1/* Round to integer type. Common helper functions.
2 Copyright (C) 2016-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <errno.h>
20#include <fenv.h>
21#include <float.h>
22#include <math.h>
23#include <math-barriers.h>
24#include <stdbool.h>
25#include <stdint.h>
26
27/* The including file should have defined UNSIGNED to 0 (signed return
28 type) or 1 (unsigned return type), INEXACT to 0 (no inexact
29 exceptions) or 1 (raise inexact exceptions) and RET_TYPE to the
30 return type (intmax_t or uintmax_t). */
31
32/* Return the maximum unbiased exponent for an argument (negative if
33 NEGATIVE is set) that might be in range for a call to a fromfp
34 function with width WIDTH (greater than 0, and not exceeding that
35 of intmax_t). The truncated argument may still be out of range in
36 the case of negative arguments, and if not out of range it may
37 become out of range as a result of rounding. */
38
39static int
40fromfp_max_exponent (bool negative, int width)
41{
42 if (UNSIGNED)
43 return negative ? -1 : width - 1;
44 else
45 return negative ? width - 1 : width - 2;
46}
47
48/* Return the result of rounding an integer value X (passed as the
49 absolute value; NEGATIVE is true if the value is negative), where
50 HALF_BIT is true if the bit with value 0.5 is set and MORE_BITS is
51 true if any lower bits are set, in the rounding direction
52 ROUND. */
53
54static uintmax_t
55fromfp_round (bool negative, uintmax_t x, bool half_bit, bool more_bits,
56 int round)
57{
58 switch (round)
59 {
60 case FP_INT_UPWARD:
61 return x + (!negative && (half_bit || more_bits));
62
63 case FP_INT_DOWNWARD:
64 return x + (negative && (half_bit || more_bits));
65
66 case FP_INT_TOWARDZERO:
67 default:
68 /* Unknown rounding directions are defined to mean unspecified
69 rounding; treat this as truncation. */
70 return x;
71
72 case FP_INT_TONEARESTFROMZERO:
73 return x + half_bit;
74
75 case FP_INT_TONEAREST:
76 return x + (half_bit && ((x & 1) || more_bits));
77 }
78}
79
80/* Integer rounding, of a value whose exponent EXPONENT did not exceed
81 the maximum exponent MAX_EXPONENT and so did not necessarily
82 overflow, has produced X (possibly wrapping to 0); the sign is
83 negative if NEGATIVE is true. Return whether this overflowed the
84 allowed width. */
85
86static bool
87fromfp_overflowed (bool negative, uintmax_t x, int exponent, int max_exponent)
88{
89 if (UNSIGNED)
90 {
91 if (negative)
92 return x != 0;
93 else if (max_exponent == INTMAX_WIDTH - 1)
94 return exponent == INTMAX_WIDTH - 1 && x == 0;
95 else
96 return x == (1ULL << (max_exponent + 1));
97 }
98 else
99 {
100 if (negative)
101 return exponent == max_exponent && x != (1ULL << max_exponent);
102 else
103 return x == (1ULL << (max_exponent + 1));
104 }
105}
106
107/* Handle a domain error for a call to a fromfp function with an
108 argument which is negative if NEGATIVE is set, and specified width
109 (not exceeding that of intmax_t) WIDTH. The return value is
110 unspecified (with it being unclear if the result needs to fit
111 within WIDTH bits in this case); we choose to saturate to the given
112 number of bits (treating NaNs like any other value). */
113
114static RET_TYPE
115fromfp_domain_error (bool negative, unsigned int width)
116{
117 feraiseexcept (FE_INVALID);
118 __set_errno (EDOM);
119 /* The return value is unspecified; we choose to saturate to the
120 given number of bits (treating NaNs like any other value). */
121 if (UNSIGNED)
122 {
123 if (negative)
124 return 0;
125 else if (width == INTMAX_WIDTH)
126 return -1;
127 else
128 return (1ULL << width) - 1;
129 }
130 else
131 {
132 if (width == 0)
133 return 0;
134 else if (negative)
135 return -(1ULL << (width - 1));
136 else
137 return (1ULL << (width - 1)) - 1;
138 }
139}
140
141/* Given X, the absolute value of a floating-point number (negative if
142 NEGATIVE is set) truncated towards zero, where HALF_BIT is true if
143 the bit with value 0.5 is set and MORE_BITS is true if any lower
144 bits are set, round it in the rounding direction ROUND, handle
145 errors and exceptions and return the appropriate return value for a
146 fromfp function. X originally had floating-point exponent
147 EXPONENT, which does not exceed MAX_EXPONENT, the return value from
148 fromfp_max_exponent with width WIDTH. */
149
150static RET_TYPE
151fromfp_round_and_return (bool negative, uintmax_t x, bool half_bit,
152 bool more_bits, int round, int exponent,
153 int max_exponent, unsigned int width)
154{
155 uintmax_t uret = fromfp_round (negative, x, half_bit, more_bits, round);
156 if (fromfp_overflowed (negative, uret, exponent, max_exponent))
157 return fromfp_domain_error (negative, width);
158
159 if (INEXACT && (half_bit || more_bits))
160 {
161 /* There is no need for this to use the specific floating-point
162 type for which this header is included, and there is no need
163 for this header to know that type at all, so just use float
164 here. */
165 float force_inexact = 1.0f + FLT_MIN;
166 math_force_eval (force_inexact);
167 }
168 if (UNSIGNED)
169 /* A negative argument not rounding to zero will already have
170 produced a domain error. */
171 return uret;
172 else
173 return negative ? -uret : uret;
174}
175