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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#include "src/__support/macros/config.h"
20
21namespace LIBC_NAMESPACE_DECL {
22namespace fputil {
23
24template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
25LIBC_INLINE T trunc(T x) {
26 using StorageType = typename FPBits<T>::StorageType;
27 FPBits<T> bits(x);
28
29 // If x is infinity or NaN, return it.
30 // If it is zero also we should return it as is, but the logic
31 // later in this function takes care of it. But not doing a zero
32 // check, we improve the run time of non-zero values.
33 if (bits.is_inf_or_nan())
34 return x;
35
36 int exponent = bits.get_exponent();
37
38 // If the exponent is greater than the most negative mantissa
39 // exponent, then x is already an integer.
40 if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN))
41 return x;
42
43 // If the exponent is such that abs(x) is less than 1, then return 0.
44 if (exponent <= -1)
45 return FPBits<T>::zero(bits.sign()).get_val();
46
47 int trim_size = FPBits<T>::FRACTION_LEN - exponent;
48 StorageType trunc_mantissa =
49 static_cast<StorageType>((bits.get_mantissa() >> trim_size) << trim_size);
50 bits.set_mantissa(trunc_mantissa);
51 return bits.get_val();
52}
53
54template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
55LIBC_INLINE T ceil(T x) {
56 using StorageType = typename FPBits<T>::StorageType;
57 FPBits<T> bits(x);
58
59 // If x is infinity NaN or zero, return it.
60 if (bits.is_inf_or_nan() || bits.is_zero())
61 return x;
62
63 bool is_neg = bits.is_neg();
64 int exponent = bits.get_exponent();
65
66 // If the exponent is greater than the most negative mantissa
67 // exponent, then x is already an integer.
68 if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN))
69 return x;
70
71 if (exponent <= -1) {
72 if (is_neg)
73 return T(-0.0);
74 else
75 return T(1.0);
76 }
77
78 uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent;
79 StorageType x_u = bits.uintval();
80 StorageType trunc_u =
81 static_cast<StorageType>((x_u >> trim_size) << trim_size);
82
83 // If x is already an integer, return it.
84 if (trunc_u == x_u)
85 return x;
86
87 bits.set_uintval(trunc_u);
88 T trunc_value = bits.get_val();
89
90 // If x is negative, the ceil operation is equivalent to the trunc operation.
91 if (is_neg)
92 return trunc_value;
93
94 return trunc_value + T(1.0);
95}
96
97template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
98LIBC_INLINE T floor(T x) {
99 FPBits<T> bits(x);
100 if (bits.is_neg()) {
101 return -ceil(-x);
102 } else {
103 return trunc(x);
104 }
105}
106
107template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
108LIBC_INLINE T round(T x) {
109 using StorageType = typename FPBits<T>::StorageType;
110 FPBits<T> bits(x);
111
112 // If x is infinity NaN or zero, return it.
113 if (bits.is_inf_or_nan() || bits.is_zero())
114 return x;
115
116 int exponent = bits.get_exponent();
117
118 // If the exponent is greater than the most negative mantissa
119 // exponent, then x is already an integer.
120 if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN))
121 return x;
122
123 if (exponent == -1) {
124 // Absolute value of x is greater than equal to 0.5 but less than 1.
125 return FPBits<T>::one(bits.sign()).get_val();
126 }
127
128 if (exponent <= -2) {
129 // Absolute value of x is less than 0.5.
130 return FPBits<T>::zero(bits.sign()).get_val();
131 }
132
133 uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent;
134 bool half_bit_set =
135 bool(bits.get_mantissa() & (StorageType(1) << (trim_size - 1)));
136 StorageType x_u = bits.uintval();
137 StorageType trunc_u =
138 static_cast<StorageType>((x_u >> trim_size) << trim_size);
139
140 // If x is already an integer, return it.
141 if (trunc_u == x_u)
142 return x;
143
144 bits.set_uintval(trunc_u);
145 T trunc_value = bits.get_val();
146
147 if (!half_bit_set) {
148 // Franctional part is less than 0.5 so round value is the
149 // same as the trunc value.
150 return trunc_value;
151 } else {
152 return bits.is_neg() ? trunc_value - T(1.0) : trunc_value + T(1.0);
153 }
154}
155
156template <typename T>
157LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T>
158round_using_specific_rounding_mode(T x, int rnd) {
159 using StorageType = typename FPBits<T>::StorageType;
160 FPBits<T> bits(x);
161
162 // If x is infinity NaN or zero, return it.
163 if (bits.is_inf_or_nan() || bits.is_zero())
164 return x;
165
166 bool is_neg = bits.is_neg();
167 int exponent = bits.get_exponent();
168
169 // If the exponent is greater than the most negative mantissa
170 // exponent, then x is already an integer.
