1 | 1 |
2 | stwotox.sa 3.1 12/10/90 2 | stwotox.sa 3.1 12/10/90
3 | 3 |
4 | stwotox --- 2**X 4 | stwotox --- 2**X
5 | stwotoxd --- 2**X for denormalized X 5 | stwotoxd --- 2**X for denormalized X
6 | stentox --- 10**X 6 | stentox --- 10**X
7 | stentoxd --- 10**X for denormalized X 7 | stentoxd --- 10**X for denormalized X
8 | 8 |
9 | Input: Double-extended number X in loc 9 | Input: Double-extended number X in location pointed to
10 | by address register a0. 10 | by address register a0.
11 | 11 |
12 | Output: The function values are return 12 | Output: The function values are returned in Fp0.
13 | 13 |
14 | Accuracy and Monotonicity: The returne 14 | Accuracy and Monotonicity: The returned result is within 2 ulps in
15 | 64 significant bit, i.e. withi 15 | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
16 | result is subsequently rounded 16 | result is subsequently rounded to double precision. The
17 | result is provably monotonic i 17 | result is provably monotonic in double precision.
18 | 18 |
19 | Speed: The program stwotox takes appro 19 | Speed: The program stwotox takes approximately 190 cycles and the
20 | program stentox takes approxim 20 | program stentox takes approximately 200 cycles.
21 | 21 |
22 | Algorithm: 22 | Algorithm:
23 | 23 |
24 | twotox 24 | twotox
25 | 1. If |X| > 16480, go to ExpBig. 25 | 1. If |X| > 16480, go to ExpBig.
26 | 26 |
27 | 2. If |X| < 2**(-70), go to ExpSm. 27 | 2. If |X| < 2**(-70), go to ExpSm.
28 | 28 |
29 | 3. Decompose X as X = N/64 + r where | 29 | 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore
30 | decompose N as 30 | decompose N as
31 | N = 64(M + M') + j, j = 0,1, 31 | N = 64(M + M') + j, j = 0,1,2,...,63.
32 | 32 |
33 | 4. Overwrite r := r * log2. Then 33 | 4. Overwrite r := r * log2. Then
34 | 2**X = 2**(M') * 2**(M) * 2**( 34 | 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
35 | Go to expr to compute that exp 35 | Go to expr to compute that expression.
36 | 36 |
37 | tentox 37 | tentox
38 | 1. If |X| > 16480*log_10(2) (base 10 l 38 | 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig.
39 | 39 |
40 | 2. If |X| < 2**(-70), go to ExpSm. 40 | 2. If |X| < 2**(-70), go to ExpSm.
41 | 41 |
42 | 3. Set y := X*log_2(10)*64 (base 2 log 42 | 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set
43 | N := round-to-int(y). Decompos 43 | N := round-to-int(y). Decompose N as
44 | N = 64(M + M') + j, j = 0,1, 44 | N = 64(M + M') + j, j = 0,1,2,...,63.
45 | 45 |
46 | 4. Define r as 46 | 4. Define r as
47 | r := ((X - N*L1)-N*L2) * L10 47 | r := ((X - N*L1)-N*L2) * L10
48 | where L1, L2 are the leading a 48 | where L1, L2 are the leading and trailing parts of log_10(2)/64
49 | and L10 is the natural log of 49 | and L10 is the natural log of 10. Then
50 | 10**X = 2**(M') * 2**(M) * 2** 50 | 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
51 | Go to expr to compute that exp 51 | Go to expr to compute that expression.
52 | 52 |
53 | expr 53 | expr
54 | 1. Fetch 2**(j/64) from table as Fact1 54 | 1. Fetch 2**(j/64) from table as Fact1 and Fact2.
55 | 55 |
56 | 2. Overwrite Fact1 and Fact2 by 56 | 2. Overwrite Fact1 and Fact2 by
57 | Fact1 := 2**(M) * Fact1 57 | Fact1 := 2**(M) * Fact1
58 | Fact2 := 2**(M) * Fact2 58 | Fact2 := 2**(M) * Fact2
59 | Thus Fact1 + Fact2 = 2**(M) * 59 | Thus Fact1 + Fact2 = 2**(M) * 2**(j/64).
