[libc-commits] [libc] [llvm] [libc][math] Refactor sinf implementation to header-only in src/__support/math folder. (PR #177963)
Muhammad Bassiouni via libc-commits
libc-commits at lists.llvm.org
Mon Jan 26 09:00:36 PST 2026
================
@@ -0,0 +1,194 @@
+//===-- Single-precision sin 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LIBC_SRC___SUPPORT_MATH_SINF_H
+#define LIBC_SRC___SUPPORT_MATH_SINF_H
+
+#include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+
+#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS) && \
+ defined(LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT) && \
+ defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
+
+#include "sincosf_float_eval.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE static float sinf(float x) {
+ return math::sincosf_float_eval::sincosf_eval</*IS_SIN*/ true>(x);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#else // !LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT
+
+#include "src/__support/math/sincosf_utils.h"
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+#include "src/__support/math/range_reduction_fma.h"
+#else // !LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+#include "src/__support/math/range_reduction.h"
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE static float sinf(float x) {
+ using FPBits = typename fputil::FPBits<float>;
+ FPBits xbits(x);
+
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & 0x7fff'ffffU;
+ double xd = static_cast<double>(x);
+
+ // Range reduction:
+ // For |x| > pi/32, we perform range reduction as follows:
+ // Find k and y such that:
+ // x = (k + y) * pi/32
+ // k is an integer
+ // |y| < 0.5
+ // For small range (|x| < 2^45 when FMA instructions are available, 2^22
+ // otherwise), this is done by performing:
+ // k = round(x * 32/pi)
+ // y = x * 32/pi - k
+ // For large range, we will omit all the higher parts of 32/pi such that the
+ // least significant bits of their full products with x are larger than 63,
+ // since sin((k + y + 64*i) * pi/32) = sin(x + i * 2pi) = sin(x).
+ //
+ // When FMA instructions are not available, we store the digits of 32/pi in
+ // chunks of 28-bit precision. This will make sure that the products:
+ // x * THIRTYTWO_OVER_PI_28[i] are all exact.
+ // When FMA instructions are available, we simply store the digits of 32/pi in
+ // chunks of doubles (53-bit of precision).
+ // So when multiplying by the largest values of single precision, the
+ // resulting output should be correct up to 2^(-208 + 128) ~ 2^-80. By the
+ // worst-case analysis of range reduction, |y| >= 2^-38, so this should give
+ // us more than 40 bits of accuracy. For the worst-case estimation of range
+ // reduction, see for instances:
+ // Elementary Functions by J-M. Muller, Chapter 11,
+ // Handbook of Floating-Point Arithmetic by J-M. Muller et. al.,
+ // Chapter 10.2.
+ //
+ // Once k and y are computed, we then deduce the answer by the sine of sum
+ // formula:
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
+ // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
+ // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
+ // computed using degree-7 and degree-6 minimax polynomials generated by
+ // Sollya respectively.
+
+ // |x| <= pi/16
+ if (LIBC_UNLIKELY(x_abs <= 0x3e49'0fdbU)) {
+
+ // |x| < 0x1.d12ed2p-12f
+ if (LIBC_UNLIKELY(x_abs < 0x39e8'9769U)) {
+ if (LIBC_UNLIKELY(x_abs == 0U)) {
+ // For signed zeros.
+ return x;
+ }
+ // When |x| < 2^-12, the relative error of the approximation sin(x) ~ x
+ // is:
+ // |sin(x) - x| / |sin(x)| < |x^3| / (6|x|)
+ // = x^2 / 6
+ // < 2^-25
+ // < epsilon(1)/2.
+ // So the correctly rounded values of sin(x) are:
+ // = x - sign(x)*eps(x) if rounding mode = FE_TOWARDZERO,
+ // or (rounding mode = FE_UPWARD and x is
+ // negative),
+ // = x otherwise.
+ // To simplify the rounding decision and make it more efficient, we use
+ // fma(x, -2^-25, x) instead.
+ // An exhaustive test shows that this formula work correctly for all
+ // rounding modes up to |x| < 0x1.c555dep-11f.
+ // Note: to use the formula x - 2^-25*x to decide the correct rounding, we
+ // do need fma(x, -2^-25, x) to prevent underflow caused by -2^-25*x when
+ // |x| < 2^-125. For targets without FMA instructions, we simply use
+ // double for intermediate results as it is more efficient than using an
+ // emulated version of FMA.
+#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
+ return fputil::multiply_add(x, -0x1.0p-25f, x);
+#else
+ return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, xd));
+#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT
+ }
+
+ // |x| < pi/16.
+ double xsq = xd * xd;
+
+ // Degree-9 polynomial approximation:
+ // sin(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9
+ // = x (1 + a_3 x^2 + ... + a_9 x^8)
+ // = x * P(x^2)
+ // generated by Sollya with the following commands:
+ // > display = hexadecimal;
+ // > Q = fpminimax(sin(x)/x, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/16]);
+ double result =
+ fputil::polyeval(xsq, 1.0, -0x1.55555555554c6p-3, 0x1.1111111085e65p-7,
+ -0x1.a019f70fb4d4fp-13, 0x1.718d179815e74p-19);
+ return static_cast<float>(xd * result);
+ }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ if (LIBC_UNLIKELY(x_abs == 0x4619'9998U)) { // x = 0x1.33333p13
+ float r = -0x1.63f4bap-2f;
+ int rounding = fputil::quick_get_round();
+ if ((rounding == FE_DOWNWARD && xbits.is_pos()) ||
+ (rounding == FE_UPWARD && xbits.is_neg()))
+ r = -0x1.63f4bcp-2f;
+ return xbits.is_neg() ? -r : r;
+ }
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ if (x_abs == 0x7f80'0000U) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+ return x + FPBits::quiet_nan().get_val();
+ }
+
+ // Combine the results with the sine of sum formula:
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
+ // = sin_y * cos_k + (1 + cosm1_y) * sin_k
+ // = sin_y * cos_k + (cosm1_y * sin_k + sin_k)
+ double sin_k, cos_k, sin_y, cosm1_y;
+
+ sincosf_eval(xd, x_abs, sin_k, cos_k, sin_y, cosm1_y);
+
+ return static_cast<float>(fputil::multiply_add(
+ sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT
+
+#endif // LIBC_SRC___SUPPORT_MATH_SINF_H
----------------
bassiounix wrote:
```suggestion
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_SINF_H
```
https://github.com/llvm/llvm-project/pull/177963
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