| 1 |
1623 |
jcastillo |
|
|
| 2 |
|
|
| stwotox.sa 3.1 12/10/90
|
| 3 |
|
|
|
|
| 4 |
|
|
| stwotox --- 2**X
|
| 5 |
|
|
| stwotoxd --- 2**X for denormalized X
|
| 6 |
|
|
| stentox --- 10**X
|
| 7 |
|
|
| stentoxd --- 10**X for denormalized X
|
| 8 |
|
|
|
|
| 9 |
|
|
| Input: Double-extended number X in location pointed to
|
| 10 |
|
|
| by address register a0.
|
| 11 |
|
|
|
|
| 12 |
|
|
| Output: The function values are returned in Fp0.
|
| 13 |
|
|
|
|
| 14 |
|
|
| Accuracy and Monotonicity: The returned result is within 2 ulps in
|
| 15 |
|
|
| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|
| 16 |
|
|
| result is subsequently rounded to double precision. The
|
| 17 |
|
|
| result is provably monotonic in double precision.
|
| 18 |
|
|
|
|
| 19 |
|
|
| Speed: The program stwotox takes approximately 190 cycles and the
|
| 20 |
|
|
| program stentox takes approximately 200 cycles.
|
| 21 |
|
|
|
|
| 22 |
|
|
| Algorithm:
|
| 23 |
|
|
|
|
| 24 |
|
|
| twotox
|
| 25 |
|
|
| 1. If |X| > 16480, go to ExpBig.
|
| 26 |
|
|
|
|
| 27 |
|
|
| 2. If |X| < 2**(-70), go to ExpSm.
|
| 28 |
|
|
|
|
| 29 |
|
|
| 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore
|
| 30 |
|
|
| decompose N as
|
| 31 |
|
|
| N = 64(M + M') + j, j = 0,1,2,...,63.
|
| 32 |
|
|
|
|
| 33 |
|
|
| 4. Overwrite r := r * log2. Then
|
| 34 |
|
|
| 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
|
| 35 |
|
|
| Go to expr to compute that expression.
|
| 36 |
|
|
|
|
| 37 |
|
|
| tentox
|
| 38 |
|
|
| 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig.
|
| 39 |
|
|
|
|
| 40 |
|
|
| 2. If |X| < 2**(-70), go to ExpSm.
|
| 41 |
|
|
|
|
| 42 |
|
|
| 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set
|
| 43 |
|
|
| N := round-to-int(y). Decompose N as
|
| 44 |
|
|
| N = 64(M + M') + j, j = 0,1,2,...,63.
|
| 45 |
|
|
|
|
| 46 |
|
|
| 4. Define r as
|
| 47 |
|
|
| r := ((X - N*L1)-N*L2) * L10
|
| 48 |
|
|
| where L1, L2 are the leading and trailing parts of log_10(2)/64
|
| 49 |
|
|
| and L10 is the natural log of 10. Then
|
| 50 |
|
|
| 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
|
| 51 |
|
|
| Go to expr to compute that expression.
|
| 52 |
|
|
|
|
| 53 |
|
|
| expr
|
| 54 |
|
|
| 1. Fetch 2**(j/64) from table as Fact1 and Fact2.
|
| 55 |
|
|
|
|
| 56 |
|
|
| 2. Overwrite Fact1 and Fact2 by
|
| 57 |
|
|
| Fact1 := 2**(M) * Fact1
|
| 58 |
|
|
| Fact2 := 2**(M) * Fact2
|
| 59 |
|
|
| Thus Fact1 + Fact2 = 2**(M) * 2**(j/64).
|
| 60 |
|
|
|
|
| 61 |
|
|
| 3. Calculate P where 1 + P approximates exp(r):
|
| 62 |
|
|
| P = r + r*r*(A1+r*(A2+...+r*A5)).
|
| 63 |
|
|
|
|
| 64 |
|
|
| 4. Let AdjFact := 2**(M'). Return
|
| 65 |
|
|
| AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ).
|
| 66 |
|
|
| Exit.