60 | 60 |
61 | 3. Calculate P where 1 + P approximate 61 | 3. Calculate P where 1 + P approximates exp(r):
62 | P = r + r*r*(A1+r*(A2+...+r*A5 62 | P = r + r*r*(A1+r*(A2+...+r*A5)).
63 | 63 |
64 | 4. Let AdjFact := 2**(M'). Return 64 | 4. Let AdjFact := 2**(M'). Return
65 | AdjFact * ( Fact1 + ((Fact1*P) 65 | AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ).
66 | Exit. 66 | Exit.
67 | 67 |
68 | ExpBig 68 | ExpBig
69 | 1. Generate overflow by Huge * Huge if 69 | 1. Generate overflow by Huge * Huge if X > 0; otherwise, generate
70 | underflow by Tiny * Tiny. 70 | underflow by Tiny * Tiny.
71 | 71 |
72 | ExpSm 72 | ExpSm
73 | 1. Return 1 + X. 73 | 1. Return 1 + X.
74 | 74 |
75 75
76 | Copyright (C) Motorola, Inc. 1 76 | Copyright (C) Motorola, Inc. 1990
77 | All Rights Reserved 77 | All Rights Reserved
78 | 78 |
79 | For details on the license for this fi 79 | For details on the license for this file, please see the
80 | file, README, in this same directory. 80 | file, README, in this same directory.
81 81
82 |STWOTOX idnt 2,1 | Motorola 040 Flo 82 |STWOTOX idnt 2,1 | Motorola 040 Floating Point Software Package
83 83
84 |section 8 84 |section 8
85 85
86 #include "fpsp.h" 86 #include "fpsp.h"
87 87
88 BOUNDS1: .long 0x3FB98000,0x400D80C0 | 88 BOUNDS1: .long 0x3FB98000,0x400D80C0 | ... 2^(-70),16480
89 BOUNDS2: .long 0x3FB98000,0x400B9B07 | 89 BOUNDS2: .long 0x3FB98000,0x400B9B07 | ... 2^(-70),16480 LOG2/LOG10
90 90
91 L2TEN64: .long 0x406A934F,0x0979A371 | 91 L2TEN64: .long 0x406A934F,0x0979A371 | ... 64LOG10/LOG2
92 L10TWO1: .long 0x3F734413,0x509F8000 | 92 L10TWO1: .long 0x3F734413,0x509F8000 | ... LOG2/64LOG10
93 93
94 L10TWO2: .long 0xBFCD0000,0xC0219DC1,0x 94 L10TWO2: .long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
95 95
96 LOG10: .long 0x40000000,0x935D8DDD,0xAAA8AC17 96 LOG10: .long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
97 97
98 LOG2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC 98 LOG2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
99 99
100 EXPA5: .long 0x3F56C16D,0x6F7BD0B2 100 EXPA5: .long 0x3F56C16D,0x6F7BD0B2
101 EXPA4: .long 0x3F811112,0x302C712C 101 EXPA4: .long 0x3F811112,0x302C712C
102 EXPA3: .long 0x3FA55555,0x55554CC1 102 EXPA3: .long 0x3FA55555,0x55554CC1
103 EXPA2: .long 0x3FC55555,0x55554A54 103 EXPA2: .long 0x3FC55555,0x55554A54
104 EXPA1: .long 0x3FE00000,0x00000000,0x00000000 104 EXPA1: .long 0x3FE00000,0x00000000,0x00000000,0x00000000
105 105
106 HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF 106 HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
107 TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF 107 TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
108 108
109 EXPTBL: 109 EXPTBL:
110 .long 0x3FFF0000,0x80000000,0x0000000 110 .long 0x3FFF0000,0x80000000,0x00000000,0x3F738000
111 .long 0x3FFF0000,0x8164D1F3,0xBC03077 111 .long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
112 .long 0x3FFF0000,0x82CD8698,0xAC2BA1D 112 .long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
113 .long 0x3FFF0000,0x843A28C3,0xACDE404 113 .long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
114 .long 0x3FFF0000,0x85AAC367,0xCC487B1 114 .long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
115 .long 0x3FFF0000,0x871F6196,0x9E8D101 115 .long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
116 .long 0x3FFF0000,0x88980E80,0x92DA852 116 .long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
117 .long 0x3FFF0000,0x8A14D575,0x496EFD9 117 .long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
118 .long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E 118 .long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
119 .long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E 119 .long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
120 .long 0x3FFF0000,0x8EA4398B,0x45CD53C 120 .long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
121 .long 0x3FFF0000,0x9031DC43,0x1466B1D 121 .long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
122 .long 0x3FFF0000,0x91C3D373,0xAB11C33 122 .long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
123 .long 0x3FFF0000,0x935A2B2F,0x13E6E92 123 .long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
124 .long 0x3FFF0000,0x94F4EFA8,0xFEF7096 124 .long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
