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