2  * Single-precision inverse error function (AdvSIMD variant).
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
18       formats to allow for table-based (vector-to-vector) lookup.
25       P_10 and Q_10 are also stored in homogenous vectors to allow better
35   .P29_3 = V4 (0x1.b13626p-2),
36   .tailshift = V4 (-0.87890625),
37   .Plo = { -0x1.a31268p+3, -0x1.fc0252p-4, 0x1.ac9048p+4, 0x1.119d44p+0 },
38   .PQ = { -0x1.293ff6p+3, -0x1.f59ee2p+0, -0x1.8265eep+3, -0x1.69952p-4 },
39   .Qhi = { 0x1.ef5eaep+4, 0x1.c7b7d2p-1, -0x1.12665p+4, -0x1.167d7p+1 },
40   .P_50 = { V4 (0x1.3d8948p-3), V4 (0x1.61f9eap+0), V4 (0x1.61c6bcp-1),
41 	    V4 (-0x1.20c9f2p+0), V4 (0x1.5c704cp-1), V4 (-0x1.50c6bep-3) },
42   .Q_50 = { V4 (0x1.3d7dacp-3), V4 (0x1.629e5p+0) },
43   .P_10 = { V4 (-0x1.a31268p+3), V4 (0x1.ac9048p+4), V4 (-0x1.293ff6p+3) },
44   .Q_10 = { V4 (-0x1.8265eep+3), V4 (0x1.ef5eaep+4), V4 (-0x1.12665p+4) },
53      these inputs, and values outside [-1, 1]. This is non-compliant, but is an  in special()
55      values use the log1pf_inline helper on -abs(x) - note that erfinvf(inf)  in special()
59 		     vsubq_f32 (v_f32 (1), vabsq_f32 (x)), &d->logf_tbl))));  in special()
61   float32x4_t q = vfmaq_f32 (d->Q_50[0], vaddq_f32 (t, d->Q_50[1]), t);  in special()
62   return vdivq_f32 (v_horner_5_f32 (t, d->P_50), vmulq_f32 (ts, q));  in special()
68   /* Shortcut when no input is in a tail region - no need to gather shift or  in notails()
70   float32x4_t t = vfmaq_f32 (v_f32 (-0.5625), x, x);  in notails()
71   float32x4_t q = vaddq_f32 (t, d->Q_10[2]);  in notails()
72   q = vfmaq_f32 (d->Q_10[1], t, q);  in notails()
73   q = vfmaq_f32 (d->Q_10[0], t, q);  in notails()
75   return vdivq_f32 (vmulq_f32 (x, v_horner_2_f32 (t, d->P_10)), q);  in notails()
85    error function in single-precision. Worst-case error is 4.98 ULP, in the
87    _ZGVnN4v_erfinvf(0x1.f7dbeep-1) got 0x1.b4793p+0
96       function", Math. Comp. 30, pp. 827--830 (1976).  in V_NAME_F1()
97      https://doi.org/10.1090/S0025-5718-1976-0421040-7.  in V_NAME_F1()
100      - 'Normal' region [-0.75, 0.75]  in V_NAME_F1()
101      - Tail region [0.75, 0.9375] U [-0.9375, -0.75]  in V_NAME_F1()
102      - Extreme tail [-1, -0.9375] U [0.9375, 1]  in V_NAME_F1()
104      shifted input - these are typically performed in parallel using gather  in V_NAME_F1()
110     /* Shortcut for if all lanes are in [-0.75, 0.75] - can avoid having to  in V_NAME_F1()
111        gather coefficients. If input is uniform in [-1, 1] then likelihood of  in V_NAME_F1()
116      x * x - shift.  in V_NAME_F1()
120       = vfmaq_f32 (vbslq_f32 (is_tail, d->tailshift, v_f32 (-0.5625)), x, x);  in V_NAME_F1()
122   /* Calculate indexes for tbl: tbl is byte-wise, so:  in V_NAME_F1()
124      Add 4 * i to a group of 4 lanes to copy 32-bit lane i. Each vector stores  in V_NAME_F1()
125      two pairs of coeffs, so we need two idx vectors - one for each pair.  */  in V_NAME_F1()
127   uint8x16_t idx_lo = vaddq_u8 (d->idxlo, off);  in V_NAME_F1()
128   uint8x16_t idx_hi = vaddq_u8 (d->idxhi, off);  in V_NAME_F1()
131   float32x4_t p_lo = d->Plo;  in V_NAME_F1()
132   float32x4_t pq = d->PQ;  in V_NAME_F1()
133   float32x4_t qhi = d->Qhi;  in V_NAME_F1()
135   /* Do the lookup (and calculate p3 by masking non-tail lanes).  */  in V_NAME_F1()
137       vandq_u32 (is_tail, vreinterpretq_u32_f32 (d->P29_3)));  in V_NAME_F1()
151     /* At least one lane is in the extreme tail - if input is uniform in  in V_NAME_F1()
152        [-1, 1] the likelihood of this is ~0.23.  */  in V_NAME_F1()
158 PL_SIG (V, F, 1, erfinv, -0.99, 0.99)
161 PL_TEST_SYM_INTERVAL_C (V_NAME_F1 (erfinv), 0, 0x1.fffffep-1, 40000, 0.5)
162 PL_TEST_SYM_INTERVAL_C (V_NAME_F1 (erfinv), 0, 0x1.fffffep-1, 40000, 0.8)
163 PL_TEST_SYM_INTERVAL_C (V_NAME_F1 (erfinv), 0, 0x1.fffffep-1, 40000, 0.95)