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
18ARM_EABI_FNALIAS(fadd, addsf3)
19
20fp_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}
152