171 if (exponent >= static_cast<int>(FPBits<T>::FRACTION_LEN))
172 return x;
173
174 if (exponent <= -1) {
175 switch (rnd) {
176 case FP_INT_DOWNWARD:
177 return is_neg ? T(-1.0) : T(0.0);
178 case FP_INT_UPWARD:
179 return is_neg ? T(-0.0) : T(1.0);
180 case FP_INT_TOWARDZERO:
181 return is_neg ? T(-0.0) : T(0.0);
182 case FP_INT_TONEARESTFROMZERO:
183 if (exponent < -1)
184 return is_neg ? T(-0.0) : T(0.0); // abs(x) < 0.5
185 return is_neg ? T(-1.0) : T(1.0); // abs(x) >= 0.5
186 case FP_INT_TONEAREST:
187 default:
188 if (exponent <= -2 || bits.get_mantissa() == 0)
189 return is_neg ? T(-0.0) : T(0.0); // abs(x) <= 0.5
190 else
191 return is_neg ? T(-1.0) : T(1.0); // abs(x) > 0.5
192 }
193 }
194
195 uint32_t trim_size = FPBits<T>::FRACTION_LEN - exponent;
196 StorageType x_u = bits.uintval();
197 StorageType trunc_u =
198 static_cast<StorageType>((x_u >> trim_size) << trim_size);
199
200 // If x is already an integer, return it.
201 if (trunc_u == x_u)
202 return x;
203
204 FPBits<T> new_bits(trunc_u);
205 T trunc_value = new_bits.get_val();
206
207 StorageType trim_value =
208 bits.get_mantissa() &
209 static_cast<StorageType>(((StorageType(1) << trim_size) - 1));
210 StorageType half_value =
211 static_cast<StorageType>((StorageType(1) << (trim_size - 1)));
212 // If exponent is 0, trimSize will be equal to the mantissa width, and
213 // truncIsOdd` will not be correct. So, we handle it as a special case
214 // below.
215 StorageType trunc_is_odd =
216 new_bits.get_mantissa() & (StorageType(1) << trim_size);
217
218 switch (rnd) {
219 case FP_INT_DOWNWARD:
220 return is_neg ? trunc_value - T(1.0) : trunc_value;
221 case FP_INT_UPWARD:
222 return is_neg ? trunc_value : trunc_value + T(1.0);
223 case FP_INT_TOWARDZERO:
224 return trunc_value;
225 case FP_INT_TONEARESTFROMZERO:
226 if (trim_value >= half_value)
227 return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0);
228 return trunc_value;
229 case FP_INT_TONEAREST:
230 default:
231 if (trim_value > half_value) {
232 return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0);
233 } else if (trim_value == half_value) {
234 if (exponent == 0)
235 return is_neg ? T(-2.0) : T(2.0);
236 if (trunc_is_odd)
237 return is_neg ? trunc_value - T(1.0) : trunc_value + T(1.0);
238 else
239 return trunc_value;
240 } else {
241 return trunc_value;
242 }
243 }
244}
245
246template <typename T>
247LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<T>, T>
248round_using_current_rounding_mode(T x) {
249 int rounding_mode = quick_get_round();
250
251 switch (rounding_mode) {
252 case FE_DOWNWARD:
253 return round_using_specific_rounding_mode(x, FP_INT_DOWNWARD);
254 case FE_UPWARD:
255 return round_using_specific_rounding_mode(x, FP_INT_UPWARD);
256 case FE_TOWARDZERO:
257 return round_using_specific_rounding_mode(x, FP_INT_TOWARDZERO);
258 case FE_TONEAREST:
259 return round_using_specific_rounding_mode(x, FP_INT_TONEAREST);
260 default:
261 __builtin_unreachable();
262 }
263}
264
265template <bool IsSigned, typename T>
266LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T>
267fromfp(T x, int rnd, unsigned int width) {
268 using StorageType = typename FPBits<T>::StorageType;
269
270 constexpr StorageType EXPLICIT_BIT =
271 FPBits<T>::SIG_MASK - FPBits<T>::FRACTION_MASK;
272
273 if (width == 0U) {
274 raise_except_if_required(FE_INVALID);
275 return FPBits<T>::quiet_nan().get_val();
276 }
277
278 FPBits<T> bits(x);
279
280 if (bits.is_inf_or_nan()) {
281 raise_except_if_required(FE_INVALID);
282 return FPBits<T>::quiet_nan().get_val();
283 }
284
285 T rounded_value = round_using_specific_rounding_mode(x, rnd);
286
287 if constexpr (IsSigned) {
288 // T can't hold a finite number >= 2.0 * 2^EXP_BIAS.
