lib/builtins/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 COMPILER_RT_ABI fp_t
  21 __addsf3(fp_t a, fp_t b) {
  22
  23     rep_t aRep = toRep(a);
  24     rep_t bRep = toRep(b);
  25     const rep_t aAbs = aRep & absMask;
  26     const rep_t bAbs = bRep & absMask;
  27
  28     // Detect if a or b is zero, infinity, or NaN.
  29     if (aAbs - 1U >= infRep - 1U || bAbs - 1U >= infRep - 1U) {
  30
  31         // NaN + anything = qNaN
  32         if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
  33         // anything + NaN = qNaN
  34         if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
  35
  36         if (aAbs == infRep) {
  37             // +/-infinity + -/+infinity = qNaN
  38             if ((toRep(a) ^ toRep(b)) == signBit) return fromRep(qnanRep);
  39             // +/-infinity + anything remaining = +/- infinity
  40             else return a;
  41         }
  42
  43         // anything remaining + +/-infinity = +/-infinity
  44         if (bAbs == infRep) return b;
  45
  46         // zero + anything = anything
  47         if (!aAbs) {
  48             // but we need to get the sign right for zero + zero
  49             if (!bAbs) return fromRep(toRep(a) & toRep(b));
  50             else return b;
  51         }
  52
  53         // anything + zero = anything
  54         if (!bAbs) return a;
  55     }
  56
  57     // Swap a and b if necessary so that a has the larger absolute value.
  58     if (bAbs > aAbs) {
  59         const rep_t temp = aRep;
  60         aRep = bRep;
  61         bRep = temp;
  62     }
  63
  64     // Extract the exponent and significand from the (possibly swapped) a and b.
  65     int aExponent = aRep >> significandBits & maxExponent;
  66     int bExponent = bRep >> significandBits & maxExponent;
  67     rep_t aSignificand = aRep & significandMask;
  68     rep_t bSignificand = bRep & significandMask;
  69
  70     // Normalize any denormals, and adjust the exponent accordingly.
  71     if (aExponent == 0) aExponent = normalize(&aSignificand);
  72     if (bExponent == 0) bExponent = normalize(&bSignificand);
  73
  74     // The sign of the result is the sign of the larger operand, a.  If they
  75     // have opposite signs, we are performing a subtraction; otherwise addition.
  76     const rep_t resultSign = aRep & signBit;
  77     const bool subtraction = (aRep ^ bRep) & signBit;
  78
  79     // Shift the significands to give us round, guard and sticky, and or in the
  80     // implicit significand bit.  (If we fell through from the denormal path it
  81     // was already set by normalize( ), but setting it twice won't hurt
  82     // anything.)
  83     aSignificand = (aSignificand | implicitBit) << 3;
  84     bSignificand = (bSignificand | implicitBit) << 3;
  85
  86     // Shift the significand of b by the difference in exponents, with a sticky
  87     // bottom bit to get rounding correct.
  88     const unsigned int align = aExponent - bExponent;
  89     if (align) {
  90         if (align < typeWidth) {
  91             const bool sticky = bSignificand << (typeWidth - align);
  92             bSignificand = bSignificand >> align | sticky;
  93         } else {
  94             bSignificand = 1; // sticky; b is known to be non-zero.
  95         }
  96     }
  97
  98     if (subtraction) {
  99         aSignificand -= bSignificand;
 100
 101         // If a == -b, return +zero.
 102         if (aSignificand == 0) return fromRep(0);
 103
 104         // If partial cancellation occured, we need to left-shift the result
 105         // and adjust the exponent:
 106         if (aSignificand < implicitBit << 3) {
 107             const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);
 108             aSignificand <<= shift;
 109             aExponent -= shift;
 110         }
 111     }
 112
 113     else /* addition */ {
 114         aSignificand += bSignificand;
 115
 116         // If the addition carried up, we need to right-shift the result and
 117         // adjust the exponent:
 118         if (aSignificand & implicitBit << 4) {
 119             const bool sticky = aSignificand & 1;
 120             aSignificand = aSignificand >> 1 | sticky;
 121             aExponent += 1;
 122         }
 123     }
 124
 125     // If we have overflowed the type, return +/- infinity:
 126     if (aExponent >= maxExponent) return fromRep(infRep | resultSign);
 127
 128     if (aExponent <= 0) {
 129         // Result is denormal before rounding; the exponent is zero and we
 130         // need to shift the significand.
 131         const int shift = 1 - aExponent;
 132         const bool sticky = aSignificand << (typeWidth - shift);
 133         aSignificand = aSignificand >> shift | sticky;
 134         aExponent = 0;
 135     }
 136
 137     // Low three bits are round, guard, and sticky.
 138     const int roundGuardSticky = aSignificand & 0x7;
 139
 140     // Shift the significand into place, and mask off the implicit bit.
 141     rep_t result = aSignificand >> 3 & significandMask;
 142
 143     // Insert the exponent and sign.
 144     result |= (rep_t)aExponent << significandBits;
 145     result |= resultSign;
 146
 147     // Final rounding.  The result may overflow to infinity, but that is the
 148     // correct result in that case.
 149     if (roundGuardSticky > 0x4) result++;
 150     if (roundGuardSticky == 0x4) result += result & 1;
 151     return fromRep(result);
 152 }