[libc-commits] [libc] [libc] Add sinpif16 function (PR #110994)
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Fri Oct 11 07:05:46 PDT 2024
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@@ -0,0 +1,187 @@
+//===-- Half-precision sinpif 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/sinpif16.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/nearest_integer.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
+// Table is generated with Sollya as follows:
+// > display = hexadecimmal;
+// > for k from 0 to 63 do { round(sin(k * pi/32), SG, RN); };
+const float SIN_K_PI_OVER_32[64] = {0,
+ 0x1.917a6cp-4,
+ 0x1.8f8b84p-3,
+ 0x1.294062p-2,
+ 0x1.87de2ap-2,
+ 0x1.e2b5d4p-2,
+ 0x1.1c73b4p-1,
+ 0x1.44cf32p-1,
+ 0x1.6a09e6p-1,
+ 0x1.8bc806p-1,
+ 0x1.a9b662p-1,
+ 0x1.c38b3p-1,
+ 0x1.d906bcp-1,
+ 0x1.e9f416p-1,
+ 0x1.f6297cp-1,
+ 0x1.fd88dap-1,
+ 0x1p0,
+ 0x1.fd88dap-1,
+ 0x1.f6297cp-1,
+ 0x1.e9f416p-1,
+ 0x1.d906bcp-1,
+ 0x1.c38b3p-1,
+ 0x1.a9b662p-1,
+ 0x1.8bc806p-1,
+ 0x1.6a09e6p-1,
+ 0x1.44cf32p-1,
+ 0x1.1c73b4p-1,
+ 0x1.e2b5d4p-2,
+ 0x1.87de2ap-2,
+ 0x1.294062p-2,
+ 0x1.8f8b84p-3,
+ 0x1.917a6cp-4,
+ 0,
+ -0x1.917a6cp-4,
+ -0x1.8f8b84p-3,
+ -0x1.294062p-2,
+ -0x1.87de2ap-2,
+ -0x1.e2b5d4p-2,
+ -0x1.1c73b4p-1,
+ -0x1.44cf32p-1,
+ -0x1.6a09e6p-1,
+ -0x1.8bc806p-1,
+ -0x1.a9b662p-1,
+ -0x1.c38b3p-1,
+ -0x1.d906bcp-1,
+ -0x1.e9f416p-1,
+ -0x1.f6297ep-1,
+ -0x1.fd88dap-1,
+ -0x1p0,
+ -0x1.fd88dap-1,
+ -0x1.f6297cp-1,
+ -0x1.e9f416p-1,
+ -0x1.d906bcp-1,
+ -0x1.c38b3p-1,
+ -0x1.a9b662p-1,
+ -0x1.8bc806p-1,
+ -0x1.6a09e6p-1,
+ -0x1.44cf32p-1,
+ -0x1.1c73b4p-1,
+ -0x1.e2b5d4p-2,
+ -0x1.87de2ap-2,
+ -0x1.294062p-2,
+ -0x1.8f8b84p-3,
+ -0x1.917a6cp-4};
+
+int32_t range_reduction(float x, float &y) {
+ float kf = fputil::nearest_integer(x * 32);
+ y = fputil::multiply_add<float>(x, 32.0, -kf);
+
+ return static_cast<int32_t>(kf);
+}
+
+LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
+ using FPBits = typename fputil::FPBits<float16>;
+ FPBits xbits(x);
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_abs = x_u & 0x7fff;
+
+ // Range reduction:
+ // For |x| > 1/32, we perform range reduction as follows:
+ // Find k and y such that:
+ // x = (k + y) * 1/32
+ // k is an integer
+ // |y| < 0.5
+ //
+ // This is done by performing:
+ // k = round(x * 32)
+ // y = x * 32 - k
+ //
+ // Once k and y are computed, we then deduce the answer by the sine of sum
+ // formula:
+ // sin(x * pi) = sin((k + y) * pi/32)
+ // = sin(k * pi/32) * cos(y * pi/32) + sin (y * pi/32) * cos (k *
+ // pi/32)
+ // The values of sin(k * pi/32) and cos (k * pi/32) for k = 0...63 are
+ // precomputed and stored using a vector of 64 single precision floats. sin(y
+ // * pi/32) and cos(y * pi/32) are computed using degree-9 chebyshev
+ // polynomials generated by Sollya.
+
+ if (LIBC_UNLIKELY(x_abs == 0U)) {
+ // For signed zeros
+ return x;
+ }
+
+ // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
+ if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
+ // Check for NaN or infinity values
+ if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
+ // If value is equal to infinity
+ if (x_abs == 0x7c00) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+
+ return x + FPBits::quiet_nan().get_val();
+ }
+ return FPBits::zero(xbits.sign()).get_val();
+ }
+
+ float f32 = x;
+ float y;
+ int32_t k = range_reduction(f32, y);
+
+ float sin_k = SIN_K_PI_OVER_32[k & 63];
+ float cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
+
+ float cosm1_y, sin_y;
+
+ // Recall;
+ // sin(x * pi/32) = sin((k + y) * pi/32)
+ // = sin(y * pi/32) * cos(k * pi/32) + cos(y * pi/32) * sin(k *
+ // pi/32) Recall, after range reduction, -0.5 <= y <= 0.5. For very small
+ // values of y, calculating sin(y * p/32) can be inaccurate. Generating a
+ // polynomial for sin(y * p/32)/y instead significantly reduces the relative
+ // errors.
+ float ysq = y * y;
+
+ // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
+ // with:
+ // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
+ sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
+ 0x1.a03354p-21f, -0x1.ad02d2p-20f);
+
+ // Note that cosm1_y = cos(y*pi/32) - 1 = cos_y - 1
+ // Derivation: // sin(x * pi)
----------------
lntue wrote:
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https://github.com/llvm/llvm-project/pull/110994
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