1 | //===-- Abstract class for bit manipulation of float numbers. ---*- C++ -*-===// |
2 | // |
3 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
4 | // See https://llvm.org/LICENSE.txt for license information. |
5 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
6 | // |
7 | //===----------------------------------------------------------------------===// |
8 | |
9 | #ifndef LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
10 | #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
11 | |
12 | #include "src/__support/CPP/bit.h" |
13 | #include "src/__support/CPP/type_traits.h" |
14 | #include "src/__support/common.h" |
15 | #include "src/__support/libc_assert.h" // LIBC_ASSERT |
16 | #include "src/__support/macros/attributes.h" // LIBC_INLINE, LIBC_INLINE_VAR |
17 | #include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_FLOAT128 |
18 | #include "src/__support/math_extras.h" // mask_trailing_ones |
19 | #include "src/__support/sign.h" // Sign |
20 | #include "src/__support/uint128.h" |
21 | |
22 | #include <stdint.h> |
23 | |
24 | namespace LIBC_NAMESPACE { |
25 | namespace fputil { |
26 | |
27 | // The supported floating point types. |
28 | enum class FPType { |
29 | IEEE754_Binary16, |
30 | IEEE754_Binary32, |
31 | IEEE754_Binary64, |
32 | IEEE754_Binary128, |
33 | X86_Binary80, |
34 | }; |
35 | |
36 | // The classes hierarchy is as follows: |
37 | // |
38 | // ┌───────────────────┐ |
39 | // │ FPLayout<FPType> │ |
40 | // └─────────▲─────────┘ |
41 | // │ |
42 | // ┌─────────┴─────────┐ |
43 | // │ FPStorage<FPType> │ |
44 | // └─────────▲─────────┘ |
45 | // │ |
46 | // ┌────────────┴─────────────┐ |
47 | // │ │ |
48 | // ┌────────┴─────────┐ ┌──────────────┴──────────────────┐ |
49 | // │ FPRepSem<FPType> │ │ FPRepSem<FPType::X86_Binary80 │ |
50 | // └────────▲─────────┘ └──────────────▲──────────────────┘ |
51 | // │ │ |
52 | // └────────────┬─────────────┘ |
53 | // │ |
54 | // ┌───────┴───────┐ |
55 | // │ FPRepImpl<T> │ |
56 | // └───────▲───────┘ |
57 | // │ |
58 | // ┌────────┴────────┐ |
59 | // ┌─────┴─────┐ ┌─────┴─────┐ |
60 | // │ FPRep<T> │ │ FPBits<T> │ |
61 | // └───────────┘ └───────────┘ |
62 | // |
63 | // - 'FPLayout' defines only a few constants, namely the 'StorageType' and |
64 | // length of the sign, the exponent, fraction and significand parts. |
65 | // - 'FPStorage' builds more constants on top of those from 'FPLayout' like |
66 | // exponent bias and masks. It also holds the bit representation of the |
67 | // floating point as a 'StorageType' type and defines tools to assemble or |
68 | // test these parts. |
69 | // - 'FPRepSem' defines functions to interact semantically with the floating |
70 | // point representation. The default implementation is the one for 'IEEE754', |
71 | // a specialization is provided for X86 Extended Precision. |
72 | // - 'FPRepImpl' derives from 'FPRepSem' and adds functions that are common to |
73 | // all implementations or build on the ones in 'FPRepSem'. |
74 | // - 'FPRep' exposes all functions from 'FPRepImpl' and returns 'FPRep' |
75 | // instances when using Builders (static functions to create values). |
76 | // - 'FPBits' exposes all the functions from 'FPRepImpl' but operates on the |
77 | // native C++ floating point type instead of 'FPType'. An additional 'get_val' |
78 | // function allows getting the C++ floating point type value back. Builders |
79 | // called from 'FPBits' return 'FPBits' instances. |
80 | |
81 | namespace internal { |
82 | |
83 | // Defines the layout (sign, exponent, significand) of a floating point type in |
84 | // memory. It also defines its associated StorageType, i.e., the unsigned |
85 | // integer type used to manipulate its representation. |
86 | // Additionally we provide the fractional part length, i.e., the number of bits |
87 | // after the decimal dot when the number is in normal form. |
88 | template <FPType> struct FPLayout {}; |
89 | |
90 | template <> struct FPLayout<FPType::IEEE754_Binary16> { |
91 | using StorageType = uint16_t; |
92 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
93 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 5; |
94 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 10; |
95 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
96 | }; |
97 | |
98 | template <> struct FPLayout<FPType::IEEE754_Binary32> { |