|
| 67 |
|
|
|
|
| 68 |
|
|
| ExpBig
|
| 69 |
|
|
| 1. Generate overflow by Huge * Huge if X > 0; otherwise, generate
|
| 70 |
|
|
| underflow by Tiny * Tiny.
|
| 71 |
|
|
|
|
| 72 |
|
|
| ExpSm
|
| 73 |
|
|
| 1. Return 1 + X.
|
| 74 |
|
|
|
|
| 75 |
|
|
|
| 76 |
|
|
| Copyright (C) Motorola, Inc. 1990
|
| 77 |
|
|
| All Rights Reserved
|
| 78 |
|
|
|
|
| 79 |
|
|
| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|
| 80 |
|
|
| The copyright notice above does not evidence any
|
| 81 |
|
|
| actual or intended publication of such source code.
|
| 82 |
|
|
|
| 83 |
|
|
|STWOTOX idnt 2,1 | Motorola 040 Floating Point Software Package
|
| 84 |
|
|
|
| 85 |
|
|
|section 8
|
| 86 |
|
|
|
| 87 |
|
|
.include "fpsp.h"
|
| 88 |
|
|
|
| 89 |
|
|
BOUNDS1: .long 0x3FB98000,0x400D80C0 | ... 2^(-70),16480
|
| 90 |
|
|
BOUNDS2: .long 0x3FB98000,0x400B9B07 | ... 2^(-70),16480 LOG2/LOG10
|
| 91 |
|
|
|
| 92 |
|
|
L2TEN64: .long 0x406A934F,0x0979A371 | ... 64LOG10/LOG2
|
| 93 |
|
|
L10TWO1: .long 0x3F734413,0x509F8000 | ... LOG2/64LOG10
|
| 94 |
|
|
|
| 95 |
|
|
L10TWO2: .long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
|
| 96 |
|
|
|
| 97 |
|
|
LOG10: .long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
|
| 98 |
|
|
|
| 99 |
|
|
LOG2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
|
| 100 |
|
|
|
| 101 |
|
|
EXPA5: .long 0x3F56C16D,0x6F7BD0B2
|
| 102 |
|
|
EXPA4: .long 0x3F811112,0x302C712C
|
| 103 |
|
|
EXPA3: .long 0x3FA55555,0x55554CC1
|
| 104 |
|
|
EXPA2: .long 0x3FC55555,0x55554A54
|
| 105 |
|
|
EXPA1: .long 0x3FE00000,0x00000000,0x00000000,0x00000000
|
| 106 |
|
|
|
| 107 |
|
|
HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
|
| 108 |
|
|
TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
|
| 109 |
|
|
|
| 110 |
|
|
EXPTBL:
|
| 111 |
|
|
.long 0x3FFF0000,0x80000000,0x00000000,0x3F738000
|
| 112 |
|
|
.long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
|
| 113 |
|
|
.long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
|
| 114 |
|
|
.long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
|
| 115 |
|
|
.long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
|
| 116 |
|
|
.long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
|
| 117 |
|
|
.long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
|
| 118 |
|
|
.long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
|
| 119 |
|
|
.long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
|
| 120 |
|
|
.long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
|
| 121 |
|
|
.long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
|
| 122 |
|
|
.long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
|
| 123 |
|
|
.long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
|
| 124 |
|
|
.long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
|
| 125 |
|
|
.long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
|
| 126 |
|
|
.long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
|
| 127 |
|
|
.long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
|
| 128 |
|
|
.long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
|
| 129 |
|
|
.long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
|
| 130 |
|
|
.long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
|
| 131 |
|
|
.long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
|
| 132 |
|
|
.long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
|
| 133 |
|
|
.long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
|
| 134 |
|
|
.long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
|
| 135 |
|
|
.long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
|
| 136 |
|
|
.long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
|
| 137 |
|
|
.long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
|
| 138 |
|
|
.long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
|
| 139 |
|
|
.long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
|
| 140 |
|
|
.long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
|
| 141 |
|
|
