| | | |
| | 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 |