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authorJoel Sherrill <joel.sherrill@OARcorp.com>1997-04-16 17:33:04 +0000
committerJoel Sherrill <joel.sherrill@OARcorp.com>1997-04-16 17:33:04 +0000
commitf9b93da8b47ff7ea4d6573b75b6077f6efb8dbc6 (patch)
tree46e2747b2b8f04d36d530daad59481f4f79e3c00 /c/src/lib/libcpu/m68k/m68040/fpsp/stan.s
parentAdded --disable-tcpip option. (diff)
downloadrtems-f9b93da8b47ff7ea4d6573b75b6077f6efb8dbc6.tar.bz2
Added the MC68040 Floating Point Support Package. This was ported
to RTEMS by Eric Norum. It is freely distributable and was acquired from the Motorola WWW site. More info is in the FPSP README.
Diffstat (limited to 'c/src/lib/libcpu/m68k/m68040/fpsp/stan.s')
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diff --git a/c/src/lib/libcpu/m68k/m68040/fpsp/stan.s b/c/src/lib/libcpu/m68k/m68040/fpsp/stan.s
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+++ b/c/src/lib/libcpu/m68k/m68040/fpsp/stan.s
@@ -0,0 +1,455 @@
+//
+// stan.sa 3.3 7/29/91
+//
+// The entry point stan computes the tangent of
+// an input argument;
+// stand does the same except for denormalized input.
+//
+// Input: Double-extended number X in location pointed to
+// by address register a0.
+//
+// Output: The value tan(X) returned in floating-point register Fp0.
+//
+// Accuracy and Monotonicity: The returned result is within 3 ulp 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 sTAN takes approximately 170 cycles for
+// input argument X such that |X| < 15Pi, which is the the usual
+// situation.
+//
+// Algorithm:
+//
+// 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
+//
+// 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
+// k = N mod 2, so in particular, k = 0 or 1.
+//
+// 3. If k is odd, go to 5.
+//
+// 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a
+// rational function U/V where
+// U = r + r*s*(P1 + s*(P2 + s*P3)), and
+// V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r.
+// Exit.
+//
+// 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a
+// rational function U/V where
+// U = r + r*s*(P1 + s*(P2 + s*P3)), and
+// V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r,
+// -Cot(r) = -V/U. Exit.
+//
+// 6. If |X| > 1, go to 8.
+//
+// 7. (|X|<2**(-40)) Tan(X) = X. Exit.
+//
+// 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
+//
+
+// 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.
+
+//STAN idnt 2,1 | Motorola 040 Floating Point Software Package
+
+ |section 8
+
+ .include "fpsp.defs"
+
+BOUNDS1: .long 0x3FD78000,0x4004BC7E
+TWOBYPI: .long 0x3FE45F30,0x6DC9C883
+
+TANQ4: .long 0x3EA0B759,0xF50F8688
+TANP3: .long 0xBEF2BAA5,0xA8924F04
+
+TANQ3: .long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000
+
+TANP2: .long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000
+
+TANQ2: .long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000
+
+TANP1: .long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000
+
+TANQ1: .long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000
+
+INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000
+
+TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
+TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
+
+//--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
+//--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
+//--MOST 69 BITS LONG.
