?? l_scosh.s
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/* l_scosh - Motorola 68040 FP hyperbolic cosine routines (LIB) *//* Copyright 1991-1993 Wind River Systems, Inc. */ .data .globl _copyright_wind_river .long _copyright_wind_river/*modification history--------------------01e,21jul93,kdl added .text (SPR #2372).01d,23aug92,jcf changed bxxx to jxx.01c,26may92,rrr the tree shuffle01b,09jan92,kdl added modification history; general cleanup.01a,15aug91,kdl original version, from Motorola FPSP v2.0.*//*DESCRIPTION scoshsa 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 Copyright (C) Motorola, Inc. 1990 All Rights Reserved THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA The copyright notice above does not evidence any actual or intended publication of such source code.SCOSH idnt 2,1 Motorola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 8NOMANUAL*/| xref __l_t_ovfl| xref __l_t_frcinx| xref __l_setoxT1: .long 0x40C62D38,0xD3D64634 |... 16381 LOG2 LEADT2: .long 0x3D6F90AE,0xB1E75CC7 |... 16381 LOG2 TRAILTWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000 .text .globl __l_scoshd__l_scoshd:|--COSH(X) = 1 FOR DENORMALIZED X .long 0xf23c4400,0x3f800000 /* fmoves &0x3F800000,fp0 */ fmovel d1,fpcr .long 0xf23c4422,0x00800000 /* fadds &0x00800000,fp0 */ jra __l_t_frcinx .globl __l_scosh__l_scosh: fmovex a0@,fp0 |...lOAD INPUT movel a0@,d0 movew a0@(4),d0 andil #0x7FFFFFFF,d0 cmpil #0x400CB167,d0 jgt COSHBIG|--THIS IS THE USUAL CASE, |X| < 16380 LOG2|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) fabsx fp0,fp0 |...|X| movel d1,a7@- clrl d1 fmovemx fp0-fp0,a0@ | pass parameter to __l_setox bsrl __l_setox |...FP0 IS EXP(|X|) .long 0xf23c4423,0x3f000000 /* fmuls &0x3F000000,fp0 */ movel a7@+,d1 .long 0xf23c4480,0x3e800000 /* fmoves &0x3E800000,fp1 */ fdivx fp0,fp1 |...1/(2 EXP(|X|)) fmovel d1,fpcr faddx fp1,fp0 jra __l_t_frcinxCOSHBIG: cmpil #0x400CB2B3,d0 jgt COSHHUGE fabsx fp0,fp0 fsubd pc@(T1),fp0 |...(|X|-16381LOG2_LEAD) fsubd pc@(T2),fp0 |...|X| - 16381 LOG2, ACCURATE movel d1,a7@- clrl d1 fmovemx fp0-fp0,a0@ bsrl __l_setox fmovel a7@+,fpcr fmulx pc@(TWO16380),fp0 jra __l_t_frcinxCOSHHUGE: fmovel #0,fpsr | clr N bit if set by source bclr #7,a0@ | always return positive value fmovemx a0@,fp0-fp0 jra __l_t_ovfl| end
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