Loading...
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 | | | stanh.sa 3.1 12/10/90 | | The entry point sTanh computes the hyperbolic tangent of | an input argument; sTanhd does the same except for denormalized | input. | | Input: Double-extended number X in location pointed to | by address register a0. | | Output: The value tanh(X) returned in floating-point register Fp0. | | Accuracy and Monotonicity: The returned result is within 3 ulps in | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the | result is subsequently rounded to double precision. The | result is provably monotonic in double precision. | | Speed: The program stanh takes approximately 270 cycles. | | Algorithm: | | TANH | 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. | | 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by | sgn := sign(X), y := 2|X|, z := expm1(Y), and | tanh(X) = sgn*( z/(2+z) ). | Exit. | | 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, | go to 7. | | 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. | | 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by | sgn := sign(X), y := 2|X|, z := exp(Y), | tanh(X) = sgn - [ sgn*2/(1+z) ]. | Exit. | | 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we | calculate Tanh(X) by | sgn := sign(X), Tiny := 2**(-126), | tanh(X) := sgn - sgn*Tiny. | Exit. | | 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | For details on the license for this file, please see the | file, README, in this same directory. |STANH idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 #include "fpsp.h" .set X,FP_SCR5 .set XDCARE,X+2 .set XFRAC,X+4 .set SGN,L_SCR3 .set V,FP_SCR6 BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2 |xref t_frcinx |xref t_extdnrm |xref setox |xref setoxm1 .global stanhd stanhd: |--TANH(X) = X FOR DENORMALIZED X bra t_extdnrm .global stanh stanh: fmovex (%a0),%fp0 | ...LOAD INPUT fmovex %fp0,X(%a6) movel (%a0),%d0 movew 4(%a0),%d0 movel %d0,X(%a6) andl #0x7FFFFFFF,%d0 cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ? bcss TANHBORS |--THIS IS THE USUAL CASE |--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). movel X(%a6),%d0 movel %d0,SGN(%a6) andl #0x7FFF0000,%d0 addl #0x00010000,%d0 | ...EXPONENT OF 2|X| movel %d0,X(%a6) andl #0x80000000,SGN(%a6) fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X| movel %d1,-(%a7) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) movel (%a7)+,%d1 fmovex %fp0,%fp1 fadds #0x40000000,%fp1 | ...Z+2 movel SGN(%a6),%d0 fmovex %fp1,V(%a6) eorl %d0,V(%a6) fmovel %d1,%FPCR |restore users exceptions fdivx V(%a6),%fp0 bra t_frcinx TANHBORS: cmpl #0x3FFF8000,%d0 blt TANHSM cmpl #0x40048AA1,%d0 bgt TANHHUGE |-- (5/2) LOG2 < |X| < 50 LOG2, |--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), |--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. movel X(%a6),%d0 movel %d0,SGN(%a6) andl #0x7FFF0000,%d0 addl #0x00010000,%d0 | ...EXPO OF 2|X| movel %d0,X(%a6) | ...Y = 2|X| andl #0x80000000,SGN(%a6) movel SGN(%a6),%d0 fmovex X(%a6),%fp0 | ...Y = 2|X| movel %d1,-(%a7) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setox | ...FP0 IS EXP(Y) movel (%a7)+,%d1 movel SGN(%a6),%d0 fadds #0x3F800000,%fp0 | ...EXP(Y)+1 eorl #0xC0000000,%d0 | ...-SIGN(X)*2 fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ] movel SGN(%a6),%d0 orl #0x3F800000,%d0 | ...SGN fmoves %d0,%fp0 | ...SGN IN SGL FMT fmovel %d1,%FPCR |restore users exceptions faddx %fp1,%fp0 bra t_frcinx TANHSM: movew #0x0000,XDCARE(%a6) fmovel %d1,%FPCR |restore users exceptions fmovex X(%a6),%fp0 |last inst - possible exception set bra t_frcinx TANHHUGE: |---RETURN SGN(X) - SGN(X)EPS movel X(%a6),%d0 andl #0x80000000,%d0 orl #0x3F800000,%d0 fmoves %d0,%fp0 andl #0x80000000,%d0 eorl #0x80800000,%d0 | ...-SIGN(X)*EPS fmovel %d1,%FPCR |restore users exceptions fadds %d0,%fp0 bra t_frcinx |end |