+ .global PITBL
+PITBL:
+ .long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000
+ .long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000
+ .long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000
+ .long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000
+ .long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000
+ .long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000
+ .long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000
+ .long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000
+ .long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000
+ .long 0xC0040000,0x90836524,0x88034B96,0x20B00000
+ .long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000
+ .long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000
+ .long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000
+ .long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000
+ .long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000
+ .long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000
+ .long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000
+ .long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000
+ .long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000
+ .long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000
+ .long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000
+ .long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000
+ .long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000
+ .long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000
+ .long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000
+ .long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000
+ .long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000
+ .long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000
+ .long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000
+ .long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000
+ .long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000
+ .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000
+ .long 0x00000000,0x00000000,0x00000000,0x00000000
+ .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000
+ .long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000
+ .long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000
+ .long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000
+ .long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000
+ .long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000
+ .long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000
+ .long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000
+ .long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000
+ .long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000
+ .long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000
+ .long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000
+ .long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000
+ .long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000
+ .long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000
+ .long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000
+ .long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000
+ .long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000
+ .long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000
+ .long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000
+ .long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000
+ .long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000
+ .long 0x40040000,0x90836524,0x88034B96,0xA0B00000
+ .long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000
+ .long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000
+ .long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000
+ .long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000
+ .long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000
+ .long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000
+ .long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000
+ .long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000
+ .long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000
+
+ .set INARG,FP_SCR4
+
+ .set TWOTO63,L_SCR1
+ .set ENDFLAG,L_SCR2
+ .set N,L_SCR3
+
+ | xref t_frcinx
+ |xref t_extdnrm
+
+ .global stand
+stand:
+//--TAN(X) = X FOR DENORMALIZED X
+
+ bra t_extdnrm
+
+ .global stan
+stan:
+ fmovex (%a0),%fp0 // ...LOAD INPUT
+
+ movel (%a0),%d0
+ movew 4(%a0),%d0
+ andil #0x7FFFFFFF,%d0
+
+ cmpil #0x3FD78000,%d0 // ...|X| >= 2**(-40)?
+ bges TANOK1
+ bra TANSM
+TANOK1:
+ cmpil #0x4004BC7E,%d0 // ...|X| < 15 PI?
+ blts TANMAIN
+ bra REDUCEX
+
+
+TANMAIN:
+//--THIS IS THE USUAL CASE, |X| <= 15 PI.
+//--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
+ fmovex %fp0,%fp1
+ fmuld TWOBYPI,%fp1 // ...X*2/PI
+
+//--HIDE THE NEXT TWO INSTRUCTIONS
+ leal PITBL+0x200,%a1 // ...TABLE OF N*PI/2, N = -32,...,32
+
+//--FP1 IS NOW READY
+ fmovel %fp1,%d0 // ...CONVERT TO INTEGER
+
+ asll #4,%d0
+ addal %d0,%a1 // ...ADDRESS N*PIBY2 IN Y1, Y2
+
+ fsubx (%a1)+,%fp0 // ...X-Y1
+//--HIDE THE NEXT ONE
+
+ fsubs (%a1),%fp0 // ...FP0 IS R = (X-Y1)-Y2
+
+ rorl #5,%d0
+ andil #0x80000000,%d0 // ...D0 WAS ODD IFF D0 < 0
+
+TANCONT:
+
+ cmpil #0,%d0
+ blt NODD
+
+ fmovex %fp0,%fp1
+ fmulx %fp1,%fp1 // ...S = R*R
+
+ fmoved TANQ4,%fp3
+ fmoved TANP3,%fp2
+
+ fmulx %fp1,%fp3 // ...SQ4
+ fmulx %fp1,%fp2 // ...SP3
+
+ faddd TANQ3,%fp3 // ...Q3+SQ4
+ faddx TANP2,%fp2 // ...P2+SP3
+
+ fmulx %fp1,%fp3 // ...S(Q3+SQ4)
+ fmulx %fp1,%fp2 // ...S(P2+SP3)
+
+ faddx TANQ2,%fp3 // ...Q2+S(Q3+SQ4)
+ faddx TANP1,%fp2 // ...P1+S(P2+SP3)
+
+ fmulx %fp1,%fp3 // ...S(Q2+S(Q3+SQ4))
+ fmulx %fp1,%fp2 // ...S(P1+S(P2+SP3))
+
+ faddx TANQ1,%fp3 // ...Q1+S(Q2+S(Q3+SQ4))
+ fmulx %fp0,%fp2 // ...RS(P1+S(P2+SP3))
+
+ fmulx %fp3,%fp1 // ...S(Q1+S(Q2+S(Q3+SQ4)))
+
+
+ faddx %fp2,%fp0 // ...R+RS(P1+S(P2+SP3))
+
+
+ fadds #0x3F800000,%fp1 // ...1+S(Q1+...)
