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 81STANH IDNT 2,1 Motorola 040 Floating Point Software Package 82 83 section 8 84 85 include fpsp.h 86 87X equ FP_SCR5 88XDCARE equ X+2 89XFRAC equ X+4 90 91SGN equ L_SCR3 92 93V equ FP_SCR6 94 95BOUNDS1 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 103stanhd: 104*--TANH(X) = X FOR DENORMALIZED X 105 106 bra t_extdnrm 107 108 xdef stanh 109stanh: 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 147TANHBORS: 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 188TANHSM: 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 196TANHHUGE: 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