const_soft_float/soft_f64/
mul.rs

1use crate::soft_f64::{u64_widen_mul, SoftF64};
2
3type F = SoftF64;
4
5type FInt = u64;
6
7const fn widen_mul(a: FInt, b: FInt) -> (FInt, FInt) {
8    u64_widen_mul(a, b)
9}
10
11pub(crate) const fn mul(a: F, b: F) -> F {
12    let one: FInt = 1;
13    let zero: FInt = 0;
14
15    let bits = F::BITS;
16    let significand_bits = F::SIGNIFICAND_BITS;
17    let max_exponent = F::EXPONENT_MAX;
18
19    let exponent_bias = F::EXPONENT_BIAS;
20
21    let implicit_bit = F::IMPLICIT_BIT;
22    let significand_mask = F::SIGNIFICAND_MASK;
23    let sign_bit = F::SIGN_MASK as FInt;
24    let abs_mask = sign_bit - one;
25    let exponent_mask = F::EXPONENT_MASK;
26    let inf_rep = exponent_mask;
27    let quiet_bit = implicit_bit >> 1;
28    let qnan_rep = exponent_mask | quiet_bit;
29    let exponent_bits = F::EXPONENT_BITS;
30
31    let a_rep = a.repr();
32    let b_rep = b.repr();
33
34    let a_exponent = (a_rep >> significand_bits) & max_exponent as FInt;
35    let b_exponent = (b_rep >> significand_bits) & max_exponent as FInt;
36    let product_sign = (a_rep ^ b_rep) & sign_bit;
37
38    let mut a_significand = a_rep & significand_mask;
39    let mut b_significand = b_rep & significand_mask;
40    let mut scale = 0;
41
42    // Detect if a or b is zero, denormal, infinity, or NaN.
43    if a_exponent.wrapping_sub(one) >= (max_exponent - 1) as FInt
44        || b_exponent.wrapping_sub(one) >= (max_exponent - 1) as FInt
45    {
46        let a_abs = a_rep & abs_mask;
47        let b_abs = b_rep & abs_mask;
48
49        // NaN + anything = qNaN
50        if a_abs > inf_rep {
51            return F::from_repr(a_rep | quiet_bit);
52        }
53        // anything + NaN = qNaN
54        if b_abs > inf_rep {
55            return F::from_repr(b_rep | quiet_bit);
56        }
57
58        if a_abs == inf_rep {
59            if b_abs != zero {
60                // infinity * non-zero = +/- infinity
61                return F::from_repr(a_abs | product_sign);
62            } else {
63                // infinity * zero = NaN
64                return F::from_repr(qnan_rep);
65            }
66        }
67
68        if b_abs == inf_rep {
69            if a_abs != zero {
70                // infinity * non-zero = +/- infinity
71                return F::from_repr(b_abs | product_sign);
72            } else {
73                // infinity * zero = NaN
74                return F::from_repr(qnan_rep);
75            }
76        }
77
78        // zero * anything = +/- zero
79        if a_abs == zero {
80            return F::from_repr(product_sign);
81        }
82
83        // anything * zero = +/- zero
84        if b_abs == zero {
85            return F::from_repr(product_sign);
86        }
87
88        // one or both of a or b is denormal, the other (if applicable) is a
89        // normal number.  Renormalize one or both of a and b, and set scale to
90        // include the necessary exponent adjustment.
91        if a_abs < implicit_bit {
92            let (exponent, significand) = F::normalize(a_significand);
93            scale += exponent;
94            a_significand = significand;
95        }
96
97        if b_abs < implicit_bit {
98            let (exponent, significand) = F::normalize(b_significand);
99            scale += exponent;
100            b_significand = significand;
101        }
102    }
103
104    // Or in the implicit significand bit.  (If we fell through from the
105    // denormal path it was already set by normalize( ), but setting it twice
106    // won't hurt anything.)
107    a_significand |= implicit_bit;
108    b_significand |= implicit_bit;
109
110    // Get the significand of a*b.  Before multiplying the significands, shift
111    // one of them left to left-align it in the field.  Thus, the product will
112    // have (exponentBits + 2) integral digits, all but two of which must be
113    // zero.  Normalizing this result is just a conditional left-shift by one
114    // and bumping the exponent accordingly.
115    let (mut product_low, mut product_high) =
116        widen_mul(a_significand, b_significand << exponent_bits);
117
118    let a_exponent_i32: i32 = a_exponent as _;
119    let b_exponent_i32: i32 = b_exponent as _;
120    let mut product_exponent: i32 = a_exponent_i32
121        .wrapping_add(b_exponent_i32)
122        .wrapping_add(scale)
123        .wrapping_sub(exponent_bias as i32);
124
125    // Normalize the significand, adjust exponent if needed.
126    if (product_high & implicit_bit) != zero {
127        product_exponent = product_exponent.wrapping_add(1);
128    } else {
129        product_high = (product_high << 1) | (product_low >> (bits - 1));
130        product_low <<= 1;
131    }
132
133    // If we have overflowed the type, return +/- infinity.
134    if product_exponent >= max_exponent as i32 {
135        return F::from_repr(inf_rep | product_sign);
136    }
137
138    if product_exponent <= 0 {
139        // Result is denormal before rounding
140        //
141        // If the result is so small that it just underflows to zero, return
142        // a zero of the appropriate sign.  Mathematically there is no need to
143        // handle this case separately, but we make it a special case to
144        // simplify the shift logic.
145        let shift = one.wrapping_sub(product_exponent as FInt) as u32;
146        if shift >= bits {
147            return F::from_repr(product_sign);
148        }
149
150        // Otherwise, shift the significand of the result so that the round
151        // bit is the high bit of productLo.
152        if shift < bits {
153            let sticky = product_low << (bits - shift);
154            product_low = product_high << (bits - shift) | product_low >> shift | sticky;
155            product_high >>= shift;
156        } else if shift < (2 * bits) {
157            let sticky = product_high << (2 * bits - shift) | product_low;
158            product_low = product_high >> (shift - bits) | sticky;
159            product_high = zero;
160        } else {
161            product_high = zero;
162        }
163    } else {
164        // Result is normal before rounding; insert the exponent.
165        product_high &= significand_mask;
166        product_high |= (product_exponent as FInt) << significand_bits;
167    }
168
169    // Insert the sign of the result:
170    product_high |= product_sign;
171
172    // Final rounding.  The final result may overflow to infinity, or underflow
173    // to zero, but those are the correct results in those cases.  We use the
174    // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
175    if product_low > sign_bit {
176        product_high += one;
177    }
178
179    if product_low == sign_bit {
180        product_high += product_high & one;
181    }
182
183    F::from_repr(product_high)
184}
185
186#[cfg(test)]
187mod test {
188    use crate::soft_f64::SoftF64;
189
190    #[test]
191    fn sanity_check() {
192        assert_eq!(SoftF64(2.0).mul(SoftF64(2.0)).0, 4.0)
193    }
194}