| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame^] | 1 | | |
| 2 | | satanh.sa 3.3 12/19/90 |
| 3 | | |
| 4 | | The entry point satanh computes the inverse |
| 5 | | hyperbolic tangent of |
| 6 | | an input argument; satanhd does the same except for denormalized |
| 7 | | input. |
| 8 | | |
| 9 | | Input: Double-extended number X in location pointed to |
| 10 | | by address register a0. |
| 11 | | |
| 12 | | Output: The value arctanh(X) returned in floating-point register Fp0. |
| 13 | | |
| 14 | | Accuracy and Monotonicity: The returned result is within 3 ulps in |
| 15 | | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the |
| 16 | | result is subsequently rounded to double precision. The |
| 17 | | result is provably monotonic in double precision. |
| 18 | | |
| 19 | | Speed: The program satanh takes approximately 270 cycles. |
| 20 | | |
| 21 | | Algorithm: |
| 22 | | |
| 23 | | ATANH |
| 24 | | 1. If |X| >= 1, go to 3. |
| 25 | | |
| 26 | | 2. (|X| < 1) Calculate atanh(X) by |
| 27 | | sgn := sign(X) |
| 28 | | y := |X| |
| 29 | | z := 2y/(1-y) |
| 30 | | atanh(X) := sgn * (1/2) * logp1(z) |
| 31 | | Exit. |
| 32 | | |
| 33 | | 3. If |X| > 1, go to 5. |
| 34 | | |
| 35 | | 4. (|X| = 1) Generate infinity with an appropriate sign and |
| 36 | | divide-by-zero by |
| 37 | | sgn := sign(X) |
| 38 | | atan(X) := sgn / (+0). |
| 39 | | Exit. |
| 40 | | |
| 41 | | 5. (|X| > 1) Generate an invalid operation by 0 * infinity. |
| 42 | | Exit. |
| 43 | | |
| 44 | |
| 45 | | Copyright (C) Motorola, Inc. 1990 |
| 46 | | All Rights Reserved |
| 47 | | |
| 48 | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA |
| 49 | | The copyright notice above does not evidence any |
| 50 | | actual or intended publication of such source code. |
| 51 | |
| 52 | |satanh idnt 2,1 | Motorola 040 Floating Point Software Package |
| 53 | |
| 54 | |section 8 |
| 55 | |
| 56 | |xref t_dz |
| 57 | |xref t_operr |
| 58 | |xref t_frcinx |
| 59 | |xref t_extdnrm |
| 60 | |xref slognp1 |
| 61 | |
| 62 | .global satanhd |
| 63 | satanhd: |
| 64 | |--ATANH(X) = X FOR DENORMALIZED X |
| 65 | |
| 66 | bra t_extdnrm |
| 67 | |
| 68 | .global satanh |
| 69 | satanh: |
| 70 | movel (%a0),%d0 |
| 71 | movew 4(%a0),%d0 |
| 72 | andil #0x7FFFFFFF,%d0 |
| 73 | cmpil #0x3FFF8000,%d0 |
| 74 | bges ATANHBIG |
| 75 | |
| 76 | |--THIS IS THE USUAL CASE, |X| < 1 |
| 77 | |--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z). |
| 78 | |
| 79 | fabsx (%a0),%fp0 | ...Y = |X| |
| 80 | fmovex %fp0,%fp1 |
| 81 | fnegx %fp1 | ...-Y |
| 82 | faddx %fp0,%fp0 | ...2Y |
| 83 | fadds #0x3F800000,%fp1 | ...1-Y |
| 84 | fdivx %fp1,%fp0 | ...2Y/(1-Y) |
| 85 | movel (%a0),%d0 |
| 86 | andil #0x80000000,%d0 |
| 87 | oril #0x3F000000,%d0 | ...SIGN(X)*HALF |
| 88 | movel %d0,-(%sp) |
| 89 | |
| 90 | fmovemx %fp0-%fp0,(%a0) | ...overwrite input |
| 91 | movel %d1,-(%sp) |
| 92 | clrl %d1 |
| 93 | bsr slognp1 | ...LOG1P(Z) |
| 94 | fmovel (%sp)+,%fpcr |
| 95 | fmuls (%sp)+,%fp0 |
| 96 | bra t_frcinx |
| 97 | |
| 98 | ATANHBIG: |
| 99 | fabsx (%a0),%fp0 | ...|X| |
| 100 | fcmps #0x3F800000,%fp0 |
| 101 | fbgt t_operr |
| 102 | bra t_dz |
| 103 | |
| 104 | |end |