@@ -23,7 +23,7 @@ static const struct data
{
float64_t poly[3];
float64_t inv_ln2, ln2_hi, ln2_lo, shift, thres;
- uint64_t index_mask, special_bound;
+ uint64_t special_bound;
} data = {
.poly = { 0x1.fffffffffffd4p-2, 0x1.5555571d6b68cp-3,
0x1.5555576a59599p-5, },
@@ -35,14 +35,16 @@ static const struct data
.shift = 0x1.8p+52,
.thres = 704.0,
- .index_mask = 0xff,
/* 0x1.6p9, above which exp overflows. */
.special_bound = 0x4086000000000000,
};
static svfloat64_t NOINLINE
-special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
+special_case (svfloat64_t x, svbool_t pg, svfloat64_t t, svbool_t special)
{
+ svfloat64_t half_t = svmul_x (svptrue_b64 (), t, 0.5);
+ svfloat64_t half_over_t = svdivr_x (pg, t, 0.5);
+ svfloat64_t y = svadd_x (pg, half_t, half_over_t);
return sv_call_f64 (cosh, x, y, special);
}
@@ -60,12 +62,12 @@ exp_inline (svfloat64_t x, const svbool_t pg, const struct data *d)
svuint64_t u = svreinterpret_u64 (z);
svuint64_t e = svlsl_x (pg, u, 52 - V_EXP_TAIL_TABLE_BITS);
- svuint64_t i = svand_x (pg, u, d->index_mask);
+ svuint64_t i = svand_x (svptrue_b64 (), u, 0xff);
svfloat64_t y = svmla_x (pg, sv_f64 (d->poly[1]), r, d->poly[2]);
y = svmla_x (pg, sv_f64 (d->poly[0]), r, y);
y = svmla_x (pg, sv_f64 (1.0), r, y);
- y = svmul_x (pg, r, y);
+ y = svmul_x (svptrue_b64 (), r, y);
/* s = 2^(n/N). */
u = svld1_gather_index (pg, __v_exp_tail_data, i);
@@ -94,12 +96,12 @@ svfloat64_t SV_NAME_D1 (cosh) (svfloat64_t x, const svbool_t pg)
/* Up to the point that exp overflows, we can use it to calculate cosh by
exp(|x|) / 2 + 1 / (2 * exp(|x|)). */
svfloat64_t t = exp_inline (ax, pg, d);
- svfloat64_t half_t = svmul_x (pg, t, 0.5);
- svfloat64_t half_over_t = svdivr_x (pg, t, 0.5);
/* Fall back to scalar for any special cases. */
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svadd_x (pg, half_t, half_over_t), special);
+ return special_case (x, pg, t, special);
+ svfloat64_t half_t = svmul_x (svptrue_b64 (), t, 0.5);
+ svfloat64_t half_over_t = svdivr_x (pg, t, 0.5);
return svadd_x (pg, half_t, half_over_t);
}
@@ -18,21 +18,23 @@
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
-#include "poly_sve_f64.h"
#define SpecialBound 307.0 /* floor (log10 (2^1023)). */
static const struct data
{
- double poly[5];
+ double c1, c3, c2, c4, c0;
double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
} data = {
/* Coefficients generated using Remez algorithm.
rel error: 0x1.9fcb9b3p-60
abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
max ulp err 0.52 +0.5. */
- .poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
- 0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
+ .c0 = 0x1.26bb1bbb55516p1,
+ .c1 = 0x1.53524c73cd32ap1,
+ .c2 = 0x1.0470591daeafbp1,
+ .c3 = 0x1.2bd77b1361ef6p0,
+ .c4 = 0x1.142b5d54e9621p-1,
/* 1.5*2^46+1023. This value is further explained below. */
.shift = 0x1.800000000ffc0p+46,
.log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */
@@ -70,9 +72,9 @@ special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
/* |n| > 1280 => 2^(n) overflows. */
svbool_t p_cmp = svacgt (pg, n, d->scale_thres);
- svfloat64_t r1 = svmul_x (pg, s1, s1);
+ svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
svfloat64_t r2 = svmla_x (pg, s2, s2, y);
- svfloat64_t r0 = svmul_x (pg, r2, s1);
+ svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
return svsel (p_cmp, r1, r0);
}
@@ -103,11 +105,14 @@ svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
comes at significant performance cost. */
svuint64_t u = svreinterpret_u64 (z);
svfloat64_t scale = svexpa (u);
-
+ svfloat64_t c24 = svld1rq (svptrue_b64 (), &d->c2);
/* Approximate exp10(r) using polynomial. */
- svfloat64_t r2 = svmul_x (pg, r, r);
- svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
- sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly + 1));
+ svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+ svfloat64_t p12 = svmla_lane (sv_f64 (d->c1), r, c24, 0);
+ svfloat64_t p34 = svmla_lane (sv_f64 (d->c3), r, c24, 1);
+ svfloat64_t p14 = svmla_x (pg, p12, p34, r2);
+
+ svfloat64_t y = svmla_x (pg, svmul_x (svptrue_b64 (), r, d->c0), r2, p14);
/* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
multiplication may overflow, so use special case routine. */
@@ -18,7 +18,6 @@
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
-#include "poly_sve_f64.h"
#define N (1 << V_EXP_TABLE_BITS)
@@ -27,15 +26,15 @@
static const struct data
{
- double poly[4];
+ double c0, c2;
+ double c1, c3;
double shift, big_bound, uoflow_bound;
} data = {
/* Coefficients are computed using Remez algorithm with
minimisation of the absolute error. */
- .poly = { 0x1.62e42fefa3686p-1, 0x1.ebfbdff82c241p-3, 0x1.c6b09b16de99ap-5,
- 0x1.3b2abf5571ad8p-7 },
- .shift = 0x1.8p52 / N,
- .uoflow_bound = UOFlowBound,
+ .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3,
