x = vbslq_f64 (special, vreinterpretq_f64_u64 (d->one), x);
#endif
- float64x2_t xm1 = vsubq_f64 (x, v_f64 (1));
- float64x2_t y;
- y = vaddq_f64 (x, v_f64 (1));
+ float64x2_t xm1 = vsubq_f64 (x, v_f64 (1.0));
+ float64x2_t y = vaddq_f64 (x, v_f64 (1.0));
y = vmulq_f64 (y, xm1);
y = vsqrtq_f64 (y);
y = vaddq_f64 (xm1, y);
const static struct data
{
struct v_log1p_data log1p_consts;
- uint64x2_t one, half;
+ uint64x2_t one;
+ uint64x2_t sign_mask;
} data = { .log1p_consts = V_LOG1P_CONSTANTS_TABLE,
.one = V2 (0x3ff0000000000000),
- .half = V2 (0x3fe0000000000000) };
+ .sign_mask = V2 (0x8000000000000000) };
static float64x2_t VPCS_ATTR NOINLINE
-special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
+special_case (float64x2_t x, float64x2_t halfsign, float64x2_t y,
+ uint64x2_t special, const struct data *d)
{
- return v_call_f64 (atanh, x, y, special);
+ y = log1p_inline (y, &d->log1p_consts);
+ return v_call_f64 (atanh, vbslq_f64 (d->sign_mask, halfsign, x),
+ vmulq_f64 (halfsign, y), special);
}
/* Approximation for vector double-precision atanh(x) using modified log1p.
{
const struct data *d = ptr_barrier (&data);
+ float64x2_t halfsign = vbslq_f64 (d->sign_mask, x, v_f64 (0.5));
float64x2_t ax = vabsq_f64 (x);
uint64x2_t ia = vreinterpretq_u64_f64 (ax);
- uint64x2_t sign = veorq_u64 (vreinterpretq_u64_f64 (x), ia);
uint64x2_t special = vcgeq_u64 (ia, d->one);
- float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->half));
#if WANT_SIMD_EXCEPT
ax = v_zerofy_f64 (ax, special);
float64x2_t y;
y = vaddq_f64 (ax, ax);
- y = vdivq_f64 (y, vsubq_f64 (v_f64 (1), ax));
- y = log1p_inline (y, &d->log1p_consts);
+ y = vdivq_f64 (y, vsubq_f64 (vreinterpretq_f64_u64 (d->one), ax));
if (__glibc_unlikely (v_any_u64 (special)))
- return special_case (x, vmulq_f64 (y, halfsign), special);
+#if WANT_SIMD_EXCEPT
+ return special_case (x, halfsign, y, special, d);
+#else
+ return special_case (ax, halfsign, y, special, d);
+#endif
+
+ y = log1p_inline (y, &d->log1p_consts);
return vmulq_f64 (y, halfsign);
}
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
-#include "v_math.h"
-#include "poly_advsimd_f64.h"
+#define WANT_V_LOG1P_K0_SHORTCUT 0
+#include "v_log1p_inline.h"
const static struct data
{
- float64x2_t poly[19], ln2[2];
- uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask, inf, minus_one;
- int64x2_t one_top;
-} data = {
- /* Generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */
- .poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2),
- V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3),
- V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3),
- V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4),
- V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4),
- V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4),
- V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4),
- V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5),
- V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4),
- V2 (-0x1.cfa7385bdb37ep-6) },
- .ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) },
- /* top32(asuint64(sqrt(2)/2)) << 32. */
- .hf_rt2_top = V2 (0x3fe6a09e00000000),
- /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */
- .one_m_hf_rt2_top = V2 (0x00095f6200000000),
- .umask = V2 (0x000fffff00000000),
- .one_top = V2 (0x3ff),
- .inf = V2 (0x7ff0000000000000),
- .minus_one = V2 (0xbff0000000000000)
-};
+ struct v_log1p_data d;
+ uint64x2_t inf, minus_one;
+} data = { .d = V_LOG1P_CONSTANTS_TABLE,
+ .inf = V2 (0x7ff0000000000000),
+ .minus_one = V2 (0xbff0000000000000) };
#define BottomMask v_u64 (0xffffffff)
-static float64x2_t VPCS_ATTR NOINLINE
-special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
+static float64x2_t NOINLINE VPCS_ATTR
+special_case (float64x2_t x, uint64x2_t cmp, const struct data *d)
{
- return v_call_f64 (log1p, x, y, special);
+ /* Side-step special lanes so fenv exceptions are not triggered
+ inadvertently. */
+ float64x2_t x_nospecial = v_zerofy_f64 (x, cmp);
+ return v_call_f64 (log1p, x, log1p_inline (x_nospecial, &d->d), cmp);
}
/* Vector log1p approximation using polynomial on reduced interval. Routine is
const struct data *d = ptr_barrier (&data);
uint64x2_t ix = vreinterpretq_u64_f64 (x);
uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
- uint64x2_t special = vcgeq_u64 (ia, d->inf);
-#if WANT_SIMD_EXCEPT
- special = vorrq_u64 (special,
- vcgeq_u64 (ix, vreinterpretq_u64_f64 (v_f64 (-1))));
- if (__glibc_unlikely (v_any_u64 (special)))
- x = v_zerofy_f64 (x, special);
-#else
- special = vorrq_u64 (special, vcleq_f64 (x, v_f64 (-1)));
-#endif
+ uint64x2_t special_cases
+ = vorrq_u64 (vcgeq_u64 (ia, d->inf), vcgeq_u64 (ix, d->minus_one));
- /* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f
- is in [sqrt(2)/2, sqrt(2)]):
- log1p(x) = k*log(2) + log1p(f).