+
+ fmovel %d1,%fpcr //restore users exceptions
+ fdivx %fp1,%fp0 //last inst - possible exception set
+
+ bra t_frcinx
+
+NODD:
+ fmovex %fp0,%fp1
+ fmulx %fp0,%fp0 // ...S = R*R
+
+ fmoved TANQ4,%fp3
+ fmoved TANP3,%fp2
+
+ fmulx %fp0,%fp3 // ...SQ4
+ fmulx %fp0,%fp2 // ...SP3
+
+ faddd TANQ3,%fp3 // ...Q3+SQ4
+ faddx TANP2,%fp2 // ...P2+SP3
+
+ fmulx %fp0,%fp3 // ...S(Q3+SQ4)
+ fmulx %fp0,%fp2 // ...S(P2+SP3)
+
+ faddx TANQ2,%fp3 // ...Q2+S(Q3+SQ4)
+ faddx TANP1,%fp2 // ...P1+S(P2+SP3)
+
+ fmulx %fp0,%fp3 // ...S(Q2+S(Q3+SQ4))
+ fmulx %fp0,%fp2 // ...S(P1+S(P2+SP3))
+
+ faddx TANQ1,%fp3 // ...Q1+S(Q2+S(Q3+SQ4))
+ fmulx %fp1,%fp2 // ...RS(P1+S(P2+SP3))
+
+ fmulx %fp3,%fp0 // ...S(Q1+S(Q2+S(Q3+SQ4)))
+
+
+ faddx %fp2,%fp1 // ...R+RS(P1+S(P2+SP3))
+ fadds #0x3F800000,%fp0 // ...1+S(Q1+...)
+
+
+ fmovex %fp1,-(%sp)
+ eoril #0x80000000,(%sp)
+
+ fmovel %d1,%fpcr //restore users exceptions
+ fdivx (%sp)+,%fp0 //last inst - possible exception set
+
+ bra t_frcinx
+
+TANBORS:
+//--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
+//--IF |X| < 2**(-40), RETURN X OR 1.
+ cmpil #0x3FFF8000,%d0
+ bgts REDUCEX
+
+TANSM:
+
+ fmovex %fp0,-(%sp)
+ fmovel %d1,%fpcr //restore users exceptions
+ fmovex (%sp)+,%fp0 //last inst - possible exception set
+
+ bra t_frcinx
+
+
+REDUCEX:
+//--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
+//--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
+//--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
+
+ fmovemx %fp2-%fp5,-(%a7) // ...save FP2 through FP5
+ movel %d2,-(%a7)
+ fmoves #0x00000000,%fp1
+
+//--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
+//--there is a danger of unwanted overflow in first LOOP iteration. In this
+//--case, reduce argument by one remainder step to make subsequent reduction
+//--safe.
+ cmpil #0x7ffeffff,%d0 //is argument dangerously large?
+ bnes LOOP
+ movel #0x7ffe0000,FP_SCR2(%a6) //yes
+// ;create 2**16383*PI/2
+ movel #0xc90fdaa2,FP_SCR2+4(%a6)
+ clrl FP_SCR2+8(%a6)
+ ftstx %fp0 //test sign of argument
+ movel #0x7fdc0000,FP_SCR3(%a6) //create low half of 2**16383*
+// ;PI/2 at FP_SCR3
+ movel #0x85a308d3,FP_SCR3+4(%a6)
+ clrl FP_SCR3+8(%a6)
+ fblt red_neg
+ orw #0x8000,FP_SCR2(%a6) //positive arg
+ orw #0x8000,FP_SCR3(%a6)
+red_neg:
+ faddx FP_SCR2(%a6),%fp0 //high part of reduction is exact
+ fmovex %fp0,%fp1 //save high result in fp1
+ faddx FP_SCR3(%a6),%fp0 //low part of reduction
+ fsubx %fp0,%fp1 //determine low component of result
+ faddx FP_SCR3(%a6),%fp1 //fp0/fp1 are reduced argument.
