1 * $NetBSD: stanh.sa,v 1.3 1994/10/26 07:50:12 cgd Exp $ 2 3 * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP 4 * M68000 Hi-Performance Microprocessor Division 5 * M68040 Software Package 6 * 7 * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. 8 * All rights reserved. 9 * 10 * THE SOFTWARE is provided on an "AS IS" basis and without warranty. 11 * To the maximum extent permitted by applicable law, 12 * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, 13 * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A 14 * PARTICULAR PURPOSE and any warranty against infringement with 15 * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) 16 * and any accompanying written materials. 17 * 18 * To the maximum extent permitted by applicable law, 19 * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER 20 * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS 21 * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR 22 * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE 23 * SOFTWARE. Motorola assumes no responsibility for the maintenance 24 * and support of the SOFTWARE. 25 * 26 * You are hereby granted a copyright license to use, modify, and 27 * distribute the SOFTWARE so long as this entire notice is retained 28 * without alteration in any modified and/or redistributed versions, 29 * and that such modified versions are clearly identified as such. 30 * No licenses are granted by implication, estoppel or otherwise 31 * under any patents or trademarks of Motorola, Inc. 32 33 * 34 * stanh.sa 3.1 12/10/90 35 * 36 * The entry point sTanh computes the hyperbolic tangent of 37 * an input argument; sTanhd does the same except for denormalized 38 * input. 39 * 40 * Input: Double-extended number X in location pointed to 41 * by address register a0. 42 * 43 * Output: The value tanh(X) returned in floating-point register Fp0. 44 * 45 * Accuracy and Monotonicity: The returned result is within 3 ulps in 46 * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 47 * result is subsequently rounded to double precision. The 48 * result is provably monotonic in double precision. 49 * 50 * Speed: The program stanh takes approximately 270 cycles. 51 * 52 * Algorithm: 53 * 54 * TANH 55 * 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. 56 * 57 * 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by 58 * sgn := sign(X), y := 2|X|, z := expm1(Y), and 59 * tanh(X) = sgn*( z/(2+z) ). 60 * Exit. 61 * 62 * 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, 63 * go to 7. 64 * 65 * 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. 66 * 67 * 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by 68 * sgn := sign(X), y := 2|X|, z := exp(Y), 69 * tanh(X) = sgn - [ sgn*2/(1+z) ]. 70 * Exit. 71 * 72 * 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we 73 * calculate Tanh(X) by 74 * sgn := sign(X), Tiny := 2**(-126), 75 * tanh(X) := sgn - sgn*Tiny. 76 * Exit. 77 * 78 * 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. 79 * 80 81 STANH IDNT 2,1 Motorola 040 Floating Point Software Package 82 83 section 8 84 85 include fpsp.h 86 87 X equ FP_SCR5 88 XDCARE equ X+2 89 XFRAC equ X+4 90 91 SGN equ L_SCR3 92 93 V equ FP_SCR6 94 95 BOUNDS1 DC.L $3FD78000,$3FFFDDCE ... 2^(-40), (5/2)LOG2 96 97 xref t_frcinx 98 xref t_extdnrm 99 xref setox 100 xref setoxm1 101 102 xdef stanhd 103 stanhd: 104 *--TANH(X) = X FOR DENORMALIZED X 105 106 bra t_extdnrm 107 108 xdef stanh 109 stanh: 110 FMOVE.X (a0),FP0 ...LOAD INPUT 111 112 FMOVE.X FP0,X(a6) 113 move.l (a0),d0 114 move.w 4(a0),d0 115 MOVE.L D0,X(a6) 116 AND.L #$7FFFFFFF,D0 117 CMP2.L BOUNDS1(pc),D0 ...2**(-40) < |X| < (5/2)LOG2 ? 118 BCS.B TANHBORS 119 120 *--THIS IS THE USUAL CASE 121 *--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). 122 123 MOVE.L X(a6),D0 124 MOVE.L D0,SGN(a6) 125 AND.L #$7FFF0000,D0 126 ADD.L #$00010000,D0 ...EXPONENT OF 2|X| 127 MOVE.L D0,X(a6) 128 AND.L #$80000000,SGN(a6) 129 FMOVE.X X(a6),FP0 ...FP0 IS Y = 2|X| 130 131 move.l d1,-(a7) 132 clr.l d1 133 fmovem.x fp0,(a0) 134 bsr setoxm1 ...FP0 IS Z = EXPM1(Y) 135 move.l (a7)+,d1 136 137 FMOVE.X FP0,FP1 138 FADD.S #:40000000,FP1 ...Z+2 139 MOVE.L SGN(a6),D0 140 FMOVE.X FP1,V(a6) 141 EOR.L D0,V(a6) 142 143 FMOVE.L d1,FPCR ;restore users exceptions 144 FDIV.X V(a6),FP0 145 bra t_frcinx 146 147 TANHBORS: 148 CMP.L #$3FFF8000,D0 149 BLT.W TANHSM 150 151 CMP.L #$40048AA1,D0 152 BGT.W TANHHUGE 153 154 *-- (5/2) LOG2 < |X| < 50 LOG2, 155 *--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), 156 *--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. 157 158 MOVE.L X(a6),D0 159 MOVE.L D0,SGN(a6) 160 AND.L #$7FFF0000,D0 161 ADD.L #$00010000,D0 ...EXPO OF 2|X| 162 MOVE.L D0,X(a6) ...Y = 2|X| 163 AND.L #$80000000,SGN(a6) 164 MOVE.L SGN(a6),D0 165 FMOVE.X X(a6),FP0 ...Y = 2|X| 166 167 move.l d1,-(a7) 168 clr.l d1 169 fmovem.x fp0,(a0) 170 bsr setox ...FP0 IS EXP(Y) 171 move.l (a7)+,d1 172 move.l SGN(a6),d0 173 FADD.S #:3F800000,FP0 ...EXP(Y)+1 174 175 EOR.L #$C0000000,D0 ...-SIGN(X)*2 176 FMOVE.S d0,FP1 ...-SIGN(X)*2 IN SGL FMT 177 FDIV.X FP0,FP1 ...-SIGN(X)2 / [EXP(Y)+1 ] 178 179 MOVE.L SGN(a6),D0 180 OR.L #$3F800000,D0 ...SGN 181 FMOVE.S d0,FP0 ...SGN IN SGL FMT 182 183 FMOVE.L d1,FPCR ;restore users exceptions 184 FADD.X fp1,FP0 185 186 bra t_frcinx 187 188 TANHSM: 189 CLR.W XDCARE(a6) 190 191 FMOVE.L d1,FPCR ;restore users exceptions 192 FMOVE.X X(a6),FP0 ;last inst - possible exception set 193 194 bra t_frcinx 195 196 TANHHUGE: 197 *---RETURN SGN(X) - SGN(X)EPS 198 MOVE.L X(a6),D0 199 AND.L #$80000000,D0 200 OR.L #$3F800000,D0 201 FMOVE.S d0,FP0 202 AND.L #$80000000,D0 203 EOR.L #$80800000,D0 ...-SIGN(X)*EPS 204 205 FMOVE.L d1,FPCR ;restore users exceptions 206 FADD.S d0,FP0 207 208 bra t_frcinx 209 210 end 211
Indexes created Tue Oct 14 21:09:58 GMT 2025