@@ -22,11 +22,11 @@
static const struct data
{
- uint32x4_t min_norm;
+ uint32x4_t off, offset_lower_bound;
uint16x8_t special_bound;
+ uint32x4_t mantissa_mask;
float32x4_t poly[8];
float32x4_t inv_ln10, ln2;
- uint32x4_t off, mantissa_mask;
} data = {
/* Use order 9 for log10(1+x), i.e. order 8 for log10(1+x)/x, with x in
[-1/3, 1/3] (offset=2/3). Max. relative error: 0x1.068ee468p-25. */
@@ -35,18 +35,22 @@ static const struct data
V4 (-0x1.0fc92cp-4f), V4 (0x1.f5f76ap-5f) },
.ln2 = V4 (0x1.62e43p-1f),
.inv_ln10 = V4 (0x1.bcb7b2p-2f),
- .min_norm = V4 (0x00800000),
- .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
+ /* Lower bound is the smallest positive normal float 0x00800000. For
+ optimised register use subnormals are detected after offset has been
+ subtracted, so lower bound is 0x0080000 - offset (which wraps around). */
+ .offset_lower_bound = V4 (0x00800000 - 0x3f2aaaab),
+ .special_bound = V8 (0x7f00), /* top16(asuint32(inf) - 0x00800000). */
.off = V4 (0x3f2aaaab), /* 0.666667. */
.mantissa_mask = V4 (0x007fffff),
};
static float32x4_t VPCS_ATTR NOINLINE
-special_case (float32x4_t x, float32x4_t y, float32x4_t p, float32x4_t r2,
- uint16x4_t cmp)
+special_case (float32x4_t y, uint32x4_t u_off, float32x4_t p, float32x4_t r2,
+ uint16x4_t cmp, const struct data *d)
{
/* Fall back to scalar code. */
- return v_call_f32 (log10f, x, vfmaq_f32 (y, p, r2), vmovl_u16 (cmp));
+ return v_call_f32 (log10f, vreinterpretq_f32_u32 (vaddq_u32 (u_off, d->off)),
+ vfmaq_f32 (y, p, r2), vmovl_u16 (cmp));
}
/* Fast implementation of AdvSIMD log10f,
@@ -58,15 +62,21 @@ special_case (float32x4_t x, float32x4_t y, float32x4_t p, float32x4_t r2,
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log10) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
- uint32x4_t u = vreinterpretq_u32_f32 (x);
- uint16x4_t special = vcge_u16 (vsubhn_u32 (u, d->min_norm),
- vget_low_u16 (d->special_bound));
+
+ /* To avoid having to mov x out of the way, keep u after offset has been
+ applied, and recover x by adding the offset back in the special-case
+ handler. */
+ uint32x4_t u_off = vreinterpretq_u32_f32 (x);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
- u = vsubq_u32 (u, d->off);
+ u_off = vsubq_u32 (u_off, d->off);
float32x4_t n = vcvtq_f32_s32 (
- vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
- u = vaddq_u32 (vandq_u32 (u, d->mantissa_mask), d->off);
+ vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend. */
+
+ uint16x4_t special = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
+ vget_low_u16 (d->special_bound));
+
+ uint32x4_t u = vaddq_u32 (vandq_u32 (u_off, d->mantissa_mask), d->off);
float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
/* y = log10(1+r) + n * log10(2). */
@@ -77,7 +87,7 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log10) (float32x4_t x)
y = vmulq_f32 (y, d->inv_ln10);
if (__glibc_unlikely (v_any_u16h (special)))
- return special_case (x, y, poly, r2, special);
+ return special_case (y, u_off, poly, r2, special, d);
return vfmaq_f32 (y, poly, r2);
}
libmvec_hidden_def (V_NAME_F1 (log10))
@@ -22,9 +22,9 @@
static const struct data
{
- uint32x4_t min_norm;
+ uint32x4_t off, offset_lower_bound;
uint16x8_t special_bound;
- uint32x4_t off, mantissa_mask;
+ uint32x4_t mantissa_mask;
float32x4_t poly[9];
} data = {
/* Coefficients generated using Remez algorithm approximate
@@ -34,18 +34,22 @@ static const struct data
V4 (-0x1.715458p-1f), V4 (0x1.ec701cp-2f), V4 (-0x1.7171a4p-2f),
V4 (0x1.27a0b8p-2f), V4 (-0x1.e5143ep-3f), V4 (0x1.9d8ecap-3f),
V4 (-0x1.c675bp-3f), V4 (0x1.9e495p-3f) },
- .min_norm = V4 (0x00800000),
- .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
+ /* Lower bound is the smallest positive normal float 0x00800000. For
+ optimised register use subnormals are detected after offset has been
+ subtracted, so lower bound is 0x0080000 - offset (which wraps around). */
+ .offset_lower_bound = V4 (0x00800000 - 0x3f2aaaab),
+ .special_bound = V8 (0x7f00), /* top16(asuint32(inf) - 0x00800000). */
.off = V4 (0x3f2aaaab), /* 0.666667. */
.mantissa_mask = V4 (0x007fffff),
};
static float32x4_t VPCS_ATTR NOINLINE
-special_case (float32x4_t x, float32x4_t n, float32x4_t p, float32x4_t r,
- uint16x4_t cmp)
+special_case (float32x4_t n, uint32x4_t u_off, float32x4_t p, float32x4_t r,
+ uint16x4_t cmp, const struct data *d)
{
/* Fall back to scalar code. */
- return v_call_f32 (log2f, x, vfmaq_f32 (n, p, r), vmovl_u16 (cmp));
+ return v_call_f32 (log2f, vreinterpretq_f32_u32 (vaddq_u32 (u_off, d->off)),
+ vfmaq_f32 (n, p, r), vmovl_u16 (cmp));
