1//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===//
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 "fp_trunc.h"
41
42static inline dst_t __truncXfYf2__(src_t a) {
43    // Various constants whose values follow from the type parameters.
44    // Any reasonable optimizer will fold and propagate all of these.
45    const int srcBits = sizeof(src_t)*CHAR_BIT;
46    const int srcExpBits = srcBits - srcSigBits - 1;
47    const int srcInfExp = (1 << srcExpBits) - 1;
48    const int srcExpBias = srcInfExp >> 1;
49
50    const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
51    const src_rep_t srcSignificandMask = srcMinNormal - 1;
52    const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
53    const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
54    const src_rep_t srcAbsMask = srcSignMask - 1;
55    const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
56    const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
57    const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigBits - 1);
58    const src_rep_t srcNaNCode = srcQNaN - 1;
59
60    const int dstBits = sizeof(dst_t)*CHAR_BIT;
61    const int dstExpBits = dstBits - dstSigBits - 1;
62    const int dstInfExp = (1 << dstExpBits) - 1;
63    const int dstExpBias = dstInfExp >> 1;
64
65    const int underflowExponent = srcExpBias + 1 - dstExpBias;
66    const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
67    const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
68    const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
69
70    const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
71    const dst_rep_t dstNaNCode = dstQNaN - 1;
72
73    // Break a into a sign and representation of the absolute value
74    const src_rep_t aRep = srcToRep(a);
75    const src_rep_t aAbs = aRep & srcAbsMask;
76    const src_rep_t sign = aRep & srcSignMask;
77    dst_rep_t absResult;
78
79    if (aAbs - underflow < aAbs - overflow) {
80        // The exponent of a is within the range of normal numbers in the
81        // destination format.  We can convert by simply right-shifting with
82        // rounding and adjusting the exponent.
83        absResult = aAbs >> (srcSigBits - dstSigBits);
84        absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
85
86        const src_rep_t roundBits = aAbs & roundMask;
87        // Round to nearest
88        if (roundBits > halfway)
89            absResult++;
90        // Ties to even
91        else if (roundBits == halfway)
92            absResult += absResult & 1;
93    }
94    else if (aAbs > srcInfinity) {
95        // a is NaN.
96        // Conjure the result by beginning with infinity, setting the qNaN
97        // bit and inserting the (truncated) trailing NaN field.
98        absResult = (dst_rep_t)dstInfExp << dstSigBits;
99        absResult |= dstQNaN;
100        absResult |= ((aAbs & srcNaNCode) >> (srcSigBits - dstSigBits)) & dstNaNCode;
101    }
102    else if (aAbs >= overflow) {
103        // a overflows to infinity.
104        absResult = (dst_rep_t)dstInfExp << dstSigBits;
105    }
106    else {
107        // a underflows on conversion to the destination type or is an exact
108        // zero.  The result may be a denormal or zero.  Extract the exponent
109        // to get the shift amount for the denormalization.
110        const int aExp = aAbs >> srcSigBits;
111        const int shift = srcExpBias - dstExpBias - aExp + 1;
112
113        const src_rep_t significand = (aRep & srcSignificandMask) | srcMinNormal;
114
115        // Right shift by the denormalization amount with sticky.
116        if (shift > srcSigBits) {
117            absResult = 0;
118        } else {
119            const bool sticky = significand << (srcBits - shift);
120            src_rep_t denormalizedSignificand = significand >> shift | sticky;
121            absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
122            const src_rep_t roundBits = denormalizedSignificand & roundMask;
123            // Round to nearest
124            if (roundBits > halfway)
125                absResult++;
126            // Ties to even
127            else if (roundBits == halfway)
128                absResult += absResult & 1;
129        }
130    }
131
132    // Apply the signbit to (dst_t)abs(a).
133    const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
134    return dstFromRep(result);
135}
136