289 if (width - 1 > FPBits<T>::EXP_BIAS)
290 return rounded_value;
291
292 StorageType range_exp =
293 static_cast<StorageType>(width - 1 + FPBits<T>::EXP_BIAS);
294 // rounded_value < -2^(width - 1)
295 T range_min =
296 FPBits<T>::create_value(Sign::NEG, range_exp, EXPLICIT_BIT).get_val();
297 if (rounded_value < range_min) {
298 raise_except_if_required(FE_INVALID);
299 return FPBits<T>::quiet_nan().get_val();
300 }
301 // rounded_value > 2^(width - 1) - 1
302 T range_max =
303 FPBits<T>::create_value(Sign::POS, range_exp, EXPLICIT_BIT).get_val() -
304 T(1.0);
305 if (rounded_value > range_max) {
306 raise_except_if_required(FE_INVALID);
307 return FPBits<T>::quiet_nan().get_val();
308 }
309
310 return rounded_value;
311 }
312
313 if (rounded_value < T(0.0)) {
314 raise_except_if_required(FE_INVALID);
315 return FPBits<T>::quiet_nan().get_val();
316 }
317
318 // T can't hold a finite number >= 2.0 * 2^EXP_BIAS.
319 if (width > FPBits<T>::EXP_BIAS)
320 return rounded_value;
321
322 StorageType range_exp = static_cast<StorageType>(width + FPBits<T>::EXP_BIAS);
323 // rounded_value > 2^width - 1
324 T range_max =
325 FPBits<T>::create_value(Sign::POS, range_exp, EXPLICIT_BIT).get_val() -
326 T(1.0);
327 if (rounded_value > range_max) {
328 raise_except_if_required(FE_INVALID);
329 return FPBits<T>::quiet_nan().get_val();
330 }
331
332 return rounded_value;
333}
334
335template <bool IsSigned, typename T>
336LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_floating_point_v<T>, T>
337fromfpx(T x, int rnd, unsigned int width) {
338 T rounded_value = fromfp<IsSigned>(x, rnd, width);
339 FPBits<T> bits(rounded_value);
340
341 if (!bits.is_nan() && rounded_value != x)
342 raise_except_if_required(FE_INEXACT);
343
344 return rounded_value;
345}
346
347namespace internal {
348
349template <typename FloatType, typename IntType,
350 cpp::enable_if_t<cpp::is_floating_point_v<FloatType> &&
351 cpp::is_integral_v<IntType>,
352 int> = 0>
353LIBC_INLINE IntType rounded_float_to_signed_integer(FloatType x) {
354 constexpr IntType INTEGER_MIN = (IntType(1) << (sizeof(IntType) * 8 - 1));
355 constexpr IntType INTEGER_MAX = -(INTEGER_MIN + 1);
356 FPBits<FloatType> bits(x);
357 auto set_domain_error_and_raise_invalid = []() {
358 set_errno_if_required(EDOM);
359 raise_except_if_required(FE_INVALID);
360 };
361
362 if (bits.is_inf_or_nan()) {
363 set_domain_error_and_raise_invalid();
364 return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX;
365 }
366
367 int exponent = bits.get_exponent();
368 constexpr int EXPONENT_LIMIT = sizeof(IntType) * 8 - 1;
369 if (exponent > EXPONENT_LIMIT) {
370 set_domain_error_and_raise_invalid();
371 return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX;
372 } else if (exponent == EXPONENT_LIMIT) {
373 if (bits.is_pos() || bits.get_mantissa() != 0) {
374 set_domain_error_and_raise_invalid();
375 return bits.is_neg() ? INTEGER_MIN : INTEGER_MAX;
376 }
377 // If the control reaches here, then it means that the rounded
378 // value is the most negative number for the signed integer type IntType.
379 }
380
381 // For all other cases, if `x` can fit in the integer type `IntType`,
382 // we just return `x`. static_cast will convert the floating
383 // point value to the exact integer value.
384 return static_cast<IntType>(x);
385}
386
387} // namespace internal
388
389template <typename FloatType, typename IntType,
390 cpp::enable_if_t<cpp::is_floating_point_v<FloatType> &&
391 cpp::is_integral_v<IntType>,
392 int> = 0>
393LIBC_INLINE IntType round_to_signed_integer(FloatType x) {
394 return internal::rounded_float_to_signed_integer<FloatType, IntType>(
395 round(x));
396}
397
398template <typename FloatType, typename IntType,
399 cpp::enable_if_t<cpp::is_floating_point_v<FloatType> &&
400 cpp::is_integral_v<IntType>,
401 int> = 0>
402LIBC_INLINE IntType
403round_to_signed_integer_using_current_rounding_mode(FloatType x) {
404 return internal::rounded_float_to_signed_integer<FloatType, IntType>(
405 round_using_current_rounding_mode(x));
406}
407
408} // namespace fputil
409} // namespace LIBC_NAMESPACE_DECL
410
411#endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_NEARESTINTEGEROPERATIONS_H
412

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source code of libc/src/__support/FPUtil/NearestIntegerOperations.h