1 //===-- lib/truncdfsf2.c - double -> single conversion ------------*- C -*-===//
2 //
3 // The LLVM Compiler Infrastructure
4 //
5 // This file is dual licensed under the MIT and the University of Illinois Open
6 // Source Licenses. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // This file implements a fairly generic conversion from a wider to a narrower
11 // IEEE-754 floating-point type in the default (round to nearest, ties to even)
12 // rounding mode. The constants and types defined following the includes below
13 // parameterize the conversion.
14 //
15 // This routine can be trivially adapted to support conversions to
16 // half-precision or from quad-precision. It does not support types that don't
17 // use the usual IEEE-754 interchange formats; specifically, some work would be
18 // needed to adapt it to (for example) the Intel 80-bit format or PowerPC
19 // double-double format.
20 //
21 // Note please, however, that this implementation is only intended to support
22 // *narrowing* operations; if you need to convert to a *wider* floating-point
23 // type (e.g. float -> double), then this routine will not do what you want it
24 // to.
25 //
26 // It also requires that integer types at least as large as both formats
27 // are available on the target platform; this may pose a problem when trying
28 // to add support for quad on some 32-bit systems, for example.
29 //
30 // Finally, the following assumptions are made:
31 //
32 // 1. floating-point types and integer types have the same endianness on the
33 // target platform
34 //
35 // 2. quiet NaNs, if supported, are indicated by the leading bit of the
36 // significand field being set
37 //
38 //===----------------------------------------------------------------------===//
39
40 #include "int_lib.h"
41
42 typedef double src_t;
43 typedef uint64_t src_rep_t;
44 #define SRC_REP_C UINT64_C
45 static const int srcSigBits = 52;
46
47 typedef float dst_t;
48 typedef uint32_t dst_rep_t;
49 #define DST_REP_C UINT32_C
50 static const int dstSigBits = 23;
51
52 // End of specialization parameters. Two helper routines for conversion to and
53 // from the representation of floating-point data as integer values follow.
54
srcToRep(src_t x)55 static inline src_rep_t srcToRep(src_t x) {
56 const union { src_t f; src_rep_t i; } rep = {.f = x};
57 return rep.i;
58 }
59
dstFromRep(dst_rep_t x)60 static inline dst_t dstFromRep(dst_rep_t x) {
61 const union { dst_t f; dst_rep_t i; } rep = {.i = x};
62 return rep.f;
63 }
64
65 // End helper routines. Conversion implementation follows.
66
ARM_EABI_FNALIAS(d2f,truncdfsf2)67 ARM_EABI_FNALIAS(d2f, truncdfsf2)
68
69 COMPILER_RT_ABI dst_t
70 __truncdfsf2(src_t a) {
71
72 // Various constants whose values follow from the type parameters.
73 // Any reasonable optimizer will fold and propagate all of these.
74 const int srcBits = sizeof(src_t)*CHAR_BIT;
75 const int srcExpBits = srcBits - srcSigBits - 1;
76 const int srcInfExp = (1 << srcExpBits) - 1;
77 const int srcExpBias = srcInfExp >> 1;
78
79 const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
80 const src_rep_t significandMask = srcMinNormal - 1;
81 const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
82 const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
83 const src_rep_t srcAbsMask = srcSignMask - 1;
84 const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
85 const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
86
87 const int dstBits = sizeof(dst_t)*CHAR_BIT;
88 const int dstExpBits = dstBits - dstSigBits - 1;
89 const int dstInfExp = (1 << dstExpBits) - 1;
90 const int dstExpBias = dstInfExp >> 1;
91
92 const int underflowExponent = srcExpBias + 1 - dstExpBias;
93 const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
94 const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
95 const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
96
97 const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
98 const dst_rep_t dstNaNCode = dstQNaN - 1;
99
100 // Break a into a sign and representation of the absolute value
101 const src_rep_t aRep = srcToRep(a);
102 const src_rep_t aAbs = aRep & srcAbsMask;
103 const src_rep_t sign = aRep & srcSignMask;
104 dst_rep_t absResult;
105
106 if (aAbs - underflow < aAbs - overflow) {
107 // The exponent of a is within the range of normal numbers in the
108 // destination format. We can convert by simply right-shifting with
109 // rounding and adjusting the exponent.
110 absResult = aAbs >> (srcSigBits - dstSigBits);
111 absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
112
113 const src_rep_t roundBits = aAbs & roundMask;
114
115 // Round to nearest
116 if (roundBits > halfway)
117 absResult++;
118
119 // Ties to even
120 else if (roundBits == halfway)
121 absResult += absResult & 1;
122 }
123
124 else if (aAbs > srcInfinity) {
125 // a is NaN.
126 // Conjure the result by beginning with infinity, setting the qNaN
127 // bit and inserting the (truncated) trailing NaN field.
128 absResult = (dst_rep_t)dstInfExp << dstSigBits;
129 absResult |= dstQNaN;
130 absResult |= aAbs & dstNaNCode;
131 }
132
133 else if (aAbs > overflow) {
134 // a overflows to infinity.
135 absResult = (dst_rep_t)dstInfExp << dstSigBits;
136 }
137
138 else {
139 // a underflows on conversion to the destination type or is an exact
140 // zero. The result may be a denormal or zero. Extract the exponent
141 // to get the shift amount for the denormalization.
142 const int aExp = aAbs >> srcSigBits;
143 const int shift = srcExpBias - dstExpBias - aExp + 1;
144
145 const src_rep_t significand = (aRep & significandMask) | srcMinNormal;
146
147 // Right shift by the denormalization amount with sticky.
148 if (shift > srcSigBits) {
149 absResult = 0;
150 } else {
151 const bool sticky = significand << (srcBits - shift);
152 src_rep_t denormalizedSignificand = significand >> shift | sticky;
153 absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
154 const src_rep_t roundBits = denormalizedSignificand & roundMask;
155 // Round to nearest
156 if (roundBits > halfway)
157 absResult++;
158 // Ties to even
159 else if (roundBits == halfway)
160 absResult += absResult & 1;
161 }
162 }
163
164 // Apply the signbit to (dst_t)abs(a).
165 const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
166 return dstFromRep(result);
167
168 }
169