1 | //===-- Nearest integer floating-point operations ---------------*- 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_NEARESTINTEGEROPERATIONS_H |
10 | #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_NEARESTINTEGEROPERATIONS_H |
11 | |
12 | #include "FEnvImpl.h" |
13 | #include "FPBits.h" |
14 | #include "rounding_mode.h" |
15 | |
16 | #include "hdr/math_macros.h" |
17 | #include "src/__support/CPP/type_traits.h" |
18 | #include "src/__support/common.h" |
19 | |
20 | namespace LIBC_NAMESPACE { |
21 | namespace fputil { |
22 | |
23 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
24 | LIBC_INLINE T trunc(T x) { |
25 | FPBits<T> bits(x); |
26 | |
27 | // If x is infinity or NaN, return it. |
28 | // If it is zero also we should return it as is, but the logic |
29 | // later in this function takes care of it. But not doing a zero |
30 | // check, we improve the run time of non-zero values. |
31 | if (bits.is_inf_or_nan()) |
32 | return x; |
33 | |
34 | int exponent = bits.get_exponent(); |
35 | |
36 | // If the exponent is greater than the most negative mantissa |
37 | // exponent, then x is already an integer. |
38 | if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN)) |
39 | return x; |
40 | |
41 | // If the exponent is such that abs(x) is less than 1, then return 0. |
42 | if (exponent <= -1) |
43 | return FPBits<T>::zero(bits.sign()).get_val(); |
44 | |
45 | int trim_size = FPBits<T>::FRACTION_LEN - exponent; |
46 | bits.set_mantissa((bits.get_mantissa() >> trim_size) << trim_size); |
47 | return bits.get_val(); |
48 | } |
49 | |
50 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
51 | LIBC_INLINE T ceil(T x) { |
52 | FPBits<T> bits(x); |
53 | |
54 | // If x is infinity NaN or zero, return it. |
55 | if (bits.is_inf_or_nan() || bits.is_zero()) |
56 | return x; |
57 | |
58 | bool is_neg = bits.is_neg(); |
59 | int exponent = bits.get_exponent(); |
60 | |
61 | // If the exponent is greater than the most negative mantissa |
62 | // exponent, then x is already an integer. |
63 | if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN)) |
64 | return x; |
65 | |
66 | if (exponent <= -1) { |
67 | if (is_neg) |
68 | return T(-0.0); |
69 | else |
70 | return T(1.0); |
71 | } |
72 | |
73 | uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent; |
74 | bits.set_mantissa((bits.get_mantissa() >> trim_size) << trim_size); |
75 | T trunc_value = bits.get_val(); |
76 | |
77 | // If x is already an integer, return it. |
78 | if (trunc_value == x) |
79 | return x; |
80 | |
81 | // If x is negative, the ceil operation is equivalent to the trunc operation. |
82 | if (is_neg) |
83 | return trunc_value; |
84 | |
85 | return trunc_value + T(1.0); |
86 | } |
87 | |
88 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
89 | LIBC_INLINE T floor(T x) { |
90 | FPBits<T> bits(x); |
91 | if (bits.is_neg()) { |
92 | return -ceil(-x); |
93 | } else { |
94 | return trunc(x); |
95 | } |
96 | } |
97 | |
98 | template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0> |
99 | LIBC_INLINE T round(T x) { |
100 | using StorageType = typename FPBits<T>::StorageType; |
101 | FPBits<T> bits(x); |
102 | |
103 | // If x is infinity NaN or zero, return it. |
104 | if (bits.is_inf_or_nan() || bits.is_zero()) |
105 | return x; |
106 | |
107 | int exponent = bits.get_exponent(); |
108 | |
109 | // If the exponent is greater than the most negative mantissa |
