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/*
* Single-precision vector log10 function.
*
* Copyright (c) 2020-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "mathlib.h"
#include "pl_sig.h"
#include "pl_test.h"
#if V_SUPPORTED
#define P(i) v_f32 (__v_log10f_poly[i])
#define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218. */
#define InvLn10 v_f32 (0x1.bcb7b2p-2f)
#define Min v_u32 (0x00800000)
#define Max v_u32 (0x7f800000)
#define Mask v_u32 (0x007fffff)
#define Off v_u32 (0x3f2aaaab) /* 0.666667. */
VPCS_ATTR
NOINLINE static v_f32_t
specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
{
/* Fall back to scalar code. */
return v_call_f32 (log10f, x, y, cmp);
}
/* Our fast implementation of v_log10f uses a similar approach as v_logf.
With the same offset as v_logf (i.e., 2/3) it delivers about 3.3ulps with
order 9. This is more efficient than using a low order polynomial computed in
double precision.
Maximum error: 3.305ulps (nearest rounding.)
__v_log10f(0x1.555c16p+0) got 0x1.ffe2fap-4
want 0x1.ffe2f4p-4 -0.304916 ulp err 2.80492. */
VPCS_ATTR
v_f32_t V_NAME (log10f) (v_f32_t x)
{
v_f32_t n, o, p, q, r, r2, y;
v_u32_t u, cmp;
u = v_as_u32_f32 (x);
cmp = v_cond_u32 (u - Min >= Max - Min);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
u -= Off;
n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend. */
u &= Mask;
u += Off;
r = v_as_f32_u32 (u) - v_f32 (1.0f);
/* y = log10(1+r) + n*log10(2). */
r2 = r * r;
/* (n*ln2 + r)*InvLn10 + r2*(P0 + r*P1 + r2*(P2 + r*P3 + r2*(P4 + r*P5 +
r2*(P6+r*P7))). */
o = v_fma_f32 (P (7), r, P (6));
p = v_fma_f32 (P (5), r, P (4));
q = v_fma_f32 (P (3), r, P (2));
y = v_fma_f32 (P (1), r, P (0));
p = v_fma_f32 (o, r2, p);
q = v_fma_f32 (p, r2, q);
y = v_fma_f32 (q, r2, y);
/* Using p = Log10(2)*n + r*InvLn(10) is slightly faster
but less accurate. */
p = v_fma_f32 (Ln2, n, r);
y = v_fma_f32 (y, r2, p * InvLn10);
if (unlikely (v_any_u32 (cmp)))
return specialcase (x, y, cmp);
return y;
}
VPCS_ALIAS
PL_SIG (V, F, 1, log10, 0.01, 11.1)
PL_TEST_ULP (V_NAME (log10f), 2.81)
PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log10f))
PL_TEST_INTERVAL (V_NAME (log10f), 0, 0xffff0000, 10000)
PL_TEST_INTERVAL (V_NAME (log10f), 0x1p-4, 0x1p4, 500000)
#endif
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