<https://www.gnu.org/licenses/>. */
#include "v_math.h"
-#include "poly_advsimd_f64.h"
+#include "v_expm1_inline.h"
static const struct data
{
- float64x2_t poly[11];
- float64x2_t invln2;
- double ln2[2];
- float64x2_t shift;
- int64x2_t exponent_bias;
+ struct v_expm1_data d;
#if WANT_SIMD_EXCEPT
uint64x2_t thresh, tiny_bound;
#else
float64x2_t oflow_bound;
#endif
} data = {
- /* Generated using fpminimax, with degree=12 in [log(2)/2, log(2)/2]. */
- .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
- V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
- V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
- V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
- V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29) },
- .invln2 = V2 (0x1.71547652b82fep0),
- .ln2 = { 0x1.62e42fefa39efp-1, 0x1.abc9e3b39803fp-56 },
- .shift = V2 (0x1.8p52),
- .exponent_bias = V2 (0x3ff0000000000000),
+ .d = V_EXPM1_DATA,
#if WANT_SIMD_EXCEPT
/* asuint64(oflow_bound) - asuint64(0x1p-51), shifted left by 1 for abs
compare. */
};
static float64x2_t VPCS_ATTR NOINLINE
-special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
+special_case (float64x2_t x, uint64x2_t special, const struct data *d)
{
- return v_call_f64 (expm1, x, y, special);
+ return v_call_f64 (expm1, x, expm1_inline (v_zerofy_f64 (x, special), &d->d),
+ special);
}
/* Double-precision vector exp(x) - 1 function.
- The maximum error observed error is 2.18 ULP:
- _ZGVnN2v_expm1 (0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2
- want 0x1.a8b9ea8d66e2p-2. */
+ The maximum error observed error is 2.05 ULP:
+ _ZGVnN2v_expm1(0x1.634902eaff3adp-2) got 0x1.a8b636e2a9388p-2
+ want 0x1.a8b636e2a9386p-2. */
float64x2_t VPCS_ATTR V_NAME_D1 (expm1) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
- uint64x2_t ix = vreinterpretq_u64_f64 (x);
-
#if WANT_SIMD_EXCEPT
+ uint64x2_t ix = vreinterpretq_u64_f64 (x);
/* If fp exceptions are to be triggered correctly, fall back to scalar for
|x| < 2^-51, |x| > oflow_bound, Inf & NaN. Add ix to itself for
shift-left by 1, and compare with thresh which was left-shifted offline -
this is effectively an absolute compare. */
uint64x2_t special
= vcgeq_u64 (vsubq_u64 (vaddq_u64 (ix, ix), d->tiny_bound), d->thresh);
- if (__glibc_unlikely (v_any_u64 (special)))
- x = v_zerofy_f64 (x, special);
#else
/* Large input, NaNs and Infs. */
uint64x2_t special = vcageq_f64 (x, d->oflow_bound);
#endif
- /* Reduce argument to smaller range:
- Let i = round(x / ln2)
- and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
- exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
- where 2^i is exact because i is an integer. */
- float64x2_t n = vsubq_f64 (vfmaq_f64 (d->shift, d->invln2, x), d->shift);
- int64x2_t i = vcvtq_s64_f64 (n);
- float64x2_t ln2 = vld1q_f64 (&d->ln2[0]);
- float64x2_t f = vfmsq_laneq_f64 (x, n, ln2, 0);
- f = vfmsq_laneq_f64 (f, n, ln2, 1);
-
- /* Approximate expm1(f) using polynomial.
- Taylor expansion for expm1(x) has the form:
- x + ax^2 + bx^3 + cx^4 ....
- So we calculate the polynomial P(f) = a + bf + cf^2 + ...
- and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
- float64x2_t f2 = vmulq_f64 (f, f);
- float64x2_t f4 = vmulq_f64 (f2, f2);
- float64x2_t f8 = vmulq_f64 (f4, f4);
- float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly));
-
- /* Assemble the result.