125 .long 0x3FFF0000,0x96942D37,0x20185A0 125 .long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
126 .long 0x3FFF0000,0x9837F051,0x8DB8A96 126 .long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
127 .long 0x3FFF0000,0x99E04593,0x20B7FA6 127 .long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
128 .long 0x3FFF0000,0x9B8D39B9,0xD54E553 128 .long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
129 .long 0x3FFF0000,0x9D3ED9A7,0x2CFFB75 129 .long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
130 .long 0x3FFF0000,0x9EF53260,0x91A111A 130 .long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
131 .long 0x3FFF0000,0xA0B0510F,0xB9714FC 131 .long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
132 .long 0x3FFF0000,0xA2704303,0x0C49681 132 .long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
133 .long 0x3FFF0000,0xA43515AE,0x09E6809 133 .long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
134 .long 0x3FFF0000,0xA5FED6A9,0xB15138E 134 .long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
135 .long 0x3FFF0000,0xA7CD93B4,0xE965356 135 .long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
136 .long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF 136 .long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
137 .long 0x3FFF0000,0xAB7A39B5,0xA93ED33 137 .long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
138 .long 0x3FFF0000,0xAD583EEA,0x42A14AC 138 .long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
139 .long 0x3FFF0000,0xAF3B78AD,0x690A437 139 .long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
140 .long 0x3FFF0000,0xB123F581,0xD2AC259 140 .long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
141 .long 0x3FFF0000,0xB311C412,0xA911248 141 .long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
142 .long 0x3FFF0000,0xB504F333,0xF9DE648 142 .long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
143 .long 0x3FFF0000,0xB6FD91E3,0x28D1779 143 .long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
144 .long 0x3FFF0000,0xB8FBAF47,0x62FB9EE 144 .long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
145 .long 0x3FFF0000,0xBAFF5AB2,0x133E45F 145 .long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
146 .long 0x3FFF0000,0xBD08A39F,0x580C36B 146 .long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
147 .long 0x3FFF0000,0xBF1799B6,0x7A73108 147 .long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
148 .long 0x3FFF0000,0xC12C4CCA,0x6670945 148 .long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
149 .long 0x3FFF0000,0xC346CCDA,0x2497640 149 .long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
150 .long 0x3FFF0000,0xC5672A11,0x5506DAD 150 .long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
151 .long 0x3FFF0000,0xC78D74C8,0xABB9B15 151 .long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
152 .long 0x3FFF0000,0xC9B9BD86,0x6E2F27A 152 .long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
153 .long 0x3FFF0000,0xCBEC14FE,0xF2727C5 153 .long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
154 .long 0x3FFF0000,0xCE248C15,0x1F8480E 154 .long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
155 .long 0x3FFF0000,0xD06333DA,0xEF2B259 155 .long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
156 .long 0x3FFF0000,0xD2A81D91,0xF12AE45 156 .long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
157 .long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1 157 .long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
158 .long 0x3FFF0000,0xD744FCCA,0xD69D6AF 158 .long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
159 .long 0x3FFF0000,0xD99D15C2,0x78AFD7B 159 .long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
160 .long 0x3FFF0000,0xDBFBB797,0xDAF2375 160 .long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
161 .long 0x3FFF0000,0xDE60F482,0x5E0E912 161 .long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
162 .long 0x3FFF0000,0xE0CCDEEC,0x2A94E11 162 .long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
163 .long 0x3FFF0000,0xE33F8972,0xBE8A5A5 163 .long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
164 .long 0x3FFF0000,0xE5B906E7,0x7C8348A 164 .long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
165 .long 0x3FFF0000,0xE8396A50,0x3C4BDC6 165 .long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
166 .long 0x3FFF0000,0xEAC0C6E7,0xDD24392 166 .long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
