1 | use crate::common::*; |
2 | use crate::d2s; |
3 | use crate::d2s_intrinsics::*; |
4 | use crate::parse::Error; |
5 | #[cfg (feature = "no-panic" )] |
6 | use no_panic::no_panic; |
7 | |
8 | const DOUBLE_EXPONENT_BIAS: usize = 1023; |
9 | |
10 | fn floor_log2(value: u64) -> u32 { |
11 | 63_u32.wrapping_sub(value.leading_zeros()) |
12 | } |
13 | |
14 | #[cfg_attr (feature = "no-panic" , no_panic)] |
15 | pub fn s2d(buffer: &[u8]) -> Result<f64, Error> { |
16 | let len = buffer.len(); |
17 | if len == 0 { |
18 | return Err(Error::InputTooShort); |
19 | } |
20 | |
21 | let mut m10digits = 0; |
22 | let mut e10digits = 0; |
23 | let mut dot_index = len; |
24 | let mut e_index = len; |
25 | let mut m10 = 0u64; |
26 | let mut e10 = 0i32; |
27 | let mut signed_m = false; |
28 | let mut signed_e = false; |
29 | |
30 | let mut i = 0; |
31 | if unsafe { *buffer.get_unchecked(0) } == b'-' { |
32 | signed_m = true; |
33 | i += 1; |
34 | } |
35 | |
36 | while let Some(c) = buffer.get(i).copied() { |
37 | if c == b'.' { |
38 | if dot_index != len { |
39 | return Err(Error::MalformedInput); |
40 | } |
41 | dot_index = i; |
42 | i += 1; |
43 | continue; |
44 | } |
45 | if c < b'0' || c > b'9' { |
46 | break; |
47 | } |
48 | if m10digits >= 17 { |
49 | return Err(Error::InputTooLong); |
50 | } |
51 | m10 = 10 * m10 + (c - b'0' ) as u64; |
52 | if m10 != 0 { |
53 | m10digits += 1; |
54 | } |
55 | i += 1; |
56 | } |
57 | |
58 | if let Some(b'e' ) | Some(b'E' ) = buffer.get(i) { |
59 | e_index = i; |
60 | i += 1; |
61 | match buffer.get(i) { |
62 | Some(b'-' ) => { |
63 | signed_e = true; |
64 | i += 1; |
65 | } |
66 | Some(b'+' ) => i += 1, |
67 | _ => {} |
68 | } |
69 | while let Some(c) = buffer.get(i).copied() { |
70 | if c < b'0' || c > b'9' { |
71 | return Err(Error::MalformedInput); |
72 | } |
73 | if e10digits > 3 { |
74 | // TODO: Be more lenient. Return +/-Infinity or +/-0 instead. |
75 | return Err(Error::InputTooLong); |
76 | } |
77 | e10 = 10 * e10 + (c - b'0' ) as i32; |
78 | if e10 != 0 { |
79 | e10digits += 1; |
80 | } |
81 | i += 1; |
82 | } |
83 | } |
84 | |
85 | if i < len { |
86 | return Err(Error::MalformedInput); |
87 | } |
88 | if signed_e { |
89 | e10 = -e10; |
90 | } |
91 | e10 -= if dot_index < e_index { |
92 | (e_index - dot_index - 1) as i32 |
93 | } else { |
94 | 0 |
95 | }; |
96 | if m10 == 0 { |
97 | return Ok(if signed_m { -0.0 } else { 0.0 }); |
98 | } |
99 | |
100 | if m10digits + e10 <= -324 || m10 == 0 { |
101 | // Number is less than 1e-324, which should be rounded down to 0; return |
102 | // +/-0.0. |
103 | let ieee = (signed_m as u64) << (d2s::DOUBLE_EXPONENT_BITS + d2s::DOUBLE_MANTISSA_BITS); |
104 | return Ok(f64::from_bits(ieee)); |
105 | } |
106 | if m10digits + e10 >= 310 { |
107 | // Number is larger than 1e+309, which should be rounded to +/-Infinity. |
108 | let ieee = ((signed_m as u64) << (d2s::DOUBLE_EXPONENT_BITS + d2s::DOUBLE_MANTISSA_BITS)) |
109 | | (0x7ff_u64 << d2s::DOUBLE_MANTISSA_BITS); |
110 | return Ok(f64::from_bits(ieee)); |
111 | } |
112 | |
113 | // Convert to binary float m2 * 2^e2, while retaining information about |
114 | // whether the conversion was exact (trailing_zeros). |
115 | let e2: i32; |
116 | let m2: u64; |
117 | let mut trailing_zeros: bool; |
118 | if e10 >= 0 { |
119 | // The length of m * 10^e in bits is: |
120 | // log2(m10 * 10^e10) = log2(m10) + e10 log2(10) = log2(m10) + e10 + e10 * log2(5) |
121 | // |
122 | // We want to compute the DOUBLE_MANTISSA_BITS + 1 top-most bits (+1 for |
123 | // the implicit leading one in IEEE format). We therefore choose a |
124 | // binary output exponent of |
125 | // log2(m10 * 10^e10) - (DOUBLE_MANTISSA_BITS + 1). |
126 | // |
127 | // We use floor(log2(5^e10)) so that we get at least this many bits; |
128 | // better to have an additional bit than to not have enough bits. |
129 | e2 = floor_log2(m10) |
130 | .wrapping_add(e10 as u32) |
131 | .wrapping_add(log2_pow5(e10) as u32) |
