| | scosh.sa 3.1 12/10/90 | | The entry point sCosh computes the hyperbolic cosine of | an input argument; sCoshd does the same except for denormalized | input. | | Input: Double-extended number X in location pointed to | by address register a0. | | Output: The value cosh(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 sCOSH takes approximately 250 cycles. | | Algorithm: | | COSH | 1. If |X| > 16380 log2, go to 3. | | 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae | y = |X|, z = exp(Y), and | cosh(X) = (1/2)*( z + 1/z ). | Exit. | | 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. | | 4. (16380 log2 < |X| <= 16480 log2) | cosh(X) = sign(X) * exp(|X|)/2. | However, invoking exp(|X|) may cause premature overflow. | Thus, we calculate sinh(X) as follows: | Y := |X| | Fact := 2**(16380) | Y' := Y - 16381 log2 | cosh(X) := Fact * exp(Y'). | Exit. | | 5. (|X| > 16480 log2) sinh(X) must overflow. Return | Huge*Huge to generate overflow and an infinity with | the appropriate sign. Huge is the largest finite number in | extended format. 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. |SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 |xref t_ovfl |xref t_frcinx |xref setox T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000 .global scoshd scoshd: |--COSH(X) = 1 FOR DENORMALIZED X fmoves #0x3F800000,%fp0 fmovel %d1,%FPCR fadds #0x00800000,%fp0 bra t_frcinx .global scosh scosh: fmovex (%a0),%fp0 | ...LOAD INPUT movel (%a0),%d0 movew 4(%a0),%d0 andil #0x7FFFFFFF,%d0 cmpil #0x400CB167,%d0 bgts COSHBIG |--THIS IS THE USUAL CASE, |X| < 16380 LOG2 |--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) fabsx %fp0 | ...|X| movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) |pass parameter to setox bsr setox | ...FP0 IS EXP(|X|) fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|) movel (%sp)+,%d1 fmoves #0x3E800000,%fp1 | ...(1/4) fdivx %fp0,%fp1 | ...1/(2 EXP(|X|)) fmovel %d1,%FPCR faddx %fp1,%fp0 bra t_frcinx COSHBIG: cmpil #0x400CB2B3,%d0 bgts COSHHUGE fabsx %fp0 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD) fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setox fmovel (%sp)+,%fpcr fmulx TWO16380(%pc),%fp0 bra t_frcinx COSHHUGE: fmovel #0,%fpsr |clr N bit if set by source bclrb #7,(%a0) |always return positive value fmovemx (%a0),%fp0-%fp0 bra t_ovfl |end