1//===-- Implementation header for exp10m1f ----------------------*- 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_MATH_EXP10M1F_H
10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F_H
11
12#include "exp10f_utils.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/PolyEval.h"
16#include "src/__support/FPUtil/except_value_utils.h"
17#include "src/__support/FPUtil/multiply_add.h"
18#include "src/__support/FPUtil/rounding_mode.h"
19#include "src/__support/common.h"
20#include "src/__support/libc_errno.h"
21#include "src/__support/macros/config.h"
22#include "src/__support/macros/optimization.h"
23
24namespace LIBC_NAMESPACE_DECL {
25
26namespace math {
27
28namespace exp10m1f_internal {
29
30#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
31LIBC_INLINE_VAR constexpr size_t N_EXCEPTS_LO = 11;
32
33LIBC_INLINE_VAR constexpr fputil::ExceptValues<float, N_EXCEPTS_LO>
34 EXP10M1F_EXCEPTS_LO = {.values: {
35 // x = 0x1.0fe54ep-11, exp10m1f(x) = 0x1.3937eep-10 (RZ)
36 {.input: 0x3a07'f2a7U, .rnd_towardzero_result: 0x3a9c'9bf7U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 1U},
37 // x = 0x1.80e6eap-11, exp10m1f(x) = 0x1.bb8272p-10 (RZ)
38 {.input: 0x3a40'7375U, .rnd_towardzero_result: 0x3add'c139U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 1U},
39 // x = -0x1.2a33bcp-51, exp10m1f(x) = -0x1.57515ep-50 (RZ)
40 {.input: 0xa615'19deU, .rnd_towardzero_result: 0xa6ab'a8afU, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
41 // x = -0x0p+0, exp10m1f(x) = -0x0p+0 (RZ)
42 {.input: 0x8000'0000U, .rnd_towardzero_result: 0x8000'0000U, .rnd_upward_offset: 0U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
43 // x = -0x1.b59e08p-31, exp10m1f(x) = -0x1.f7d356p-30 (RZ)
44 {.input: 0xb05a'cf04U, .rnd_towardzero_result: 0xb0fb'e9abU, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
45 // x = -0x1.bf342p-12, exp10m1f(x) = -0x1.014e02p-10 (RZ)
46 {.input: 0xb9df'9a10U, .rnd_towardzero_result: 0xba80'a701U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
47 // x = -0x1.6207fp-11, exp10m1f(x) = -0x1.9746cap-10 (RZ)
48 {.input: 0xba31'03f8U, .rnd_towardzero_result: 0xbacb'a365U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
49 // x = -0x1.bd0c66p-11, exp10m1f(x) = -0x1.ffe168p-10 (RZ)
50 {.input: 0xba5e'8633U, .rnd_towardzero_result: 0xbaff'f0b4U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
51 // x = -0x1.ffd84cp-10, exp10m1f(x) = -0x1.25faf2p-8 (RZ)
52 {.input: 0xbaff'ec26U, .rnd_towardzero_result: 0xbb92'fd79U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
53 // x = -0x1.a74172p-9, exp10m1f(x) = -0x1.e57be2p-8 (RZ)
54 {.input: 0xbb53'a0b9U, .rnd_towardzero_result: 0xbbf2'bdf1U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
55 // x = -0x1.cb694cp-9, exp10m1f(x) = -0x1.0764e4p-7 (RZ)
56 {.input: 0xbb65'b4a6U, .rnd_towardzero_result: 0xbc03'b272U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
57 }};
58
59LIBC_INLINE_VAR constexpr size_t N_EXCEPTS_HI = 19;
60
61LIBC_INLINE_VAR constexpr fputil::ExceptValues<float, N_EXCEPTS_HI>
62 EXP10M1F_EXCEPTS_HI = {.values: {
63 // (input, RZ output, RU offset, RD offset, RN offset)
64 // x = 0x1.8d31eep-8, exp10m1f(x) = 0x1.cc7e4cp-7 (RZ)
65 {.input: 0x3bc6'98f7U, .rnd_towardzero_result: 0x3c66'3f26U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 1U},
66 // x = 0x1.915fcep-8, exp10m1f(x) = 0x1.d15f72p-7 (RZ)
67 {.input: 0x3bc8'afe7U, .rnd_towardzero_result: 0x3c68'afb9U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
68 // x = 0x1.bcf982p-8, exp10m1f(x) = 0x1.022928p-6 (RZ)
69 {.input: 0x3bde'7cc1U, .rnd_towardzero_result: 0x3c81'1494U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 1U},
70 // x = 0x1.99ff0ap-7, exp10m1f(x) = 0x1.dee416p-6 (RZ)
71 {.input: 0x3c4c'ff85U, .rnd_towardzero_result: 0x3cef'720bU, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
72 // x = 0x1.75ea14p-6, exp10m1f(x) = 0x1.b9ff16p-5 (RZ)
73 {.input: 0x3cba'f50aU, .rnd_towardzero_result: 0x3d5c'ff8bU, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
