1/*
2 * Single-precision vector powf function.
3 *
4 * Copyright (c) 2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8#include "mathlib.h"
9#include "v_math.h"
10#if V_SUPPORTED
11
12#define Min v_u32 (0x00800000)
13#define Max v_u32 (0x7f800000)
14#define SBITS 5
15#define Tlog v__powf_log2_data.tab
16#define Texp v__exp2f_data.tab
17#define A v__powf_log2_data.poly
18#define C v__exp2f_data.poly
19#define LOGDEG 4
20
21#if LOGDEG == 5
22/* 1.01 ulp */
23#define OFF v_u32 (0x3f330000)
24#define TBITS 4
25#elif LOGDEG == 4
26/* 2.6 ulp ~ 0.5 + 2^24 (128*Ln2*relerr_log2 + relerr_exp2) */
27#define OFF v_u32 (0x3f35d000)
28#define TBITS 5
29#endif
30
31#define V_EXP2F_TABLE_BITS SBITS
32#define V_EXP2F_POLY_ORDER 3
33struct v_exp2f_data
34{
35  uint64_t tab[1 << V_EXP2F_TABLE_BITS];
36  double poly[V_EXP2F_POLY_ORDER];
37};
38
39#define V_POWF_LOG2_TABLE_BITS TBITS
40#define V_POWF_LOG2_POLY_ORDER LOGDEG
41#define SCALE ((double) (1 << SBITS))
42struct v_powf_log2_data
43{
44  struct
45  {
46    double invc, logc;
47  } tab[1 << V_POWF_LOG2_TABLE_BITS];
48  double poly[V_POWF_LOG2_POLY_ORDER];
49};
50
51static const struct v_powf_log2_data v__powf_log2_data = {
52#if LOGDEG == 5
53  .tab = {
54{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * SCALE },
55{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * SCALE },
56{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * SCALE },
57{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * SCALE },
58{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * SCALE },
59{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * SCALE },
60{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * SCALE },
61{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * SCALE },
62{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * SCALE },
63{ 0x1p+0, 0x0p+0 * SCALE },
64{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * SCALE },
65{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * SCALE },
66{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * SCALE },
67{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * SCALE },
68{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * SCALE },
69{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * SCALE },
70  },
71/* rel err: 1.46 * 2^-32 */
72  .poly = {
730x1.27616c9496e0bp-2 * SCALE, -0x1.71969a075c67ap-2 * SCALE,
740x1.ec70a6ca7baddp-2 * SCALE, -0x1.7154748bef6c8p-1 * SCALE,
750x1.71547652ab82bp0 * SCALE,
76  }
77#elif LOGDEG == 4
78  .tab = {
79{0x1.6489890582816p+0, -0x1.e960f97b22702p-2 * SCALE},
80{0x1.5cf19b35e3472p+0, -0x1.c993406cd4db6p-2 * SCALE},
81{0x1.55aac0e956d65p+0, -0x1.aa711d9a7d0f3p-2 * SCALE},
82{0x1.4eb0022977e01p+0, -0x1.8bf37bacdce9bp-2 * SCALE},
83{0x1.47fcccda1dd1fp+0, -0x1.6e13b3519946ep-2 * SCALE},
84{0x1.418ceabab68c1p+0, -0x1.50cb8281e4089p-2 * SCALE},
85{0x1.3b5c788f1edb3p+0, -0x1.341504a237e2bp-2 * SCALE},
86{0x1.3567de48e9c9ap+0, -0x1.17eaab624ffbbp-2 * SCALE},
87{0x1.2fabc80fd19bap+0, -0x1.f88e708f8c853p-3 * SCALE},
88{0x1.2a25200ce536bp+0, -0x1.c24b6da113914p-3 * SCALE},
89{0x1.24d108e0152e3p+0, -0x1.8d02ee397cb1dp-3 * SCALE},
90{0x1.1facd8ab2fbe1p+0, -0x1.58ac1223408b3p-3 * SCALE},
91{0x1.1ab614a03efdfp+0, -0x1.253e6fd190e89p-3 * SCALE},
92{0x1.15ea6d03af9ffp+0, -0x1.e5641882c12ffp-4 * SCALE},
93{0x1.1147b994bb776p+0, -0x1.81fea712926f7p-4 * SCALE},
94{0x1.0ccbf650593aap+0, -0x1.203e240de64a3p-4 * SCALE},
95{0x1.0875408477302p+0, -0x1.8029b86a78281p-5 * SCALE},
96{0x1.0441d42a93328p+0, -0x1.85d713190fb9p-6 * SCALE},
97{0x1p+0, 0x0p+0 * SCALE},
98{0x1.f1d006c855e86p-1, 0x1.4c1cc07312997p-5 * SCALE},
99{0x1.e28c3341aa301p-1, 0x1.5e1848ccec948p-4 * SCALE},
100{0x1.d4bdf9aa64747p-1, 0x1.04cfcb7f1196fp-3 * SCALE},
101{0x1.c7b45a24e5803p-1, 0x1.582813d463c21p-3 * SCALE},
102{0x1.bb5f5eb2ed60ap-1, 0x1.a936fa68760ccp-3 * SCALE},
103{0x1.afb0bff8fe6b4p-1, 0x1.f81bc31d6cc4ep-3 * SCALE},
104{0x1.a49badf7ab1f5p-1, 0x1.2279a09fae6b1p-2 * SCALE},