167 .long 0x3FFF0000,0xED4F301E,0xD9942B8 167 .long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
168 .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5C 168 .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
169 .long 0x3FFF0000,0xF281773C,0x59FFB13 169 .long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
170 .long 0x3FFF0000,0xF5257D15,0x2486CC2 170 .long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
171 .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB 171 .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
172 .long 0x3FFF0000,0xFA83B2DB,0x722A033 172 .long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
173 .long 0x3FFF0000,0xFD3E0C0C,0xF486C17 173 .long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
174 174
175 .set N,L_SCR1 175 .set N,L_SCR1
176 176
177 .set X,FP_SCR1 177 .set X,FP_SCR1
178 .set XDCARE,X+2 178 .set XDCARE,X+2
179 .set XFRAC,X+4 179 .set XFRAC,X+4
180 180
181 .set ADJFACT,FP_SCR2 181 .set ADJFACT,FP_SCR2
182 182
183 .set FACT1,FP_SCR3 183 .set FACT1,FP_SCR3
184 .set FACT1HI,FACT1+4 184 .set FACT1HI,FACT1+4
185 .set FACT1LOW,FACT1+8 185 .set FACT1LOW,FACT1+8
186 186
187 .set FACT2,FP_SCR4 187 .set FACT2,FP_SCR4
188 .set FACT2HI,FACT2+4 188 .set FACT2HI,FACT2+4
189 .set FACT2LOW,FACT2+8 189 .set FACT2LOW,FACT2+8
190 190
191 | xref t_unfl 191 | xref t_unfl
192 |xref t_ovfl 192 |xref t_ovfl
193 |xref t_frcinx 193 |xref t_frcinx
194 194
195 .global stwotoxd 195 .global stwotoxd
196 stwotoxd: 196 stwotoxd:
197 |--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARG 197 |--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
198 198
199 fmovel %d1,%fpcr 199 fmovel %d1,%fpcr | ...set user's rounding mode/precision
200 fmoves #0x3F800000,%fp0 | .. 200 fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
201 movel (%a0),%d0 201 movel (%a0),%d0
202 orl #0x00800001,%d0 202 orl #0x00800001,%d0
203 fadds %d0,%fp0 203 fadds %d0,%fp0
204 bra t_frcinx 204 bra t_frcinx
205 205
206 .global stwotox 206 .global stwotox
207 stwotox: 207 stwotox:
208 |--ENTRY POINT FOR 2**(X), HERE X IS FINITE, N 208 |--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
209 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPU 209 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
210 210
211 movel (%a0),%d0 211 movel (%a0),%d0
212 movew 4(%a0),%d0 212 movew 4(%a0),%d0
213 fmovex %fp0,X(%a6) 213 fmovex %fp0,X(%a6)
214 andil #0x7FFFFFFF,%d0 214 andil #0x7FFFFFFF,%d0
215 215
216 cmpil #0x3FB98000,%d0 216 cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
217 bges TWOOK1 217 bges TWOOK1
218 bra EXPBORS 218 bra EXPBORS
219 219
220 TWOOK1: 220 TWOOK1:
221 cmpil #0x400D80C0,%d0 221 cmpil #0x400D80C0,%d0 | ...|X| > 16480?
222 bles TWOMAIN 222 bles TWOMAIN
223 bra EXPBORS 223 bra EXPBORS
224 224
225 225
226 TWOMAIN: 226 TWOMAIN:
227 |--USUAL CASE, 2^(-70) <= |X| <= 16480 227 |--USUAL CASE, 2^(-70) <= |X| <= 16480
228 228
229 fmovex %fp0,%fp1 229 fmovex %fp0,%fp1
230 fmuls #0x42800000,%fp1 | .. 230 fmuls #0x42800000,%fp1 | ...64 * X
231 231
232 fmovel %fp1,N(%a6) 232 fmovel %fp1,N(%a6) | ...N = ROUND-TO-INT(64 X)
233 movel %d2,-(%sp) 233 movel %d2,-(%sp)
234 lea EXPTBL,%a1 | ...L 234 lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
235 fmovel N(%a6),%fp1 235 fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
236 movel N(%a6),%d0 236 movel N(%a6),%d0
237 movel %d0,%d2 237 movel %d0,%d2
238 andil #0x3F,%d0 238 andil #0x3F,%d0 | ...D0 IS J
239 asll #4,%d0 | ...D 239 asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
240 addal %d0,%a1 | ...A 240 addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
241 asrl #6,%d2 | ...d 241 asrl #6,%d2 | ...d2 IS L, N = 64L + J
242 movel %d2,%d0 242 movel %d2,%d0
243 asrl #1,%d0 | ...D 243 asrl #1,%d0 | ...D0 IS M
244 subl %d0,%d2 | ...d 244 subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
245 addil #0x3FFF,%d2 245 addil #0x3FFF,%d2
246 movew %d2,ADJFACT(%a6) 246 movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
247 movel (%sp)+,%d2 247 movel (%sp)+,%d2
248 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORT 248 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
249 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT | 249 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
250 |--ADJFACT = 2^(M'). 250 |--ADJFACT = 2^(M').
