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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+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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