1| 2| stanh.sa 3.1 12/10/90 3| 4| The entry point sTanh computes the hyperbolic tangent of 5| an input argument; sTanhd does the same except for denormalized 6| input. 7| 8| Input: Double-extended number X in location pointed to 9| by address register a0. 10| 11| Output: The value tanh(X) returned in floating-point register Fp0. 12| 13| Accuracy and Monotonicity: The returned result is within 3 ulps in 14| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 15| result is subsequently rounded to double precision. The 16| result is provably monotonic in double precision. 17| 18| Speed: The program stanh takes approximately 270 cycles. 19| 20| Algorithm: 21| 22| TANH 23| 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. 24| 25| 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by 26| sgn := sign(X), y := 2|X|, z := expm1(Y), and 27| tanh(X) = sgn*( z/(2+z) ). 28| Exit. 29| 30| 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, 31| go to 7. 32| 33| 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. 34| 35| 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by 36| sgn := sign(X), y := 2|X|, z := exp(Y), 37| tanh(X) = sgn - [ sgn*2/(1+z) ]. 38| Exit. 39| 40| 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we 41| calculate Tanh(X) by 42| sgn := sign(X), Tiny := 2**(-126), 43| tanh(X) := sgn - sgn*Tiny. 44| Exit. 45| 46| 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. 47| 48 49| Copyright (C) Motorola, Inc. 1990 50| All Rights Reserved 51| 52| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 53| The copyright notice above does not evidence any 54| actual or intended publication of such source code. 55 56|STANH idnt 2,1 | Motorola 040 Floating Point Software Package 57 58 |section 8 59 60#include "fpsp.h" 61 62 .set X,FP_SCR5 63 .set XDCARE,X+2 64 .set XFRAC,X+4 65 66 .set SGN,L_SCR3 67 68 .set V,FP_SCR6 69 70BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2 71 72 |xref t_frcinx 73 |xref t_extdnrm 74 |xref setox 75 |xref setoxm1 76 77 .global stanhd 78stanhd: 79|--TANH(X) = X FOR DENORMALIZED X 80 81 bra t_extdnrm 82 83 .global stanh 84stanh: 85 fmovex (%a0),%fp0 | ...LOAD INPUT 86 87 fmovex %fp0,X(%a6) 88 movel (%a0),%d0 89 movew 4(%a0),%d0 90 movel %d0,X(%a6) 91 andl #0x7FFFFFFF,%d0 92 cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ? 93 bcss TANHBORS 94 95|--THIS IS THE USUAL CASE 96|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). 97 98 movel X(%a6),%d0 99 movel %d0,SGN(%a6) 100 andl #0x7FFF0000,%d0 101 addl #0x00010000,%d0 | ...EXPONENT OF 2|X| 102 movel %d0,X(%a6) 103 andl #0x80000000,SGN(%a6) 104 fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X| 105 106 movel %d1,-(%a7) 107 clrl %d1 108 fmovemx %fp0-%fp0,(%a0) 109 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) 110 movel (%a7)+,%d1 111 112 fmovex %fp0,%fp1 113 fadds #0x40000000,%fp1 | ...Z+2 114 movel SGN(%a6),%d0 115 fmovex %fp1,V(%a6) 116 eorl %d0,V(%a6) 117 118 fmovel %d1,%FPCR |restore users exceptions 119 fdivx V(%a6),%fp0 120 bra t_frcinx 121 122TANHBORS: 123 cmpl #0x3FFF8000,%d0 124 blt TANHSM 125 126 cmpl #0x40048AA1,%d0 127 bgt TANHHUGE 128 129|-- (5/2) LOG2 < |X| < 50 LOG2, 130|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), 131|--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. 132 133 movel X(%a6),%d0 134 movel %d0,SGN(%a6) 135 andl #0x7FFF0000,%d0 136 addl #0x00010000,%d0 | ...EXPO OF 2|X| 137 movel %d0,X(%a6) | ...Y = 2|X| 138 andl #0x80000000,SGN(%a6) 139 movel SGN(%a6),%d0 140 fmovex X(%a6),%fp0 | ...Y = 2|X| 141 142 movel %d1,-(%a7) 143 clrl %d1 144 fmovemx %fp0-%fp0,(%a0) 145 bsr setox | ...FP0 IS EXP(Y) 146 movel (%a7)+,%d1 147 movel SGN(%a6),%d0 148 fadds #0x3F800000,%fp0 | ...EXP(Y)+1 149 150 eorl #0xC0000000,%d0 | ...-SIGN(X)*2 151 fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT 152 fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ] 153 154 movel SGN(%a6),%d0 155 orl #0x3F800000,%d0 | ...SGN 156 fmoves %d0,%fp0 | ...SGN IN SGL FMT 157 158 fmovel %d1,%FPCR |restore users exceptions 159 faddx %fp1,%fp0 160 161 bra t_frcinx 162 163TANHSM: 164 movew #0x0000,XDCARE(%a6) 165 166 fmovel %d1,%FPCR |restore users exceptions 167 fmovex X(%a6),%fp0 |last inst - possible exception set 168 169 bra t_frcinx 170 171TANHHUGE: 172|---RETURN SGN(X) - SGN(X)EPS 173 movel X(%a6),%d0 174 andl #0x80000000,%d0 175 orl #0x3F800000,%d0 176 fmoves %d0,%fp0 177 andl #0x80000000,%d0 178 eorl #0x80800000,%d0 | ...-SIGN(X)*EPS 179 180 fmovel %d1,%FPCR |restore users exceptions 181 fadds %d0,%fp0 182 183 bra t_frcinx 184 185 |end 186