.long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
|
| 142 |
|
|
.long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
|
| 143 |
|
|
.long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
|
| 144 |
|
|
.long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
|
| 145 |
|
|
.long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
|
| 146 |
|
|
.long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
|
| 147 |
|
|
.long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
|
| 148 |
|
|
.long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
|
| 149 |
|
|
.long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
|
| 150 |
|
|
.long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
|
| 151 |
|
|
.long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
|
| 152 |
|
|
.long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
|
| 153 |
|
|
.long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
|
| 154 |
|
|
.long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
|
| 155 |
|
|
.long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
|
| 156 |
|
|
.long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
|
| 157 |
|
|
.long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
|
| 158 |
|
|
.long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
|
| 159 |
|
|
.long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
|
| 160 |
|
|
.long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
|
| 161 |
|
|
.long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
|
| 162 |
|
|
.long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
|
| 163 |
|
|
.long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
|
| 164 |
|
|
.long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
|
| 165 |
|
|
.long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
|
| 166 |
|
|
.long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
|
| 167 |
|
|
.long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
|
| 168 |
|
|
.long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
|
| 169 |
|
|
.long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
|
| 170 |
|
|
.long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
|
| 171 |
|
|
.long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
|
| 172 |
|
|
.long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
|
| 173 |
|
|
.long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
|
| 174 |
|
|
.long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
|
| 175 |
|
|
|
| 176 |
|
|
.set N,L_SCR1
|
| 177 |
|
|
|
| 178 |
|
|
.set X,FP_SCR1
|
| 179 |
|
|
.set XDCARE,X+2
|
| 180 |
|
|
.set XFRAC,X+4
|
| 181 |
|
|
|
| 182 |
|
|
.set ADJFACT,FP_SCR2
|
| 183 |
|
|
|
| 184 |
|
|
.set FACT1,FP_SCR3
|
| 185 |
|
|
.set FACT1HI,FACT1+4
|
| 186 |
|
|
.set FACT1LOW,FACT1+8
|
| 187 |
|
|
|
| 188 |
|
|
.set FACT2,FP_SCR4
|
| 189 |
|
|
.set FACT2HI,FACT2+4
|
| 190 |
|
|
.set FACT2LOW,FACT2+8
|
| 191 |
|
|
|
| 192 |
|
|
| xref t_unfl
|
| 193 |
|
|
|xref t_ovfl
|
| 194 |
|
|
|xref t_frcinx
|
| 195 |
|
|
|
| 196 |
|
|
.global stwotoxd
|
| 197 |
|
|
stwotoxd:
|
| 198 |
|
|
|--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
|
| 199 |
|
|
|
| 200 |
|
|
fmovel %d1,%fpcr | ...set user's rounding mode/precision
|
| 201 |
|
|
fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
|
| 202 |
|
|
movel (%a0),%d0
|
| 203 |
|
|
orl #0x00800001,%d0
|
| 204 |
|
|
fadds %d0,%fp0
|
| 205 |
|
|
bra t_frcinx
|
| 206 |
|
|
|
| 207 |
|
|
.global stwotox
|
| 208 |
|
|
stwotox:
|
| 209 |
|
|
|--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
|
| 210 |
|
|
fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
|
| 211 |
|
|
|
| 212 |
|
|
movel (%a0),%d0
|
| 213 |
|
|
movew 4(%a0),%d0
|
| 214 |
|
|
fmovex %fp0,X(%a6)
|
| 215 |
|
|
andil #0x7FFFFFFF,%d0
|
| 216 |
|
|
|
| 217 |
|
|
cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
|
| 218 |
|
|
bges TWOOK1
|
| 219 |
|
|
bra EXPBORS
|
| 220 |
|
|
|
| 221 |
|
|
TWOOK1:
|
| 222 |
|
|
cmpil #0x400D80C0,%d0 | ...|X| > 16480?
