113 lines
3.8 KiB
C
113 lines
3.8 KiB
C
/*
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* Single-precision vector tan(x) function.
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*
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* Copyright (c) 2020-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "sv_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if SV_SUPPORTED
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/* Constants. */
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#define NegPio2_1 (sv_f32 (-0x1.921fb6p+0f))
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#define NegPio2_2 (sv_f32 (0x1.777a5cp-25f))
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#define NegPio2_3 (sv_f32 (0x1.ee59dap-50f))
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#define InvPio2 (sv_f32 (0x1.45f306p-1f))
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#define RangeVal (sv_f32 (0x1p15f))
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#define Shift (sv_f32 (0x1.8p+23f))
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#define poly(i) sv_f32 (__tanf_poly_data.poly_tan[i])
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/* Use full Estrin's scheme to evaluate polynomial. */
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static inline sv_f32_t
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eval_poly (svbool_t pg, sv_f32_t z)
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{
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sv_f32_t z2 = svmul_f32_x (pg, z, z);
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sv_f32_t z4 = svmul_f32_x (pg, z2, z2);
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sv_f32_t y_10 = sv_fma_f32_x (pg, z, poly (1), poly (0));
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sv_f32_t y_32 = sv_fma_f32_x (pg, z, poly (3), poly (2));
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sv_f32_t y_54 = sv_fma_f32_x (pg, z, poly (5), poly (4));
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sv_f32_t y_32_10 = sv_fma_f32_x (pg, z2, y_32, y_10);
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sv_f32_t y = sv_fma_f32_x (pg, z4, y_54, y_32_10);
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return y;
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}
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static NOINLINE sv_f32_t
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__sv_tanf_specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp)
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{
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return sv_call_f32 (tanf, x, y, cmp);
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}
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/* Fast implementation of SVE tanf.
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Maximum error is 3.45 ULP:
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__sv_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
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want 0x1.ff9850p-1. */
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sv_f32_t
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__sv_tanf_x (sv_f32_t x, const svbool_t pg)
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{
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/* Determine whether input is too large to perform fast regression. */
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svbool_t cmp = svacge_f32 (pg, x, RangeVal);
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svbool_t pred_minuszero = svcmpeq_f32 (pg, x, sv_f32 (-0.0));
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/* n = rint(x/(pi/2)). */
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sv_f32_t q = sv_fma_f32_x (pg, InvPio2, x, Shift);
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sv_f32_t n = svsub_f32_x (pg, q, Shift);
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/* n is already a signed integer, simply convert it. */
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sv_s32_t in = sv_to_s32_f32_x (pg, n);
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/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
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sv_s32_t alt = svand_s32_x (pg, in, sv_s32 (1));
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svbool_t pred_alt = svcmpne_s32 (pg, alt, sv_s32 (0));
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/* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
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sv_f32_t r;
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r = sv_fma_f32_x (pg, NegPio2_1, n, x);
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r = sv_fma_f32_x (pg, NegPio2_2, n, r);
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r = sv_fma_f32_x (pg, NegPio2_3, n, r);
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/* If x lives in an interval, where |tan(x)|
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- is finite, then use a polynomial approximation of the form
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tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
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- grows to infinity then use symmetries of tangent and the identity
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tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
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the same polynomial approximation of tan as above. */
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/* Perform additional reduction if required. */
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sv_f32_t z = svneg_f32_m (r, pred_alt, r);
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/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
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sv_f32_t z2 = svmul_f32_x (pg, z, z);
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sv_f32_t p = eval_poly (pg, z2);
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sv_f32_t y = sv_fma_f32_x (pg, svmul_f32_x (pg, z, z2), p, z);
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/* Transform result back, if necessary. */
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sv_f32_t inv_y = svdiv_f32_x (pg, sv_f32 (1.0f), y);
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y = svsel_f32 (pred_alt, inv_y, y);
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/* Fast reduction does not handle the x = -0.0 case well,
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therefore it is fixed here. */
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y = svsel_f32 (pred_minuszero, x, y);
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/* No need to pass pg to specialcase here since cmp is a strict subset,
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guaranteed by the cmpge above. */
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if (unlikely (svptest_any (pg, cmp)))
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return __sv_tanf_specialcase (x, y, cmp);
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return y;
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}
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PL_ALIAS (__sv_tanf_x, _ZGVsMxv_tanf)
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PL_SIG (SV, F, 1, tan, -3.1, 3.1)
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PL_TEST_ULP (__sv_tanf, 2.96)
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PL_TEST_INTERVAL (__sv_tanf, -0.0, -0x1p126, 100)
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PL_TEST_INTERVAL (__sv_tanf, 0x1p-149, 0x1p-126, 4000)
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PL_TEST_INTERVAL (__sv_tanf, 0x1p-126, 0x1p-23, 50000)
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PL_TEST_INTERVAL (__sv_tanf, 0x1p-23, 0.7, 50000)
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PL_TEST_INTERVAL (__sv_tanf, 0.7, 1.5, 50000)
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PL_TEST_INTERVAL (__sv_tanf, 1.5, 100, 50000)
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PL_TEST_INTERVAL (__sv_tanf, 100, 0x1p17, 50000)
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PL_TEST_INTERVAL (__sv_tanf, 0x1p17, inf, 50000)
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#endif
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