+ if (__glibc_unlikely (v_any_u64 (special_cases)))
+ return special_case (x, special_cases, d);
- f may not be representable exactly, so we need a correction term:
- let m = round(1 + x), c = (1 + x) - m.
- c << m: at very small x, log1p(x) ~ x, hence:
- log(1+x) - log(m) ~ c/m.
-
- We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */
-
- /* Obtain correctly scaled k by manipulation in the exponent.
- The scalar algorithm casts down to 32-bit at this point to calculate k and
- u_red. We stay in double-width to obtain f and k, using the same constants
- as the scalar algorithm but shifted left by 32. */
- float64x2_t m = vaddq_f64 (x, v_f64 (1));
- uint64x2_t mi = vreinterpretq_u64_f64 (m);
- uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top);
-
- int64x2_t ki
- = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top);
- float64x2_t k = vcvtq_f64_s64 (ki);
-
- /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
- uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top);
- uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask));
- float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1));
-
- /* Correction term c/m. */
- float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m);
-
- /* Approximate log1p(x) on the reduced input using a polynomial. Because
- log1p(0)=0 we choose an approximation of the form:
- x + C0*x^2 + C1*x^3 + C2x^4 + ...
- Hence approximation has the form f + f^2 * P(f)
- where P(x) = C0 + C1*x + C2x^2 + ...
- Assembling this all correctly is dealt with at the final step. */
- float64x2_t f2 = vmulq_f64 (f, f);
- float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly);
-
- float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]);
- float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]);
- float64x2_t y = vaddq_f64 (ylo, yhi);
-
- if (__glibc_unlikely (v_any_u64 (special)))
- return special_case (vreinterpretq_f64_u64 (ix), vfmaq_f64 (y, f2, p),
- special);
-
- return vfmaq_f64 (y, f2, p);
+ return log1p_inline (x, &d->d);
}
strong_alias (V_NAME_D1 (log1p), V_NAME_D1 (logp1))
#define AARCH64_FPU_V_LOG1P_INLINE_H
#include "v_math.h"
-#include "poly_advsimd_f64.h"
struct v_log1p_data
{
- float64x2_t poly[19], ln2[2];
+ float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16;
uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask;
int64x2_t one_top;
+ double c1, c3, c5, c7, c9, c11, c13, c15, c17, c18;
+ double ln2[2];
};
/* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */
#define V_LOG1P_CONSTANTS_TABLE \
{ \
- .poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2), \
- V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3), \
- V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3), \
- V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4), \
- V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4), \
- V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4), \
- V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4), \
- V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5), \
- V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4), \
- V2 (-0x1.cfa7385bdb37ep-6) }, \
- .ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) }, \
+ .c0 = V2 (-0x1.ffffffffffffbp-2), .c1 = 0x1.55555555551a9p-2, \
+ .c2 = V2 (-0x1.00000000008e3p-2), .c3 = 0x1.9999999a32797p-3, \
+ .c4 = V2 (-0x1.555555552fecfp-3), .c5 = 0x1.249248e071e5ap-3, \
+ .c6 = V2 (-0x1.ffffff8bf8482p-4), .c7 = 0x1.c71c8f07da57ap-4, \
+ .c8 = V2 (-0x1.9999ca4ccb617p-4), .c9 = 0x1.7459ad2e1dfa3p-4, \
+ .c10 = V2 (-0x1.554d2680a3ff2p-4), .c11 = 0x1.3b4c54d487455p-4, \
+ .c12 = V2 (-0x1.2548a9ffe80e6p-4), .c13 = 0x1.0f389a24b2e07p-4, \
+ .c14 = V2 (-0x1.eee4db15db335p-5), .c15 = 0x1.e95b494d4a5ddp-5, \
+ .c16 = V2 (-0x1.15fdf07cb7c73p-4), .c17 = 0x1.0310b70800fcfp-4, \
+ .c18 = -0x1.cfa7385bdb37ep-6, \
+ .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 }, \
