COMPILER_RT_ABI fp_t __floatditf(di_int a) {
const int aWidth = sizeof a * CHAR_BIT;
// Handle zero as a special case to protect clz
if (a == 0)
return fromRep(0);
// All other cases begin by extracting the sign and absolute value of a
rep_t sign = 0;
du_int aAbs = (du_int)a;
if (a < 0) {
sign = signBit;
aAbs = ~(du_int)a + 1U;
}
// Exponent of (fp_t)a is the width of abs(a).
const int exponent = (aWidth - 1) - __builtin_clzll(aAbs);
rep_t result;
// Shift a into the significand field, rounding if it is a right-shift
const int shift = significandBits - exponent;
result = (rep_t)aAbs << shift ^ implicitBit;
// Insert the exponent
result += (rep_t)(exponent + exponentBias) << significandBits;
// Insert the sign bit and return
return fromRep(result | sign);
}
COMPILER_RT_ABI fp_t __floatunsitf(unsigned int a) {
const int aWidth = sizeof a * CHAR_BIT;
// Handle zero as a special case to protect clz
if (a == 0) return fromRep(0);
// Exponent of (fp_t)a is the width of abs(a).
const int exponent = (aWidth - 1) - __builtin_clz(a);
rep_t result;
// Shift a into the significand field and clear the implicit bit.
const int shift = significandBits - exponent;
result = (rep_t)a << shift ^ implicitBit;
// Insert the exponent
result += (rep_t)(exponent + exponentBias) << significandBits;
return fromRep(result);
}
// Subtraction; flip the sign bit of b and add.
COMPILER_RT_ABI fp_t
__subsf3(fp_t a, fp_t b) {
return __addsf3(a, fromRep(toRep(b) ^ signBit));
}
COMPILER_RT_ABI fp_t
__negdf2(fp_t a) {
return fromRep(toRep(a) ^ signBit);
}
fp_t __addsf3(fp_t a, fp_t b) {
rep_t aRep = toRep(a);
rep_t bRep = toRep(b);
const rep_t aAbs = aRep & absMask;
const rep_t bAbs = bRep & absMask;
// Detect if a or b is zero, infinity, or NaN.
if (aAbs - 1U >= infRep - 1U || bAbs - 1U >= infRep - 1U) {
// NaN + anything = qNaN
if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
// anything + NaN = qNaN
if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
if (aAbs == infRep) {
// +/-infinity + -/+infinity = qNaN
if ((toRep(a) ^ toRep(b)) == signBit) return fromRep(qnanRep);
// +/-infinity + anything remaining = +/- infinity
else return a;
}
// anything remaining + +/-infinity = +/-infinity
if (bAbs == infRep) return b;
// zero + anything = anything
if (!aAbs) {
// but we need to get the sign right for zero + zero
if (!bAbs) return fromRep(toRep(a) & toRep(b));
else return b;
}
// anything + zero = anything
if (!bAbs) return a;
}
// Swap a and b if necessary so that a has the larger absolute value.
if (bAbs > aAbs) {
const rep_t temp = aRep;
aRep = bRep;
bRep = temp;
}
// Extract the exponent and significand from the (possibly swapped) a and b.
int aExponent = aRep >> significandBits & maxExponent;
int bExponent = bRep >> significandBits & maxExponent;
rep_t aSignificand = aRep & significandMask;
rep_t bSignificand = bRep & significandMask;
// Normalize any denormals, and adjust the exponent accordingly.
if (aExponent == 0) aExponent = normalize(&aSignificand);
if (bExponent == 0) bExponent = normalize(&bSignificand);
// The sign of the result is the sign of the larger operand, a. If they
// have opposite signs, we are performing a subtraction; otherwise addition.
const rep_t resultSign = aRep & signBit;
const bool subtraction = (aRep ^ bRep) & signBit;
// Shift the significands to give us round, guard and sticky, and or in the
// implicit significand bit. (If we fell through from the denormal path it
// was already set by normalize( ), but setting it twice won't hurt
// anything.)
aSignificand = (aSignificand | implicitBit) << 3;
bSignificand = (bSignificand | implicitBit) << 3;
// Shift the significand of b by the difference in exponents, with a sticky
// bottom bit to get rounding correct.
const int align = aExponent - bExponent;
if (align) {
if (align < typeWidth) {
const bool sticky = bSignificand << (typeWidth - align);
bSignificand = bSignificand >> align | sticky;
} else {
bSignificand = 1; // sticky; b is known to be non-zero.