99 | using StorageType = uint32_t; |
100 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
101 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 8; |
102 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 23; |
103 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
104 | }; |
105 | |
106 | template <> struct FPLayout<FPType::IEEE754_Binary64> { |
107 | using StorageType = uint64_t; |
108 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
109 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 11; |
110 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 52; |
111 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
112 | }; |
113 | |
114 | template <> struct FPLayout<FPType::IEEE754_Binary128> { |
115 | using StorageType = UInt128; |
116 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
117 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 15; |
118 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 112; |
119 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN; |
120 | }; |
121 | |
122 | template <> struct FPLayout<FPType::X86_Binary80> { |
123 | using StorageType = UInt128; |
124 | LIBC_INLINE_VAR static constexpr int SIGN_LEN = 1; |
125 | LIBC_INLINE_VAR static constexpr int EXP_LEN = 15; |
126 | LIBC_INLINE_VAR static constexpr int SIG_LEN = 64; |
127 | LIBC_INLINE_VAR static constexpr int FRACTION_LEN = SIG_LEN - 1; |
128 | }; |
129 | |
130 | // FPStorage derives useful constants from the FPLayout above. |
131 | template <FPType fp_type> struct FPStorage : public FPLayout<fp_type> { |
132 | using UP = FPLayout<fp_type>; |
133 | |
134 | using UP::EXP_LEN; // The number of bits for the *exponent* part |
135 | using UP::SIG_LEN; // The number of bits for the *significand* part |
136 | using UP::SIGN_LEN; // The number of bits for the *sign* part |
137 | // For convenience, the sum of `SIG_LEN`, `EXP_LEN`, and `SIGN_LEN`. |
138 | LIBC_INLINE_VAR static constexpr int TOTAL_LEN = SIGN_LEN + EXP_LEN + SIG_LEN; |
139 | |
140 | // The number of bits after the decimal dot when the number is in normal form. |
141 | using UP::FRACTION_LEN; |
142 | |
143 | // An unsigned integer that is wide enough to contain all of the floating |
144 | // point bits. |
145 | using StorageType = typename UP::StorageType; |
146 | |
147 | // The number of bits in StorageType. |
148 | LIBC_INLINE_VAR static constexpr int STORAGE_LEN = |
149 | sizeof(StorageType) * CHAR_BIT; |
150 | static_assert(STORAGE_LEN >= TOTAL_LEN); |
151 | |
152 | // The exponent bias. Always positive. |
153 | LIBC_INLINE_VAR static constexpr int32_t EXP_BIAS = |
154 | (1U << (EXP_LEN - 1U)) - 1U; |
155 | static_assert(EXP_BIAS > 0); |
156 | |
157 | // The bit pattern that keeps only the *significand* part. |
158 | LIBC_INLINE_VAR static constexpr StorageType SIG_MASK = |
159 | mask_trailing_ones<StorageType, SIG_LEN>(); |
160 | // The bit pattern that keeps only the *exponent* part. |
161 | LIBC_INLINE_VAR static constexpr StorageType EXP_MASK = |
162 | mask_trailing_ones<StorageType, EXP_LEN>() << SIG_LEN; |
163 | // The bit pattern that keeps only the *sign* part. |
164 | LIBC_INLINE_VAR static constexpr StorageType SIGN_MASK = |
165 | mask_trailing_ones<StorageType, SIGN_LEN>() << (EXP_LEN + SIG_LEN); |
166 | // The bit pattern that keeps only the *exponent + significand* part. |
167 | LIBC_INLINE_VAR static constexpr StorageType EXP_SIG_MASK = |
168 | mask_trailing_ones<StorageType, EXP_LEN + SIG_LEN>(); |
169 | // The bit pattern that keeps only the *sign + exponent + significand* part. |
170 | LIBC_INLINE_VAR static constexpr StorageType FP_MASK = |
171 | mask_trailing_ones<StorageType, TOTAL_LEN>(); |
172 | // The bit pattern that keeps only the *fraction* part. |
173 | // i.e., the *significand* without the leading one. |
174 | LIBC_INLINE_VAR static constexpr StorageType FRACTION_MASK = |
175 | mask_trailing_ones<StorageType, FRACTION_LEN>(); |
176 | |
177 | static_assert((SIG_MASK & EXP_MASK & SIGN_MASK) == 0, "masks disjoint" ); |
178 | static_assert((SIG_MASK | EXP_MASK | SIGN_MASK) == FP_MASK, "masks cover" ); |
179 | |
180 | protected: |
181 | // Merge bits from 'a' and 'b' values according to 'mask'. |
182 | // Use 'a' bits when corresponding 'mask' bits are zeroes and 'b' bits when |
183 | // corresponding bits are ones. |
