| | | |
| | 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 |