+
+//--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
+//--integer quotient will be stored in N
+//--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1)
+
+LOOP:
+ fmovex %fp0,INARG(%a6) // ...+-2**K * F, 1 <= F < 2
+ movew INARG(%a6),%d0
+ movel %d0,%a1 // ...save a copy of D0
+ andil #0x00007FFF,%d0
+ subil #0x00003FFF,%d0 // ...D0 IS K
+ cmpil #28,%d0
+ bles LASTLOOP
+CONTLOOP:
+ subil #27,%d0 // ...D0 IS L := K-27
+ movel #0,ENDFLAG(%a6)
+ bras WORK
+LASTLOOP:
+ clrl %d0 // ...D0 IS L := 0
+ movel #1,ENDFLAG(%a6)
+
+WORK:
+//--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
+//--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
+
+//--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
+//--2**L * (PIby2_1), 2**L * (PIby2_2)
+
+ movel #0x00003FFE,%d2 // ...BIASED EXPO OF 2/PI
+ subl %d0,%d2 // ...BIASED EXPO OF 2**(-L)*(2/PI)
+
+ movel #0xA2F9836E,FP_SCR1+4(%a6)
+ movel #0x4E44152A,FP_SCR1+8(%a6)
+ movew %d2,FP_SCR1(%a6) // ...FP_SCR1 is 2**(-L)*(2/PI)
+
+ fmovex %fp0,%fp2
+ fmulx FP_SCR1(%a6),%fp2
+//--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
+//--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
+//--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
+//--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
+//--US THE DESIRED VALUE IN FLOATING POINT.
+
+//--HIDE SIX CYCLES OF INSTRUCTION
+ movel %a1,%d2
+ swap %d2
+ andil #0x80000000,%d2
+ oril #0x5F000000,%d2 // ...D2 IS SIGN(INARG)*2**63 IN SGL
+ movel %d2,TWOTO63(%a6)
+
+ movel %d0,%d2
+ addil #0x00003FFF,%d2 // ...BIASED EXPO OF 2**L * (PI/2)
+
+//--FP2 IS READY
+ fadds TWOTO63(%a6),%fp2 // ...THE FRACTIONAL PART OF FP1 IS ROUNDED
+
+//--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2
+ movew %d2,FP_SCR2(%a6)
+ clrw FP_SCR2+2(%a6)
+ movel #0xC90FDAA2,FP_SCR2+4(%a6)
+ clrl FP_SCR2+8(%a6) // ...FP_SCR2 is 2**(L) * Piby2_1
+
+//--FP2 IS READY
+ fsubs TWOTO63(%a6),%fp2 // ...FP2 is N
+
+ addil #0x00003FDD,%d0
+ movew %d0,FP_SCR3(%a6)
+ clrw FP_SCR3+2(%a6)
+ movel #0x85A308D3,FP_SCR3+4(%a6)
+ clrl FP_SCR3+8(%a6) // ...FP_SCR3 is 2**(L) * Piby2_2
+
+ movel ENDFLAG(%a6),%d0
+
+//--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
+//--P2 = 2**(L) * Piby2_2
+ fmovex %fp2,%fp4
+ fmulx FP_SCR2(%a6),%fp4 // ...W = N*P1
+ fmovex %fp2,%fp5
+ fmulx FP_SCR3(%a6),%fp5 // ...w = N*P2
+ fmovex %fp4,%fp3
+//--we want P+p = W+w but |p| <= half ulp of P
+//--Then, we need to compute A := R-P and a := r-p
+ faddx %fp5,%fp3 // ...FP3 is P
+ fsubx %fp3,%fp4 // ...W-P
+
+ fsubx %fp3,%fp0 // ...FP0 is A := R - P
+ faddx %fp5,%fp4 // ...FP4 is p = (W-P)+w
+
+ fmovex %fp0,%fp3 // ...FP3 A
+ fsubx %fp4,%fp1 // ...FP1 is a := r - p
+
+//--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
+//--|r| <= half ulp of R.
+ faddx %fp1,%fp0 // ...FP0 is R := A+a
+//--No need to calculate r if this is the last loop
+ cmpil #0,%d0
+ bgt RESTORE
+
+//--Need to calculate r
+ fsubx %fp0,%fp3 // ...A-R
+ faddx %fp3,%fp1 // ...FP1 is r := (A-R)+a
+ bra LOOP
+
+RESTORE:
+ fmovel %fp2,N(%a6)
+ movel (%a7)+,%d2
+ fmovemx (%a7)+,%fp2-%fp5
+
+
+ movel N(%a6),%d0
+ rorl #1,%d0
+
+
+ bra TANCONT
+
+ |end