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 | For details on the license for this file, please see the 53 | file, README, in this same directory. 54 55 |STANH idnt 2,1 | Motorola 040 Floating Point Software Package 56 57 |section 8 58 59 #include "fpsp.h" 60 61 .set X,FP_SCR5 62 .set XDCARE,X+2 63 .set XFRAC,X+4 64 65 .set SGN,L_SCR3 66 67 .set V,FP_SCR6 68 69 BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2 70 71 |xref t_frcinx 72 |xref t_extdnrm 73 |xref setox 74 |xref setoxm1 75 76 .global stanhd 77 stanhd: 78 |--TANH(X) = X FOR DENORMALIZED X 79 80 bra t_extdnrm 81 82 .global stanh 83 stanh: 84 fmovex (%a0),%fp0 | ...LOAD INPUT 85 86 fmovex %fp0,X(%a6) 87 movel (%a0),%d0 88 movew 4(%a0),%d0 89 movel %d0,X(%a6) 90 andl #0x7FFFFFFF,%d0 91 cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ? 92 bcss TANHBORS 93 94 |--THIS IS THE USUAL CASE 95 |--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). 96 97 movel X(%a6),%d0 98 movel %d0,SGN(%a6) 99 andl #0x7FFF0000,%d0 100 addl #0x00010000,%d0 | ...EXPONENT OF 2|X| 101 movel %d0,X(%a6) 102 andl #0x80000000,SGN(%a6) 103 fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X| 104 105 movel %d1,-(%a7) 106 clrl %d1 107 fmovemx %fp0-%fp0,(%a0) 108 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) 109 movel (%a7)+,%d1 110 111 fmovex %fp0,%fp1 112 fadds #0x40000000,%fp1 | ...Z+2 113 movel SGN(%a6),%d0 114 fmovex %fp1,V(%a6) 115 eorl %d0,V(%a6) 116 117 fmovel %d1,%FPCR |restore users exceptions 118 fdivx V(%a6),%fp0 119 bra t_frcinx 120 121 TANHBORS: 122 cmpl #0x3FFF8000,%d0 123 blt TANHSM 124 125 cmpl #0x40048AA1,%d0 126 bgt TANHHUGE 127 128 |-- (5/2) LOG2 < |X| < 50 LOG2, 129 |--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), 130 |--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. 131 132 movel X(%a6),%d0 133 movel %d0,SGN(%a6) 134 andl #0x7FFF0000,%d0 135 addl #0x00010000,%d0 | ...EXPO OF 2|X| 136 movel %d0,X(%a6) | ...Y = 2|X| 137 andl #0x80000000,SGN(%a6) 138 movel SGN(%a6),%d0 139 fmovex X(%a6),%fp0 | ...Y = 2|X| 140 141 movel %d1,-(%a7) 142 clrl %d1 143 fmovemx %fp0-%fp0,(%a0) 144 bsr setox | ...FP0 IS EXP(Y) 145 movel (%a7)+,%d1 146 movel SGN(%a6),%d0 147 fadds #0x3F800000,%fp0 | ...EXP(Y)+1 148 149 eorl #0xC0000000,%d0 | ...-SIGN(X)*2 150 fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT 151 fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ] 152 153 movel SGN(%a6),%d0 154 orl #0x3F800000,%d0 | ...SGN 155 fmoves %d0,%fp0 | ...SGN IN SGL FMT 156 157 fmovel %d1,%FPCR |restore users exceptions 158 faddx %fp1,%fp0 159 160 bra t_frcinx 161 162 TANHSM: 163 movew #0x0000,XDCARE(%a6) 164 165 fmovel %d1,%FPCR |restore users exceptions 166 fmovex X(%a6),%fp0 |last inst - possible exception set 167 168 bra t_frcinx 169 170 TANHHUGE: 171 |---RETURN SGN(X) - SGN(X)EPS 172 movel X(%a6),%d0 173 andl #0x80000000,%d0 174 orl #0x3F800000,%d0 175 fmoves %d0,%fp0 176 andl #0x80000000,%d0 177 eorl #0x80800000,%d0 | ...-SIGN(X)*EPS 178 179 fmovel %d1,%FPCR |restore users exceptions 180 fadds %d0,%fp0 181 182 bra t_frcinx 183 184 |end 185