scosh.S
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- |
- | 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
- |
- | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
- | The copyright notice above does not evidence any
- | actual or intended publication of such source code.
- |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