132 lines
4.3 KiB
C
132 lines
4.3 KiB
C
/*
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* Single-precision vector tan(x) function.
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*
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* Copyright (c) 2021-2023, 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 "v_math.h"
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#include "estrinf.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if V_SUPPORTED
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/* Constants. */
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#define NegPio2_1 (v_f32 (-0x1.921fb6p+0f))
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#define NegPio2_2 (v_f32 (0x1.777a5cp-25f))
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#define NegPio2_3 (v_f32 (0x1.ee59dap-50f))
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#define InvPio2 (v_f32 (0x1.45f306p-1f))
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#define RangeVal (0x47000000) /* asuint32(0x1p15f). */
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#define TinyBound (0x30000000) /* asuint32 (0x1p-31). */
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#define Shift (v_f32 (0x1.8p+23f))
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#define AbsMask (v_u32 (0x7fffffff))
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#define poly(i) v_f32 (__tanf_poly_data.poly_tan[i])
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/* Special cases (fall back to scalar calls). */
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VPCS_ATTR
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NOINLINE static v_f32_t
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specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
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{
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return v_call_f32 (tanf, x, y, cmp);
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}
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/* Use a full Estrin scheme to evaluate polynomial. */
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static inline v_f32_t
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eval_poly (v_f32_t z)
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{
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v_f32_t z2 = z * z;
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#if WANT_SIMD_EXCEPT
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/* Tiny z (<= 0x1p-31) will underflow when calculating z^4. If fp exceptions
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are to be triggered correctly, sidestep this by fixing such lanes to 0. */
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v_u32_t will_uflow = v_cond_u32 ((v_as_u32_f32 (z) & AbsMask) <= TinyBound);
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if (unlikely (v_any_u32 (will_uflow)))
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z2 = v_sel_f32 (will_uflow, v_f32 (0), z2);
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#endif
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v_f32_t z4 = z2 * z2;
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return ESTRIN_5 (z, z2, z4, poly);
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}
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/* Fast implementation of Neon tanf.
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Maximum error is 3.45 ULP:
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__v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
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want 0x1.ff9850p-1. */
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VPCS_ATTR
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v_f32_t V_NAME (tanf) (v_f32_t x)
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{
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v_f32_t special_arg = x;
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v_u32_t ix = v_as_u32_f32 (x);
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v_u32_t iax = ix & AbsMask;
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/* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
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regression. */
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#if WANT_SIMD_EXCEPT
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/* If fp exceptions are to be triggered correctly, also special-case tiny
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input, as this will load to overflow later. Fix any special lanes to 1 to
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prevent any exceptions being triggered. */
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v_u32_t special = v_cond_u32 (iax - TinyBound >= RangeVal - TinyBound);
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if (unlikely (v_any_u32 (special)))
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x = v_sel_f32 (special, v_f32 (1.0f), x);
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#else
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/* Otherwise, special-case large and special values. */
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v_u32_t special = v_cond_u32 (iax >= RangeVal);
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#endif
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/* n = rint(x/(pi/2)). */
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v_f32_t q = v_fma_f32 (InvPio2, x, Shift);
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v_f32_t n = q - Shift;
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/* n is representable as a signed integer, simply convert it. */
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v_s32_t in = v_round_s32 (n);
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/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
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v_s32_t alt = in & 1;
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v_u32_t pred_alt = (alt != 0);
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/* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
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v_f32_t r;
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r = v_fma_f32 (NegPio2_1, n, x);
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r = v_fma_f32 (NegPio2_2, n, r);
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r = v_fma_f32 (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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v_f32_t z = v_sel_f32 (pred_alt, -r, r);
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/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
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v_f32_t z2 = r * r;
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v_f32_t p = eval_poly (z2);
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v_f32_t y = v_fma_f32 (z * z2, p, z);
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/* Compute reciprocal and apply if required. */
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v_f32_t inv_y = v_div_f32 (v_f32 (1.0f), y);
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y = v_sel_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 = v_sel_f32 (x == v_f32 (-0.0), x, y);
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if (unlikely (v_any_u32 (special)))
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return specialcase (special_arg, y, special);
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return y;
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}
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VPCS_ALIAS
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PL_SIG (V, F, 1, tan, -3.1, 3.1)
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PL_TEST_ULP (V_NAME (tanf), 2.96)
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PL_TEST_EXPECT_FENV (V_NAME (tanf), WANT_SIMD_EXCEPT)
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PL_TEST_INTERVAL (V_NAME (tanf), -0.0, -0x1p126, 100)
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PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-149, 0x1p-126, 4000)
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PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-126, 0x1p-23, 50000)
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PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-23, 0.7, 50000)
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PL_TEST_INTERVAL (V_NAME (tanf), 0.7, 1.5, 50000)
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PL_TEST_INTERVAL (V_NAME (tanf), 1.5, 100, 50000)
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PL_TEST_INTERVAL (V_NAME (tanf), 100, 0x1p17, 50000)
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PL_TEST_INTERVAL (V_NAME (tanf), 0x1p17, inf, 50000)
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#endif
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