// // $Id$ // // 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 // // Copyright (C) Motorola, Inc. 1990 // All Rights Reserved // // THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA // The copyright notice above does not evidence any // actual or intended publication of such source code. //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