- expm1(x) ~= 2^i * (p + 1) - 1
- Let t = 2^i. */
- int64x2_t u = vaddq_s64 (vshlq_n_s64 (i, 52), d->exponent_bias);
- float64x2_t t = vreinterpretq_f64_s64 (u);
-
if (__glibc_unlikely (v_any_u64 (special)))
- return special_case (vreinterpretq_f64_u64 (ix),
- vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t),
- special);
+ return special_case (x, special, d);
/* expm1(x) ~= p * t + (t - 1). */
- return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t);
+ return expm1_inline (x, &d->d);
}
<https://www.gnu.org/licenses/>. */
#include "v_math.h"
-#include "poly_advsimd_f64.h"
+#include "v_expm1_inline.h"
static const struct data
{
- float64x2_t poly[11], inv_ln2;
- double m_ln2[2];
- float64x2_t shift;
+ struct v_expm1_data d;
uint64x2_t halff;
- int64x2_t onef;
#if WANT_SIMD_EXCEPT
uint64x2_t tiny_bound, thresh;
#else
- uint64x2_t large_bound;
+ float64x2_t large_bound;
#endif
} data = {
- /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */
- .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
- V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
- V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
- V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
- V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), },
-
- .inv_ln2 = V2 (0x1.71547652b82fep0),
- .m_ln2 = {-0x1.62e42fefa39efp-1, -0x1.abc9e3b39803fp-56},
- .shift = V2 (0x1.8p52),
-
+ .d = V_EXPM1_DATA,
.halff = V2 (0x3fe0000000000000),
- .onef = V2 (0x3ff0000000000000),
#if WANT_SIMD_EXCEPT
/* 2^-26, below which sinh(x) rounds to x. */
.tiny_bound = V2 (0x3e50000000000000),
/* asuint(large_bound) - asuint(tiny_bound). */
.thresh = V2 (0x0230000000000000),
#else
-/* 2^9. expm1 helper overflows for large input. */
- .large_bound = V2 (0x4080000000000000),
+ /* 2^9. expm1 helper overflows for large input. */
+ .large_bound = V2 (0x1p+9),
#endif
};
-static inline float64x2_t
-expm1_inline (float64x2_t x)
-{
- const struct data *d = ptr_barrier (&data);
-
- /* Reduce argument:
- exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
- where i = round(x / ln2)
- and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */
- float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift);
- int64x2_t i = vcvtq_s64_f64 (j);
-
- float64x2_t m_ln2 = vld1q_f64 (d->m_ln2);
- float64x2_t f = vfmaq_laneq_f64 (x, j, m_ln2, 0);
- f = vfmaq_laneq_f64 (f, j, m_ln2, 1);
- /* Approximate expm1(f) using polynomial. */
- float64x2_t f2 = vmulq_f64 (f, f);
- float64x2_t f4 = vmulq_f64 (f2, f2);
- float64x2_t f8 = vmulq_f64 (f4, f4);
- float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly));
- /* t = 2^i. */
- float64x2_t t = vreinterpretq_f64_u64 (
- vreinterpretq_u64_s64 (vaddq_s64 (vshlq_n_s64 (i, 52), d->onef)));
- /* expm1(x) ~= p * t + (t - 1). */
- return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t);
-}
-
static float64x2_t NOINLINE VPCS_ATTR
special_case (float64x2_t x)
{
/* Approximation for vector double-precision sinh(x) using expm1.
sinh(x) = (exp(x) - exp(-x)) / 2.