105{0x1.9a14a111fc4c9p-1, 0x1.47ec0b6df5526p-2 * SCALE},
106{0x1.901131f5b2fdcp-1, 0x1.6c71762280f1p-2 * SCALE},
107{0x1.8687f73f6d865p-1, 0x1.90155070798dap-2 * SCALE},
108{0x1.7d7067eb77986p-1, 0x1.b2e23b1d3068cp-2 * SCALE},
109{0x1.74c2c1cf97b65p-1, 0x1.d4e21b0daa86ap-2 * SCALE},
110{0x1.6c77f37cff2a1p-1, 0x1.f61e2a2f67f3fp-2 * SCALE},
111  },
112/* rel err: 1.5 * 2^-30 */
113  .poly = {
114 -0x1.6ff5daa3b3d7cp-2 * SCALE,
115 0x1.ec81d03c01aebp-2 * SCALE,
116 -0x1.71547bb43f101p-1 * SCALE,
117 0x1.7154764a815cbp0 * SCALE,
118  }
119#endif
120};
121
122static const struct v_exp2f_data v__exp2f_data = {
123  .tab = {
1240x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
1250x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
1260x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
1270x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
1280x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
1290x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
1300x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
1310x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
132  },
133/* rel err: 1.69 * 2^-34 */
134  .poly = {
1350x1.c6af84b912394p-5/SCALE/SCALE/SCALE, 0x1.ebfce50fac4f3p-3/SCALE/SCALE, 0x1.62e42ff0c52d6p-1/SCALE
136  },
137};
138
139VPCS_ATTR
140__attribute__ ((noinline)) static v_f32_t
141specialcase (v_f32_t x, v_f32_t y, v_f32_t ret, v_u32_t cmp)
142{
143  return v_call2_f32 (powf, x, y, ret, cmp);
144}
145
146VPCS_ATTR
147v_f32_t
148V_NAME(powf) (v_f32_t x, v_f32_t y)
149{
150  v_u32_t u, tmp, cmp, i, top, iz;
151  v_s32_t k;
152  v_f32_t ret;
153
154  u = v_as_u32_f32 (x);
155  cmp = v_cond_u32 (u - Min >= Max - Min);
156  tmp = u - OFF;
157  i = (tmp >> (23 - TBITS)) % (1 << TBITS);
158  top = tmp & 0xff800000;
159  iz = u - top;
160  k = v_as_s32_u32 (top) >> (23 - SBITS); /* arithmetic shift */
161
162  for (int lane = 0; lane < v_lanes32 (); lane++)
163    {
164      uint32_t si, siz;
165      int32_t sk;
166      float sy;
167
168      /* Use double precision for each lane.  */
169      double invc, logc, z, r, p, y0, logx, ylogx, kd, s;
170      uint64_t ki, t;
171
172      si = v_get_u32 (i, lane);
173      siz = v_get_u32 (iz, lane);
174      sk = v_get_s32 (k, lane);
175      sy = v_get_f32 (y, lane);
176
177      invc = Tlog[si].invc;
178      logc = Tlog[si].logc;
179      z = (double) as_f32_u32 (siz);
180
181      /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
182      r = __builtin_fma (z, invc, -1.0);
183      y0 = logc + (double) sk;
184
185      /* Polynomial to approximate log1p(r)/ln2.  */
186#if LOGDEG == 5
187      logx = A[0];
188      logx = r * logx + A[1];
189      logx = r * logx + A[2];
190      logx = r * logx + A[3];
191      logx = r * logx + A[4];
192      logx = r * logx + y0;
193#elif LOGDEG == 4
194      logx = A[0];
195      logx = r * logx + A[1];
196      logx = r * logx + A[2];
197      logx = r * logx + A[3];
198      logx = r * logx + y0;
199#endif
200      ylogx = sy * logx;
201      v_set_u32 (&cmp, lane,
202		 (as_u64_f64 (ylogx) >> 47 & 0xffff)
203		     >= as_u64_f64 (126.0 * (1 << SBITS)) >> 47
204		   ? 1
205		   : v_get_u32 (cmp, lane));
206
207      /* N*x = k + r with r in [-1/2, 1/2] */
208#if TOINT_INTRINSICS
209      kd = roundtoint (ylogx); /* k */
210      ki = converttoint (ylogx);
211#else
212# define SHIFT 0x1.8p52
213      kd = eval_as_double (ylogx + SHIFT);
214      ki = asuint64 (kd);
215      kd -= SHIFT;
216#endif
217      r = ylogx - kd;
218
219      /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
220      t = Texp[ki % (1 << SBITS)];
221      t += ki << (52 - SBITS);
222      s = as_f64_u64 (t);
223      p = C[0];
224      p = __builtin_fma (p, r, C[1]);
225      p = __builtin_fma (p, r, C[2]);
226      p = __builtin_fma (p, s * r, s);
227
228      v_set_f32 (&ret, lane, p);
229    }
230  if (unlikely (v_any_u32 (cmp)))
231    return specialcase (x, y, ret, cmp);
232  return ret;
233}
234VPCS_ALIAS
235#endif
236