compiler_builtins/float/
add.rs

1use crate::float::Float;
2use crate::int::{CastInto, Int, MinInt};
3
4/// Returns `a + b`
5fn add<F: Float>(a: F, b: F) -> F
6where
7    u32: CastInto<F::Int>,
8    F::Int: CastInto<u32>,
9    i32: CastInto<F::Int>,
10    F::Int: CastInto<i32>,
11{
12    let one = F::Int::ONE;
13    let zero = F::Int::ZERO;
14
15    let bits = F::BITS.cast();
16    let significand_bits = F::SIG_BITS;
17    let max_exponent = F::EXP_SAT;
18
19    let implicit_bit = F::IMPLICIT_BIT;
20    let significand_mask = F::SIG_MASK;
21    let sign_bit = F::SIGN_MASK as F::Int;
22    let abs_mask = sign_bit - one;
23    let exponent_mask = F::EXP_MASK;
24    let inf_rep = exponent_mask;
25    let quiet_bit = implicit_bit >> 1;
26    let qnan_rep = exponent_mask | quiet_bit;
27
28    let mut a_rep = a.to_bits();
29    let mut b_rep = b.to_bits();
30    let a_abs = a_rep & abs_mask;
31    let b_abs = b_rep & abs_mask;
32
33    // Detect if a or b is zero, infinity, or NaN.
34    if a_abs.wrapping_sub(one) >= inf_rep - one || b_abs.wrapping_sub(one) >= inf_rep - one {
35        // NaN + anything = qNaN
36        if a_abs > inf_rep {
37            return F::from_bits(a_abs | quiet_bit);
38        }
39        // anything + NaN = qNaN
40        if b_abs > inf_rep {
41            return F::from_bits(b_abs | quiet_bit);
42        }
43
44        if a_abs == inf_rep {
45            // +/-infinity + -/+infinity = qNaN
46            if (a.to_bits() ^ b.to_bits()) == sign_bit {
47                return F::from_bits(qnan_rep);
48            } else {
49                // +/-infinity + anything remaining = +/- infinity
50                return a;
51            }
52        }
53
54        // anything remaining + +/-infinity = +/-infinity
55        if b_abs == inf_rep {
56            return b;
57        }
58
59        // zero + anything = anything
60        if a_abs == MinInt::ZERO {
61            // but we need to get the sign right for zero + zero
62            if b_abs == MinInt::ZERO {
63                return F::from_bits(a.to_bits() & b.to_bits());
64            } else {
65                return b;
66            }
67        }
68
69        // anything + zero = anything
70        if b_abs == MinInt::ZERO {
71            return a;
72        }
73    }
74
75    // Swap a and b if necessary so that a has the larger absolute value.
76    if b_abs > a_abs {
77        // Don't use mem::swap because it may generate references to memcpy in unoptimized code.
78        let tmp = a_rep;
79        a_rep = b_rep;
80        b_rep = tmp;
81    }
82
83    // Extract the exponent and significand from the (possibly swapped) a and b.
84    let mut a_exponent: i32 = ((a_rep & exponent_mask) >> significand_bits).cast();
85    let mut b_exponent: i32 = ((b_rep & exponent_mask) >> significand_bits).cast();
86    let mut a_significand = a_rep & significand_mask;
87    let mut b_significand = b_rep & significand_mask;
88
89    // normalize any denormals, and adjust the exponent accordingly.
90    if a_exponent == 0 {
91        let (exponent, significand) = F::normalize(a_significand);
92        a_exponent = exponent;
93        a_significand = significand;
94    }
95    if b_exponent == 0 {
96        let (exponent, significand) = F::normalize(b_significand);
97        b_exponent = exponent;
98        b_significand = significand;
99    }
100
101    // The sign of the result is the sign of the larger operand, a.  If they
102    // have opposite signs, we are performing a subtraction; otherwise addition.
