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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 | | | satanh.sa 3.3 12/19/90 | | The entry point satanh computes the inverse | hyperbolic tangent of | an input argument; satanhd does the same except for denormalized | input. | | Input: Double-extended number X in location pointed to | by address register a0. | | Output: The value arctanh(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 satanh takes approximately 270 cycles. | | Algorithm: | | ATANH | 1. If |X| >= 1, go to 3. | | 2. (|X| < 1) Calculate atanh(X) by | sgn := sign(X) | y := |X| | z := 2y/(1-y) | atanh(X) := sgn * (1/2) * logp1(z) | Exit. | | 3. If |X| > 1, go to 5. | | 4. (|X| = 1) Generate infinity with an appropriate sign and | divide-by-zero by | sgn := sign(X) | atan(X) := sgn / (+0). | Exit. | | 5. (|X| > 1) Generate an invalid operation by 0 * infinity. | Exit. | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code. |satanh idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 |xref t_dz |xref t_operr |xref t_frcinx |xref t_extdnrm |xref slognp1 .global satanhd satanhd: |--ATANH(X) = X FOR DENORMALIZED X bra t_extdnrm .global satanh satanh: movel (%a0),%d0 movew 4(%a0),%d0 andil #0x7FFFFFFF,%d0 cmpil #0x3FFF8000,%d0 bges ATANHBIG |--THIS IS THE USUAL CASE, |X| < 1 |--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z). fabsx (%a0),%fp0 | ...Y = |X| fmovex %fp0,%fp1 fnegx %fp1 | ...-Y faddx %fp0,%fp0 | ...2Y fadds #0x3F800000,%fp1 | ...1-Y fdivx %fp1,%fp0 | ...2Y/(1-Y) movel (%a0),%d0 andil #0x80000000,%d0 oril #0x3F000000,%d0 | ...SIGN(X)*HALF movel %d0,-(%sp) fmovemx %fp0-%fp0,(%a0) | ...overwrite input movel %d1,-(%sp) clrl %d1 bsr slognp1 | ...LOG1P(Z) fmovel (%sp)+,%fpcr fmuls (%sp)+,%fp0 bra t_frcinx ATANHBIG: fabsx (%a0),%fp0 | ...|X| fcmps #0x3F800000,%fp0 fbgt t_operr bra t_dz |end |