184 | LIBC_INLINE static constexpr StorageType merge(StorageType a, StorageType b, |
185 | StorageType mask) { |
186 | // https://graphics.stanford.edu/~seander/bithacks.html#MaskedMerge |
187 | return a ^ ((a ^ b) & mask); |
188 | } |
189 | |
190 | // A stongly typed integer that prevents mixing and matching integers with |
191 | // different semantics. |
192 | template <typename T> struct TypedInt { |
193 | using value_type = T; |
194 | LIBC_INLINE constexpr explicit TypedInt(T value) : value(value) {} |
195 | LIBC_INLINE constexpr TypedInt(const TypedInt &value) = default; |
196 | LIBC_INLINE constexpr TypedInt &operator=(const TypedInt &value) = default; |
197 | |
198 | LIBC_INLINE constexpr explicit operator T() const { return value; } |
199 | |
200 | LIBC_INLINE constexpr StorageType to_storage_type() const { |
201 | return StorageType(value); |
202 | } |
203 | |
204 | LIBC_INLINE friend constexpr bool operator==(TypedInt a, TypedInt b) { |
205 | return a.value == b.value; |
206 | } |
207 | LIBC_INLINE friend constexpr bool operator!=(TypedInt a, TypedInt b) { |
208 | return a.value != b.value; |
209 | } |
210 | |
211 | protected: |
212 | T value; |
213 | }; |
214 | |
215 | // An opaque type to store a floating point exponent. |
216 | // We define special values but it is valid to create arbitrary values as long |
217 | // as they are in the range [min, max]. |
218 | struct Exponent : public TypedInt<int32_t> { |
219 | using UP = TypedInt<int32_t>; |
220 | using UP::UP; |
221 | LIBC_INLINE static constexpr auto subnormal() { |
222 | return Exponent(-EXP_BIAS); |
223 | } |
224 | LIBC_INLINE static constexpr auto min() { return Exponent(1 - EXP_BIAS); } |
225 | LIBC_INLINE static constexpr auto zero() { return Exponent(0); } |
226 | LIBC_INLINE static constexpr auto max() { return Exponent(EXP_BIAS); } |
227 | LIBC_INLINE static constexpr auto inf() { return Exponent(EXP_BIAS + 1); } |
228 | }; |
229 | |
230 | // An opaque type to store a floating point biased exponent. |
231 | // We define special values but it is valid to create arbitrary values as long |
232 | // as they are in the range [zero, bits_all_ones]. |
233 | // Values greater than bits_all_ones are truncated. |
234 | struct BiasedExponent : public TypedInt<uint32_t> { |
235 | using UP = TypedInt<uint32_t>; |
236 | using UP::UP; |
237 | |
238 | LIBC_INLINE constexpr BiasedExponent(Exponent exp) |
239 | : UP(static_cast<int32_t>(exp) + EXP_BIAS) {} |
240 | |
241 | // Cast operator to get convert from BiasedExponent to Exponent. |
242 | LIBC_INLINE constexpr operator Exponent() const { |
243 | return Exponent(UP::value - EXP_BIAS); |
244 | } |
245 | |
246 | LIBC_INLINE constexpr BiasedExponent &operator++() { |
247 | LIBC_ASSERT(*this != BiasedExponent(Exponent::inf())); |
248 | ++UP::value; |
249 | return *this; |
250 | } |
251 | |
252 | LIBC_INLINE constexpr BiasedExponent &operator--() { |
253 | LIBC_ASSERT(*this != BiasedExponent(Exponent::subnormal())); |
254 | --UP::value; |
255 | return *this; |
256 | } |
257 | }; |
258 | |
259 | // An opaque type to store a floating point significand. |
260 | // We define special values but it is valid to create arbitrary values as long |
261 | // as they are in the range [zero, bits_all_ones]. |
262 | // Note that the semantics of the Significand are implementation dependent. |
263 | // Values greater than bits_all_ones are truncated. |
264 | struct Significand : public TypedInt<StorageType> { |
265 | using UP = TypedInt<StorageType>; |
266 | using UP::UP; |
267 | |
268 | LIBC_INLINE friend constexpr Significand operator|(const Significand a, |
269 | const Significand b) { |
270 | return Significand( |
271 | StorageType(a.to_storage_type() | b.to_storage_type())); |
272 | } |
273 | LIBC_INLINE friend constexpr Significand operator^(const Significand a, |
274 | const Significand b) { |
275 | return Significand( |
276 | StorageType(a.to_storage_type() ^ b.to_storage_type())); |
277 | } |
278 | LIBC_INLINE friend constexpr Significand operator>>(const Significand a, |
279 | int shift) { |
280 | return Significand(StorageType(a.to_storage_type() >> shift)); |
281 | } |
282 | |
283 | LIBC_INLINE static constexpr auto zero() { |
284 | return Significand(StorageType(0)); |
285 | } |
286 | LIBC_INLINE static constexpr auto lsb() { |
287 | return Significand(StorageType(1)); |
288 | } |