- The greatest observed error is 2.57 ULP:
- _ZGVnN2v_sinh (0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2
- want 0x1.ab34e59d678d9p-2. */
+ The greatest observed error is 2.52 ULP:
+ _ZGVnN2v_sinh(-0x1.a098a2177a2b9p-2) got -0x1.ac2f05bb66fccp-2
+ want -0x1.ac2f05bb66fc9p-2. */
float64x2_t VPCS_ATTR V_NAME_D1 (sinh) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
float64x2_t ax = vabsq_f64 (x);
- uint64x2_t sign
- = veorq_u64 (vreinterpretq_u64_f64 (x), vreinterpretq_u64_f64 (ax));
- float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->halff));
+ uint64x2_t ix = vreinterpretq_u64_f64 (x);
+ float64x2_t halfsign = vreinterpretq_f64_u64 (
+ vbslq_u64 (v_u64 (0x8000000000000000), ix, d->halff));
#if WANT_SIMD_EXCEPT
uint64x2_t special = vcgeq_u64 (
vsubq_u64 (vreinterpretq_u64_f64 (ax), d->tiny_bound), d->thresh);
#else
- uint64x2_t special = vcgeq_u64 (vreinterpretq_u64_f64 (ax), d->large_bound);
+ uint64x2_t special = vcageq_f64 (x, d->large_bound);
#endif
/* Fall back to scalar variant for all lanes if any of them are special. */
/* Up to the point that expm1 overflows, we can use it to calculate sinh
using a slight rearrangement of the definition of sinh. This allows us to
retain acceptable accuracy for very small inputs. */
- float64x2_t t = expm1_inline (ax);
+ float64x2_t t = expm1_inline (ax, &d->d);
t = vaddq_f64 (t, vdivq_f64 (t, vaddq_f64 (t, v_f64 (1.0))));
return vmulq_f64 (t, halfsign);
}
<https://www.gnu.org/licenses/>. */
#include "v_math.h"
-#include "poly_advsimd_f64.h"
+#include "v_expm1_inline.h"
static const struct data
{
- float64x2_t poly[11];
- float64x2_t inv_ln2, ln2_hi, ln2_lo, shift;
- uint64x2_t onef;
+ struct v_expm1_data d;
uint64x2_t thresh, tiny_bound;
} data = {
- /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */
- .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
- V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
- V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
- V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
- V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), },
-
- .inv_ln2 = V2 (0x1.71547652b82fep0),
- .ln2_hi = V2 (-0x1.62e42fefa39efp-1),
- .ln2_lo = V2 (-0x1.abc9e3b39803fp-56),
- .shift = V2 (0x1.8p52),
-
- .onef = V2 (0x3ff0000000000000),
+ .d = V_EXPM1_DATA,
.tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */
/* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */
.thresh = V2 (0x01f241bf835f9d5f),
};
-static inline float64x2_t
-expm1_inline (float64x2_t x, const struct data *d)
-{
- /* Helper routine for calculating exp(x) - 1. Vector port of the helper from
- the scalar variant of tanh. */
-
- /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
- float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift);
- int64x2_t i = vcvtq_s64_f64 (j);
- float64x2_t f = vfmaq_f64 (x, j, d->ln2_hi);
- f = vfmaq_f64 (f, j, d->ln2_lo);
-
- /* Approximate expm1(f) using polynomial. */
- float64x2_t f2 = vmulq_f64 (f, f);
- float64x2_t f4 = vmulq_f64 (f2, f2);
- float64x2_t p = vfmaq_f64 (
- f, f2, v_estrin_10_f64 (f, f2, f4, vmulq_f64 (f4, f4), d->poly));
-
- /* t = 2 ^ i. */
- float64x2_t t = vreinterpretq_f64_u64 (
- vaddq_u64 (vreinterpretq_u64_s64 (i << 52), d->onef));
- /* expm1(x) = p * t + (t - 1). */
- return vfmaq_f64 (vsubq_f64 (t, v_f64 (1)), p, t);
-}
-
static float64x2_t NOINLINE VPCS_ATTR
-special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
+special_case (float64x2_t x, float64x2_t q, float64x2_t qp2,
+ uint64x2_t special)
{
- return v_call_f64 (tanh, x, y, special);
+ return v_call_f64 (tanh, x, vdivq_f64 (q, qp2), special);
}
/* Vector approximation for double-precision tanh(x), using a simplified
- version of expm1. The greatest observed error is 2.77 ULP:
- _ZGVnN2v_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3
