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//===-- lib/truncdfsf2.c - double -> single conversion ------------*- C -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements a fairly generic conversion from a wider to a narrower
// IEEE-754 floating-point type in the default (round to nearest, ties to even)
// rounding mode. The constants and types defined following the includes below
// parameterize the conversion.
//
// This routine can be trivially adapted to support conversions to
// half-precision or from quad-precision. It does not support types that don't
// use the usual IEEE-754 interchange formats; specifically, some work would be
// needed to adapt it to (for example) the Intel 80-bit format or PowerPC
// double-double format.
//
// Note please, however, that this implementation is only intended to support
// *narrowing* operations; if you need to convert to a *wider* floating-point
// type (e.g. float -> double), then this routine will not do what you want it
// to.
//
// It also requires that integer types at least as large as both formats
// are available on the target platform; this may pose a problem when trying
// to add support for quad on some 32-bit systems, for example.
//
// Finally, the following assumptions are made:
//
// 1. floating-point types and integer types have the same endianness on the
// target platform
//
// 2. quiet NaNs, if supported, are indicated by the leading bit of the
// significand field being set
//
//===----------------------------------------------------------------------===//
#include "int_lib.h"
typedef double src_t;
typedef uint64_t src_rep_t;
#define SRC_REP_C UINT64_C
static const int srcSigBits = 52;
typedef float dst_t;
typedef uint32_t dst_rep_t;
#define DST_REP_C UINT32_C
static const int dstSigBits = 23;
// End of specialization parameters. Two helper routines for conversion to and
// from the representation of floating-point data as integer values follow.
static inline src_rep_t srcToRep(src_t x) {
const union { src_t f; src_rep_t i; } rep = {.f = x};
return rep.i;
}
static inline dst_t dstFromRep(dst_rep_t x) {
const union { dst_t f; dst_rep_t i; } rep = {.i = x};
return rep.f;
}
// End helper routines. Conversion implementation follows.
ARM_EABI_FNALIAS(d2f, truncdfsf2)
COMPILER_RT_ABI dst_t
__truncdfsf2(src_t a) {
// Various constants whose values follow from the type parameters.
// Any reasonable optimizer will fold and propagate all of these.
const int srcBits = sizeof(src_t)*CHAR_BIT;
const int srcExpBits = srcBits - srcSigBits - 1;
const int srcInfExp = (1 << srcExpBits) - 1;
const int srcExpBias = srcInfExp >> 1;
const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
const src_rep_t significandMask = srcMinNormal - 1;
const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
const src_rep_t srcAbsMask = srcSignMask - 1;
const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
const int dstBits = sizeof(dst_t)*CHAR_BIT;
const int dstExpBits = dstBits - dstSigBits - 1;
const int dstInfExp = (1 << dstExpBits) - 1;
const int dstExpBias = dstInfExp >> 1;
const int underflowExponent = srcExpBias + 1 - dstExpBias;
const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
const dst_rep_t dstNaNCode = dstQNaN - 1;
// Break a into a sign and representation of the absolute value
const src_rep_t aRep = srcToRep(a);
const src_rep_t aAbs = aRep & srcAbsMask;
const src_rep_t sign = aRep & srcSignMask;
dst_rep_t absResult;
if (aAbs - underflow < aAbs - overflow) {
// The exponent of a is within the range of normal numbers in the
// destination format. We can convert by simply right-shifting with
// rounding and adjusting the exponent.
absResult = aAbs >> (srcSigBits - dstSigBits);
absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
const src_rep_t roundBits = aAbs & roundMask;
// Round to nearest
if (roundBits > halfway)
absResult++;
// Ties to even
else if (roundBits == halfway)
absResult += absResult & 1;
}
else if (aAbs > srcInfinity) {
// a is NaN.
// Conjure the result by beginning with infinity, setting the qNaN
// bit and inserting the (truncated) trailing NaN field.
absResult = (dst_rep_t)dstInfExp << dstSigBits;
absResult |= dstQNaN;
absResult |= aAbs & dstNaNCode;
}
else if (aAbs > overflow) {
// a overflows to infinity.
absResult = (dst_rep_t)dstInfExp << dstSigBits;
}
else {
// a underflows on conversion to the destination type or is an exact
// zero. The result may be a denormal or zero. Extract the exponent
// to get the shift amount for the denormalization.
const int aExp = aAbs >> srcSigBits;
const int shift = srcExpBias - dstExpBias - aExp + 1;
const src_rep_t significand = (aRep & significandMask) | srcMinNormal;
// Right shift by the denormalization amount with sticky.
if (shift > srcSigBits) {
absResult = 0;
} else {
const bool sticky = significand << (srcBits - shift);
src_rep_t denormalizedSignificand = significand >> shift | sticky;
absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
const src_rep_t roundBits = denormalizedSignificand & roundMask;
// Round to nearest
if (roundBits > halfway)
absResult++;
// Ties to even
else if (roundBits == halfway)
absResult += absResult & 1;
}
}
// Apply the signbit to (dst_t)abs(a).
const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
return dstFromRep(result);
}
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