110 | // exponent, then x is already an integer. |
111 | if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN)) |
112 | return x; |
113 | |
114 | if (exponent == -1) { |
115 | // Absolute value of x is greater than equal to 0.5 but less than 1. |
116 | return FPBits<T>::one(bits.sign()).get_val(); |
117 | } |
118 | |
119 | if (exponent <= -2) { |
120 | // Absolute value of x is less than 0.5. |
121 | return FPBits<T>::zero(bits.sign()).get_val(); |
122 | } |
123 | |
124 | uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent; |
125 | bool half_bit_set = |
126 | bool(bits.get_mantissa() & (StorageType(1) << (trim_size - 1))); |
127 | bits.set_mantissa((bits.get_mantissa() >> trim_size) << trim_size); |
128 | T trunc_value = bits.get_val(); |
129 | |
130 | // If x is already an integer, return it. |
131 | if (trunc_value == x) |
132 | return x; |
133 | |
134 | if (!half_bit_set) { |
135 | // Franctional part is less than 0.5 so round value is the |
136 | // same as the trunc value. |
137 | return trunc_value; |
138 | } else { |
139 | return bits.is_neg() ? trunc_value - T(1.0) : trunc_value + T(1.0); |
140 | } |
141 | } |
142 | |
143 | template <typename T> |
144 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
145 | round_using_specific_rounding_mode(T x, int rnd) { |
146 | using StorageType = typename FPBits<T>::StorageType; |
147 | FPBits<T> bits(x); |
148 | |
149 | // If x is infinity NaN or zero, return it. |
150 | if (bits.is_inf_or_nan() || bits.is_zero()) |
151 | return x; |
152 | |
153 | bool is_neg = bits.is_neg(); |
154 | int exponent = bits.get_exponent(); |
155 | |
156 | // If the exponent is greater than the most negative mantissa |
157 | // exponent, then x is already an integer. |
158 | if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN)) |
159 | return x; |
160 | |
161 | if (exponent <= -1) { |
162 | switch (rnd) { |
163 | case FP_INT_DOWNWARD: |
164 | return is_neg ? T(-1.0) : T(0.0); |
165 | case FP_INT_UPWARD: |
166 | return is_neg ? T(-0.0) : T(1.0); |
167 | case FP_INT_TOWARDZERO: |
168 | return is_neg ? T(-0.0) : T(0.0); |
169 | case FP_INT_TONEARESTFROMZERO: |
170 | if (exponent < -1) |
171 | return is_neg ? T(-0.0) : T(0.0); // abs(x) < 0.5 |
172 | return is_neg ? T(-1.0) : T(1.0); // abs(x) >= 0.5 |
173 | case FP_INT_TONEAREST: |
174 | default: |
175 | if (exponent <= -2 || bits.get_mantissa() == 0) |
176 | return is_neg ? T(-0.0) : T(0.0); // abs(x) <= 0.5 |
177 | else |
178 | return is_neg ? T(-1.0) : T(1.0); // abs(x) > 0.5 |
179 | } |
180 | } |
181 | |
182 | uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent; |
183 | FPBits<T> new_bits = bits; |
184 | new_bits.set_mantissa((bits.get_mantissa() >> trim_size) << trim_size); |
185 | T trunc_value = new_bits.get_val(); |
186 | |
187 | // If x is already an integer, return it. |
188 | if (trunc_value == x) |
189 | return x; |
190 | |
191 | StorageType trim_value = |
192 | bits.get_mantissa() & ((StorageType(1) << trim_size) - 1); |
193 | StorageType half_value = (StorageType(1) << (trim_size - 1)); |
194 | // If exponent is 0, trimSize will be equal to the mantissa width, and |
195 | // truncIsOdd` will not be correct. So, we handle it as a special case |
196 | // below. |
197 | StorageType trunc_is_odd = |
198 | new_bits.get_mantissa() & (StorageType(1) << trim_size); |
199 | |
200 | switch (rnd) { |
201 | case FP_INT_DOWNWARD: |
