Annotation of sys/arch/m68k/fpsp/scosh.sa, Revision 1.1
1.1 ! nbrk 1: * $OpenBSD: scosh.sa,v 1.2 1996/05/29 21:05:36 niklas Exp $
! 2: * $NetBSD: scosh.sa,v 1.2 1994/10/26 07:49:39 cgd Exp $
! 3:
! 4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
! 5: * M68000 Hi-Performance Microprocessor Division
! 6: * M68040 Software Package
! 7: *
! 8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
! 9: * All rights reserved.
! 10: *
! 11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
! 12: * To the maximum extent permitted by applicable law,
! 13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
! 14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
! 15: * PARTICULAR PURPOSE and any warranty against infringement with
! 16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
! 17: * and any accompanying written materials.
! 18: *
! 19: * To the maximum extent permitted by applicable law,
! 20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
! 21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
! 22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
! 23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
! 24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
! 25: * and support of the SOFTWARE.
! 26: *
! 27: * You are hereby granted a copyright license to use, modify, and
! 28: * distribute the SOFTWARE so long as this entire notice is retained
! 29: * without alteration in any modified and/or redistributed versions,
! 30: * and that such modified versions are clearly identified as such.
! 31: * No licenses are granted by implication, estoppel or otherwise
! 32: * under any patents or trademarks of Motorola, Inc.
! 33:
! 34: *
! 35: * scosh.sa 3.1 12/10/90
! 36: *
! 37: * The entry point sCosh computes the hyperbolic cosine of
! 38: * an input argument; sCoshd does the same except for denormalized
! 39: * input.
! 40: *
! 41: * Input: Double-extended number X in location pointed to
! 42: * by address register a0.
! 43: *
! 44: * Output: The value cosh(X) returned in floating-point register Fp0.
! 45: *
! 46: * Accuracy and Monotonicity: The returned result is within 3 ulps in
! 47: * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
! 48: * result is subsequently rounded to double precision. The
! 49: * result is provably monotonic in double precision.
! 50: *
! 51: * Speed: The program sCOSH takes approximately 250 cycles.
! 52: *
! 53: * Algorithm:
! 54: *
! 55: * COSH
! 56: * 1. If |X| > 16380 log2, go to 3.
! 57: *
! 58: * 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
! 59: * y = |X|, z = exp(Y), and
! 60: * cosh(X) = (1/2)*( z + 1/z ).
! 61: * Exit.
! 62: *
! 63: * 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
! 64: *
! 65: * 4. (16380 log2 < |X| <= 16480 log2)
! 66: * cosh(X) = sign(X) * exp(|X|)/2.
! 67: * However, invoking exp(|X|) may cause premature overflow.
! 68: * Thus, we calculate sinh(X) as follows:
! 69: * Y := |X|
! 70: * Fact := 2**(16380)
! 71: * Y' := Y - 16381 log2
! 72: * cosh(X) := Fact * exp(Y').
! 73: * Exit.
! 74: *
! 75: * 5. (|X| > 16480 log2) sinh(X) must overflow. Return
! 76: * Huge*Huge to generate overflow and an infinity with
! 77: * the appropriate sign. Huge is the largest finite number in
! 78: * extended format. Exit.
! 79: *
! 80:
! 81: SCOSH IDNT 2,1 Motorola 040 Floating Point Software Package
! 82:
! 83: section 8
! 84:
! 85: xref t_ovfl
! 86: xref t_frcinx
! 87: xref setox
! 88:
! 89: T1 DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD
! 90: T2 DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL
! 91:
! 92: TWO16380 DC.L $7FFB0000,$80000000,$00000000,$00000000
! 93:
! 94: xdef scoshd
! 95: scoshd:
! 96: *--COSH(X) = 1 FOR DENORMALIZED X
! 97:
! 98: FMOVE.S #:3F800000,FP0
! 99:
! 100: FMOVE.L d1,FPCR
! 101: FADD.S #:00800000,FP0
! 102: bra t_frcinx
! 103:
! 104: xdef scosh
! 105: scosh:
! 106: FMOVE.X (a0),FP0 ...LOAD INPUT
! 107:
! 108: move.l (a0),d0
! 109: move.w 4(a0),d0
! 110: ANDI.L #$7FFFFFFF,d0
! 111: CMPI.L #$400CB167,d0
! 112: BGT.B COSHBIG
! 113:
! 114: *--THIS IS THE USUAL CASE, |X| < 16380 LOG2
! 115: *--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
! 116:
! 117: FABS.X FP0 ...|X|
! 118:
! 119: move.l d1,-(sp)
! 120: clr.l d1
! 121: fmovem.x fp0,(a0) ;pass parameter to setox
! 122: bsr setox ...FP0 IS EXP(|X|)
! 123: FMUL.S #:3F000000,FP0 ...(1/2)EXP(|X|)
! 124: move.l (sp)+,d1
! 125:
! 126: FMOVE.S #:3E800000,FP1 ...(1/4)
! 127: FDIV.X FP0,FP1 ...1/(2 EXP(|X|))
! 128:
! 129: FMOVE.L d1,FPCR
! 130: FADD.X fp1,FP0
! 131:
! 132: bra t_frcinx
! 133:
! 134: COSHBIG:
! 135: CMPI.L #$400CB2B3,d0
! 136: BGT.B COSHHUGE
! 137:
! 138: FABS.X FP0
! 139: FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD)
! 140: FSUB.D T2(pc),FP0 ...|X| - 16381 LOG2, ACCURATE
! 141:
! 142: move.l d1,-(sp)
! 143: clr.l d1
! 144: fmovem.x fp0,(a0)
! 145: bsr setox
! 146: fmove.l (sp)+,fpcr
! 147:
! 148: FMUL.X TWO16380(pc),FP0
! 149: bra t_frcinx
! 150:
! 151: COSHHUGE:
! 152: fmove.l #0,fpsr ;clr N bit if set by source
! 153: bclr.b #7,(a0) ;always return positive value
! 154: fmovem.x (a0),fp0
! 155: bra t_ovfl
! 156:
! 157: end
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