289 | LIBC_INLINE static constexpr auto msb() { |
290 | return Significand(StorageType(1) << (SIG_LEN - 1)); |
291 | } |
292 | LIBC_INLINE static constexpr auto bits_all_ones() { |
293 | return Significand(SIG_MASK); |
294 | } |
295 | }; |
296 | |
297 | LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp) { |
298 | return (exp.to_storage_type() << SIG_LEN) & EXP_MASK; |
299 | } |
300 | |
301 | LIBC_INLINE static constexpr StorageType encode(Significand value) { |
302 | return value.to_storage_type() & SIG_MASK; |
303 | } |
304 | |
305 | LIBC_INLINE static constexpr StorageType encode(BiasedExponent exp, |
306 | Significand sig) { |
307 | return encode(exp) | encode(sig); |
308 | } |
309 | |
310 | LIBC_INLINE static constexpr StorageType encode(Sign sign, BiasedExponent exp, |
311 | Significand sig) { |
312 | if (sign.is_neg()) |
313 | return SIGN_MASK | encode(exp, sig); |
314 | return encode(exp, sig); |
315 | } |
316 | |
317 | // The floating point number representation as an unsigned integer. |
318 | StorageType bits{}; |
319 | |
320 | LIBC_INLINE constexpr FPStorage() : bits(0) {} |
321 | LIBC_INLINE constexpr FPStorage(StorageType value) : bits(value) {} |
322 | |
323 | // Observers |
324 | LIBC_INLINE constexpr StorageType exp_bits() const { return bits & EXP_MASK; } |
325 | LIBC_INLINE constexpr StorageType sig_bits() const { return bits & SIG_MASK; } |
326 | LIBC_INLINE constexpr StorageType exp_sig_bits() const { |
327 | return bits & EXP_SIG_MASK; |
328 | } |
329 | |
330 | // Parts |
331 | LIBC_INLINE constexpr BiasedExponent biased_exponent() const { |
332 | return BiasedExponent(static_cast<uint32_t>(exp_bits() >> SIG_LEN)); |
333 | } |
334 | LIBC_INLINE constexpr void set_biased_exponent(BiasedExponent biased) { |
335 | bits = merge(a: bits, b: encode(biased), mask: EXP_MASK); |
336 | } |
337 | |
338 | public: |
339 | LIBC_INLINE constexpr Sign sign() const { |
340 | return (bits & SIGN_MASK) ? Sign::NEG : Sign::POS; |
341 | } |
342 | LIBC_INLINE constexpr void set_sign(Sign signVal) { |
343 | if (sign() != signVal) |
344 | bits ^= SIGN_MASK; |
345 | } |
346 | }; |
347 | |
348 | // This layer defines all functions that are specific to how the the floating |
349 | // point type is encoded. It enables constructions, modification and observation |
350 | // of values manipulated as 'StorageType'. |
351 | template <FPType fp_type, typename RetT> |
352 | struct FPRepSem : public FPStorage<fp_type> { |
353 | using UP = FPStorage<fp_type>; |
354 | using typename UP::StorageType; |
355 | using UP::FRACTION_LEN; |
356 | using UP::FRACTION_MASK; |
357 | |
358 | protected: |
359 | using typename UP::Exponent; |
360 | using typename UP::Significand; |
361 | using UP::bits; |
362 | using UP::encode; |
363 | using UP::exp_bits; |
364 | using UP::exp_sig_bits; |
365 | using UP::sig_bits; |
366 | using UP::UP; |
367 | |
368 | public: |
369 | // Builders |
370 | LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) { |
371 | return RetT(encode(sign, Exponent::subnormal(), Significand::zero())); |
372 | } |
373 | LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) { |
374 | return RetT(encode(sign, Exponent::zero(), Significand::zero())); |
375 | } |
376 | LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) { |
377 | return RetT(encode(sign, Exponent::subnormal(), Significand::lsb())); |
378 | } |
379 | LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) { |
380 | return RetT( |
381 | encode(sign, Exponent::subnormal(), Significand::bits_all_ones())); |
382 | } |
383 | LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) { |
384 | return RetT(encode(sign, Exponent::min(), Significand::zero())); |
385 | } |
386 | LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) { |
387 | return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones())); |
388 | } |
389 | LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) { |
390 | return RetT(encode(sign, Exponent::inf(), Significand::zero())); |
391 | } |
392 | LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS, |
393 | StorageType v = 0) { |
394 | return RetT(encode(sign, Exponent::inf(), |
395 | (v ? Significand(v) : (Significand::msb() >> 1)))); |
396 | } |
397 | LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS, |
398 | StorageType v = 0) { |
399 | return RetT( |
