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(l: &Xll, x: -2 - exponent) >= 0x80000000U) |
91 | Xll++; /* round up */ |
92 | } |
93 | |
94 | accumulator.lsw = accumulator.midw = accumulator.msw = 0; |
95 | polynomial_Xsig(&accumulator, x: &Xll, terms: lterms, HIPOWER - 1); |
96 | mul_Xsig_Xsig(dest: &accumulator, mult: &argSignif); |
97 | shr_Xsig(&accumulator, n: 3); |
98 | |
99 | mul_Xsig_Xsig(dest: &argSignif, mult: &hiterm); /* The leading term */ |
100 | add_two_Xsig(dest: &accumulator, x2: &argSignif, exp: &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, n: -exponent); |
107 | accumulator.msw |= 0x80000000; /* add 1.0 */ |
108 | mul_Xsig_Xsig(dest: &accumulator, mult: 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, n: -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(x1: &accumulator, x2: &Denom, dest: &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(arg: result, extent: 1, dummy: 0, FULL_PRECISION, sign); |
140 | |
141 | setsign(result, sign); |
142 | FPU_settag0(tag); |
143 | |
144 | return 0; |
145 | |
146 | } |
147 | |