stanh.sa revision 1.1.1.1
1 * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP 2 * M68000 Hi-Performance Microprocessor Division 3 * M68040 Software Package 4 * 5 * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. 6 * All rights reserved. 7 * 8 * THE SOFTWARE is provided on an "AS IS" basis and without warranty. 9 * To the maximum extent permitted by applicable law, 10 * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, 11 * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A 12 * PARTICULAR PURPOSE and any warranty against infringement with 13 * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) 14 * and any accompanying written materials. 15 * 16 * To the maximum extent permitted by applicable law, 17 * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER 18 * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS 19 * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR 20 * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE 21 * SOFTWARE. Motorola assumes no responsibility for the maintenance 22 * and support of the SOFTWARE. 23 * 24 * You are hereby granted a copyright license to use, modify, and 25 * distribute the SOFTWARE so long as this entire notice is retained 26 * without alteration in any modified and/or redistributed versions, 27 * and that such modified versions are clearly identified as such. 28 * No licenses are granted by implication, estoppel or otherwise 29 * under any patents or trademarks of Motorola, Inc. 30 31 * 32 * stanh.sa 3.1 12/10/90 33 * 34 * The entry point sTanh computes the hyperbolic tangent of 35 * an input argument; sTanhd does the same except for denormalized 36 * input. 37 * 38 * Input: Double-extended number X in location pointed to 39 * by address register a0. 40 * 41 * Output: The value tanh(X) returned in floating-point register Fp0. 42 * 43 * Accuracy and Monotonicity: The returned result is within 3 ulps in 44 * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 45 * result is subsequently rounded to double precision. The 46 * result is provably monotonic in double precision. 47 * 48 * Speed: The program stanh takes approximately 270 cycles. 49 * 50 * Algorithm: 51 * 52 * TANH 53 * 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. 54 * 55 * 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by 56 * sgn := sign(X), y := 2|X|, z := expm1(Y), and 57 * tanh(X) = sgn*( z/(2+z) ). 58 * Exit. 59 * 60 * 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, 61 * go to 7. 62 * 63 * 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. 64 * 65 * 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by 66 * sgn := sign(X), y := 2|X|, z := exp(Y), 67 * tanh(X) = sgn - [ sgn*2/(1+z) ]. 68 * Exit. 69 * 70 * 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we 71 * calculate Tanh(X) by 72 * sgn := sign(X), Tiny := 2**(-126), 73 * tanh(X) := sgn - sgn*Tiny. 74 * Exit. 75 * 76 * 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. 77 * 78 79 STANH IDNT 2,1 Motorola 040 Floating Point Software Package 80 81 section 8 82 83 include fpsp.h 84 85 X equ FP_SCR5 86 XDCARE equ X+2 87 XFRAC equ X+4 88 89 SGN equ L_SCR3 90 91 V equ FP_SCR6 92 93 BOUNDS1 DC.L $3FD78000,$3FFFDDCE ... 2^(-40), (5/2)LOG2 94 95 xref t_frcinx 96 xref t_extdnrm 97 xref setox 98 xref setoxm1 99 100 xdef stanhd 101 stanhd: 102 *--TANH(X) = X FOR DENORMALIZED X 103 104 bra t_extdnrm 105 106 xdef stanh 107 stanh: 108 FMOVE.X (a0),FP0 ...LOAD INPUT 109 110 FMOVE.X FP0,X(a6) 111 move.l (a0),d0 112 move.w 4(a0),d0 113 MOVE.L D0,X(a6) 114 AND.L #$7FFFFFFF,D0 115 CMP2.L BOUNDS1(pc),D0 ...2**(-40) < |X| < (5/2)LOG2 ? 116 BCS.B TANHBORS 117 118 *--THIS IS THE USUAL CASE 119 *--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). 120 121 MOVE.L X(a6),D0 122 MOVE.L D0,SGN(a6) 123 AND.L #$7FFF0000,D0 124 ADD.L #$00010000,D0 ...EXPONENT OF 2|X| 125 MOVE.L D0,X(a6) 126 AND.L #$80000000,SGN(a6) 127 FMOVE.X X(a6),FP0 ...FP0 IS Y = 2|X| 128 129 move.l d1,-(a7) 130 clr.l d1 131 fmovem.x fp0,(a0) 132 bsr setoxm1 ...FP0 IS Z = EXPM1(Y) 133 move.l (a7)+,d1 134 135 FMOVE.X FP0,FP1 136 FADD.S #:40000000,FP1 ...Z+2 137 MOVE.L SGN(a6),D0 138 FMOVE.X FP1,V(a6) 139 EOR.L D0,V(a6) 140 141 FMOVE.L d1,FPCR ;restore users exceptions 142 FDIV.X V(a6),FP0 143 bra t_frcinx 144 145 TANHBORS: 146 CMP.L #$3FFF8000,D0 147 BLT.W TANHSM 148 149 CMP.L #$40048AA1,D0 150 BGT.W TANHHUGE 151 152 *-- (5/2) LOG2 < |X| < 50 LOG2, 153 *--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), 154 *--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. 155 156 MOVE.L X(a6),D0 157 MOVE.L D0,SGN(a6) 158 AND.L #$7FFF0000,D0 159 ADD.L #$00010000,D0 ...EXPO OF 2|X| 160 MOVE.L D0,X(a6) ...Y = 2|X| 161 AND.L #$80000000,SGN(a6) 162 MOVE.L SGN(a6),D0 163 FMOVE.X X(a6),FP0 ...Y = 2|X| 164 165 move.l d1,-(a7) 166 clr.l d1 167 fmovem.x fp0,(a0) 168 bsr setox ...FP0 IS EXP(Y) 169 move.l (a7)+,d1 170 move.l SGN(a6),d0 171 FADD.S #:3F800000,FP0 ...EXP(Y)+1 172 173 EOR.L #$C0000000,D0 ...-SIGN(X)*2 174 FMOVE.S d0,FP1 ...-SIGN(X)*2 IN SGL FMT 175 FDIV.X FP0,FP1 ...-SIGN(X)2 / [EXP(Y)+1 ] 176 177 MOVE.L SGN(a6),D0 178 OR.L #$3F800000,D0 ...SGN 179 FMOVE.S d0,FP0 ...SGN IN SGL FMT 180 181 FMOVE.L d1,FPCR ;restore users exceptions 182 FADD.X fp1,FP0 183 184 bra t_frcinx 185 186 TANHSM: 187 MOVE.W #$0000,XDCARE(a6) 188 189 FMOVE.L d1,FPCR ;restore users exceptions 190 FMOVE.X X(a6),FP0 ;last inst - possible exception set 191 192 bra t_frcinx 193 194 TANHHUGE: 195 *---RETURN SGN(X) - SGN(X)EPS 196 MOVE.L X(a6),D0 197 AND.L #$80000000,D0 198 OR.L #$3F800000,D0 199 FMOVE.S d0,FP0 200 AND.L #$80000000,D0 201 EOR.L #$80800000,D0 ...-SIGN(X)*EPS 202 203 FMOVE.L d1,FPCR ;restore users exceptions 204 FADD.S d0,FP0 205 206 bra t_frcinx 207 208 end 209
Indexes created Sat Oct 18 23:09:54 GMT 2025