+ .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7,
+ .shift = 0x1.8p52 / N, .uoflow_bound = UOFlowBound,
.big_bound = BigBound,
};
@@ -67,9 +66,9 @@ special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
/* |n| > 1280 => 2^(n) overflows. */
svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound);
- svfloat64_t r1 = svmul_x (pg, s1, s1);
+ svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
svfloat64_t r2 = svmla_x (pg, s2, s2, y);
- svfloat64_t r0 = svmul_x (pg, r2, s1);
+ svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
return svsel (p_cmp, r1, r0);
}
@@ -99,11 +98,14 @@ svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
+ svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
/* Approximate exp2(r) using polynomial. */
- svfloat64_t r2 = svmul_x (pg, r, r);
- svfloat64_t p = sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly);
- svfloat64_t y = svmul_x (pg, r, p);
-
+ /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */
+ svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+ svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
+ svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
+ svfloat64_t p = svmla_x (pg, p01, p23, r2);
+ svfloat64_t y = svmul_x (svptrue_b64 (), r, p);
/* Assemble exp2(x) = exp2(r) * scale. */
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (pg, scale, y, kd, d);
@@ -21,12 +21,15 @@
static const struct data
{
- double poly[4];
+ double c0, c2;
+ double c1, c3;
double ln2_hi, ln2_lo, inv_ln2, shift, thres;
+
} data = {
- .poly = { /* ulp error: 0.53. */
- 0x1.fffffffffdbcdp-2, 0x1.555555555444cp-3, 0x1.555573c6a9f7dp-5,
- 0x1.1111266d28935p-7 },
+ .c0 = 0x1.fffffffffdbcdp-2,
+ .c1 = 0x1.555555555444cp-3,
+ .c2 = 0x1.555573c6a9f7dp-5,
+ .c3 = 0x1.1111266d28935p-7,
.ln2_hi = 0x1.62e42fefa3800p-1,
.ln2_lo = 0x1.ef35793c76730p-45,
/* 1/ln2. */
@@ -36,7 +39,6 @@ static const struct data
.thres = 704.0,
};
-#define C(i) sv_f64 (d->poly[i])
#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
@@ -56,20 +58,20 @@ special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n)
svuint64_t b
= svdup_u64_z (p_sign, SpecialOffset); /* Inactive lanes set to 0. */
- /* Set s1 to generate overflow depending on sign of exponent n. */
- svfloat64_t s1 = svreinterpret_f64 (
- svsubr_x (pg, b, SpecialBias1)); /* 0x70...0 - b. */
- /* Offset s to avoid overflow in final result if n is below threshold. */
+ /* Set s1 to generate overflow depending on sign of exponent n,
+ ie. s1 = 0x70...0 - b. */
+ svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
+ /* Offset s to avoid overflow in final result if n is below threshold.
+ ie. s2 = as_u64 (s) - 0x3010...0 + b. */
svfloat64_t s2 = svreinterpret_f64 (
- svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2),
- b)); /* as_u64 (s) - 0x3010...0 + b. */
+ svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
/* |n| > 1280 => 2^(n) overflows. */
svbool_t p_cmp = svacgt (pg, n, 1280.0);
- svfloat64_t r1 = svmul_x (pg, s1, s1);
+ svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
svfloat64_t r2 = svmla_x (pg, s2, s2, y);
- svfloat64_t r0 = svmul_x (pg, r2, s1);
+ svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
return svsel (p_cmp, r1, r0);
}
@@ -103,16 +105,16 @@ svfloat64_t SV_NAME_D1 (exp) (svfloat64_t x, const svbool_t pg)
svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2);
svuint64_t u = svreinterpret_u64 (z);
svfloat64_t n = svsub_x (pg, z, d->shift);
-
+ svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
/* r = x - n * ln2, r is in [-ln2/(2N), ln2/(2N)]. */
svfloat64_t ln2 = svld1rq (svptrue_b64 (), &d->ln2_hi);
svfloat64_t r = svmls_lane (x, n, ln2, 0);
r = svmls_lane (r, n, ln2, 1);
/* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5. */
- svfloat64_t r2 = svmul_x (pg, r, r);
- svfloat64_t p01 = svmla_x (pg, C (0), C (1), r);
- svfloat64_t p23 = svmla_x (pg, C (2), C (3), r);
+ svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+ svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
+ svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
svfloat64_t p04 = svmla_x (pg, p01, p23, r2);
svfloat64_t y = svmla_x (pg, r, p04, r2);
@@ -61,7 +61,7 @@ expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d)
/* scale = 2^(n/N). */
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
- /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
+ /* poly(r) = exp(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4 + C4 r^5. */
svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, lane_consts, 2);
svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, lane_consts, 3);
svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
@@ -71,5 +71,4 @@ expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d)
return svmla_x (pg, scale, scale, poly);
}
-
-#endif
+#endif
\ No newline at end of file