|
| 223 |
|
|
bles TWOMAIN
|
| 224 |
|
|
bra EXPBORS
|
| 225 |
|
|
|
| 226 |
|
|
|
| 227 |
|
|
TWOMAIN:
|
| 228 |
|
|
|--USUAL CASE, 2^(-70) <= |X| <= 16480
|
| 229 |
|
|
|
| 230 |
|
|
fmovex %fp0,%fp1
|
| 231 |
|
|
fmuls #0x42800000,%fp1 | ...64 * X
|
| 232 |
|
|
|
| 233 |
|
|
fmovel %fp1,N(%a6) | ...N = ROUND-TO-INT(64 X)
|
| 234 |
|
|
movel %d2,-(%sp)
|
| 235 |
|
|
lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
|
| 236 |
|
|
fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
|
| 237 |
|
|
movel N(%a6),%d0
|
| 238 |
|
|
movel %d0,%d2
|
| 239 |
|
|
andil #0x3F,%d0 | ...D0 IS J
|
| 240 |
|
|
asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
|
| 241 |
|
|
addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
|
| 242 |
|
|
asrl #6,%d2 | ...d2 IS L, N = 64L + J
|
| 243 |
|
|
movel %d2,%d0
|
| 244 |
|
|
asrl #1,%d0 | ...D0 IS M
|
| 245 |
|
|
subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
|
| 246 |
|
|
addil #0x3FFF,%d2
|
| 247 |
|
|
movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
|
| 248 |
|
|
movel (%sp)+,%d2
|
| 249 |
|
|
|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
|
| 250 |
|
|
|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
|
| 251 |
|
|
|--ADJFACT = 2^(M').
|
| 252 |
|
|
|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
|
| 253 |
|
|
|
| 254 |
|
|
fmuls #0x3C800000,%fp1 | ...(1/64)*N
|
| 255 |
|
|
movel (%a1)+,FACT1(%a6)
|
| 256 |
|
|
movel (%a1)+,FACT1HI(%a6)
|
| 257 |
|
|
movel (%a1)+,FACT1LOW(%a6)
|
| 258 |
|
|
movew (%a1)+,FACT2(%a6)
|
| 259 |
|
|
clrw FACT2+2(%a6)
|
| 260 |
|
|
|
| 261 |
|
|
fsubx %fp1,%fp0 | ...X - (1/64)*INT(64 X)
|
| 262 |
|
|
|
| 263 |
|
|
movew (%a1)+,FACT2HI(%a6)
|
| 264 |
|
|
clrw FACT2HI+2(%a6)
|
| 265 |
|
|
clrl FACT2LOW(%a6)
|
| 266 |
|
|
addw %d0,FACT1(%a6)
|
| 267 |
|
|
|
| 268 |
|
|
fmulx LOG2,%fp0 | ...FP0 IS R
|
| 269 |
|
|
addw %d0,FACT2(%a6)
|
| 270 |
|
|
|
| 271 |
|
|
bra expr
|
| 272 |
|
|
|
| 273 |
|
|
EXPBORS:
|
| 274 |
|
|
|--FPCR, D0 SAVED
|
| 275 |
|
|
cmpil #0x3FFF8000,%d0
|
| 276 |
|
|
bgts EXPBIG
|
| 277 |
|
|
|
| 278 |
|
|
EXPSM:
|
| 279 |
|
|
|--|X| IS SMALL, RETURN 1 + X
|
| 280 |
|
|
|
| 281 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 282 |
|
|
fadds #0x3F800000,%fp0 | ...RETURN 1 + X
|
| 283 |
|
|
|
| 284 |
|
|
bra t_frcinx
|
| 285 |
|
|
|
| 286 |
|
|
EXPBIG:
|
| 287 |
|
|
|--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
|
| 288 |
|
|
|--REGISTERS SAVE SO FAR ARE FPCR AND D0
|
| 289 |
|
|
movel X(%a6),%d0
|
| 290 |
|
|
cmpil #0,%d0
