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
41// The destination type may use a usual IEEE-754 interchange format or Intel
42// 80-bit format. In particular, for the destination type dstSigFracBits may be
43// not equal to dstSigBits. The source type is assumed to be one of IEEE-754
44// standard types.
45static __inline dst_t __truncXfYf2__(src_t a) {
46 // Various constants whose values follow from the type parameters.
47 // Any reasonable optimizer will fold and propagate all of these.
48 const int srcInfExp = (1 << srcExpBits) - 1;
49 const int srcExpBias = srcInfExp >> 1;
50
51 const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigFracBits;
52 const src_rep_t roundMask =
53 (SRC_REP_C(1) << (srcSigFracBits - dstSigFracBits)) - 1;
54 const src_rep_t halfway = SRC_REP_C(1)
55 << (srcSigFracBits - dstSigFracBits - 1);
56 const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigFracBits - 1);
57 const src_rep_t srcNaNCode = srcQNaN - 1;
58
59 const int dstInfExp = (1 << dstExpBits) - 1;
60 const int dstExpBias = dstInfExp >> 1;
61 const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
62
63 const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigFracBits - 1);
64 const dst_rep_t dstNaNCode = dstQNaN - 1;
65
66 const src_rep_t aRep = srcToRep(x: a);
67 const src_rep_t srcSign = extract_sign_from_src(x: aRep);
68 const src_rep_t srcExp = extract_exp_from_src(x: aRep);
69 const src_rep_t srcSigFrac = extract_sig_frac_from_src(x: aRep);
70
71 dst_rep_t dstSign = srcSign;
72 dst_rep_t dstExp;
73 dst_rep_t dstSigFrac;
74
75 // Same size exponents and a's significand tail is 0.
76 // The significand can be truncated and the exponent can be copied over.
77 const int sigFracTailBits = srcSigFracBits - dstSigFracBits;
78 if (srcExpBits == dstExpBits &&
79 ((aRep >> sigFracTailBits) << sigFracTailBits) == aRep) {
80 dstExp = srcExp;
81 dstSigFrac = (dst_rep_t)(srcSigFrac >> sigFracTailBits);
82 return dstFromRep(x: construct_dst_rep(sign: dstSign, exp: dstExp, sigFrac: dstSigFrac));
83 }
84
85 const int dstExpCandidate = ((int)srcExp - srcExpBias) + dstExpBias;
86 if (dstExpCandidate >= 1 && dstExpCandidate < dstInfExp) {
87 // The exponent of a is within the range of normal numbers in the
88 // destination format. We can convert by simply right-shifting with
89 // rounding and adjusting the exponent.
90 dstExp = dstExpCandidate;
91 dstSigFrac = (dst_rep_t)(srcSigFrac >> sigFracTailBits);
92
93 const src_rep_t roundBits = srcSigFrac & roundMask;
94 // Round to nearest.
95 if (roundBits > halfway)
96 dstSigFrac++;
97 // Tie to even.
98 else if (roundBits == halfway)
99 dstSigFrac += dstSigFrac & 1;
100
101 // Rounding has changed the exponent.
102 if (dstSigFrac >= (DST_REP_C(1) << dstSigFracBits)) {
103 dstExp += 1;
104 dstSigFrac ^= (DST_REP_C(1) << dstSigFracBits);
105 }
106 } else if (srcExp == srcInfExp && srcSigFrac) {
107 // a is NaN.
108 // Conjure the result by beginning with infinity, setting the qNaN
109 // bit and inserting the (truncated) trailing NaN field.
110 dstExp = dstInfExp;
111 dstSigFrac = dstQNaN;
112 dstSigFrac |= ((srcSigFrac & srcNaNCode) >> sigFracTailBits) & dstNaNCode;
113 } else if ((int)srcExp >= overflowExponent) {
114 dstExp = dstInfExp;
115 dstSigFrac = 0;
116 } else {
117 // a underflows on conversion to the destination type or is an exact
118 // zero. The result may be a denormal or zero. Extract the exponent
119 // to get the shift amount for the denormalization.
120 src_rep_t significand = srcSigFrac;
121 int shift = srcExpBias - dstExpBias - srcExp;
122
123 if (srcExp) {
124 // Set the implicit integer bit if the source is a normal number.
125 significand |= srcMinNormal;
126 shift += 1;
127 }
128
129 // Right shift by the denormalization amount with sticky.
130 if (shift > srcSigFracBits) {
131 dstExp = 0;
132 dstSigFrac = 0;
133 } else {
134 dstExp = 0;
135 const bool sticky = shift && ((significand << (srcBits - shift)) != 0);
136 src_rep_t denormalizedSignificand = significand >> shift | sticky;
137 dstSigFrac = denormalizedSignificand >> sigFracTailBits;
138 const src_rep_t roundBits = denormalizedSignificand & roundMask;
139 // Round to nearest
140 if (roundBits > halfway)
141 dstSigFrac++;
142 // Ties to even
143 else if (roundBits == halfway)
144 dstSigFrac += dstSigFrac & 1;
145
146 // Rounding has changed the exponent.
147 if (dstSigFrac >= (DST_REP_C(1) << dstSigFracBits)) {
148 dstExp += 1;
149 dstSigFrac ^= (DST_REP_C(1) << dstSigFracBits);
150 }
151 }
152 }
153
154 return dstFromRep(x: construct_dst_rep(sign: dstSign, exp: dstExp, sigFrac: dstSigFrac));
155}
156

source code of compiler-rt/lib/builtins/fp_trunc_impl.inc