| | |
| | 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 |
| | |
| | For details on the license for this file, please see the |
| | file, README, in this same directory. |
| |
| |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 |