code / linux / torvalds / linux / 97eeb4d9d755605385fa329da9afa38729f3413c / . / arch / m68k / fpsp040 / satanh.S

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| satanh.sa 3.3 12/19/90 | |

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| The entry point satanh computes the inverse | |

| hyperbolic tangent of | |

| an input argument; satanhd does the same except for denormalized | |

| input. | |

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| Input: Double-extended number X in location pointed to | |

| by address register a0. | |

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| Output: The value arctanh(X) returned in floating-point register Fp0. | |

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| 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. | |

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| Speed: The program satanh takes approximately 270 cycles. | |

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| Algorithm: | |

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| ATANH | |

| 1. If |X| >= 1, go to 3. | |

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| 2. (|X| < 1) Calculate atanh(X) by | |

| sgn := sign(X) | |

| y := |X| | |

| z := 2y/(1-y) | |

| atanh(X) := sgn * (1/2) * logp1(z) | |

| Exit. | |

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| 3. If |X| > 1, go to 5. | |

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| 4. (|X| = 1) Generate infinity with an appropriate sign and | |

| divide-by-zero by | |

| sgn := sign(X) | |

| atan(X) := sgn / (+0). | |

| Exit. | |

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| 5. (|X| > 1) Generate an invalid operation by 0 * infinity. | |

| Exit. | |

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| Copyright (C) Motorola, Inc. 1990 | |

| All Rights Reserved | |

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| 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 |