251 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, 251 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
252 252
253 fmuls #0x3C800000,%fp1 | .. 253 fmuls #0x3C800000,%fp1 | ...(1/64)*N
254 movel (%a1)+,FACT1(%a6) 254 movel (%a1)+,FACT1(%a6)
255 movel (%a1)+,FACT1HI(%a6) 255 movel (%a1)+,FACT1HI(%a6)
256 movel (%a1)+,FACT1LOW(%a6) 256 movel (%a1)+,FACT1LOW(%a6)
257 movew (%a1)+,FACT2(%a6) 257 movew (%a1)+,FACT2(%a6)
258 clrw FACT2+2(%a6) 258 clrw FACT2+2(%a6)
259 259
260 fsubx %fp1,%fp0 260 fsubx %fp1,%fp0 | ...X - (1/64)*INT(64 X)
261 261
262 movew (%a1)+,FACT2HI(%a6) 262 movew (%a1)+,FACT2HI(%a6)
263 clrw FACT2HI+2(%a6) 263 clrw FACT2HI+2(%a6)
264 clrl FACT2LOW(%a6) 264 clrl FACT2LOW(%a6)
265 addw %d0,FACT1(%a6) 265 addw %d0,FACT1(%a6)
266 266
267 fmulx LOG2,%fp0 | ...F 267 fmulx LOG2,%fp0 | ...FP0 IS R
268 addw %d0,FACT2(%a6) 268 addw %d0,FACT2(%a6)
269 269
270 bra expr 270 bra expr
271 271
272 EXPBORS: 272 EXPBORS:
273 |--FPCR, D0 SAVED 273 |--FPCR, D0 SAVED
274 cmpil #0x3FFF8000,%d0 274 cmpil #0x3FFF8000,%d0
275 bgts EXPBIG 275 bgts EXPBIG
276 276
277 EXPSM: 277 EXPSM:
278 |--|X| IS SMALL, RETURN 1 + X 278 |--|X| IS SMALL, RETURN 1 + X
279 279
280 fmovel %d1,%FPCR 280 fmovel %d1,%FPCR |restore users exceptions
281 fadds #0x3F800000,%fp0 | .. 281 fadds #0x3F800000,%fp0 | ...RETURN 1 + X
282 282
283 bra t_frcinx 283 bra t_frcinx
284 284
285 EXPBIG: 285 EXPBIG:
286 |--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; E 286 |--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
287 |--REGISTERS SAVE SO FAR ARE FPCR AND D0 287 |--REGISTERS SAVE SO FAR ARE FPCR AND D0
288 movel X(%a6),%d0 288 movel X(%a6),%d0
289 cmpil #0,%d0 289 cmpil #0,%d0
290 blts EXPNEG 290 blts EXPNEG
291 291
292 bclrb #7,(%a0) 292 bclrb #7,(%a0) |t_ovfl expects positive value
293 bra t_ovfl 293 bra t_ovfl
294 294
295 EXPNEG: 295 EXPNEG:
296 bclrb #7,(%a0) 296 bclrb #7,(%a0) |t_unfl expects positive value
297 bra t_unfl 297 bra t_unfl
298 298
299 .global stentoxd 299 .global stentoxd
300 stentoxd: 300 stentoxd:
301 |--ENTRY POINT FOR 10**(X) FOR DENORMALIZED AR 301 |--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
302 302
303 fmovel %d1,%fpcr 303 fmovel %d1,%fpcr | ...set user's rounding mode/precision
304 fmoves #0x3F800000,%fp0 | .. 304 fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
305 movel (%a0),%d0 305 movel (%a0),%d0
306 orl #0x00800001,%d0 306 orl #0x00800001,%d0
307 fadds %d0,%fp0 307 fadds %d0,%fp0
308 bra t_frcinx 308 bra t_frcinx
309 309
310 .global stentox 310 .global stentox
311 stentox: 311 stentox:
312 |--ENTRY POINT FOR 10**(X), HERE X IS FINITE, 312 |--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
313 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPU 313 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
314 314
315 movel (%a0),%d0 315 movel (%a0),%d0
316 movew 4(%a0),%d0 316 movew 4(%a0),%d0
317 fmovex %fp0,X(%a6) 317 fmovex %fp0,X(%a6)
318 andil #0x7FFFFFFF,%d0 318 andil #0x7FFFFFFF,%d0
319 319
320 cmpil #0x3FB98000,%d0 320 cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
321 bges TENOK1 321 bges TENOK1
322 bra EXPBORS 322 bra EXPBORS
323 323
324 TENOK1: 324 TENOK1:
325 cmpil #0x400B9B07,%d0 325 cmpil #0x400B9B07,%d0 | ...|X| <= 16480*log2/log10 ?