400 | encode(sign, Exponent::inf(), Significand::msb() | Significand(v))); |
401 | } |
402 | |
403 | // Observers |
404 | LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; } |
405 | LIBC_INLINE constexpr bool is_nan() const { |
406 | return exp_sig_bits() > encode(Exponent::inf(), Significand::zero()); |
407 | } |
408 | LIBC_INLINE constexpr bool is_quiet_nan() const { |
409 | return exp_sig_bits() >= encode(Exponent::inf(), Significand::msb()); |
410 | } |
411 | LIBC_INLINE constexpr bool is_signaling_nan() const { |
412 | return is_nan() && !is_quiet_nan(); |
413 | } |
414 | LIBC_INLINE constexpr bool is_inf() const { |
415 | return exp_sig_bits() == encode(Exponent::inf(), Significand::zero()); |
416 | } |
417 | LIBC_INLINE constexpr bool is_finite() const { |
418 | return exp_bits() != encode(Exponent::inf()); |
419 | } |
420 | LIBC_INLINE |
421 | constexpr bool is_subnormal() const { |
422 | return exp_bits() == encode(Exponent::subnormal()); |
423 | } |
424 | LIBC_INLINE constexpr bool is_normal() const { |
425 | return is_finite() && !is_subnormal(); |
426 | } |
427 | LIBC_INLINE constexpr RetT next_toward_inf() const { |
428 | if (is_finite()) |
429 | return RetT(bits + StorageType(1)); |
430 | return RetT(bits); |
431 | } |
432 | |
433 | // Returns the mantissa with the implicit bit set iff the current |
434 | // value is a valid normal number. |
435 | LIBC_INLINE constexpr StorageType get_explicit_mantissa() const { |
436 | if (is_subnormal()) |
437 | return sig_bits(); |
438 | return (StorageType(1) << UP::SIG_LEN) | sig_bits(); |
439 | } |
440 | }; |
441 | |
442 | // Specialization for the X86 Extended Precision type. |
443 | template <typename RetT> |
444 | struct FPRepSem<FPType::X86_Binary80, RetT> |
445 | : public FPStorage<FPType::X86_Binary80> { |
446 | using UP = FPStorage<FPType::X86_Binary80>; |
447 | using typename UP::StorageType; |
448 | using UP::FRACTION_LEN; |
449 | using UP::FRACTION_MASK; |
450 | |
451 | // The x86 80 bit float represents the leading digit of the mantissa |
452 | // explicitly. This is the mask for that bit. |
453 | static constexpr StorageType EXPLICIT_BIT_MASK = StorageType(1) |
454 | << FRACTION_LEN; |
455 | // The X80 significand is made of an explicit bit and the fractional part. |
456 | static_assert((EXPLICIT_BIT_MASK & FRACTION_MASK) == 0, |
457 | "the explicit bit and the fractional part should not overlap" ); |
458 | static_assert((EXPLICIT_BIT_MASK | FRACTION_MASK) == SIG_MASK, |
459 | "the explicit bit and the fractional part should cover the " |
460 | "whole significand" ); |
461 | |
462 | protected: |
463 | using typename UP::Exponent; |
464 | using typename UP::Significand; |
465 | using UP::encode; |
466 | using UP::UP; |
467 | |
468 | public: |
469 | // Builders |
470 | LIBC_INLINE static constexpr RetT zero(Sign sign = Sign::POS) { |
471 | return RetT(encode(sign, Exponent::subnormal(), Significand::zero())); |
472 | } |
473 | LIBC_INLINE static constexpr RetT one(Sign sign = Sign::POS) { |
474 | return RetT(encode(sign, Exponent::zero(), Significand::msb())); |
475 | } |
476 | LIBC_INLINE static constexpr RetT min_subnormal(Sign sign = Sign::POS) { |
477 | return RetT(encode(sign, Exponent::subnormal(), Significand::lsb())); |
478 | } |
479 | LIBC_INLINE static constexpr RetT max_subnormal(Sign sign = Sign::POS) { |
480 | return RetT(encode(sign, Exponent::subnormal(), |
481 | Significand::bits_all_ones() ^ Significand::msb())); |
482 | } |
483 | LIBC_INLINE static constexpr RetT min_normal(Sign sign = Sign::POS) { |
484 | return RetT(encode(sign, Exponent::min(), Significand::msb())); |
485 | } |
486 | LIBC_INLINE static constexpr RetT max_normal(Sign sign = Sign::POS) { |
487 | return RetT(encode(sign, Exponent::max(), Significand::bits_all_ones())); |
488 | } |
489 | LIBC_INLINE static constexpr RetT inf(Sign sign = Sign::POS) { |
490 | return RetT(encode(sign, Exponent::inf(), Significand::msb())); |
491 | } |
492 | LIBC_INLINE static constexpr RetT signaling_nan(Sign sign = Sign::POS, |
493 | StorageType v = 0) { |
494 | return RetT(encode(sign, Exponent::inf(), |
495 | Significand::msb() | |
496 | (v ? Significand(v) : (Significand::msb() >> 2)))); |
497 | } |
498 | LIBC_INLINE static constexpr RetT quiet_nan(Sign sign = Sign::POS, |
499 | StorageType v = 0) { |
500 | return RetT(encode(sign, Exponent::inf(), |
