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      1 //===-- lib/muldf3.c - Double-precision multiplication ------------*- 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 double-precision soft-float multiplication
     11 // with the IEEE-754 default rounding (to nearest, ties to even).
     12 //
     13 //===----------------------------------------------------------------------===//
     14 
     15 #define DOUBLE_PRECISION
     16 #include "fp_lib.h"
     17 
     18 ARM_EABI_FNALIAS(dmul, muldf3)
     19 
     20 COMPILER_RT_ABI fp_t
     21 __muldf3(fp_t a, fp_t b) {
     22 
     23     const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
     24     const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
     25     const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
     26 
     27     rep_t aSignificand = toRep(a) & significandMask;
     28     rep_t bSignificand = toRep(b) & significandMask;
     29     int scale = 0;
     30 
     31     // Detect if a or b is zero, denormal, infinity, or NaN.
     32     if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
     33 
     34         const rep_t aAbs = toRep(a) & absMask;
     35         const rep_t bAbs = toRep(b) & absMask;
     36 
     37         // NaN * anything = qNaN
     38         if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
     39         // anything * NaN = qNaN
     40         if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
     41 
     42         if (aAbs == infRep) {
     43             // infinity * non-zero = +/- infinity
     44             if (bAbs) return fromRep(aAbs | productSign);
     45             // infinity * zero = NaN
     46             else return fromRep(qnanRep);
     47         }
     48 
     49         if (bAbs == infRep) {
     50             // non-zero * infinity = +/- infinity
     51             if (aAbs) return fromRep(bAbs | productSign);
     52             // zero * infinity = NaN
     53             else return fromRep(qnanRep);
     54         }
     55 
     56         // zero * anything = +/- zero
     57         if (!aAbs) return fromRep(productSign);
     58         // anything * zero = +/- zero
     59         if (!bAbs) return fromRep(productSign);
     60 
     61         // one or both of a or b is denormal, the other (if applicable) is a
     62         // normal number.  Renormalize one or both of a and b, and set scale to
     63         // include the necessary exponent adjustment.
     64         if (aAbs < implicitBit) scale += normalize(&aSignificand);
     65         if (bAbs < implicitBit) scale += normalize(&bSignificand);
     66     }
     67 
     68     // Or in the implicit significand bit.  (If we fell through from the
     69     // denormal path it was already set by normalize( ), but setting it twice
     70     // won't hurt anything.)
     71     aSignificand |= implicitBit;
     72     bSignificand |= implicitBit;
     73 
     74     // Get the significand of a*b.  Before multiplying the significands, shift
     75     // one of them left to left-align it in the field.  Thus, the product will
     76     // have (exponentBits + 2) integral digits, all but two of which must be
     77     // zero.  Normalizing this result is just a conditional left-shift by one
     78     // and bumping the exponent accordingly.
     79     rep_t productHi, productLo;
     80     wideMultiply(aSignificand, bSignificand << exponentBits,
     81                  &productHi, &productLo);
     82 
     83     int productExponent = aExponent + bExponent - exponentBias + scale;
     84 
     85     // Normalize the significand, adjust exponent if needed.
     86     if (productHi & implicitBit) productExponent++;
     87     else wideLeftShift(&productHi, &productLo, 1);
     88 
     89     // If we have overflowed the type, return +/- infinity.
     90     if (productExponent >= maxExponent) return fromRep(infRep | productSign);
     91 
     92     if (productExponent <= 0) {
     93         // Result is denormal before rounding
     94         //
     95         // If the result is so small that it just underflows to zero, return
     96         // a zero of the appropriate sign.  Mathematically there is no need to
     97         // handle this case separately, but we make it a special case to
     98         // simplify the shift logic.
     99         const unsigned int shift = 1U - (unsigned int)productExponent;
    100         if (shift >= typeWidth) return fromRep(productSign);
    101 
    102         // Otherwise, shift the significand of the result so that the round
    103         // bit is the high bit of productLo.
    104         wideRightShiftWithSticky(&productHi, &productLo, shift);
    105     }
    106 
    107     else {
    108         // Result is normal before rounding; insert the exponent.
    109         productHi &= significandMask;
    110         productHi |= (rep_t)productExponent << significandBits;
    111     }
    112 
    113     // Insert the sign of the result:
    114     productHi |= productSign;
    115 
    116     // Final rounding.  The final result may overflow to infinity, or underflow
    117     // to zero, but those are the correct results in those cases.  We use the
    118     // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
    119     if (productLo > signBit) productHi++;
    120     if (productLo == signBit) productHi += productHi & 1;
    121     return fromRep(productHi);
    122 }
    123