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b2441318 | 1 | // SPDX-License-Identifier: GPL-2.0 |
1da177e4 LT |
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 | ||
1da177e4 | 21 | #define HIPOWER 11 |
3d0d14f9 IM |
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 | |
1da177e4 LT |
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, | |
3d0d14f9 IM |
47 | &shiftterm2, &shiftterm3 |
48 | }; | |
1da177e4 LT |
49 | |
50 | /*--- poly_2xm1() -----------------------------------------------------------+ | |
51 | | Requires st(0) which is TAG_Valid and < 1. | | |
52 | +---------------------------------------------------------------------------*/ | |
e8d591dc | 53 | int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) |
1da177e4 | 54 | { |
3d0d14f9 IM |
55 | long int exponent, shift; |
56 | unsigned long long Xll; | |
57 | Xsig accumulator, Denom, argSignif; | |
58 | u_char tag; | |
1da177e4 | 59 | |
3d0d14f9 | 60 | exponent = exponent16(arg); |
1da177e4 LT |
61 | |
62 | #ifdef PARANOID | |
3d0d14f9 IM |
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 | } | |
1da177e4 LT |
68 | #endif /* PARANOID */ |
69 | ||
3d0d14f9 IM |
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); | |
1da177e4 | 130 | } |
1da177e4 | 131 | |
3d0d14f9 IM |
132 | /* Convert to 64 bit signed-compatible */ |
133 | exponent += round_Xsig(&accumulator); | |
1da177e4 | 134 | |
3d0d14f9 IM |
135 | result = &st(0); |
136 | significand(result) = XSIG_LL(accumulator); | |
137 | setexponent16(result, exponent); | |
1da177e4 | 138 | |
3d0d14f9 | 139 | tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); |
1da177e4 | 140 | |
3d0d14f9 IM |
141 | setsign(result, sign); |
142 | FPU_settag0(tag); | |
1da177e4 | 143 | |
3d0d14f9 | 144 | return 0; |
1da177e4 LT |
145 | |
146 | } |