|
| 291 |
|
|
blts EXPNEG
|
| 292 |
|
|
|
| 293 |
|
|
bclrb #7,(%a0) |t_ovfl expects positive value
|
| 294 |
|
|
bra t_ovfl
|
| 295 |
|
|
|
| 296 |
|
|
EXPNEG:
|
| 297 |
|
|
bclrb #7,(%a0) |t_unfl expects positive value
|
| 298 |
|
|
bra t_unfl
|
| 299 |
|
|
|
| 300 |
|
|
.global stentoxd
|
| 301 |
|
|
stentoxd:
|
| 302 |
|
|
|--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
|
| 303 |
|
|
|
| 304 |
|
|
fmovel %d1,%fpcr | ...set user's rounding mode/precision
|
| 305 |
|
|
fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
|
| 306 |
|
|
movel (%a0),%d0
|
| 307 |
|
|
orl #0x00800001,%d0
|
| 308 |
|
|
fadds %d0,%fp0
|
| 309 |
|
|
bra t_frcinx
|
| 310 |
|
|
|
| 311 |
|
|
.global stentox
|
| 312 |
|
|
stentox:
|
| 313 |
|
|
|--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
|
| 314 |
|
|
fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
|
| 315 |
|
|
|
| 316 |
|
|
movel (%a0),%d0
|
| 317 |
|
|
movew 4(%a0),%d0
|
| 318 |
|
|
fmovex %fp0,X(%a6)
|
| 319 |
|
|
andil #0x7FFFFFFF,%d0
|
| 320 |
|
|
|
| 321 |
|
|
cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
|
| 322 |
|
|
bges TENOK1
|
| 323 |
|
|
bra EXPBORS
|
| 324 |
|
|
|
| 325 |
|
|
TENOK1:
|
| 326 |
|
|
cmpil #0x400B9B07,%d0 | ...|X| <= 16480*log2/log10 ?
|
| 327 |
|
|
bles TENMAIN
|
| 328 |
|
|
bra EXPBORS
|
| 329 |
|
|
|
| 330 |
|
|
TENMAIN:
|
| 331 |
|
|
|--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
|
| 332 |
|
|
|
| 333 |
|
|
fmovex %fp0,%fp1
|
| 334 |
|
|
fmuld L2TEN64,%fp1 | ...X*64*LOG10/LOG2
|
| 335 |
|
|
|
| 336 |
|
|
fmovel %fp1,N(%a6) | ...N=INT(X*64*LOG10/LOG2)
|
| 337 |
|
|
movel %d2,-(%sp)
|
| 338 |
|
|
lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
|
| 339 |
|
|
fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
|
| 340 |
|
|
movel N(%a6),%d0
|
| 341 |
|
|
movel %d0,%d2
|
| 342 |
|
|
andil #0x3F,%d0 | ...D0 IS J
|
| 343 |
|
|
asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
|
| 344 |
|
|
addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
|
| 345 |
|
|
asrl #6,%d2 | ...d2 IS L, N = 64L + J
|
| 346 |
|
|
movel %d2,%d0
|
| 347 |
|
|
asrl #1,%d0 | ...D0 IS M
|
| 348 |
|
|
subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
|
| 349 |
|
|
addil #0x3FFF,%d2
|
| 350 |
|
|
movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
|
| 351 |
|
|
movel (%sp)+,%d2
|
| 352 |
|
|
|
| 353 |
|
|
|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
|
| 354 |
|
|
|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
|
| 355 |
|
|
|--ADJFACT = 2^(M').