132 | .wrapping_sub(d2s::DOUBLE_MANTISSA_BITS + 1) as i32; |
133 | |
134 | // We now compute [m10 * 10^e10 / 2^e2] = [m10 * 5^e10 / 2^(e2-e10)]. |
135 | // To that end, we use the DOUBLE_POW5_SPLIT table. |
136 | let j = e2 |
137 | .wrapping_sub(e10) |
138 | .wrapping_sub(ceil_log2_pow5(e10)) |
139 | .wrapping_add(d2s::DOUBLE_POW5_BITCOUNT); |
140 | debug_assert!(j >= 0); |
141 | debug_assert!(e10 < d2s::DOUBLE_POW5_SPLIT.len() as i32); |
142 | m2 = mul_shift_64( |
143 | m10, |
144 | unsafe { d2s::DOUBLE_POW5_SPLIT.get_unchecked(e10 as usize) }, |
145 | j as u32, |
146 | ); |
147 | |
148 | // We also compute if the result is exact, i.e., |
149 | // [m10 * 10^e10 / 2^e2] == m10 * 10^e10 / 2^e2. |
150 | // This can only be the case if 2^e2 divides m10 * 10^e10, which in turn |
151 | // requires that the largest power of 2 that divides m10 + e10 is |
152 | // greater than e2. If e2 is less than e10, then the result must be |
153 | // exact. Otherwise we use the existing multiple_of_power_of_2 function. |
154 | trailing_zeros = |
155 | e2 < e10 || e2 - e10 < 64 && multiple_of_power_of_2(m10, (e2 - e10) as u32); |
156 | } else { |
157 | e2 = floor_log2(m10) |
158 | .wrapping_add(e10 as u32) |
159 | .wrapping_sub(ceil_log2_pow5(-e10) as u32) |
160 | .wrapping_sub(d2s::DOUBLE_MANTISSA_BITS + 1) as i32; |
161 | let j = e2 |
162 | .wrapping_sub(e10) |
163 | .wrapping_add(ceil_log2_pow5(-e10)) |
164 | .wrapping_sub(1) |
165 | .wrapping_add(d2s::DOUBLE_POW5_INV_BITCOUNT); |
166 | debug_assert!(-e10 < d2s::DOUBLE_POW5_INV_SPLIT.len() as i32); |
167 | m2 = mul_shift_64( |
168 | m10, |
169 | unsafe { d2s::DOUBLE_POW5_INV_SPLIT.get_unchecked(-e10 as usize) }, |
170 | j as u32, |
171 | ); |
172 | trailing_zeros = multiple_of_power_of_5(m10, -e10 as u32); |
173 | } |
174 | |
175 | // Compute the final IEEE exponent. |
176 | let mut ieee_e2 = i32::max(0, e2 + DOUBLE_EXPONENT_BIAS as i32 + floor_log2(m2) as i32) as u32; |
177 | |
178 | if ieee_e2 > 0x7fe { |
179 | // Final IEEE exponent is larger than the maximum representable; return +/-Infinity. |
180 | let ieee = ((signed_m as u64) << (d2s::DOUBLE_EXPONENT_BITS + d2s::DOUBLE_MANTISSA_BITS)) |
181 | | (0x7ff_u64 << d2s::DOUBLE_MANTISSA_BITS); |
182 | return Ok(f64::from_bits(ieee)); |
183 | } |
184 | |
185 | // We need to figure out how much we need to shift m2. The tricky part is |
186 | // that we need to take the final IEEE exponent into account, so we need to |
187 | // reverse the bias and also special-case the value 0. |
188 | let shift = if ieee_e2 == 0 { 1 } else { ieee_e2 as i32 } |
189 | .wrapping_sub(e2) |
190 | .wrapping_sub(DOUBLE_EXPONENT_BIAS as i32) |
191 | .wrapping_sub(d2s::DOUBLE_MANTISSA_BITS as i32); |
192 | debug_assert!(shift >= 0); |
193 | |
194 | // We need to round up if the exact value is more than 0.5 above the value |
195 | // we computed. That's equivalent to checking if the last removed bit was 1 |
196 | // and either the value was not just trailing zeros or the result would |
197 | // otherwise be odd. |
198 | // |
199 | // We need to update trailing_zeros given that we have the exact output |
200 | // exponent ieee_e2 now. |
201 | trailing_zeros &= (m2 & ((1_u64 << (shift - 1)) - 1)) == 0; |
202 | let last_removed_bit = (m2 >> (shift - 1)) & 1; |
203 | let round_up = last_removed_bit != 0 && (!trailing_zeros || ((m2 >> shift) & 1) != 0); |
204 | |
205 | let mut ieee_m2 = (m2 >> shift).wrapping_add(round_up as u64); |
206 | debug_assert!(ieee_m2 <= 1_u64 << (d2s::DOUBLE_MANTISSA_BITS + 1)); |
207 | ieee_m2 &= (1_u64 << d2s::DOUBLE_MANTISSA_BITS) - 1; |
208 | if ieee_m2 == 0 && round_up { |
209 | // Due to how the IEEE represents +/-Infinity, we don't need to check |
210 | // for overflow here. |
211 | ieee_e2 += 1; |
212 | } |
213 | let ieee = ((((signed_m as u64) << d2s::DOUBLE_EXPONENT_BITS) | ieee_e2 as u64) |
214 | << d2s::DOUBLE_MANTISSA_BITS) |
215 | | ieee_m2; |
216 | Ok(f64::from_bits(ieee)) |
217 | } |
218 | |