202 | return is_neg ? trunc_value - T(1.0) : trunc_value; |
203 | case FP_INT_UPWARD: |
204 | return is_neg ? trunc_value : trunc_value + T(1.0); |
205 | case FP_INT_TOWARDZERO: |
206 | return trunc_value; |
207 | case FP_INT_TONEARESTFROMZERO: |
208 | if (trim_value >= half_value) |
209 | return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0); |
210 | return trunc_value; |
211 | case FP_INT_TONEAREST: |
212 | default: |
213 | if (trim_value > half_value) { |
214 | return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0); |
215 | } else if (trim_value == half_value) { |
216 | if (exponent == 0) |
217 | return is_neg ? T(-2.0) : T(2.0); |
218 | if (trunc_is_odd) |
219 | return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0); |
220 | else |
221 | return trunc_value; |
222 | } else { |
223 | return trunc_value; |
224 | } |
225 | } |
226 | } |
227 | |
228 | template <typename T> |
229 | LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
230 | round_using_current_rounding_mode(T x) { |
231 | int rounding_mode = quick_get_round(); |
232 | |
233 | switch (rounding_mode) { |
234 | case FE_DOWNWARD: |
235 | return round_using_specific_rounding_mode(x, FP_INT_DOWNWARD); |
236 | case FE_UPWARD: |
237 | return round_using_specific_rounding_mode(x, FP_INT_UPWARD); |
238 | case FE_TOWARDZERO: |
239 | return round_using_specific_rounding_mode(x, FP_INT_TOWARDZERO); |
240 | case FE_TONEAREST: |
241 | return round_using_specific_rounding_mode(x, FP_INT_TONEAREST); |
242 | default: |
243 | __builtin_unreachable(); |
244 | } |
245 | } |
246 | |
247 | template <bool IsSigned, typename T> |
248 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
249 | fromfp(T x, int rnd, unsigned int width) { |
250 | using StorageType = typename FPBits<T>::StorageType; |
251 | |
252 | constexpr StorageType EXPLICIT_BIT = |
253 | FPBits<T>::SIG_MASK - FPBits<T>::FRACTION_MASK; |
254 | |
255 | if (width == 0U) { |
256 | raise_except_if_required(FE_INVALID); |
257 | return FPBits<T>::quiet_nan().get_val(); |
258 | } |
259 | |
260 | FPBits<T> bits(x); |
261 | |
262 | if (bits.is_inf_or_nan()) { |
263 | raise_except_if_required(FE_INVALID); |
264 | return FPBits<T>::quiet_nan().get_val(); |
265 | } |
266 | |
267 | T rounded_value = round_using_specific_rounding_mode(x, rnd); |
268 | |
269 | if constexpr (IsSigned) { |
270 | // T can't hold a finite number >= 2.0 * 2^EXP_BIAS. |
271 | if (width - 1 > FPBits<T>::EXP_BIAS) |
272 | return rounded_value; |
273 | |
274 | StorageType range_exp = width - 1U + FPBits<T>::EXP_BIAS; |
275 | // rounded_value < -2^(width - 1) |
276 | T range_min = |
277 | FPBits<T>::create_value(Sign::NEG, range_exp, EXPLICIT_BIT).get_val(); |
278 | if (rounded_value < range_min) { |
279 | raise_except_if_required(FE_INVALID); |
280 | return FPBits<T>::quiet_nan().get_val(); |
281 | } |
282 | // rounded_value > 2^(width - 1) - 1 |
283 | T range_max = |
284 | FPBits<T>::create_value(Sign::POS, range_exp, EXPLICIT_BIT).get_val() - |
285 | T(1.0); |
286 | if (rounded_value > range_max) { |
287 | raise_except_if_required(FE_INVALID); |
288 | return FPBits<T>::quiet_nan().get_val(); |
289 | } |
290 | |
291 | return rounded_value; |
292 | } |
293 | |
294 | if (rounded_value < T(0.0)) { |
295 | raise_except_if_required(FE_INVALID); |
296 | return FPBits<T>::quiet_nan().get_val(); |
297 | } |
298 | |
299 | // T can't hold a finite number >= 2.0 * 2^EXP_BIAS. |