|
| 356 |
|
|
|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
|
| 357 |
|
|
|
| 358 |
|
|
fmovex %fp1,%fp2
|
| 359 |
|
|
|
| 360 |
|
|
fmuld L10TWO1,%fp1 | ...N*(LOG2/64LOG10)_LEAD
|
| 361 |
|
|
movel (%a1)+,FACT1(%a6)
|
| 362 |
|
|
|
| 363 |
|
|
fmulx L10TWO2,%fp2 | ...N*(LOG2/64LOG10)_TRAIL
|
| 364 |
|
|
|
| 365 |
|
|
movel (%a1)+,FACT1HI(%a6)
|
| 366 |
|
|
movel (%a1)+,FACT1LOW(%a6)
|
| 367 |
|
|
fsubx %fp1,%fp0 | ...X - N L_LEAD
|
| 368 |
|
|
movew (%a1)+,FACT2(%a6)
|
| 369 |
|
|
|
| 370 |
|
|
fsubx %fp2,%fp0 | ...X - N L_TRAIL
|
| 371 |
|
|
|
| 372 |
|
|
clrw FACT2+2(%a6)
|
| 373 |
|
|
movew (%a1)+,FACT2HI(%a6)
|
| 374 |
|
|
clrw FACT2HI+2(%a6)
|
| 375 |
|
|
clrl FACT2LOW(%a6)
|
| 376 |
|
|
|
| 377 |
|
|
fmulx LOG10,%fp0 | ...FP0 IS R
|
| 378 |
|
|
|
| 379 |
|
|
addw %d0,FACT1(%a6)
|
| 380 |
|
|
addw %d0,FACT2(%a6)
|
| 381 |
|
|
|
| 382 |
|
|
expr:
|
| 383 |
|
|
|--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
|
| 384 |
|
|
|--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
|
| 385 |
|
|
|--FP0 IS R. THE FOLLOWING CODE COMPUTES
|
| 386 |
|
|
|-- 2**(M'+M) * 2**(J/64) * EXP(R)
|
| 387 |
|
|
|
| 388 |
|
|
fmovex %fp0,%fp1
|
| 389 |
|
|
fmulx %fp1,%fp1 | ...FP1 IS S = R*R
|
| 390 |
|
|
|
| 391 |
|
|
fmoved EXPA5,%fp2 | ...FP2 IS A5
|
| 392 |
|
|
fmoved EXPA4,%fp3 | ...FP3 IS A4
|
| 393 |
|
|
|
| 394 |
|
|
fmulx %fp1,%fp2 | ...FP2 IS S*A5
|
| 395 |
|
|
fmulx %fp1,%fp3 | ...FP3 IS S*A4
|
| 396 |
|
|
|
| 397 |
|
|
faddd EXPA3,%fp2 | ...FP2 IS A3+S*A5
|
| 398 |
|
|
faddd EXPA2,%fp3 | ...FP3 IS A2+S*A4
|
| 399 |
|
|
|
| 400 |
|
|
fmulx %fp1,%fp2 | ...FP2 IS S*(A3+S*A5)
|
| 401 |
|
|
fmulx %fp1,%fp3 | ...FP3 IS S*(A2+S*A4)
|
| 402 |
|
|
|
| 403 |
|
|
faddd EXPA1,%fp2 | ...FP2 IS A1+S*(A3+S*A5)
|
| 404 |
|
|
fmulx %fp0,%fp3 | ...FP3 IS R*S*(A2+S*A4)
|
| 405 |
|
|
|
| 406 |
|
|
fmulx %fp1,%fp2 | ...FP2 IS S*(A1+S*(A3+S*A5))
|
| 407 |
|
|
faddx %fp3,%fp0 | ...FP0 IS R+R*S*(A2+S*A4)
|
| 408 |
|
|
|
| 409 |
|
|
faddx %fp2,%fp0 | ...FP0 IS EXP(R) - 1
|
| 410 |
|
|
|
| 411 |
|
|
|
| 412 |
|
|
|--FINAL RECONSTRUCTION PROCESS
|
| 413 |
|
|
|--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0)
|
| 414 |
|
|
|
| 415 |
|
|
fmulx FACT1(%a6),%fp0
|
| 416 |
|
|
faddx FACT2(%a6),%fp0
|
| 417 |
|
|
faddx FACT1(%a6),%fp0
|
| 418 |
|
|
|
| 419 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 420 |
|
|
clrw ADJFACT+2(%a6)
|
| 421 |
|
|
movel #0x80000000,ADJFACT+4(%a6)
|
| 422 |
|
|
clrl ADJFACT+8(%a6)
|
| 423 |
|
|
fmulx ADJFACT(%a6),%fp0 | ...FINAL ADJUSTMENT
|
| 424 |
|
|
|
| 425 |
|
|
bra t_frcinx
|
| 426 |
|
|
|
| 427 |
|
|
|end
|