}
}
COMPILER_RT_ABI fp_t
__muldf3(fp_t a, fp_t b) {
const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
rep_t aSignificand = toRep(a) & significandMask;
rep_t bSignificand = toRep(b) & significandMask;
int scale = 0;
// Detect if a or b is zero, denormal, infinity, or NaN.
if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
const rep_t aAbs = toRep(a) & absMask;
const rep_t bAbs = toRep(b) & absMask;
// NaN * anything = qNaN
if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
// anything * NaN = qNaN
if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
if (aAbs == infRep) {
// infinity * non-zero = +/- infinity
if (bAbs) return fromRep(aAbs | productSign);
// infinity * zero = NaN
else return fromRep(qnanRep);
}
if (bAbs == infRep) {
// non-zero * infinity = +/- infinity
if (aAbs) return fromRep(bAbs | productSign);
// zero * infinity = NaN
else return fromRep(qnanRep);
}
// zero * anything = +/- zero
if (!aAbs) return fromRep(productSign);
// anything * zero = +/- zero
if (!bAbs) return fromRep(productSign);
// one or both of a or b is denormal, the other (if applicable) is a
// normal number. Renormalize one or both of a and b, and set scale to
// include the necessary exponent adjustment.
if (aAbs < implicitBit) scale += normalize(&aSignificand);
if (bAbs < implicitBit) scale += normalize(&bSignificand);
}
// Or in the implicit significand bit. (If we fell through from the
// denormal path it was already set by normalize( ), but setting it twice
// won't hurt anything.)
aSignificand |= implicitBit;
bSignificand |= implicitBit;
// Get the significand of a*b. Before multiplying the significands, shift
// one of them left to left-align it in the field. Thus, the product will
// have (exponentBits + 2) integral digits, all but two of which must be
// zero. Normalizing this result is just a conditional left-shift by one
// and bumping the exponent accordingly.
rep_t productHi, productLo;
wideMultiply(aSignificand, bSignificand << exponentBits,
&productHi, &productLo);
int productExponent = aExponent + bExponent - exponentBias + scale;
// Normalize the significand, adjust exponent if needed.
if (productHi & implicitBit) productExponent++;
else wideLeftShift(&productHi, &productLo, 1);
// If we have overflowed the type, return +/- infinity.
if (productExponent >= maxExponent) return fromRep(infRep | productSign);
if (productExponent <= 0) {
// Result is denormal before rounding
//
// If the result is so small that it just underflows to zero, return
// a zero of the appropriate sign. Mathematically there is no need to
// handle this case separately, but we make it a special case to
// simplify the shift logic.
const unsigned int shift = 1U - (unsigned int)productExponent;
if (shift >= typeWidth) return fromRep(productSign);
// Otherwise, shift the significand of the result so that the round
// bit is the high bit of productLo.
wideRightShiftWithSticky(&productHi, &productLo, shift);
}
else {
// Result is normal before rounding; insert the exponent.
productHi &= significandMask;
productHi |= (rep_t)productExponent << significandBits;
}
// Insert the sign of the result:
productHi |= productSign;
// Final rounding. The final result may overflow to infinity, or underflow
// to zero, but those are the correct results in those cases. We use the
// default IEEE-754 round-to-nearest, ties-to-even rounding mode.
if (productLo > signBit) productHi++;
if (productLo == signBit) productHi += productHi & 1;
return fromRep(productHi);
}
