[libc-commits] [libc] [libc][math] Implement double precision sincos correctly rounded to all rounding modes. (PR #96719)
Nick Desaulniers via libc-commits
libc-commits at lists.llvm.org
Wed Jun 26 10:11:12 PDT 2024
================
@@ -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);
----------------
nickdesaulniers wrote:
```c
bool sin_upper_is_lower = sin_upper == sin_lower;
bool cos_upper_is_lower = cos_upper == cos_lower;
if (sin_upper_is_lower || cos_upper_is_lower):
if (sin_upper_is_lower)
*sin_x = sin_upper
if (cos_upper_is_lower)
*cos_x = cos_upper
return
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);
```
maybe some likely/unlikely macros can be used, too?
https://github.com/llvm/llvm-project/pull/96719
More information about the libc-commits
mailing list