326 bles TENMAIN 326 bles TENMAIN
327 bra EXPBORS 327 bra EXPBORS
328 328
329 TENMAIN: 329 TENMAIN:
330 |--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / 330 |--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
331 331
332 fmovex %fp0,%fp1 332 fmovex %fp0,%fp1
333 fmuld L2TEN64,%fp1 | ...X 333 fmuld L2TEN64,%fp1 | ...X*64*LOG10/LOG2
334 334
335 fmovel %fp1,N(%a6) 335 fmovel %fp1,N(%a6) | ...N=INT(X*64*LOG10/LOG2)
336 movel %d2,-(%sp) 336 movel %d2,-(%sp)
337 lea EXPTBL,%a1 | ...L 337 lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
338 fmovel N(%a6),%fp1 338 fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
339 movel N(%a6),%d0 339 movel N(%a6),%d0
340 movel %d0,%d2 340 movel %d0,%d2
341 andil #0x3F,%d0 341 andil #0x3F,%d0 | ...D0 IS J
342 asll #4,%d0 | ...D 342 asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
343 addal %d0,%a1 | ...A 343 addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
344 asrl #6,%d2 | ...d 344 asrl #6,%d2 | ...d2 IS L, N = 64L + J
345 movel %d2,%d0 345 movel %d2,%d0
346 asrl #1,%d0 | ...D 346 asrl #1,%d0 | ...D0 IS M
347 subl %d0,%d2 | ...d 347 subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
348 addil #0x3FFF,%d2 348 addil #0x3FFF,%d2
349 movew %d2,ADJFACT(%a6) 349 movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
350 movel (%sp)+,%d2 350 movel (%sp)+,%d2
351 351
352 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORT 352 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
353 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT | 353 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
354 |--ADJFACT = 2^(M'). 354 |--ADJFACT = 2^(M').
