| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | | |
| 2 | | sasin.sa 3.3 12/19/90 |
| 3 | | |
| 4 | | Description: The entry point sAsin computes the inverse sine of |
| 5 | | an input argument; sAsind does the same except for denormalized |
| 6 | | input. |
| 7 | | |
| 8 | | Input: Double-extended number X in location pointed to |
| 9 | | by address register a0. |
| 10 | | |
| 11 | | Output: The value arcsin(X) returned in floating-point register Fp0. |
| 12 | | |
| 13 | | Accuracy and Monotonicity: The returned result is within 3 ulps in |
| 14 | | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the |
| 15 | | result is subsequently rounded to double precision. The |
| 16 | | result is provably monotonic in double precision. |
| 17 | | |
| 18 | | Speed: The program sASIN takes approximately 310 cycles. |
| 19 | | |
| 20 | | Algorithm: |
| 21 | | |
| 22 | | ASIN |
| 23 | | 1. If |X| >= 1, go to 3. |
| 24 | | |
| 25 | | 2. (|X| < 1) Calculate asin(X) by |
| 26 | | z := sqrt( [1-X][1+X] ) |
| 27 | | asin(X) = atan( x / z ). |
| 28 | | Exit. |
| 29 | | |
| 30 | | 3. If |X| > 1, go to 5. |
| 31 | | |
| 32 | | 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit. |
| 33 | | |
| 34 | | 5. (|X| > 1) Generate an invalid operation by 0 * infinity. |
| 35 | | Exit. |
| 36 | | |
| 37 | |
| 38 | | Copyright (C) Motorola, Inc. 1990 |
| 39 | | All Rights Reserved |
| 40 | | |
| Matt Waddel | e00d82d | 2006-02-11 17:55:48 -0800 | [diff] [blame] | 41 | | For details on the license for this file, please see the |
| 42 | | file, README, in this same directory. |
| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 43 | |
| 44 | |SASIN idnt 2,1 | Motorola 040 Floating Point Software Package |
| 45 | |
| 46 | |section 8 |
| 47 | |
| 48 | PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 |
| 49 | |
| 50 | |xref t_operr |
| 51 | |xref t_frcinx |
| 52 | |xref t_extdnrm |
| 53 | |xref satan |
| 54 | |
| 55 | .global sasind |
| 56 | sasind: |
| 57 | |--ASIN(X) = X FOR DENORMALIZED X |
| 58 | |
| 59 | bra t_extdnrm |
| 60 | |
| 61 | .global sasin |
| 62 | sasin: |
| 63 | fmovex (%a0),%fp0 | ...LOAD INPUT |
| 64 | |
| 65 | movel (%a0),%d0 |
| 66 | movew 4(%a0),%d0 |
| 67 | andil #0x7FFFFFFF,%d0 |
| 68 | cmpil #0x3FFF8000,%d0 |
| 69 | bges asinbig |
| 70 | |
| 71 | |--THIS IS THE USUAL CASE, |X| < 1 |
| 72 | |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) ) |
| 73 | |
| 74 | fmoves #0x3F800000,%fp1 |
| 75 | fsubx %fp0,%fp1 | ...1-X |
| 76 | fmovemx %fp2-%fp2,-(%a7) |
| 77 | fmoves #0x3F800000,%fp2 |
| 78 | faddx %fp0,%fp2 | ...1+X |
| 79 | fmulx %fp2,%fp1 | ...(1+X)(1-X) |
| 80 | fmovemx (%a7)+,%fp2-%fp2 |
| 81 | fsqrtx %fp1 | ...SQRT([1-X][1+X]) |
| 82 | fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X]) |
| 83 | fmovemx %fp0-%fp0,(%a0) |
| 84 | bsr satan |
| 85 | bra t_frcinx |
| 86 | |
| 87 | asinbig: |
| 88 | fabsx %fp0 | ...|X| |
| 89 | fcmps #0x3F800000,%fp0 |
| 90 | fbgt t_operr |cause an operr exception |
| 91 | |
| 92 | |--|X| = 1, ASIN(X) = +- PI/2. |
| 93 | |
| 94 | fmovex PIBY2,%fp0 |
| 95 | movel (%a0),%d0 |
| 96 | andil #0x80000000,%d0 | ...SIGN BIT OF X |
| 97 | oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT |
| 98 | movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT |
| 99 | fmovel %d1,%FPCR |
| 100 | fmuls (%sp)+,%fp0 |
| 101 | bra t_frcinx |
| 102 | |
| 103 | |end |