74 // x = 0x1.f81b64p-6, exp10m1f(x) = 0x1.2cb6bcp-4 (RZ)
75 {.input: 0x3cfc'0db2U, .rnd_towardzero_result: 0x3d96'5b5eU, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
76 // x = 0x1.fafecp+3, exp10m1f(x) = 0x1.8c880ap+52 (RZ)
77 {.input: 0x417d'7f60U, .rnd_towardzero_result: 0x59c6'4405U, .rnd_upward_offset: 1U, .rnd_downward_offset: 0U, .rnd_tonearest_offset: 0U},
78 // x = -0x1.3bf094p-8, exp10m1f(x) = -0x1.69ba4ap-7 (RZ)
79 {.input: 0xbb9d'f84aU, .rnd_towardzero_result: 0xbc34'dd25U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
80 // x = -0x1.4558bcp-8, exp10m1f(x) = -0x1.746fb8p-7 (RZ)
81 {.input: 0xbba2'ac5eU, .rnd_towardzero_result: 0xbc3a'37dcU, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
82 // x = -0x1.4bb43p-8, exp10m1f(x) = -0x1.7babe4p-7 (RZ)
83 {.input: 0xbba5'da18U, .rnd_towardzero_result: 0xbc3d'd5f2U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
84 // x = -0x1.776cc8p-8, exp10m1f(x) = -0x1.ad62c4p-7 (RZ)
85 {.input: 0xbbbb'b664U, .rnd_towardzero_result: 0xbc56'b162U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
86 // x = -0x1.f024cp-8, exp10m1f(x) = -0x1.1b20d6p-6 (RZ)
87 {.input: 0xbbf8'1260U, .rnd_towardzero_result: 0xbc8d'906bU, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
88 // x = -0x1.f510eep-8, exp10m1f(x) = -0x1.1de9aap-6 (RZ)
89 {.input: 0xbbfa'8877U, .rnd_towardzero_result: 0xbc8e'f4d5U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
90 // x = -0x1.0b43c4p-7, exp10m1f(x) = -0x1.30d418p-6 (RZ)
91 {.input: 0xbc05'a1e2U, .rnd_towardzero_result: 0xbc98'6a0cU, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
92 // x = -0x1.245ee4p-7, exp10m1f(x) = -0x1.4d2b86p-6 (RZ)
93 {.input: 0xbc12'2f72U, .rnd_towardzero_result: 0xbca6'95c3U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
94 // x = -0x1.f9f2dap-7, exp10m1f(x) = -0x1.1e2186p-5 (RZ)
95 {.input: 0xbc7c'f96dU, .rnd_towardzero_result: 0xbd0f'10c3U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 0U},
96 // x = -0x1.08e42p-6, exp10m1f(x) = -0x1.2b5c4p-5 (RZ)
97 {.input: 0xbc84'7210U, .rnd_towardzero_result: 0xbd15'ae20U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
98 // x = -0x1.0cdc44p-5, exp10m1f(x) = -0x1.2a2152p-4 (RZ)
99 {.input: 0xbd06'6e22U, .rnd_towardzero_result: 0xbd95'10a9U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
100 // x = -0x1.ca4322p-5, exp10m1f(x) = -0x1.ef073p-4 (RZ)
101 {.input: 0xbd65'2191U, .rnd_towardzero_result: 0xbdf7'8398U, .rnd_upward_offset: 0U, .rnd_downward_offset: 1U, .rnd_tonearest_offset: 1U},
102 }};
103#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
104
105} // namespace exp10m1f_internal
106
107LIBC_INLINE float exp10m1f(float x) {
108 using namespace exp10m1f_internal;
109 using FPBits = fputil::FPBits<float>;
110 FPBits xbits(x);
111
112 uint32_t x_u = xbits.uintval();
113 uint32_t x_abs = x_u & 0x7fff'ffffU;
114
115 // When x >= log10(2^128), or x is nan
116 if (LIBC_UNLIKELY(xbits.is_pos() && x_u >= 0x421a'209bU)) {
117 if (xbits.is_finite()) {
118#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
119 int rounding = fputil::quick_get_round();
120 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
121 return FPBits::max_normal().get_val();
122#endif
123
124 fputil::set_errno_if_required(ERANGE);
125 fputil::raise_except_if_required(FE_OVERFLOW);
126 }
127
128 // x >= log10(2^128) and 10^x - 1 rounds to +inf, or x is +inf or nan
129 return x + FPBits::inf().get_val();
130 }
131
132 // When |x| <= log10(2) * 2^(-6)
133 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
134#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
135 if (auto r = EXP10M1F_EXCEPTS_LO.lookup(x_bits: x_u); LIBC_UNLIKELY(r.has_value()))
136 return r.value();
137#else
138 // Even if we're not checking for the misrounded cases in this interval, we
139 // must still check for -0 as input and return -0 as output, rather than +0
140 // as the code below would compute.
