1 //= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===//
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
7 //===----------------------------------------------------------------------===//
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.
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.
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
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.
29 // Finally, the following assumptions are made:
31 // 1. Floating-point types and integer types have the same endianness on the
34 // 2. Quiet NaNs, if supported, are indicated by the leading bit of the
35 // significand field being set.
37 //===----------------------------------------------------------------------===//
41 static __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;
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;
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;
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;
69 const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
70 const dst_rep_t dstNaNCode = dstQNaN - 1;
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;
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;
85 const src_rep_t roundBits = aAbs & roundMask;
87 if (roundBits > halfway)
90 else if (roundBits == halfway)
91 absResult += absResult & 1;
92 } else if (aAbs > srcInfinity) {
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;
99 ((aAbs & srcNaNCode) >> (srcSigBits - dstSigBits)) & dstNaNCode;
100 } else if (aAbs >= overflow) {
101 // a overflows to infinity.
102 absResult = (dst_rep_t)dstInfExp << dstSigBits;
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;
110 const src_rep_t significand = (aRep & srcSignificandMask) | srcMinNormal;
112 // Right shift by the denormalization amount with sticky.
113 if (shift > srcSigBits) {
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;
121 if (roundBits > halfway)
124 else if (roundBits == halfway)
125 absResult += absResult & 1;
129 // Apply the signbit to the absolute value.
130 const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
131 return dstFromRep(result);