501 | Significand::msb() | (Significand::msb() >> 1) | |
502 | Significand(v))); |
503 | } |
504 | |
505 | // Observers |
506 | LIBC_INLINE constexpr bool is_zero() const { return exp_sig_bits() == 0; } |
507 | LIBC_INLINE constexpr bool is_nan() const { |
508 | // Most encoding forms from the table found in |
509 | // https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format |
510 | // are interpreted as NaN. |
511 | // More precisely : |
512 | // - Pseudo-Infinity |
513 | // - Pseudo Not a Number |
514 | // - Signalling Not a Number |
515 | // - Floating-point Indefinite |
516 | // - Quiet Not a Number |
517 | // - Unnormal |
518 | // This can be reduced to the following logic: |
519 | if (exp_bits() == encode(Exponent::inf())) |
520 | return !is_inf(); |
521 | if (exp_bits() != encode(Exponent::subnormal())) |
522 | return (sig_bits() & encode(Significand::msb())) == 0; |
523 | return false; |
524 | } |
525 | LIBC_INLINE constexpr bool is_quiet_nan() const { |
526 | return exp_sig_bits() >= |
527 | encode(Exponent::inf(), |
528 | Significand::msb() | (Significand::msb() >> 1)); |
529 | } |
530 | LIBC_INLINE constexpr bool is_signaling_nan() const { |
531 | return is_nan() && !is_quiet_nan(); |
532 | } |
533 | LIBC_INLINE constexpr bool is_inf() const { |
534 | return exp_sig_bits() == encode(Exponent::inf(), Significand::msb()); |
535 | } |
536 | LIBC_INLINE constexpr bool is_finite() const { |
537 | return !is_inf() && !is_nan(); |
538 | } |
539 | LIBC_INLINE |
540 | constexpr bool is_subnormal() const { |
541 | return exp_bits() == encode(Exponent::subnormal()); |
542 | } |
543 | LIBC_INLINE constexpr bool is_normal() const { |
544 | const auto exp = exp_bits(); |
545 | if (exp == encode(Exponent::subnormal()) || exp == encode(Exponent::inf())) |
546 | return false; |
547 | return get_implicit_bit(); |
548 | } |
549 | LIBC_INLINE constexpr RetT next_toward_inf() const { |
550 | if (is_finite()) { |
551 | if (exp_sig_bits() == max_normal().uintval()) { |
552 | return inf(sign: sign()); |
553 | } else if (exp_sig_bits() == max_subnormal().uintval()) { |
554 | return min_normal(sign: sign()); |
555 | } else if (sig_bits() == SIG_MASK) { |
556 | return RetT(encode(sign(), ++biased_exponent(), Significand::zero())); |
557 | } else { |
558 | return RetT(bits + StorageType(1)); |
559 | } |
560 | } |
561 | return RetT(bits); |
562 | } |
563 | |
564 | LIBC_INLINE constexpr StorageType get_explicit_mantissa() const { |
565 | return sig_bits(); |
566 | } |
567 | |
568 | // This functions is specific to FPRepSem<FPType::X86_Binary80>. |
569 | // TODO: Remove if possible. |
570 | LIBC_INLINE constexpr bool get_implicit_bit() const { |
571 | return static_cast<bool>(bits & EXPLICIT_BIT_MASK); |
572 | } |
573 | |
574 | // This functions is specific to FPRepSem<FPType::X86_Binary80>. |
575 | // TODO: Remove if possible. |
576 | LIBC_INLINE constexpr void set_implicit_bit(bool implicitVal) { |
577 | if (get_implicit_bit() != implicitVal) |
578 | bits ^= EXPLICIT_BIT_MASK; |
579 | } |
580 | }; |
581 | |
582 | // 'FPRepImpl' is the bottom of the class hierarchy that only deals with |
583 | // 'FPType'. The operations dealing with specific float semantics are |
584 | // implemented by 'FPRepSem' above and specialized when needed. |
585 | // |
586 | // The 'RetT' type is being propagated up to 'FPRepSem' so that the functions |
587 | // creating new values (Builders) can return the appropriate type. That is, when |
588 | // creating a value through 'FPBits' below the builder will return an 'FPBits' |
589 | // value. |
590 | // FPBits<float>::zero(); // returns an FPBits<> |
591 | // |
592 | // When we don't care about specific C++ floating point type we can use |
593 | // 'FPRep' and specify the 'FPType' directly. |
594 | // FPRep<FPType::IEEE754_Binary32:>::zero() // returns an FPRep<> |
595 | template <FPType fp_type, typename RetT> |
596 | struct FPRepImpl : public FPRepSem<fp_type, RetT> { |
597 | using UP = FPRepSem<fp_type, RetT>; |
598 | using StorageType = typename UP::StorageType; |
599 | |
600 | protected: |
601 | using UP::bits; |
602 | using UP::encode; |
603 | using UP::exp_bits; |
604 | using UP::exp_sig_bits; |
605 | |
606 | using typename UP::BiasedExponent; |
607 | using typename UP::Exponent; |
608 | using typename UP::Significand; |
609 | |
610 | using UP::FP_MASK; |
