExp = (1 << srcExpBits) - 1;
47  const int srcExpBias = srcInfExp >> 1;
48
49  const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
50  const src_rep_t srcSignificandMask = srcMinNormal - 1;
51  const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
52  const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
53  const src_rep_t srcAbsMask = srcSignMask - 1;
54  const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
55  const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
56  const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigBits - 1);
57  const src_rep_t srcNaNCode = srcQNaN - 1;
58
59  const int dstBits = sizeof(dst_t) * CHAR_BIT;
60  const int dstExpBits = dstBits - dstSigBits - 1;
61  const int dstInfExp = (1 << dstExpBits) - 1;
62  const int dstExpBias = dstInfExp >> 1;
63
64  const int underflowExponent = srcExpBias + 1 - dstExpBias;
65  const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
66  const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
67  const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
68
69  const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
70  const dst_rep_t dstNaNCode = dstQNaN - 1;
71
72  // Break a into a sign and representation of the absolute value.
73  const src_rep_t aRep = srcToRep(a);
74  const src_rep_t aAbs = aRep & srcAbsMask;
75  const src_rep_t sign = aRep & srcSignMask;
76  dst_rep_t absResult;
77
78  if (aAbs - underflow < aAbs - overflow) {
79    // The exponent of a is within the range of normal numbers in the
80    // destination format.  We can convert by simply right-shifting with
81    // rounding and adjusting the exponent.
82    absResult = aAbs >> (srcSigBits - dstSigBits);
83    absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
84
85    const src_rep_t roundBits = aAbs & roundMask;
86    // Round to nearest.
87    if (roundBits > halfway)
88      absResult++;
89    // Tie to even.
90    else if (roundBits == halfway)
91      absResult += absResult & 1;
92  } else if (aAbs > srcInfinity) {
93    // a is NaN.
94    // Conjure the result by beginning with infinity, setting the qNaN
95    // bit and inserting the (truncated) trailing NaN field.
96    absResult = (dst_rep_t)dstInfExp << dstSigBits;
97    absResult |= dstQNaN;
98    absResult |=
99        ((aAbs & srcNaNCode) >> (srcSigBits - dstSigBits)) & dstNaNCode;
100  } else if (aAbs >= overflow) {
101    // a overflows to infinity.
102    absResult = (dst_rep_t)dstInfExp << dstSigBits;
103  } else {
104    // a underflows on conversion to the destination type or is an exact
105    // zero.  The result may be a denormal or zero.  Extract the exponent
106    // to get the shift amount for the denormalization.
107    const int aExp = aAbs >> srcSigBits;
108    const int shift = srcExpBias - dstExpBias - aExp + 1;
109
110    const src_rep_t significand = (aRep & srcSignificandMask) | srcMinNormal;
111
112    // Right shift by the denormalization amount with sticky.
113    if (shift > srcSigBits) {
114      absResult = 0;
115    } else {
116      const bool sticky = (significand << (srcBits - shift)) != 0;
117      src_rep_t denormalizedSignificand = significand >> shift | sticky;
118      absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
119      const src_rep_t roundBits = denormalizedSignificand & roundMask;
120      // Round to nearest
121      if (roundBits > halfway)
122        absResult++;
123      // Ties to even
124      else if (roundBits == halfway)
125        absResult += absResult & 1;
126    }
127  }
128
129  // Apply the signbit to the absolute value.
130  const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
131  return dstFromRep(result);
132}
133