300 | if (width > FPBits<T>::EXP_BIAS) |
301 | return rounded_value; |
302 | |
303 | StorageType range_exp = width + FPBits<T>::EXP_BIAS; |
304 | // rounded_value > 2^width - 1 |
305 | T range_max = |
306 | FPBits<T>::create_value(Sign::POS, range_exp, EXPLICIT_BIT).get_val() - |
307 | T(1.0); |
308 | if (rounded_value > range_max) { |
309 | raise_except_if_required(FE_INVALID); |
310 | return FPBits<T>::quiet_nan().get_val(); |
311 | } |
312 | |
313 | return rounded_value; |
314 | } |
315 | |
316 | template <bool IsSigned, typename T> |
317 | LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T> |
318 | fromfpx(T x, int rnd, unsigned int width) { |
319 | T rounded_value = fromfp<IsSigned>(x, rnd, width); |
320 | FPBits<T> bits(rounded_value); |
321 | |
322 | if (!bits.is_nan() && rounded_value != x) |
323 | raise_except_if_required(FE_INEXACT); |
324 | |
325 | return rounded_value; |
326 | } |
327 | |
328 | namespace internal { |
329 | |
330 | template <typename F, typename I, |
331 | cpp::enable_if_t<cpp::is_floating_point_v<F> && cpp::is_integral_v<I>, |
332 | int> = 0> |
333 | LIBC_INLINE I rounded_float_to_signed_integer(F x) { |
334 | constexpr I INTEGER_MIN = (I(1) << (sizeof(I) * 8 - 1)); |
335 | constexpr I INTEGER_MAX = -(INTEGER_MIN + 1); |
336 | FPBits<F> bits(x); |
337 | auto set_domain_error_and_raise_invalid = []() { |
338 | set_errno_if_required(EDOM); |
339 | raise_except_if_required(FE_INVALID); |
340 | }; |
341 | |
342 | if (bits.is_inf_or_nan()) { |
343 | set_domain_error_and_raise_invalid(); |
344 | return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX; |
345 | } |
346 | |
347 | int exponent = bits.get_exponent(); |
348 | constexpr int EXPONENT_LIMIT = sizeof(I) * 8 - 1; |
349 | if (exponent > EXPONENT_LIMIT) { |
350 | set_domain_error_and_raise_invalid(); |
351 | return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX; |
352 | } else if (exponent == EXPONENT_LIMIT) { |
353 | if (bits.is_pos() || bits.get_mantissa() != 0) { |
354 | set_domain_error_and_raise_invalid(); |
355 | return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX; |
356 | } |
357 | // If the control reaches here, then it means that the rounded |
358 | // value is the most negative number for the signed integer type I. |
359 | } |
360 | |
361 | // For all other cases, if `x` can fit in the integer type `I`, |
362 | // we just return `x`. static_cast will convert the floating |
363 | // point value to the exact integer value. |
364 | return static_cast<I>(x); |
365 | } |
366 | |
367 | } // namespace internal |
368 | |
369 | template <typename F, typename I, |
370 | cpp::enable_if_t<cpp::is_floating_point_v<F> && cpp::is_integral_v<I>, |
371 | int> = 0> |
372 | LIBC_INLINE I round_to_signed_integer(F x) { |
373 | return internal::rounded_float_to_signed_integer<F, I>(round(x)); |
374 | } |
375 | |
376 | template <typename F, typename I, |
377 | cpp::enable_if_t<cpp::is_floating_point_v<F> && cpp::is_integral_v<I>, |
378 | int> = 0> |
379 | LIBC_INLINE I round_to_signed_integer_using_current_rounding_mode(F x) { |
380 | return internal::rounded_float_to_signed_integer<F, I>( |
381 | round_using_current_rounding_mode(x)); |
382 | } |
383 | |
384 | } // namespace fputil |
385 | } // namespace LIBC_NAMESPACE |
386 | |
387 | #endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_NEARESTINTEGEROPERATIONS_H |
388 | |