- want -0x1.bd6a21a163624p-3. */
+ version of expm1. The greatest observed error is 2.70 ULP:
+ _ZGVnN2v_tanh(-0x1.c59aa220cb177p-3) got -0x1.be5452a6459fep-3
+ want -0x1.be5452a6459fbp-3. */
float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
u = vaddq_f64 (u, u);
/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
- float64x2_t q = expm1_inline (u, d);
- float64x2_t qp2 = vaddq_f64 (q, v_f64 (2));
+ float64x2_t q = expm1_inline (u, &d->d);
+ float64x2_t qp2 = vaddq_f64 (q, v_f64 (2.0));
if (__glibc_unlikely (v_any_u64 (special)))
- return special_case (x, vdivq_f64 (q, qp2), special);
+ return special_case (x, q, qp2, special);
return vdivq_f64 (q, qp2);
}
--- /dev/null
+/* Double-precision inline helper for vector (Advanced SIMD) expm1 function
+
+ Copyright (C) 2024 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#ifndef AARCH64_FPU_V_EXPM1_INLINE_H
+#define AARCH64_FPU_V_EXPM1_INLINE_H
+
+#include "v_math.h"
+
+struct v_expm1_data
+{
+ float64x2_t c2, c4, c6, c8;
+ float64x2_t invln2;
+ int64x2_t exponent_bias;
+ double c1, c3, c5, c7, c9, c10;
+ double ln2[2];
+};
+
+/* Generated using fpminimax, with degree=12 in [log(2)/2, log(2)/2]. */
+#define V_EXPM1_DATA \
+ { \
+ .c1 = 0x1.5555555555559p-3, .c2 = V2 (0x1.555555555554bp-5), \
+ .c3 = 0x1.111111110f663p-7, .c4 = V2 (0x1.6c16c16c1b5f3p-10), \
+ .c5 = 0x1.a01a01affa35dp-13, .c6 = V2 (0x1.a01a018b4ecbbp-16), \
+ .c7 = 0x1.71ddf82db5bb4p-19, .c8 = V2 (0x1.27e517fc0d54bp-22), \
+ .c9 = 0x1.af5eedae67435p-26, .c10 = 0x1.1f143d060a28ap-29, \
+ .ln2 = { 0x1.62e42fefa39efp-1, 0x1.abc9e3b39803fp-56 }, \
+ .invln2 = V2 (0x1.71547652b82fep0), \
+ .exponent_bias = V2 (0x3ff0000000000000), \
+ }
+
+static inline float64x2_t
+expm1_inline (float64x2_t x, const struct v_expm1_data *d)
+{
+ /* Helper routine for calculating exp(x) - 1. */
+
+ float64x2_t ln2 = vld1q_f64 (&d->ln2[0]);
+
+ /* Reduce argument to smaller range:
+ Let i = round(x / ln2)
+ and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
+ exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
+ where 2^i is exact because i is an integer. */
+ float64x2_t n = vrndaq_f64 (vmulq_f64 (x, d->invln2));
+ int64x2_t i = vcvtq_s64_f64 (n);
+ float64x2_t f = vfmsq_laneq_f64 (x, n, ln2, 0);
+ f = vfmsq_laneq_f64 (f, n, ln2, 1);
+
+ /* Approximate expm1(f) using polynomial.
+ Taylor expansion for expm1(x) has the form:
+ x + ax^2 + bx^3 + cx^4 ....
+ So we calculate the polynomial P(f) = a + bf + cf^2 + ...
+ and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
+ float64x2_t f2 = vmulq_f64 (f, f);
+ float64x2_t f4 = vmulq_f64 (f2, f2);
+ float64x2_t lane_consts_13 = vld1q_f64 (&d->c1);
+ float64x2_t lane_consts_57 = vld1q_f64 (&d->c5);
+ float64x2_t lane_consts_910 = vld1q_f64 (&d->c9);
+ float64x2_t p01 = vfmaq_laneq_f64 (v_f64 (0.5), f, lane_consts_13, 0);
+ float64x2_t p23 = vfmaq_laneq_f64 (d->c2, f, lane_consts_13, 1);
+ float64x2_t p45 = vfmaq_laneq_f64 (d->c4, f, lane_consts_57, 0);
+ float64x2_t p67 = vfmaq_laneq_f64 (d->c6, f, lane_consts_57, 1);
+ float64x2_t p03 = vfmaq_f64 (p01, f2, p23);
+ float64x2_t p47 = vfmaq_f64 (p45, f2, p67);
+ float64x2_t p89 = vfmaq_laneq_f64 (d->c8, f, lane_consts_910, 0);
+ float64x2_t p = vfmaq_laneq_f64 (p89, f2, lane_consts_910, 1);
+ p = vfmaq_f64 (p47, f4, p);
+ p = vfmaq_f64 (p03, f4, p);
+
+ p = vfmaq_f64 (f, f2, p);
+
+ /* Assemble the result.
+ expm1(x) ~= 2^i * (p + 1) - 1
+ Let t = 2^i. */
+ int64x2_t u = vaddq_s64 (vshlq_n_s64 (i, 52), d->exponent_bias);
+ float64x2_t t = vreinterpretq_f64_s64 (u);
+
+ /* expm1(x) ~= p * t + (t - 1). */
+ return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t);
+}
+
+#endif
#define AARCH64_FPU_V_EXPM1F_INLINE_H
#include "v_math.h"
-#include "math_config.h"
struct v_expm1f_data
{
projects / thirdparty / glibc.git / commitdiff