}
/* Fast implementation for single precision AdvSIMD log2,
@@ -56,15 +60,21 @@ special_case (float32x4_t x, float32x4_t n, float32x4_t p, float32x4_t r,
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log2) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
- uint32x4_t u = vreinterpretq_u32_f32 (x);
- uint16x4_t special = vcge_u16 (vsubhn_u32 (u, d->min_norm),
- vget_low_u16 (d->special_bound));
+
+ /* To avoid having to mov x out of the way, keep u after offset has been
+ applied, and recover x by adding the offset back in the special-case
+ handler. */
+ uint32x4_t u_off = vreinterpretq_u32_f32 (x);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
- u = vsubq_u32 (u, d->off);
+ u_off = vsubq_u32 (u_off, d->off);
float32x4_t n = vcvtq_f32_s32 (
- vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
- u = vaddq_u32 (vandq_u32 (u, d->mantissa_mask), d->off);
+ vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend. */
+
+ uint16x4_t special = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
+ vget_low_u16 (d->special_bound));
+
+ uint32x4_t u = vaddq_u32 (vandq_u32 (u_off, d->mantissa_mask), d->off);
float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
/* y = log2(1+r) + n. */
@@ -72,7 +82,7 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log2) (float32x4_t x)
float32x4_t p = v_pw_horner_8_f32 (r, r2, d->poly);
if (__glibc_unlikely (v_any_u16h (special)))
- return special_case (x, n, p, r, special);
+ return special_case (n, u_off, p, r, special, d);
return vfmaq_f32 (n, p, r);
}
libmvec_hidden_def (V_NAME_F1 (log2))
@@ -21,20 +21,22 @@
static const struct data
{
- uint32x4_t min_norm;
+ uint32x4_t off, offset_lower_bound;
uint16x8_t special_bound;
+ uint32x4_t mantissa_mask;
float32x4_t poly[7];
- float32x4_t ln2, tiny_bound;
- uint32x4_t off, mantissa_mask;
+ float32x4_t ln2;
} data = {
/* 3.34 ulp error. */
.poly = { V4 (-0x1.3e737cp-3f), V4 (0x1.5a9aa2p-3f), V4 (-0x1.4f9934p-3f),
V4 (0x1.961348p-3f), V4 (-0x1.00187cp-2f), V4 (0x1.555d7cp-2f),
V4 (-0x1.ffffc8p-2f) },
.ln2 = V4 (0x1.62e43p-1f),
- .tiny_bound = V4 (0x1p-126),
- .min_norm = V4 (0x00800000),
- .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
+ /* Lower bound is the smallest positive normal float 0x00800000. For
+ optimised register use subnormals are detected after offset has been
+ subtracted, so lower bound is 0x0080000 - offset (which wraps around). */
+ .offset_lower_bound = V4 (0x00800000 - 0x3f2aaaab),
+ .special_bound = V8 (0x7f00), /* top16(asuint32(inf) - 0x00800000). */
.off = V4 (0x3f2aaaab), /* 0.666667. */
.mantissa_mask = V4 (0x007fffff)
};
@@ -42,32 +44,37 @@ static const struct data
#define P(i) d->poly[7 - i]
static float32x4_t VPCS_ATTR NOINLINE
-special_case (float32x4_t x, float32x4_t y, float32x4_t r2, float32x4_t p,
- uint16x4_t cmp)
+special_case (float32x4_t p, uint32x4_t u_off, float32x4_t y, float32x4_t r2,
+ uint16x4_t cmp, const struct data *d)
{
/* Fall back to scalar code. */
- return v_call_f32 (logf, x, vfmaq_f32 (p, y, r2), vmovl_u16 (cmp));
+ return v_call_f32 (logf, vreinterpretq_f32_u32 (vaddq_u32 (u_off, d->off)),
+ vfmaq_f32 (p, y, r2), vmovl_u16 (cmp));
}
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
float32x4_t n, p, q, r, r2, y;
- uint32x4_t u;
+ uint32x4_t u, u_off;
uint16x4_t cmp;
- u = vreinterpretq_u32_f32 (x);
- cmp = vcge_u16 (vsubhn_u32 (u, d->min_norm),
- vget_low_u16 (d->special_bound));
+ /* To avoid having to mov x out of the way, keep u after offset has been
+ applied, and recover x by adding the offset back in the special-case
+ handler. */
+ u_off = vreinterpretq_u32_f32 (x);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
- u = vsubq_u32 (u, d->off);
+ u_off = vsubq_u32 (u_off, d->off);
n = vcvtq_f32_s32 (
- vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
- u = vandq_u32 (u, d->mantissa_mask);
+ vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend. */
+ u = vandq_u32 (u_off, d->mantissa_mask);
u = vaddq_u32 (u, d->off);
r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
+ cmp = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
+ vget_low_u16 (d->special_bound));
+
/* y = log(1+r) + n*ln2. */
r2 = vmulq_f32 (r, r);
/* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
@@ -80,7 +87,7 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log) (float32x4_t x)
p = vfmaq_f32 (r, d->ln2, n);
if (__glibc_unlikely (v_any_u16h (cmp)))
- return special_case (x, y, r2, p, cmp);
+ return special_case (p, u_off, y, r2, cmp, d);
return vfmaq_f32 (p, y, r2);
}
libmvec_hidden_def (V_NAME_F1 (log))