611 | |
612 | public: |
613 | // Constants. |
614 | using UP::EXP_BIAS; |
615 | using UP::EXP_MASK; |
616 | using UP::FRACTION_MASK; |
617 | using UP::SIG_LEN; |
618 | using UP::SIG_MASK; |
619 | using UP::SIGN_MASK; |
620 | LIBC_INLINE_VAR static constexpr int MAX_BIASED_EXPONENT = |
621 | (1 << UP::EXP_LEN) - 1; |
622 | |
623 | // CTors |
624 | LIBC_INLINE constexpr FPRepImpl() = default; |
625 | LIBC_INLINE constexpr explicit FPRepImpl(StorageType x) : UP(x) {} |
626 | |
627 | // Comparison |
628 | LIBC_INLINE constexpr friend bool operator==(FPRepImpl a, FPRepImpl b) { |
629 | return a.uintval() == b.uintval(); |
630 | } |
631 | LIBC_INLINE constexpr friend bool operator!=(FPRepImpl a, FPRepImpl b) { |
632 | return a.uintval() != b.uintval(); |
633 | } |
634 | |
635 | // Representation |
636 | LIBC_INLINE constexpr StorageType uintval() const { return bits & FP_MASK; } |
637 | LIBC_INLINE constexpr void set_uintval(StorageType value) { |
638 | bits = (value & FP_MASK); |
639 | } |
640 | |
641 | // Builders |
642 | using UP::inf; |
643 | using UP::max_normal; |
644 | using UP::max_subnormal; |
645 | using UP::min_normal; |
646 | using UP::min_subnormal; |
647 | using UP::one; |
648 | using UP::quiet_nan; |
649 | using UP::signaling_nan; |
650 | using UP::zero; |
651 | |
652 | // Modifiers |
653 | LIBC_INLINE constexpr RetT abs() const { |
654 | return RetT(bits & UP::EXP_SIG_MASK); |
655 | } |
656 | |
657 | // Observers |
658 | using UP::get_explicit_mantissa; |
659 | using UP::is_finite; |
660 | using UP::is_inf; |
661 | using UP::is_nan; |
662 | using UP::is_normal; |
663 | using UP::is_quiet_nan; |
664 | using UP::is_signaling_nan; |
665 | using UP::is_subnormal; |
666 | using UP::is_zero; |
667 | using UP::next_toward_inf; |
668 | using UP::sign; |
669 | LIBC_INLINE constexpr bool is_inf_or_nan() const { return !is_finite(); } |
670 | LIBC_INLINE constexpr bool is_neg() const { return sign().is_neg(); } |
671 | LIBC_INLINE constexpr bool is_pos() const { return sign().is_pos(); } |
672 | |
673 | LIBC_INLINE constexpr uint16_t get_biased_exponent() const { |
674 | return static_cast<uint16_t>(static_cast<uint32_t>(UP::biased_exponent())); |
675 | } |
676 | |
677 | LIBC_INLINE constexpr void set_biased_exponent(StorageType biased) { |
678 | UP::set_biased_exponent(BiasedExponent((int32_t)biased)); |
679 | } |
680 | |
681 | LIBC_INLINE constexpr int get_exponent() const { |
682 | return static_cast<int32_t>(Exponent(UP::biased_exponent())); |
683 | } |
684 | |
685 | // If the number is subnormal, the exponent is treated as if it were the |
686 | // minimum exponent for a normal number. This is to keep continuity between |
687 | // the normal and subnormal ranges, but it causes problems for functions where |
688 | // values are calculated from the exponent, since just subtracting the bias |
689 | // will give a slightly incorrect result. Additionally, zero has an exponent |
690 | // of zero, and that should actually be treated as zero. |
691 | LIBC_INLINE constexpr int get_explicit_exponent() const { |
692 | Exponent exponent(UP::biased_exponent()); |
693 | if (is_zero()) |
694 | exponent = Exponent::zero(); |
695 | if (exponent == Exponent::subnormal()) |
696 | exponent = Exponent::min(); |
697 | return static_cast<int32_t>(exponent); |
698 | } |
699 | |
700 | LIBC_INLINE constexpr StorageType get_mantissa() const { |
701 | return bits & FRACTION_MASK; |
702 | } |
703 | |
704 | LIBC_INLINE constexpr void set_mantissa(StorageType mantVal) { |
705 | bits = UP::merge(bits, mantVal, FRACTION_MASK); |
706 | } |
707 | |
708 | LIBC_INLINE constexpr void set_significand(StorageType sigVal) { |
709 | bits = UP::merge(bits, sigVal, SIG_MASK); |
710 | } |
711 | // Unsafe function to create a floating point representation. |
712 | // It simply packs the sign, biased exponent and mantissa values without |
713 | // checking bound nor normalization. |
714 | // |
715 | // WARNING: For X86 Extended Precision, implicit bit needs to be set correctly |
716 | // in the 'mantissa' by the caller. This function will not check for its |
717 | // validity. |
718 | // |
719 | // FIXME: Use an uint32_t for 'biased_exp'. |
720 | LIBC_INLINE static constexpr RetT |
721 | create_value(Sign sign, StorageType biased_exp, StorageType mantissa) { |
722 | return RetT(encode(sign, BiasedExponent(static_cast<uint32_t>(biased_exp)), |
