| | |
| | sasin.sa 3.3 12/19/90 |
| | |
| | Description: The entry point sAsin computes the inverse sine of |
| | an input argument; sAsind does the same except for denormalized |
| | input. |
| | |
| | Input: Double-extended number X in location pointed to |
| | by address register a0. |
| | |
| | Output: The value arcsin(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 sASIN takes approximately 310 cycles. |
| | |
| | Algorithm: |
| | |
| | ASIN |
| | 1. If |X| >= 1, go to 3. |
| | |
| | 2. (|X| < 1) Calculate asin(X) by |
| | z := sqrt( [1-X][1+X] ) |
| | asin(X) = atan( x / z ). |
| | Exit. |
| | |
| | 3. If |X| > 1, go to 5. |
| | |
| | 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. 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. |
| |
| |SASIN idnt 2,1 | Motorola 040 Floating Point Software Package |
| |
| |section 8 |
| |
| PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 |
| |
| |xref t_operr |
| |xref t_frcinx |
| |xref t_extdnrm |
| |xref satan |
| |
| .global sasind |
| sasind: |
| |--ASIN(X) = X FOR DENORMALIZED X |
| |
| bra t_extdnrm |
| |
| .global sasin |
| sasin: |
| fmovex (%a0),%fp0 | ...LOAD INPUT |
| |
| movel (%a0),%d0 |
| movew 4(%a0),%d0 |
| andil #0x7FFFFFFF,%d0 |
| cmpil #0x3FFF8000,%d0 |
| bges asinbig |
| |
| |--THIS IS THE USUAL CASE, |X| < 1 |
| |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) ) |
| |
| fmoves #0x3F800000,%fp1 |
| fsubx %fp0,%fp1 | ...1-X |
| fmovemx %fp2-%fp2,-(%a7) |
| fmoves #0x3F800000,%fp2 |
| faddx %fp0,%fp2 | ...1+X |
| fmulx %fp2,%fp1 | ...(1+X)(1-X) |
| fmovemx (%a7)+,%fp2-%fp2 |
| fsqrtx %fp1 | ...SQRT([1-X][1+X]) |
| fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X]) |
| fmovemx %fp0-%fp0,(%a0) |
| bsr satan |
| bra t_frcinx |
| |
| asinbig: |
| fabsx %fp0 | ...|X| |
| fcmps #0x3F800000,%fp0 |
| fbgt t_operr |cause an operr exception |
| |
| |--|X| = 1, ASIN(X) = +- PI/2. |
| |
| fmovex PIBY2,%fp0 |
| movel (%a0),%d0 |
| andil #0x80000000,%d0 | ...SIGN BIT OF X |
| oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT |
| movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT |
| fmovel %d1,%FPCR |
| fmuls (%sp)+,%fp0 |
| bra t_frcinx |
| |
| |end |
