forked from OSchip/llvm-project
96 lines
2.6 KiB
C
96 lines
2.6 KiB
C
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/*
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* Double-precision vector e^x function.
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*
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* Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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* See https://llvm.org/LICENSE.txt for license information.
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* SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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*/
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#include "mathlib.h"
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#include "v_math.h"
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#if V_SUPPORTED
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#include "v_exp.h"
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#if V_EXP_TABLE_BITS == 7
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/* maxerr: 1.88 +0.5 ulp
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rel error: 1.4337*2^-53
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abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
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#define C1 v_f64 (0x1.ffffffffffd43p-2)
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#define C2 v_f64 (0x1.55555c75adbb2p-3)
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#define C3 v_f64 (0x1.55555da646206p-5)
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#define InvLn2 v_f64 (0x1.71547652b82fep7) /* N/ln2. */
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#define Ln2hi v_f64 (0x1.62e42fefa39efp-8) /* ln2/N. */
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#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-63)
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#elif V_EXP_TABLE_BITS == 8
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/* maxerr: 0.54 +0.5 ulp
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rel error: 1.4318*2^-58
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abs error: 1.4299*2^-58 in [ -ln2/512, ln2/512 ]. */
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#define C1 v_f64 (0x1.fffffffffffd4p-2)
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#define C2 v_f64 (0x1.5555571d6b68cp-3)
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#define C3 v_f64 (0x1.5555576a59599p-5)
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#define InvLn2 v_f64 (0x1.71547652b82fep8)
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#define Ln2hi v_f64 (0x1.62e42fefa39efp-9)
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#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-64)
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#endif
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#define N (1 << V_EXP_TABLE_BITS)
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#define Tab __v_exp_data
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#define IndexMask v_u64 (N - 1)
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#define Shift v_f64 (0x1.8p+52)
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#define Thres v_f64 (704.0)
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VPCS_ATTR
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static v_f64_t
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specialcase (v_f64_t s, v_f64_t y, v_f64_t n)
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{
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v_f64_t absn = v_abs_f64 (n);
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/* 2^(n/N) may overflow, break it up into s1*s2. */
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v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);
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v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);
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v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);
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v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));
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v_f64_t r1 = s1 * s1;
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v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;
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return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));
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}
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VPCS_ATTR
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v_f64_t
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V_NAME(exp) (v_f64_t x)
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{
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v_f64_t n, r, r2, s, y, z;
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v_u64_t cmp, u, e, i;
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cmp = v_cond_u64 (v_abs_f64 (x) > Thres);
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/* n = round(x/(ln2/N)). */
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z = v_fma_f64 (x, InvLn2, Shift);
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u = v_as_u64_f64 (z);
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n = z - Shift;
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/* r = x - n*ln2/N. */
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r = x;
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r = v_fma_f64 (-Ln2hi, n, r);
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r = v_fma_f64 (-Ln2lo, n, r);
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e = u << (52 - V_EXP_TABLE_BITS);
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i = u & IndexMask;
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/* y = exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
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r2 = r * r;
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y = v_fma_f64 (C2, r, C1);
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y = v_fma_f64 (C3, r2, y);
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y = v_fma_f64 (y, r2, r);
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/* s = 2^(n/N). */
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u = v_lookup_u64 (Tab, i);
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s = v_as_f64_u64 (u + e);
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if (unlikely (v_any_u64 (cmp)))
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return specialcase (s, y, n);
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return v_fma_f64 (y, s, s);
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}
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VPCS_ALIAS
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#endif
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