723 | Significand(mantissa))); |
724 | } |
725 | |
726 | // The function converts integer number and unbiased exponent to proper |
727 | // float T type: |
728 | // Result = number * 2^(ep+1 - exponent_bias) |
729 | // Be careful! |
730 | // 1) "ep" is the raw exponent value. |
731 | // 2) The function adds +1 to ep for seamless normalized to denormalized |
732 | // transition. |
733 | // 3) The function does not check exponent high limit. |
734 | // 4) "number" zero value is not processed correctly. |
735 | // 5) Number is unsigned, so the result can be only positive. |
736 | LIBC_INLINE static constexpr RetT make_value(StorageType number, int ep) { |
737 | FPRepImpl result(0); |
738 | int lz = |
739 | UP::FRACTION_LEN + 1 - (UP::STORAGE_LEN - cpp::countl_zero(number)); |
740 | |
741 | number <<= lz; |
742 | ep -= lz; |
743 | |
744 | if (LIBC_LIKELY(ep >= 0)) { |
745 | // Implicit number bit will be removed by mask |
746 | result.set_significand(number); |
747 | result.set_biased_exponent(ep + 1); |
748 | } else { |
749 | result.set_significand(number >> -ep); |
750 | } |
751 | return RetT(result.uintval()); |
752 | } |
753 | }; |
754 | |
755 | // A generic class to manipulate floating point formats. |
756 | // It derives its functionality to FPRepImpl above. |
757 | template <FPType fp_type> |
758 | struct FPRep : public FPRepImpl<fp_type, FPRep<fp_type>> { |
759 | using UP = FPRepImpl<fp_type, FPRep<fp_type>>; |
760 | using StorageType = typename UP::StorageType; |
761 | using UP::UP; |
762 | |
763 | LIBC_INLINE constexpr explicit operator StorageType() const { |
764 | return UP::uintval(); |
765 | } |
766 | }; |
767 | |
768 | } // namespace internal |
769 | |
770 | // Returns the FPType corresponding to C++ type T on the host. |
771 | template <typename T> LIBC_INLINE static constexpr FPType get_fp_type() { |
772 | using UnqualT = cpp::remove_cv_t<T>; |
773 | if constexpr (cpp::is_same_v<UnqualT, float> && __FLT_MANT_DIG__ == 24) |
774 | return FPType::IEEE754_Binary32; |
775 | else if constexpr (cpp::is_same_v<UnqualT, double> && __DBL_MANT_DIG__ == 53) |
776 | return FPType::IEEE754_Binary64; |
777 | else if constexpr (cpp::is_same_v<UnqualT, long double>) { |
778 | if constexpr (__LDBL_MANT_DIG__ == 53) |
779 | return FPType::IEEE754_Binary64; |
780 | else if constexpr (__LDBL_MANT_DIG__ == 64) |
781 | return FPType::X86_Binary80; |
782 | else if constexpr (__LDBL_MANT_DIG__ == 113) |
783 | return FPType::IEEE754_Binary128; |
784 | } |
785 | #if defined(LIBC_TYPES_HAS_FLOAT16) |
786 | else if constexpr (cpp::is_same_v<UnqualT, float16>) |
787 | return FPType::IEEE754_Binary16; |
788 | #endif |
789 | #if defined(LIBC_TYPES_HAS_FLOAT128) |
790 | else if constexpr (cpp::is_same_v<UnqualT, float128>) |
791 | return FPType::IEEE754_Binary128; |
792 | #endif |
793 | else |
794 | static_assert(cpp::always_false<UnqualT>, "Unsupported type" ); |
795 | } |
796 | |
797 | // A generic class to manipulate C++ floating point formats. |
798 | // It derives its functionality to FPRepImpl above. |
799 | template <typename T> |
800 | struct FPBits final : public internal::FPRepImpl<get_fp_type<T>(), FPBits<T>> { |
801 | static_assert(cpp::is_floating_point_v<T>, |
802 | "FPBits instantiated with invalid type." ); |
803 | using UP = internal::FPRepImpl<get_fp_type<T>(), FPBits<T>>; |
804 | using StorageType = typename UP::StorageType; |
805 | |
806 | // Constructors. |
807 | LIBC_INLINE constexpr FPBits() = default; |
808 | |
809 | template <typename XType> LIBC_INLINE constexpr explicit FPBits(XType x) { |
810 | using Unqual = typename cpp::remove_cv_t<XType>; |
811 | if constexpr (cpp::is_same_v<Unqual, T>) { |
812 | UP::bits = cpp::bit_cast<StorageType>(x); |
813 | } else if constexpr (cpp::is_same_v<Unqual, StorageType>) { |
814 | UP::bits = x; |
815 | } else { |
816 | // We don't want accidental type promotions/conversions, so we require |
817 | // exact type match. |
818 | static_assert(cpp::always_false<XType>); |
819 | } |
820 | } |
821 | |
822 | // Floating-point conversions. |
823 | LIBC_INLINE constexpr T get_val() const { return cpp::bit_cast<T>(UP::bits); } |
824 | }; |
825 | |
826 | } // namespace fputil |
827 | } // namespace LIBC_NAMESPACE |
828 | |
829 | #endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_FPBITS_H |
830 | |