xref: /llvm-project/libc/src/math/generic/sin.cpp (revision 0f4b3c409fbd756d826c89d5539d9ea22bcc56aa)
116903aceSlntue //===-- Double-precision sin function -------------------------------------===//
216903aceSlntue //
316903aceSlntue // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
416903aceSlntue // See https://llvm.org/LICENSE.txt for license information.
516903aceSlntue // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
616903aceSlntue //
716903aceSlntue //===----------------------------------------------------------------------===//
816903aceSlntue 
916903aceSlntue #include "src/math/sin.h"
1016903aceSlntue #include "hdr/errno_macros.h"
1116903aceSlntue #include "src/__support/FPUtil/FEnvImpl.h"
1216903aceSlntue #include "src/__support/FPUtil/FPBits.h"
1316903aceSlntue #include "src/__support/FPUtil/double_double.h"
1416903aceSlntue #include "src/__support/FPUtil/dyadic_float.h"
1516903aceSlntue #include "src/__support/FPUtil/multiply_add.h"
1616903aceSlntue #include "src/__support/FPUtil/rounding_mode.h"
1716903aceSlntue #include "src/__support/common.h"
185ff3ff33SPetr Hosek #include "src/__support/macros/config.h"
1916903aceSlntue #include "src/__support/macros/optimization.h"            // LIBC_UNLIKELY
2016903aceSlntue #include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
2151e9430aSlntue #include "src/math/generic/range_reduction_double_common.h"
2216903aceSlntue #include "src/math/generic/sincos_eval.h"
2316903aceSlntue 
2451e9430aSlntue #ifdef LIBC_TARGET_CPU_HAS_FMA
2551e9430aSlntue #include "range_reduction_double_fma.h"
2651e9430aSlntue #else
2751e9430aSlntue #include "range_reduction_double_nofma.h"
2851e9430aSlntue #endif // LIBC_TARGET_CPU_HAS_FMA
2916903aceSlntue 
305ff3ff33SPetr Hosek namespace LIBC_NAMESPACE_DECL {
3116903aceSlntue 
3216903aceSlntue using DoubleDouble = fputil::DoubleDouble;
3316903aceSlntue using Float128 = typename fputil::DyadicFloat<128>;
3416903aceSlntue 
3516903aceSlntue LLVM_LIBC_FUNCTION(double, sin, (double x)) {
3616903aceSlntue   using FPBits = typename fputil::FPBits<double>;
3716903aceSlntue   FPBits xbits(x);
3816903aceSlntue 
3916903aceSlntue   uint16_t x_e = xbits.get_biased_exponent();
4016903aceSlntue 
4116903aceSlntue   DoubleDouble y;
4216903aceSlntue   unsigned k;
4351e9430aSlntue   LargeRangeReduction range_reduction_large{};
4416903aceSlntue 
4551e9430aSlntue   // |x| < 2^16
4616903aceSlntue   if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
4751e9430aSlntue     // |x| < 2^-7
4851e9430aSlntue     if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
4951e9430aSlntue       // |x| < 2^-26, |sin(x) - x| < ulp(x)/2.
5016903aceSlntue       if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) {
5116903aceSlntue         // Signed zeros.
5216903aceSlntue         if (LIBC_UNLIKELY(x == 0.0))
53*0f4b3c40Slntue           return x + x; // Make sure it works with FTZ/DAZ.
5416903aceSlntue 
5516903aceSlntue #ifdef LIBC_TARGET_CPU_HAS_FMA
5616903aceSlntue         return fputil::multiply_add(x, -0x1.0p-54, x);
5716903aceSlntue #else
5816903aceSlntue         if (LIBC_UNLIKELY(x_e < 4)) {
5916903aceSlntue           int rounding_mode = fputil::quick_get_round();
6016903aceSlntue           if (rounding_mode == FE_TOWARDZERO ||
6116903aceSlntue               (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
6216903aceSlntue               (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
6316903aceSlntue             return FPBits(xbits.uintval() - 1).get_val();
6416903aceSlntue         }
6516903aceSlntue         return fputil::multiply_add(x, -0x1.0p-54, x);
6616903aceSlntue #endif // LIBC_TARGET_CPU_HAS_FMA
6716903aceSlntue       }
6851e9430aSlntue       // No range reduction needed.
6951e9430aSlntue       k = 0;
7051e9430aSlntue       y.lo = 0.0;
7151e9430aSlntue       y.hi = x;
7251e9430aSlntue     } else {
7351e9430aSlntue       // Small range reduction.
7416903aceSlntue       k = range_reduction_small(x, y);
7551e9430aSlntue     }
7616903aceSlntue   } else {
7716903aceSlntue     // Inf or NaN
7816903aceSlntue     if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
7916903aceSlntue       // sin(+-Inf) = NaN
8016903aceSlntue       if (xbits.get_mantissa() == 0) {
8116903aceSlntue         fputil::set_errno_if_required(EDOM);
8216903aceSlntue         fputil::raise_except_if_required(FE_INVALID);
8316903aceSlntue       }
8416903aceSlntue       return x + FPBits::quiet_nan().get_val();
8516903aceSlntue     }
8616903aceSlntue 
8716903aceSlntue     // Large range reduction.