355 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, 355 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
356 356
357 fmovex %fp1,%fp2 357 fmovex %fp1,%fp2
358 358
359 fmuld L10TWO1,%fp1 | ...N 359 fmuld L10TWO1,%fp1 | ...N*(LOG2/64LOG10)_LEAD
360 movel (%a1)+,FACT1(%a6) 360 movel (%a1)+,FACT1(%a6)
361 361
362 fmulx L10TWO2,%fp2 | ...N 362 fmulx L10TWO2,%fp2 | ...N*(LOG2/64LOG10)_TRAIL
363 363
364 movel (%a1)+,FACT1HI(%a6) 364 movel (%a1)+,FACT1HI(%a6)
365 movel (%a1)+,FACT1LOW(%a6) 365 movel (%a1)+,FACT1LOW(%a6)
366 fsubx %fp1,%fp0 366 fsubx %fp1,%fp0 | ...X - N L_LEAD
367 movew (%a1)+,FACT2(%a6) 367 movew (%a1)+,FACT2(%a6)
368 368
369 fsubx %fp2,%fp0 369 fsubx %fp2,%fp0 | ...X - N L_TRAIL
370 370
371 clrw FACT2+2(%a6) 371 clrw FACT2+2(%a6)
372 movew (%a1)+,FACT2HI(%a6) 372 movew (%a1)+,FACT2HI(%a6)
373 clrw FACT2HI+2(%a6) 373 clrw FACT2HI+2(%a6)
374 clrl FACT2LOW(%a6) 374 clrl FACT2LOW(%a6)
375 375
376 fmulx LOG10,%fp0 | ...F 376 fmulx LOG10,%fp0 | ...FP0 IS R
377 377
378 addw %d0,FACT1(%a6) 378 addw %d0,FACT1(%a6)
379 addw %d0,FACT2(%a6) 379 addw %d0,FACT2(%a6)
380 380
381 expr: 381 expr:
382 |--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN. 382 |--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
383 |--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2 383 |--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
384 |--FP0 IS R. THE FOLLOWING CODE COMPUTES 384 |--FP0 IS R. THE FOLLOWING CODE COMPUTES
385 |-- 2**(M'+M) * 2**(J/64) * EXP(R) 385 |-- 2**(M'+M) * 2**(J/64) * EXP(R)
386 386
387 fmovex %fp0,%fp1 387 fmovex %fp0,%fp1
388 fmulx %fp1,%fp1 388 fmulx %fp1,%fp1 | ...FP1 IS S = R*R
389 389
390 fmoved EXPA5,%fp2 | ...F 390 fmoved EXPA5,%fp2 | ...FP2 IS A5
391 fmoved EXPA4,%fp3 | ...F 391 fmoved EXPA4,%fp3 | ...FP3 IS A4
392 392
393 fmulx %fp1,%fp2 393 fmulx %fp1,%fp2 | ...FP2 IS S*A5
394 fmulx %fp1,%fp3 394 fmulx %fp1,%fp3 | ...FP3 IS S*A4
395 395
396 faddd EXPA3,%fp2 | ...F 396 faddd EXPA3,%fp2 | ...FP2 IS A3+S*A5
397 faddd EXPA2,%fp3 | ...F 397 faddd EXPA2,%fp3 | ...FP3 IS A2+S*A4
398 398
399 fmulx %fp1,%fp2 399 fmulx %fp1,%fp2 | ...FP2 IS S*(A3+S*A5)
400 fmulx %fp1,%fp3 400 fmulx %fp1,%fp3 | ...FP3 IS S*(A2+S*A4)
401 401
402 faddd EXPA1,%fp2 | ...F 402 faddd EXPA1,%fp2 | ...FP2 IS A1+S*(A3+S*A5)
403 fmulx %fp0,%fp3 403 fmulx %fp0,%fp3 | ...FP3 IS R*S*(A2+S*A4)
404 404
405 fmulx %fp1,%fp2 405 fmulx %fp1,%fp2 | ...FP2 IS S*(A1+S*(A3+S*A5))
406 faddx %fp3,%fp0 406 faddx %fp3,%fp0 | ...FP0 IS R+R*S*(A2+S*A4)
407 407
408 faddx %fp2,%fp0 408 faddx %fp2,%fp0 | ...FP0 IS EXP(R) - 1
409 409
410 410
411 |--FINAL RECONSTRUCTION PROCESS 411 |--FINAL RECONSTRUCTION PROCESS
412 |--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R 412 |--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0)
413 413
414 fmulx FACT1(%a6),%fp0 414 fmulx FACT1(%a6),%fp0
415 faddx FACT2(%a6),%fp0 415 faddx FACT2(%a6),%fp0
416 faddx FACT1(%a6),%fp0 416 faddx FACT1(%a6),%fp0
417 417
418 fmovel %d1,%FPCR 418 fmovel %d1,%FPCR |restore users exceptions
419 clrw ADJFACT+2(%a6) 419 clrw ADJFACT+2(%a6)
420 movel #0x80000000,ADJFACT+4( 420 movel #0x80000000,ADJFACT+4(%a6)
421 clrl ADJFACT+8(%a6) 421 clrl ADJFACT+8(%a6)
422 fmulx ADJFACT(%a6),%fp0 422 fmulx ADJFACT(%a6),%fp0 | ...FINAL ADJUSTMENT
423 423
424 bra t_frcinx 424 bra t_frcinx
425 425
426 |end 426 |end
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