xref: /llvm-project/libc/src/math/generic/cos.cpp (revision 5ff3ff33ff930e4ec49da7910612d8a41eb068cb)
1 //===-- Double-precision cos function -------------------------------------===//
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 #include "src/math/cos.h"
10 #include "hdr/errno_macros.h"
11 #include "src/__support/FPUtil/FEnvImpl.h"
12 #include "src/__support/FPUtil/FPBits.h"
13 #include "src/__support/FPUtil/double_double.h"
14 #include "src/__support/FPUtil/dyadic_float.h"
15 #include "src/__support/FPUtil/except_value_utils.h"
16 #include "src/__support/common.h"
17 #include "src/__support/macros/config.h"
18 #include "src/__support/macros/optimization.h"            // LIBC_UNLIKELY
19 #include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
20 #include "src/math/generic/sincos_eval.h"
21 
22 #ifdef LIBC_TARGET_CPU_HAS_FMA
23 #include "range_reduction_double_fma.h"
24 
25 using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
26 using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
27 using LIBC_NAMESPACE::fma::range_reduction_small;
28 using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;
29 
30 LIBC_INLINE constexpr bool NO_FMA = false;
31 #else
32 #include "range_reduction_double_nofma.h"
33 
34 using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
35 using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
36 using LIBC_NAMESPACE::nofma::range_reduction_small;
37 using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;
38 
39 LIBC_INLINE constexpr bool NO_FMA = true;
40 #endif // LIBC_TARGET_CPU_HAS_FMA
41 
42 // TODO: We might be able to improve the performance of large range reduction of
43 // non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
44 // pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
45 // those lookup table.
46 #include "range_reduction_double_common.h"
47 
48 #if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
49 #define LIBC_MATH_COS_SKIP_ACCURATE_PASS
50 #endif
51 
52 namespace LIBC_NAMESPACE_DECL {
53 
54 using DoubleDouble = fputil::DoubleDouble;
55 using Float128 = typename fputil::DyadicFloat<128>;
56 
57 LLVM_LIBC_FUNCTION(double, cos, (double x)) {
58   using FPBits = typename fputil::FPBits<double>;
59   FPBits xbits(x);
60 
61   uint16_t x_e = xbits.get_biased_exponent();
62 
63   DoubleDouble y;
64   unsigned k;
65   generic::LargeRangeReduction<NO_FMA> range_reduction_large{};
66 
67   // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
68   if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
69     // |x| < 2^-27
70     if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
71       // Signed zeros.
72       if (LIBC_UNLIKELY(x == 0.0))
73         return 1.0;
74 
75       // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
76       return fputil::round_result_slightly_down(1.0);
77     }
78 
79     // // Small range reduction.
80     k = range_reduction_small(x, y);
81   } else {
82     // Inf or NaN
83     if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
84       // sin(+-Inf) = NaN
85       if (xbits.get_mantissa() == 0) {
86         fputil::set_errno_if_required(EDOM);
87         fputil::raise_except_if_required(FE_INVALID);
88       }
89       return x + FPBits::quiet_nan().get_val();
90     }
91 
92     // Large range reduction.
93     k = range_reduction_large.compute_high_part(x);
94     y = range_reduction_large.fast();
95   }
96 
97   DoubleDouble sin_y, cos_y;
98 
99   generic::sincos_eval(y, sin_y, cos_y);
100 
101   // Look up sin(k * pi/128) and cos(k * pi/128)
102   // Memory saving versions:
103 
104   // Use 128-entry table instead:
105   // DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
106   // uint64_t sin_s = static_cast<uint64_t>((k + 128) & 128) << (63 - 7);
107   // sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
108   // sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
109   // DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
110   // uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
111   // cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
112   // cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
113 
114   // Use 64-entry table instead:
115   // auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
116   //   unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
117   //   DoubleDouble ans = SIN_K_PI_OVER_128[idx];
118   //   if (kk & 128) {
119   //     ans.hi = -ans.hi;
120   //     ans.lo = -ans.lo;
121   //   }
122   //   return ans;
123   // };
124   // DoubleDouble sin_k = get_idx_dd(k + 128);
125   // DoubleDouble cos_k = get_idx_dd(k + 64);
126 
127   // Fast look up version, but needs 256-entry table.
128   // -sin(k * pi/128) = sin((k + 128) * pi/128)
129   // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
130   DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
131   DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
132 
133   // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
134   // So k is an integer and -pi / 256 <= y <= pi / 256.
135   // Then cos(x) = cos((k * pi/128 + y)
136   //             = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
137   DoubleDouble cos_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, cos_k);
138   DoubleDouble msin_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, msin_k);
139 
140   DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
141   rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
142 
143 #ifdef LIBC_MATH_COS_SKIP_ACCURATE_PASS
144   return rr.hi + rr.lo;
145 #else
146 
147   // Accurate test and pass for correctly rounded implementation.
148 #ifdef LIBC_TARGET_CPU_HAS_FMA
149   constexpr double ERR = 0x1.0p-70;
150 #else
151   // TODO: Improve non-FMA fast pass accuracy.
152   constexpr double ERR = 0x1.0p-66;
153 #endif // LIBC_TARGET_CPU_HAS_FMA
154 
155   double rlp = rr.lo + ERR;
156   double rlm = rr.lo - ERR;
157 
158   double r_upper = rr.hi + rlp; // (rr.lo + ERR);
159   double r_lower = rr.hi + rlm; // (rr.lo - ERR);
160 
161   // Ziv's rounding test.
162   if (LIBC_LIKELY(r_upper == r_lower))
163     return r_upper;
164 
165   Float128 u_f128, sin_u, cos_u;
166   if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
167     u_f128 = generic::range_reduction_small_f128(x);
168   else
169     u_f128 = range_reduction_large.accurate();
170 
171   generic::sincos_eval(u_f128, sin_u, cos_u);
172 
173   auto get_sin_k = [](unsigned kk) -> Float128 {
174     unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
175     Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx];
176     if (kk & 128)
177       ans.sign = Sign::NEG;
178     return ans;
179   };
180 
181   // -sin(k * pi/128) = sin((k + 128) * pi/128)
182   // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
183   Float128 msin_k_f128 = get_sin_k(k + 128);
184   Float128 cos_k_f128 = get_sin_k(k + 64);
185 
186   // cos(x) = cos((k * pi/128 + u)
187   //        = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
188   Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
189                                  fputil::quick_mul(msin_k_f128, sin_u));
190 
191   // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
192   // https://github.com/llvm/llvm-project/issues/96452.
193 
194   return static_cast<double>(r);
195 #endif // !LIBC_MATH_COS_SKIP_ACCURATE_PASS
196 }
197 
198 } // namespace LIBC_NAMESPACE_DECL
199