8851e9430aSlntue     k = range_reduction_large.fast(x, y);
8916903aceSlntue   }
9016903aceSlntue 
9116903aceSlntue   DoubleDouble sin_y, cos_y;
9216903aceSlntue 
9351e9430aSlntue   [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y);
9416903aceSlntue 
9516903aceSlntue   // Look up sin(k * pi/128) and cos(k * pi/128)
9651e9430aSlntue #ifdef LIBC_MATH_HAS_SMALL_TABLES
9751e9430aSlntue   // Memory saving versions.  Use 65-entry table.
9851e9430aSlntue   auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
9951e9430aSlntue     unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
10051e9430aSlntue     DoubleDouble ans = SIN_K_PI_OVER_128[idx];
10151e9430aSlntue     if (kk & 128) {
10251e9430aSlntue       ans.hi = -ans.hi;
10351e9430aSlntue       ans.lo = -ans.lo;
10451e9430aSlntue     }
10551e9430aSlntue     return ans;
10651e9430aSlntue   };
10751e9430aSlntue   DoubleDouble sin_k = get_idx_dd(k);
10851e9430aSlntue   DoubleDouble cos_k = get_idx_dd(k + 64);
10951e9430aSlntue #else
11016903aceSlntue   // Fast look up version, but needs 256-entry table.
11116903aceSlntue   // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
11216903aceSlntue   DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
11316903aceSlntue   DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
11451e9430aSlntue #endif
11516903aceSlntue 
11616903aceSlntue   // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
11716903aceSlntue   // So k is an integer and -pi / 256 <= y <= pi / 256.
11816903aceSlntue   // Then sin(x) = sin((k * pi/128 + y)
11916903aceSlntue   //             = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
12051e9430aSlntue   DoubleDouble sin_k_cos_y = fputil::quick_mult(cos_y, sin_k);
12151e9430aSlntue   DoubleDouble cos_k_sin_y = fputil::quick_mult(sin_y, cos_k);
12216903aceSlntue 
12316903aceSlntue   DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
12416903aceSlntue   rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
12516903aceSlntue 
12651e9430aSlntue #ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
12716903aceSlntue   return rr.hi + rr.lo;
12816903aceSlntue #else
12916903aceSlntue   // Accurate test and pass for correctly rounded implementation.
13088f80aebSlntue 
13151e9430aSlntue   double rlp = rr.lo + err;
13251e9430aSlntue   double rlm = rr.lo - err;
13316903aceSlntue 
13416903aceSlntue   double r_upper = rr.hi + rlp; // (rr.lo + ERR);
13516903aceSlntue   double r_lower = rr.hi + rlm; // (rr.lo - ERR);
13616903aceSlntue 
13716903aceSlntue   // Ziv's rounding test.
13816903aceSlntue   if (LIBC_LIKELY(r_upper == r_lower))
13916903aceSlntue     return r_upper;
14016903aceSlntue 
14188f80aebSlntue   Float128 u_f128, sin_u, cos_u;
14216903aceSlntue   if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
14351e9430aSlntue     u_f128 = range_reduction_small_f128(x);
14416903aceSlntue   else
14516903aceSlntue     u_f128 = range_reduction_large.accurate();
14616903aceSlntue 
14788f80aebSlntue   generic::sincos_eval(u_f128, sin_u, cos_u);
14816903aceSlntue 
14916903aceSlntue   auto get_sin_k = [](unsigned kk) -> Float128 {
15016903aceSlntue     unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
15151e9430aSlntue     Float128 ans = SIN_K_PI_OVER_128_F128[idx];
15216903aceSlntue     if (kk & 128)
15316903aceSlntue       ans.sign = Sign::NEG;
15416903aceSlntue     return ans;
15516903aceSlntue   };
15616903aceSlntue 
15716903aceSlntue   // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
15816903aceSlntue   Float128 sin_k_f128 = get_sin_k(k);
15916903aceSlntue   Float128 cos_k_f128 = get_sin_k(k + 64);
16016903aceSlntue 
16116903aceSlntue   // sin(x) = sin((k * pi/128 + u)
16216903aceSlntue   //        = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
16316903aceSlntue   Float128 r = fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),
16416903aceSlntue                                  fputil::quick_mul(cos_k_f128, sin_u));
16516903aceSlntue 
16616903aceSlntue   // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
16716903aceSlntue   // https://github.com/llvm/llvm-project/issues/96452.
16816903aceSlntue 
16916903aceSlntue   return static_cast<double>(r);
17051e9430aSlntue #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
17116903aceSlntue }
17216903aceSlntue 
1735ff3ff33SPetr Hosek } // namespace LIBC_NAMESPACE_DECL
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