lib/addsf3.c

   1 //===-- lib/addsf3.c - Single-precision addition ------------------*- 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 single-precision soft-float addition with the IEEE-754
  11 // default rounding (to nearest, ties to even).
  12 //
  13 //===----------------------------------------------------------------------===//
  14
  15 #define SINGLE_PRECISION
  16 #include "fp_lib.h"
  17
  18 ARM_EABI_FNALIAS(fadd, addsf3)
  19
  20 fp_t __addsf3(fp_t a, fp_t b) {
  21
  22     rep_t aRep = toRep(a);
  23     rep_t bRep = toRep(b);
  24     const rep_t aAbs = aRep & absMask;
  25     const rep_t bAbs = bRep & absMask;
  26
  27     // Detect if a or b is zero, infinity, or NaN.
  28     if (aAbs - 1U >= infRep - 1U || bAbs - 1U >= infRep - 1U) {
  29
  30         // NaN + anything = qNaN
  31         if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
  32         // anything + NaN = qNaN
  33         if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
  34
  35         if (aAbs == infRep) {
  36             // +/-infinity + -/+infinity = qNaN
  37             if ((toRep(a) ^ toRep(b)) == signBit) return fromRep(qnanRep);
  38             // +/-infinity + anything remaining = +/- infinity
  39             else return a;
  40         }
  41
  42         // anything remaining + +/-infinity = +/-infinity
  43         if (bAbs == infRep) return b;
  44
  45         // zero + anything = anything
  46         if (!aAbs) {
  47             // but we need to get the sign right for zero + zero
  48             if (!bAbs) return fromRep(toRep(a) & toRep(b));
  49             else return b;
  50         }
  51
  52         // anything + zero = anything
  53         if (!bAbs) return a;
  54     }
  55
  56     // Swap a and b if necessary so that a has the larger absolute value.
  57     if (bAbs > aAbs) {
  58         const rep_t temp = aRep;
  59         aRep = bRep;
  60         bRep = temp;
  61     }
  62
  63     // Extract the exponent and significand from the (possibly swapped) a and b.
  64     int aExponent = aRep >> significandBits & maxExponent;
  65     int bExponent = bRep >> significandBits & maxExponent;
  66     rep_t aSignificand = aRep & significandMask;
  67     rep_t bSignificand = bRep & significandMask;
  68
  69     // Normalize any denormals, and adjust the exponent accordingly.
  70     if (aExponent == 0) aExponent = normalize(&aSignificand);
  71     if (bExponent == 0) bExponent = normalize(&bSignificand);
  72
  73     // The sign of the result is the sign of the larger operand, a.  If they
  74     // have opposite signs, we are performing a subtraction; otherwise addition.
  75     const rep_t resultSign = aRep & signBit;
  76     const bool subtraction = (aRep ^ bRep) & signBit;
  77
  78     // Shift the significands to give us round, guard and sticky, and or in the
  79     // implicit significand bit.  (If we fell through from the denormal path it
  80     // was already set by normalize( ), but setting it twice won't hurt
  81     // anything.)
  82     aSignificand = (aSignificand | implicitBit) << 3;
  83     bSignificand = (bSignificand | implicitBit) << 3;
  84
  85     // Shift the significand of b by the difference in exponents, with a sticky
  86     // bottom bit to get rounding correct.
  87     const unsigned int align = aExponent - bExponent;
  88     if (align) {
  89         if (align < typeWidth) {
  90             const bool sticky = bSignificand << (typeWidth - align);
  91             bSignificand = bSignificand >> align | sticky;
  92         } else {
  93             bSignificand = 1; // sticky; b is known to be non-zero.
  94         }
  95     }
  96
  97     if (subtraction) {
  98         aSignificand -= bSignificand;
  99
 100         // If a == -b, return +zero.
 101         if (aSignificand == 0) return fromRep(0);
 102
 103         // If partial cancellation occured, we need to left-shift the result
 104         // and adjust the exponent:
 105         if (aSignificand < implicitBit << 3) {
 106             const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);
 107             aSignificand <<= shift;
 108             aExponent -= shift;
 109         }
 110     }
 111
 112     else /* addition */ {
 113         aSignificand += bSignificand;
 114
 115         // If the addition carried up, we need to right-shift the result and
 116         // adjust the exponent:
 117         if (aSignificand & implicitBit << 4) {
 118             const bool sticky = aSignificand & 1;
 119             aSignificand = aSignificand >> 1 | sticky;
 120             aExponent += 1;
 121         }
 122     }
 123
 124     // If we have overflowed the type, return +/- infinity:
 125     if (aExponent >= maxExponent) return fromRep(infRep | resultSign);
 126
 127     if (aExponent <= 0) {
 128         // Result is denormal before rounding; the exponent is zero and we
 129         // need to shift the significand.
 130         const int shift = 1 - aExponent;
 131         const bool sticky = aSignificand << (typeWidth - shift);
 132         aSignificand = aSignificand >> shift | sticky;
 133         aExponent = 0;
 134     }
 135
 136     // Low three bits are round, guard, and sticky.
 137     const int roundGuardSticky = aSignificand & 0x7;
 138
 139     // Shift the significand into place, and mask off the implicit bit.
 140     rep_t result = aSignificand >> 3 & significandMask;
 141
 142     // Insert the exponent and sign.
 143     result |= (rep_t)aExponent << significandBits;
 144     result |= resultSign;
 145
 146     // Final rounding.  The result may overflow to infinity, but that is the
 147     // correct result in that case.
 148     if (roundGuardSticky > 0x4) result++;
 149     if (roundGuardSticky == 0x4) result += result & 1;
 150     return fromRep(result);
 151 }