.hf_rt2_top = V2 (0x3fe6a09e00000000), \
.one_m_hf_rt2_top = V2 (0x00095f6200000000), \
.umask = V2 (0x000fffff00000000), .one_top = V2 (0x3ff) \
#define BottomMask v_u64 (0xffffffff)
+static inline float64x2_t
+eval_poly (float64x2_t m, float64x2_t m2, const struct v_log1p_data *d)
+{
+ /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */
+ float64x2_t c13 = vld1q_f64 (&d->c1);
+ float64x2_t c57 = vld1q_f64 (&d->c5);
+ float64x2_t c911 = vld1q_f64 (&d->c9);
+ float64x2_t c1315 = vld1q_f64 (&d->c13);
+ float64x2_t c1718 = vld1q_f64 (&d->c17);
+ float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, m, c1718, 0);
+ float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, m, c1315, 1);
+ float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, m, c1315, 0);
+ float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, m, c911, 1);
+ float64x2_t p89 = vfmaq_laneq_f64 (d->c8, m, c911, 0);
+ float64x2_t p67 = vfmaq_laneq_f64 (d->c6, m, c57, 1);
+ float64x2_t p45 = vfmaq_laneq_f64 (d->c4, m, c57, 0);
+ float64x2_t p23 = vfmaq_laneq_f64 (d->c2, m, c13, 1);
+ float64x2_t p01 = vfmaq_laneq_f64 (d->c0, m, c13, 0);
+ float64x2_t p = vfmaq_laneq_f64 (p1617, m2, c1718, 1);
+ p = vfmaq_f64 (p1415, m2, p);
+ p = vfmaq_f64 (p1213, m2, p);
+ p = vfmaq_f64 (p1011, m2, p);
+ p = vfmaq_f64 (p89, m2, p);
+ p = vfmaq_f64 (p67, m2, p);
+ p = vfmaq_f64 (p45, m2, p);
+ p = vfmaq_f64 (p23, m2, p);
+ return vfmaq_f64 (p01, m2, p);
+}
+
static inline float64x2_t
log1p_inline (float64x2_t x, const struct v_log1p_data *d)
{
- /* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several
- modifications:
+ /* Helper for calculating log(x + 1):
- No special-case handling - this should be dealt with by the caller.
- - Pairwise Horner polynomial evaluation for improved accuracy.
- Optionally simulate the shortcut for k=0, used in the scalar routine,
- using v_sel, for improved accuracy when the argument to log1p is close to
- 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in
- the source of the caller before including this file.
- See v_log1pf_2u1.c for details of the algorithm. */
- float64x2_t m = vaddq_f64 (x, v_f64 (1));
+ using v_sel, for improved accuracy when the argument to log1p is close
+ to 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1
+ in the source of the caller before including this file. */
+ float64x2_t m = vaddq_f64 (x, v_f64 (1.0));
uint64x2_t mi = vreinterpretq_u64_f64 (m);
uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top);
/* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top);
uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask));
- float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1));
+ float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1.0));
/* Correction term c/m. */
- float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m);
+ float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1.0))), m);
#ifndef WANT_V_LOG1P_K0_SHORTCUT
-#error \
- "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
+# error \
+ "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
#elif WANT_V_LOG1P_K0_SHORTCUT
/* Shortcut if k is 0 - set correction term to 0 and f to x. The result is
that the approximation is solely the polynomial. */
/* Approximate log1p(f) on the reduced input using a polynomial. */
float64x2_t f2 = vmulq_f64 (f, f);
- float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly);
+ float64x2_t p = eval_poly (f, f2, d);
/* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */
- float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]);
- float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]);
+ float64x2_t ln2 = vld1q_f64 (&d->ln2[0]);
+ float64x2_t ylo = vfmaq_laneq_f64 (cm, k, ln2, 1);
+ float64x2_t yhi = vfmaq_laneq_f64 (f, k, ln2, 0);
return vfmaq_f64 (vaddq_f64 (ylo, yhi), f2, p);
}
projects / thirdparty / glibc.git / commitdiff
