TLA Line data Source code
1 : // Copyright 2020-2023 Daniel Lemire
2 : // Copyright 2023 Matt Borland
3 : // Distributed under the Boost Software License, Version 1.0.
4 : // https://www.boost.org/LICENSE_1_0.txt
5 : //
6 : // Derivative of: https://github.com/fastfloat/fast_float
7 :
8 : #ifndef BOOST_JSON_DETAIL_CHARCONV_DETAIL_FASTFLOAT_DECIMAL_TO_BINARY_HPP
9 : #define BOOST_JSON_DETAIL_CHARCONV_DETAIL_FASTFLOAT_DECIMAL_TO_BINARY_HPP
10 :
11 : #include <boost/json/detail/charconv/detail/fast_float/float_common.hpp>
12 : #include <boost/json/detail/charconv/detail/fast_float/fast_table.hpp>
13 : #include <cfloat>
14 : #include <cinttypes>
15 : #include <cmath>
16 : #include <cstdint>
17 : #include <cstdlib>
18 : #include <cstring>
19 :
20 : namespace boost { namespace json { namespace detail { namespace charconv { namespace detail { namespace fast_float {
21 :
22 : // This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
23 : // the result, with the "high" part corresponding to the most significant bits and the
24 : // low part corresponding to the least significant bits.
25 : //
26 : template <int bit_precision>
27 : BOOST_FORCEINLINE BOOST_JSON_FASTFLOAT_CONSTEXPR20
28 : value128 compute_product_approximation(int64_t q, uint64_t w) {
29 HIT 2005879 : const int index = 2 * int(q - powers::smallest_power_of_five);
30 : // For small values of q, e.g., q in [0,27], the answer is always exact because
31 : // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
32 : // gives the exact answer.
33 4011758 : value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
34 : static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]");
35 2005879 : constexpr uint64_t precision_mask = (bit_precision < 64) ?
36 : (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
37 : : uint64_t(0xFFFFFFFFFFFFFFFF);
38 2005879 : if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower)
39 : // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
40 4995 : value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
41 4995 : firstproduct.low += secondproduct.high;
42 4995 : if(secondproduct.high > firstproduct.low) {
43 1825 : firstproduct.high++;
44 : }
45 : }
46 2005879 : return firstproduct;
47 : }
48 :
49 : namespace detail {
50 : /**
51 : * For q in (0,350), we have that
52 : * f = (((152170 + 65536) * q ) >> 16);
53 : * is equal to
54 : * floor(p) + q
55 : * where
56 : * p = log(5**q)/log(2) = q * log(5)/log(2)
57 : *
58 : * For negative values of q in (-400,0), we have that
59 : * f = (((152170 + 65536) * q ) >> 16);
60 : * is equal to
61 : * -ceil(p) + q
62 : * where
63 : * p = log(5**-q)/log(2) = -q * log(5)/log(2)
64 : */
65 : constexpr BOOST_FORCEINLINE int32_t power(int32_t q) noexcept {
66 2005879 : return (((152170 + 65536) * q) >> 16) + 63;
67 : }
68 : } // namespace detail
69 :
70 : // create an adjusted mantissa, biased by the invalid power2
71 : // for significant digits already multiplied by 10 ** q.
72 : template <typename binary>
73 : BOOST_FORCEINLINE BOOST_JSON_CXX14_CONSTEXPR_NO_INLINE
74 : adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept {
75 2986 : int hilz = int(w >> 63) ^ 1;
76 2986 : adjusted_mantissa answer;
77 2986 : answer.mantissa = w << hilz;
78 2986 : int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent();
79 5972 : answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias);
80 2986 : return answer;
81 : }
82 :
83 : // w * 10 ** q, without rounding the representation up.
84 : // the power2 in the exponent will be adjusted by invalid_am_bias.
85 : template <typename binary>
86 : BOOST_FORCEINLINE BOOST_JSON_FASTFLOAT_CONSTEXPR20
87 : adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept {
88 2986 : int lz = leading_zeroes(w);
89 2986 : w <<= lz;
90 : value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
91 8958 : return compute_error_scaled<binary>(q, product.high, lz);
92 : }
93 :
94 : // w * 10 ** q
95 : // The returned value should be a valid ieee64 number that simply need to be packed.
