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1da177e4 LT |
1 | /*---------------------------------------------------------------------------+ |
2 | | poly_2xm1.c | | |
3 | | | | |
4 | | Function to compute 2^x-1 by a polynomial approximation. | | |
5 | | | | |
6 | | Copyright (C) 1992,1993,1994,1997 | | |
7 | | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | | |
8 | | E-mail billm@suburbia.net | | |
9 | | | | |
10 | | | | |
11 | +---------------------------------------------------------------------------*/ | |
12 | ||
13 | #include "exception.h" | |
14 | #include "reg_constant.h" | |
15 | #include "fpu_emu.h" | |
16 | #include "fpu_system.h" | |
17 | #include "control_w.h" | |
18 | #include "poly.h" | |
19 | ||
20 | ||
21 | #define HIPOWER 11 | |
22 | static const unsigned long long lterms[HIPOWER] = | |
23 | { | |
24 | 0x0000000000000000LL, /* This term done separately as 12 bytes */ | |
25 | 0xf5fdeffc162c7543LL, | |
26 | 0x1c6b08d704a0bfa6LL, | |
27 | 0x0276556df749cc21LL, | |
28 | 0x002bb0ffcf14f6b8LL, | |
29 | 0x0002861225ef751cLL, | |
30 | 0x00001ffcbfcd5422LL, | |
31 | 0x00000162c005d5f1LL, | |
32 | 0x0000000da96ccb1bLL, | |
33 | 0x0000000078d1b897LL, | |
34 | 0x000000000422b029LL | |
35 | }; | |
36 | ||
37 | static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194); | |
38 | ||
39 | /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0, | |
40 | These numbers are 2^(1/4), 2^(1/2), and 2^(3/4) | |
41 | */ | |
42 | static const Xsig shiftterm0 = MK_XSIG(0, 0, 0); | |
43 | static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318); | |
44 | static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3); | |
45 | static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9); | |
46 | ||
47 | static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1, | |
48 | &shiftterm2, &shiftterm3 }; | |
49 | ||
50 | ||
51 | /*--- poly_2xm1() -----------------------------------------------------------+ | |
52 | | Requires st(0) which is TAG_Valid and < 1. | | |
53 | +---------------------------------------------------------------------------*/ | |
54 | int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) | |
55 | { | |
56 | long int exponent, shift; | |
57 | unsigned long long Xll; | |
58 | Xsig accumulator, Denom, argSignif; | |
59 | u_char tag; | |
60 | ||
61 | exponent = exponent16(arg); | |
62 | ||
63 | #ifdef PARANOID | |
64 | if ( exponent >= 0 ) /* Don't want a |number| >= 1.0 */ | |
65 | { | |
66 | /* Number negative, too large, or not Valid. */ | |
67 | EXCEPTION(EX_INTERNAL|0x127); | |
68 | return 1; | |
69 | } | |
70 | #endif /* PARANOID */ | |
71 | ||
72 | argSignif.lsw = 0; | |
73 | XSIG_LL(argSignif) = Xll = significand(arg); | |
74 | ||
75 | if ( exponent == -1 ) | |
76 | { | |
77 | shift = (argSignif.msw & 0x40000000) ? 3 : 2; | |
78 | /* subtract 0.5 or 0.75 */ | |
79 | exponent -= 2; | |
80 | XSIG_LL(argSignif) <<= 2; | |
81 | Xll <<= 2; | |
82 | } | |
83 | else if ( exponent == -2 ) | |
84 | { | |
85 | shift = 1; | |
86 | /* subtract 0.25 */ | |
87 | exponent--; | |
88 | XSIG_LL(argSignif) <<= 1; | |
89 | Xll <<= 1; | |
90 | } | |
91 | else | |
92 | shift = 0; | |
93 | ||
94 | if ( exponent < -2 ) | |
95 | { | |
96 | /* Shift the argument right by the required places. */ | |
97 | if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U ) | |
98 | Xll++; /* round up */ | |
99 | } | |
100 | ||
101 | accumulator.lsw = accumulator.midw = accumulator.msw = 0; | |
102 | polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1); | |
103 | mul_Xsig_Xsig(&accumulator, &argSignif); | |
104 | shr_Xsig(&accumulator, 3); | |
105 | ||
106 | mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */ | |
107 | add_two_Xsig(&accumulator, &argSignif, &exponent); | |
108 | ||
109 | if ( shift ) | |
110 | { | |
111 | /* The argument is large, use the identity: | |
112 | f(x+a) = f(a) * (f(x) + 1) - 1; | |
113 | */ | |
114 | shr_Xsig(&accumulator, - exponent); | |
115 | accumulator.msw |= 0x80000000; /* add 1.0 */ | |
116 | mul_Xsig_Xsig(&accumulator, shiftterm[shift]); | |
117 | accumulator.msw &= 0x3fffffff; /* subtract 1.0 */ | |
118 | exponent = 1; | |
119 | } | |
120 | ||
121 | if ( sign != SIGN_POS ) | |
122 | { | |
123 | /* The argument is negative, use the identity: | |
124 | f(-x) = -f(x) / (1 + f(x)) | |
125 | */ | |
126 | Denom.lsw = accumulator.lsw; | |
127 | XSIG_LL(Denom) = XSIG_LL(accumulator); | |
128 | if ( exponent < 0 ) | |
129 | shr_Xsig(&Denom, - exponent); | |
130 | else if ( exponent > 0 ) | |
131 | { | |
132 | /* exponent must be 1 here */ | |
133 | XSIG_LL(Denom) <<= 1; | |
134 | if ( Denom.lsw & 0x80000000 ) | |
135 | XSIG_LL(Denom) |= 1; | |
136 | (Denom.lsw) <<= 1; | |
137 | } | |
138 | Denom.msw |= 0x80000000; /* add 1.0 */ | |
139 | div_Xsig(&accumulator, &Denom, &accumulator); | |
140 | } | |
141 | ||
142 | /* Convert to 64 bit signed-compatible */ | |
143 | exponent += round_Xsig(&accumulator); | |
144 | ||
145 | result = &st(0); | |
146 | significand(result) = XSIG_LL(accumulator); | |
147 | setexponent16(result, exponent); | |
148 | ||
149 | tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); | |
150 | ||
151 | setsign(result, sign); | |
152 | FPU_settag0(tag); | |
153 | ||
154 | return 0; | |
155 | ||
156 | } |