1 // SPDX-License-Identifier: GPL-2.0
2 /*---------------------------------------------------------------------------+
3 | poly_2xm1.c |
4 | |
5 | Function to compute 2^x-1 by a polynomial approximation. |
6 | |
7 | Copyright (C) 1992,1993,1994,1997 |
8 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
9 | E-mail billm@suburbia.net |
10 | |
11 | |
12 +---------------------------------------------------------------------------*/
13
14 #include "exception.h"
15 #include "reg_constant.h"
16 #include "fpu_emu.h"
17 #include "fpu_system.h"
18 #include "control_w.h"
19 #include "poly.h"
20
21 #define HIPOWER 11
22 static const unsigned long long lterms[HIPOWER] = {
23 0x0000000000000000LL, /* This term done separately as 12 bytes */
24 0xf5fdeffc162c7543LL,
25 0x1c6b08d704a0bfa6LL,
26 0x0276556df749cc21LL,
27 0x002bb0ffcf14f6b8LL,
28 0x0002861225ef751cLL,
29 0x00001ffcbfcd5422LL,
30 0x00000162c005d5f1LL,
31 0x0000000da96ccb1bLL,
32 0x0000000078d1b897LL,
33 0x000000000422b029LL
34 };
35
36 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
37
38 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
39 These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
40 */
41 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
42 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
43 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
44 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
45
46 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
47 &shiftterm2, &shiftterm3
48 };
49
50 /*--- poly_2xm1() -----------------------------------------------------------+
51 | Requires st(0) which is TAG_Valid and < 1. |
52 +---------------------------------------------------------------------------*/
53 int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
54 {
55 long int exponent, shift;
56 unsigned long long Xll;
57 Xsig accumulator, Denom, argSignif;
58 u_char tag;
59
60 exponent = exponent16(arg);
61
62 #ifdef PARANOID
63 if (exponent >= 0) { /* Don't want a |number| >= 1.0 */
64 /* Number negative, too large, or not Valid. */
65 EXCEPTION(EX_INTERNAL | 0x127);
66 return 1;
67 }
68 #endif /* PARANOID */
69
70 argSignif.lsw = 0;
71 XSIG_LL(argSignif) = Xll = significand(arg);
72
73 if (exponent == -1) {
74 shift = (argSignif.msw & 0x40000000) ? 3 : 2;
75 /* subtract 0.5 or 0.75 */
76 exponent -= 2;
77 XSIG_LL(argSignif) <<= 2;
78 Xll <<= 2;
79 } else if (exponent == -2) {
80 shift = 1;
81 /* subtract 0.25 */
82 exponent--;
83 XSIG_LL(argSignif) <<= 1;
84 Xll <<= 1;
85 } else
86 shift = 0;
87
88 if (exponent < -2) {
89 /* Shift the argument right by the required places. */
90 if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
91 Xll++; /* round up */
92 }
93
94 accumulator.lsw = accumulator.midw = accumulator.msw = 0;
95 polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
96 mul_Xsig_Xsig(&accumulator, &argSignif);
97 shr_Xsig(&accumulator, 3);
98
99 mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */
100 add_two_Xsig(&accumulator, &argSignif, &exponent);
101
102 if (shift) {
103 /* The argument is large, use the identity:
104 f(x+a) = f(a) * (f(x) + 1) - 1;
105 */
106 shr_Xsig(&accumulator, -exponent);
107 accumulator.msw |= 0x80000000; /* add 1.0 */
108 mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
109 accumulator.msw &= 0x3fffffff; /* subtract 1.0 */
110 exponent = 1;
111 }
112
113 if (sign != SIGN_POS) {
114 /* The argument is negative, use the identity:
115 f(-x) = -f(x) / (1 + f(x))
116 */
117 Denom.lsw = accumulator.lsw;
118 XSIG_LL(Denom) = XSIG_LL(accumulator);
119 if (exponent < 0)
120 shr_Xsig(&Denom, -exponent);
121 else if (exponent > 0) {
122 /* exponent must be 1 here */
123 XSIG_LL(Denom) <<= 1;
124 if (Denom.lsw & 0x80000000)
125 XSIG_LL(Denom) |= 1;
126 (Denom.lsw) <<= 1;
127 }
128 Denom.msw |= 0x80000000; /* add 1.0 */
129 div_Xsig(&accumulator, &Denom, &accumulator);
130 }
131
132 /* Convert to 64 bit signed-compatible */
133 exponent += round_Xsig(&accumulator);
134
135 result = &st(0);
136 significand(result) = XSIG_LL(accumulator);
137 setexponent16(result, exponent);
138
139 tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
140
141 setsign(result, sign);
142 FPU_settag0(tag);
143
144 return 0;
145
146 }