| | |

| | 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 |