103    let result_sign = a_rep & sign_bit;
104    let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero;
105
106    // Shift the significands to give us round, guard and sticky, and or in the
107    // implicit significand bit.  (If we fell through from the denormal path it
108    // was already set by normalize(), but setting it twice won't hurt
109    // anything.)
110    a_significand = (a_significand | implicit_bit) << 3;
111    b_significand = (b_significand | implicit_bit) << 3;
112
113    // Shift the significand of b by the difference in exponents, with a sticky
114    // bottom bit to get rounding correct.
115    let align = a_exponent.wrapping_sub(b_exponent).cast();
116    if align != MinInt::ZERO {
117        if align < bits {
118            let sticky =
119                F::Int::from_bool(b_significand << bits.wrapping_sub(align).cast() != MinInt::ZERO);
120            b_significand = (b_significand >> align.cast()) | sticky;
121        } else {
122            b_significand = one; // sticky; b is known to be non-zero.
123        }
124    }
125    if subtraction {
126        a_significand = a_significand.wrapping_sub(b_significand);
127        // If a == -b, return +zero.
128        if a_significand == MinInt::ZERO {
129            return F::from_bits(MinInt::ZERO);
130        }
131
132        // If partial cancellation occured, we need to left-shift the result
133        // and adjust the exponent:
134        if a_significand < implicit_bit << 3 {
135            let shift =
136                a_significand.leading_zeros() as i32 - (implicit_bit << 3).leading_zeros() as i32;
137            a_significand <<= shift;
138            a_exponent -= shift;
139        }
140    } else {
141        // addition
142        a_significand += b_significand;
143
144        // If the addition carried up, we need to right-shift the result and
145        // adjust the exponent:
146        if a_significand & (implicit_bit << 4) != MinInt::ZERO {
147            let sticky = F::Int::from_bool(a_significand & one != MinInt::ZERO);
148            a_significand = (a_significand >> 1) | sticky;
149            a_exponent += 1;
150        }
151    }
152
153    // If we have overflowed the type, return +/- infinity:
154    if a_exponent >= max_exponent as i32 {
155        return F::from_bits(inf_rep | result_sign);
156    }
157
158    if a_exponent <= 0 {
159        // Result is denormal before rounding; the exponent is zero and we
160        // need to shift the significand.
161        let shift = (1 - a_exponent).cast();
162        let sticky =
163            F::Int::from_bool((a_significand << bits.wrapping_sub(shift).cast()) != MinInt::ZERO);
164        a_significand = (a_significand >> shift.cast()) | sticky;
165        a_exponent = 0;
166    }
167
168    // Low three bits are round, guard, and sticky.
169    let a_significand_i32: i32 = a_significand.cast();
170    let round_guard_sticky: i32 = a_significand_i32 & 0x7;
171
172    // Shift the significand into place, and mask off the implicit bit.
173    let mut result = (a_significand >> 3) & significand_mask;
174
175    // Insert the exponent and sign.
176    result |= a_exponent.cast() << significand_bits;
177    result |= result_sign;
178
179    // Final rounding.  The result may overflow to infinity, but that is the
180    // correct result in that case.
181    if round_guard_sticky > 0x4 {
182        result += one;
183    }
184    if round_guard_sticky == 0x4 {
185        result += result & one;
186    }
187
188    F::from_bits(result)
189}
190
191intrinsics! {
192    #[aapcs_on_arm]
193    #[arm_aeabi_alias = __aeabi_fadd]
194    pub extern "C" fn __addsf3(a: f32, b: f32) -> f32 {
195        add(a, b)
196    }
197
198    #[aapcs_on_arm]
199    #[arm_aeabi_alias = __aeabi_dadd]
200    pub extern "C" fn __adddf3(a: f64, b: f64) -> f64 {
201        add(a, b)
202    }
203
204    #[ppc_alias = __addkf3]
205    #[cfg(f128_enabled)]
206    pub extern "C" fn __addtf3(a: f128, b: f128) -> f128 {
207        add(a, b)
208    }
209}
compiler_builtins/float/add.rs

compiler_builtins/float/
add.rs