96 : // However, in some very rare cases, the computation will fail. In such cases, we
97 : // return an adjusted_mantissa with a negative power of 2: the caller should recompute
98 : // in such cases.
99 : template <typename binary>
100 : BOOST_FORCEINLINE BOOST_JSON_FASTFLOAT_CONSTEXPR20
101 : adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
102 2004452 : adjusted_mantissa answer;
103 2004452 : if ((w == 0) || (q < binary::smallest_power_of_ten())) {
104 1 : answer.power2 = 0;
105 1 : answer.mantissa = 0;
106 : // result should be zero
107 1 : return answer;
108 : }
109 2004451 : if (q > binary::largest_power_of_ten()) {
110 : // we want to get infinity:
111 1558 : answer.power2 = binary::infinite_power();
112 1558 : answer.mantissa = 0;
113 1558 : return answer;
114 : }
115 : // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].
116 :
117 : // We want the most significant bit of i to be 1. Shift if needed.
118 2002893 : int lz = leading_zeroes(w);
119 2002893 : w <<= lz;
120 :
121 : // The required precision is binary::mantissa_explicit_bits() + 3 because
122 : // 1. We need the implicit bit
123 : // 2. We need an extra bit for rounding purposes
124 : // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
125 :
126 : value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
127 : // The computed 'product' is always sufficient.
128 : // Mathematical proof:
129 : // Noble Mushtak and Daniel Lemire, Fast Number Parsing Without Fallback (to appear)
130 : // See script/mushtak_lemire.py
131 :
132 : // The "compute_product_approximation" function can be slightly slower than a branchless approach:
133 : // value128 product = compute_product(q, w);
134 : // but in practice, we can win big with the compute_product_approximation if its additional branch
135 : // is easily predicted. Which is best is data specific.
136 2002893 : int upperbit = int(product.high >> 63);
137 :
138 2002893 : answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
139 :
140 4005786 : answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent());
141 2002893 : if (answer.power2 <= 0) { // we have a subnormal?
142 : // Here have that answer.power2 <= 0 so -answer.power2 >= 0
143 82 : if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
144 MIS 0 : answer.power2 = 0;
145 0 : answer.mantissa = 0;
146 : // result should be zero
147 0 : return answer;
148 : }
149 : // next line is safe because -answer.power2 + 1 < 64
150 HIT 82 : answer.mantissa >>= -answer.power2 + 1;
151 : // Thankfully, we can't have both "round-to-even" and subnormals because
152 : // "round-to-even" only occurs for powers close to 0.
153 82 : answer.mantissa += (answer.mantissa & 1); // round up
154 82 : answer.mantissa >>= 1;
155 : // There is a weird scenario where we don't have a subnormal but just.
156 : // Suppose we start with 2.2250738585072013e-308, we end up
157 : // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
158 : // whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round
159 : // up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer
160 : // subnormal, but we can only know this after rounding.
161 : // So we only declare a subnormal if we are smaller than the threshold.
162 82 : answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
163 82 : return answer;
164 : }
165 :
166 : // usually, we round *up*, but if we fall right in between and and we have an
167 : // even basis, we need to round down
168 : // We are only concerned with the cases where 5**q fits in single 64-bit word.
169 2009538 : if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
170 6727 : ((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
171 : // To be in-between two floats we need that in doing
172 : // answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
173 : // ... we dropped out only zeroes. But if this happened, then we can go back!!!
174 1857 : if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) {
175 14 : answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up
176 : }
177 : }
178 :
179 2002811 : answer.mantissa += (answer.mantissa & 1); // round up
180 2002811 : answer.mantissa >>= 1;
181 2002811 : if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
182 360 : answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
183 360 : answer.power2++; // undo previous addition
184 : }
185 :
186 2002811 : answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
187 2002811 : if (answer.power2 >= binary::infinite_power()) { // infinity
188 59658 : answer.power2 = binary::infinite_power();
189 59658 : answer.mantissa = 0;
190 : }
191 2002811 : return answer;
192 : }
193 :
194 : }}}}}} // namespace fast_float
195 :
196 : #endif
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