95 lines
3.0 KiB
C
95 lines
3.0 KiB
C
/*
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* Single-precision vector exp(x) - 1 function.
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*
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* Copyright (c) 2022-2023, 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 "pl_sig.h"
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#include "pl_test.h"
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#if V_SUPPORTED
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#define Shift v_f32 (0x1.8p23f)
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#define InvLn2 v_f32 (0x1.715476p+0f)
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#define MLn2hi v_f32 (-0x1.62e4p-1f)
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#define MLn2lo v_f32 (-0x1.7f7d1cp-20f)
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#define AbsMask (0x7fffffff)
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#define One (0x3f800000)
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#define SpecialBound \
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(0x42af5e20) /* asuint(0x1.5ebc4p+6). Largest value of x for which expm1(x) \
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should round to -1. */
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#define TinyBound (0x34000000) /* asuint(0x1p-23). */
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#define C(i) v_f32 (__expm1f_poly[i])
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/* Single-precision vector exp(x) - 1 function.
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The maximum error is 1.51 ULP:
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expm1f(0x1.8baa96p-2) got 0x1.e2fb9p-2
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want 0x1.e2fb94p-2. */
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VPCS_ATTR
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v_f32_t V_NAME (expm1f) (v_f32_t x)
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{
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v_u32_t ix = v_as_u32_f32 (x);
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v_u32_t ax = ix & AbsMask;
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#if WANT_SIMD_EXCEPT
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/* If fp exceptions are to be triggered correctly, fall back to the scalar
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variant for all lanes if any of them should trigger an exception. */
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v_u32_t special
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= v_cond_u32 ((ax >= SpecialBound) | (ix == 0x80000000) | (ax < TinyBound));
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if (unlikely (v_any_u32 (special)))
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return v_call_f32 (expm1f, x, x, v_u32 (0xffffffff));
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#else
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/* Handles very large values (+ve and -ve), +/-NaN, +/-Inf and -0. */
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v_u32_t special = v_cond_u32 ((ax >= SpecialBound) | (ix == 0x80000000));
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#endif
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/* Reduce argument to smaller range:
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Let i = round(x / ln2)
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and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
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where 2^i is exact because i is an integer. */
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v_f32_t j = v_fma_f32 (InvLn2, x, Shift) - Shift;
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v_s32_t i = v_to_s32_f32 (j);
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v_f32_t f = v_fma_f32 (j, MLn2hi, x);
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f = v_fma_f32 (j, MLn2lo, f);
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/* Approximate expm1(f) using polynomial.
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Taylor expansion for expm1(x) has the form:
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x + ax^2 + bx^3 + cx^4 ....
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So we calculate the polynomial P(f) = a + bf + cf^2 + ...
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and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
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v_f32_t p = v_fma_f32 (C (4), f, C (3));
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p = v_fma_f32 (p, f, C (2));
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p = v_fma_f32 (p, f, C (1));
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p = v_fma_f32 (p, f, C (0));
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p = v_fma_f32 (f * f, p, f);
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/* Assemble the result.
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expm1(x) ~= 2^i * (p + 1) - 1
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Let t = 2^i. */
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v_f32_t t = v_as_f32_u32 (v_as_u32_s32 (i << 23) + One);
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/* expm1(x) ~= p * t + (t - 1). */
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v_f32_t y = v_fma_f32 (p, t, t - 1);
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#if !WANT_SIMD_EXCEPT
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if (unlikely (v_any_u32 (special)))
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return v_call_f32 (expm1f, x, y, special);
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#endif
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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, expm1, -9.9, 9.9)
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PL_TEST_ULP (V_NAME (expm1f), 1.02)
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PL_TEST_EXPECT_FENV (V_NAME (expm1f), WANT_SIMD_EXCEPT)
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PL_TEST_INTERVAL (V_NAME (expm1f), 0, 0x1p-23, 1000)
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PL_TEST_INTERVAL (V_NAME (expm1f), -0, -0x1p-23, 1000)
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PL_TEST_INTERVAL (V_NAME (expm1f), 0x1p-23, 0x1.644716p6, 1000000)
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PL_TEST_INTERVAL (V_NAME (expm1f), -0x1p-23, -0x1.9bbabcp+6, 1000000)
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#endif
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