[libc-commits] [libc] [libc][math] Implement double precision sincos correctly rounded to all rounding modes. (PR #96719)
via libc-commits
libc-commits at lists.llvm.org
Wed Jun 26 13:38:57 PDT 2024
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@@ -0,0 +1,247 @@
+//===-- Double-precision sincos function ----------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/sincos.h"
+#include "hdr/errno_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+#include "src/math/generic/sincos_eval.h"
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+#include "range_reduction_double_fma.h"
+
+using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::fma::range_reduction_small;
+using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = false;
+#else
+#include "range_reduction_double_nofma.h"
+
+using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::nofma::range_reduction_small;
+using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = true;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// TODO: We might be able to improve the performance of large range reduction of
+// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
+// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
+// those lookup table.
+#include "range_reduction_double_common.h"
+
+#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
+#define LIBC_MATH_SINCOS_SKIP_ACCURATE_PASS
+#endif
+
+namespace LIBC_NAMESPACE {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+LLVM_LIBC_FUNCTION(void, sincos, (double x, double *sin_x, double *cos_x)) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint16_t x_e = xbits.get_biased_exponent();
+
+ DoubleDouble y;
+ unsigned k;
+ generic::LargeRangeReduction<NO_FMA> range_reduction_large;
+
+ // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
+ if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
+ // |x| < 2^-27
+ if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
+ // Signed zeros.
+ if (LIBC_UNLIKELY(x == 0.0)) {
+ *sin_x = x;
+ *cos_x = 1.0;
+ return;
+ }
+
+ // For |x| < 2^-27, max(|sin(x) - x|, |cos(x) - 1|) < ulp(x)/2.
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
+ *cos_x = fputil::multiply_add(x, -x, 1.0);
+#else
+ *cos_x = fputil::round_result_slightly_down(1.0);
+
+ if (LIBC_UNLIKELY(x_e < 4)) {
+ int rounding_mode = fputil::quick_get_round();
+ if (rounding_mode == FE_TOWARDZERO ||
+ (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
+ (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
+ *sin_x = FPBits(xbits.uintval() - 1).get_val();
+ }
+ *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
+#endif // LIBC_TARGET_CPU_HAS_FMA
+ return;
+ }
+
+ // // Small range reduction.
+ k = range_reduction_small(x, y);
+ } else {
+ // Inf or NaN
+ if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
+ // sin(+-Inf) = NaN
+ if (xbits.get_mantissa() == 0) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+ *sin_x = *cos_x = x + FPBits::quiet_nan().get_val();
+ return;
+ }
+
+ // Large range reduction.
+ k = range_reduction_large.compute_high_part(x);
+ y = range_reduction_large.fast();
+ }
+
+ DoubleDouble sin_y, cos_y;
+
+ generic::sincos_eval(y, sin_y, cos_y);
+
+ // Look up sin(k * pi/128) and cos(k * pi/128)
+ // Memory saving versions:
+
+ // Use 128-entry table instead:
+ // DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
+ // uint64_t sin_s = static_cast<uint64_t>(k & 128) << (63 - 7);
+ // sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+ // sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+ // DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
+ // uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
+ // cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+ // cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+
+ // Use 64-entry table instead:
+ // auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
+ // unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
+ // DoubleDouble ans = SIN_K_PI_OVER_128[idx];
+ // if (kk & 128) {
+ // ans.hi = -ans.hi;
+ // ans.lo = -ans.lo;
+ // }
+ // return ans;
+ // };
+ // DoubleDouble sin_k = get_idx_dd(k);
+ // DoubleDouble cos_k = get_idx_dd(k + 64);
+
+ // Fast look up version, but needs 256-entry table.
+ // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
+ DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
+ DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
+ DoubleDouble msin_k{-sin_k.lo, -sin_k.hi};
+
+ // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
+ // So k is an integer and -pi / 256 <= y <= pi / 256.
+ // Then sin(x) = sin((k * pi/128 + y)
+ // = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
+ DoubleDouble sin_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, sin_k);
+ DoubleDouble cos_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, cos_k);
+ // cos(x) = cos((k * pi/128 + y)
+ // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
+ DoubleDouble cos_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, cos_k);
+ DoubleDouble msin_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, msin_k);
+
+ DoubleDouble sin_dd =
+ fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
+ DoubleDouble cos_dd =
+ fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
+ sin_dd.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
+ cos_dd.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
+
+#ifdef LIBC_MATH_SINCOS_SKIP_ACCURATE_PASS
+ *sin_x = sin_dd.hi + sin_dd.lo;
+ *cos_x = cos_dd.hi + cos_dd.lo;
+ return;
+#else
+ // Accurate test and pass for correctly rounded implementation.
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ constexpr double ERR = 0x1.0p-70;
+#else
+ // TODO: Improve non-FMA fast pass accuracy.
+ constexpr double ERR = 0x1.0p-66;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+ double sin_lp = sin_dd.lo + ERR;
+ double sin_lm = sin_dd.lo - ERR;
+ double cos_lp = cos_dd.lo + ERR;
+ double cos_lm = cos_dd.lo - ERR;
+
+ double sin_upper = sin_dd.hi + sin_lp;
+ double sin_lower = sin_dd.hi + sin_lm;
+ double cos_upper = cos_dd.hi + cos_lp;
+ double cos_lower = cos_dd.hi + cos_lm;
+
+ // Ziv's rounding test.
+ if (LIBC_LIKELY(sin_upper == sin_lower && cos_upper == cos_lower)) {
+ *sin_x = sin_upper;
+ *cos_x = cos_upper;
+ return;
+ }
+
+ Float128 u_f128, sin_u, cos_u;
+ if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
+ u_f128 = generic::range_reduction_small_f128(x);
+ else
+ u_f128 = range_reduction_large.accurate();
+
+ generic::sincos_eval(u_f128, sin_u, cos_u);
+
+ auto get_sin_k = [](unsigned kk) -> Float128 {
+ unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
+ Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx];
+ if (kk & 128)
+ ans.sign = Sign::NEG;
+ return ans;
+ };
+
+ // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
+ Float128 sin_k_f128 = get_sin_k(k);
+ Float128 cos_k_f128 = get_sin_k(k + 64);
+ Float128 msin_k_f128 = get_sin_k(k + 128);
----------------
lntue wrote:
We only do fast return if both `sin_upper_is_lower` and `cos_upper_is_lower` are true. Otherwise, we still have to go through most of the accurate pass when at least one of them is false. In the logic above, if one of them fails the fast pass, it will be unset.
Also we expect both of them pass the first accuracy test with > 99.9% chance, so we optimize for that case's throughput.
https://github.com/llvm/llvm-project/pull/96719
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