141 //
142 // We might as well check for both zeroes at once, in fact, since it's no
143 // slower.
144 if (LIBC_UNLIKELY(x_abs == 0))
145 return x;
146#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
147
148 double dx = x;
149 double dx_sq = dx * dx;
150 double c0 = dx * Exp10Base::COEFFS[0];
151 double c1 =
152 fputil::multiply_add(x: dx, y: Exp10Base::COEFFS[2], z: Exp10Base::COEFFS[1]);
153 double c2 =
154 fputil::multiply_add(x: dx, y: Exp10Base::COEFFS[4], z: Exp10Base::COEFFS[3]);
155 // 10^dx - 1 ~ (1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5) - 1
156 // = COEFFS[0] * dx + ... + COEFFS[4] * dx^5
157 return static_cast<float>(fputil::polyeval(x: dx_sq, a0: c0, a: c1, a: c2));
158 }
159
160 // When x <= log10(2^-25), or x is nan
161 if (LIBC_UNLIKELY(x_u >= 0xc0f0d2f1)) {
162 // exp10m1(-inf) = -1
163 if (xbits.is_inf())
164 return -1.0f;
165 // exp10m1(nan) = nan
166 if (xbits.is_nan())
167 return x;
168
169#ifdef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
170 if (x_u == 0xc0f0d2f1) // x = log10(2^-25)
171 return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
172#else
173 int rounding = fputil::quick_get_round();
174 if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO ||
175 (rounding == FE_TONEAREST && x_u == 0xc0f0d2f1))
176 return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
177#endif
178
179 fputil::set_errno_if_required(ERANGE);
180 fputil::raise_except_if_required(FE_UNDERFLOW);
181 return -1.0f;
182 }
183
184 // Exact outputs when x = 1, 2, ..., 10.
185 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
186 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
187 switch (x_u) {
188 case 0x3f800000U: // x = 1.0f
189 return 9.0f;
190 case 0x40000000U: // x = 2.0f
191 return 99.0f;
192 case 0x40400000U: // x = 3.0f
193 return 999.0f;
194 case 0x40800000U: // x = 4.0f
195 return 9'999.0f;
196 case 0x40a00000U: // x = 5.0f
197 return 99'999.0f;
198 case 0x40c00000U: // x = 6.0f
199 return 999'999.0f;
200 case 0x40e00000U: // x = 7.0f
201 return 9'999'999.0f;
202 case 0x41000000U: { // x = 8.0f
203#ifdef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
204 return 100'000'000.0f;
205#else
206 int rounding = fputil::quick_get_round();
207 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)
208 return 100'000'000.0f;
209#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
210 return 99'999'992.0f;
211 }
212 case 0x41100000U: { // x = 9.0f
213#ifdef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
214 return 1'000'000'000.0f;
215#else
216 int rounding = fputil::quick_get_round();
217 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)
218 return 1'000'000'000.0f;
219#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
220 return 999'999'936.0f;
221 }
222 case 0x41200000U: { // x = 10.0f
223#ifdef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
224 return 10'000'000'000.0f;
225#else
226 int rounding = fputil::quick_get_round();
227 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)
228 return 10'000'000'000.0f;
229#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
230 return 9'999'998'976.0f;
231 }
232 }
233 }
234
235#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
236 if (auto r = EXP10M1F_EXCEPTS_HI.lookup(x_bits: x_u); LIBC_UNLIKELY(r.has_value()))
237 return r.value();
238#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
239
240 // Range reduction: 10^x = 2^(mid + hi) * 10^lo
241 // rr = (2^(mid + hi), lo)
242 auto rr = exp_b_range_reduc<Exp10Base>(x);
243
244 // The low part is approximated by a degree-5 minimax polynomial.
245 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
246 double lo_sq = rr.lo * rr.lo;
247 double c0 = fputil::multiply_add(x: rr.lo, y: Exp10Base::COEFFS[0], z: 1.0);
248 double c1 =
249 fputil::multiply_add(x: rr.lo, y: Exp10Base::COEFFS[2], z: Exp10Base::COEFFS[1]);
250 double c2 =
251 fputil::multiply_add(x: rr.lo, y: Exp10Base::COEFFS[4], z: Exp10Base::COEFFS[3]);
252 double exp10_lo = fputil::polyeval(x: lo_sq, a0: c0, a: c1, a: c2);
253 // 10^x - 1 = 2^(mid + hi) * 10^lo - 1
254 // ~ mh * exp10_lo - 1
255 return static_cast<float>(fputil::multiply_add(x: exp10_lo, y: rr.mh, z: -1.0));
256}
257
258} // namespace math
259
260} // namespace LIBC_NAMESPACE_DECL
261
262#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F_H
263