Merge branch 'sqrt_decn'
This commit is contained in:
Jeff Wang
commit
233f347ecc
10
README.md
10
README.md
@ -109,7 +109,7 @@ Press `Shift` (the `mode` key on the physical calculator) and then `0` to turn o
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# Building
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# Building
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There is a prebuilt binary for the calculator checked in at `binaries/main.hex` for the calculator. Building is fairly straigtforward though.
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Github releases has prebuilt binaries for the calculator. Building is fairly straigtforward though.
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- Use the Makefile for building a new firmware for the calculator.
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- Use the Makefile for building a new firmware for the calculator.
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- type `make` to build
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- type `make` to build
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@ -206,7 +206,7 @@ I sometimes use an STC15F2K60S2 for development work. This microcontroller is av
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## Programming with stcgal
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## Programming with stcgal
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Run `stcgal` as shown below, replacing `stc_rpncalc/main.hex` with the actual path to the main.hex you built. There are also prebuilt binaries in the `binaries` directory. In this example, I'm programming at a relatively high line rate of 230,400 bits/s. This works very reliably, but you may want to try at a slower speed to start (omit the `-b 230400` option).
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Run `stcgal` as shown below, replacing `stc_rpncalc/main.hex` with the actual path to the main.hex you built. There are also prebuilt binaries in the `binaries` directory. In this example, I'm programming at a relatively high line rate of 230,400 bits/s. This works very reliably, but you may want to try at a slower speed to start (omit the `-b 230400` option), especially when using an inline resistor and diode.
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~~~~
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~~~~
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$ ./stcgal.py -P stc15 -b 230400 stc_rpncalc/main.hex
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$ ./stcgal.py -P stc15 -b 230400 stc_rpncalc/main.hex
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@ -251,7 +251,7 @@ Disconnected!
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# Bugs
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# Bugs
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1. After division by 0, ln(-), over/underflow, or other operations which give an `Error`, it's possible to still do certain operations on `Error`. Many functions do check, and will not operate on `Error`, but not all of them yet. This is somewhat similar to old soviet Elektronika calculators where `Error` is just a number, and there wasn't enough ROM space to check for errors. (There are people who explore the inner-workings of these calculators by manipulating the `Error` "number".)
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1. After division by 0, ln(-), over/underflow, or other operations which give an `Error`, it's possible to still do certain operations on `Error`. Many functions do check, and will not operate on `Error`, but not all of them yet. This is somewhat similar to old soviet Elektronika calculators where `Error` is just a number, and there wasn't enough ROM space to check for errors. (There are people who explore the inner-workings of these calculators by manipulating the `Error` "number".)
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1. When shifted down, keys which do not have a shifted-down function will instead be interpreted as if there were no shift.
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1. When shifted, keys which do not have a shifted function will instead be interpreted as if there were no shift.
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1. Trigonometric functions are extremely slow and inaccurate.
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1. Trigonometric functions are extremely slow and inaccurate.
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1. There are probably more bugs waiting to be discovered.
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1. There are probably more bugs waiting to be discovered.
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@ -300,7 +300,9 @@ The number `0.135` would be stored the same way, except now the exponent is `0x7
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- Exponentials are calculated similar to the HP 35 algorithm, as described [here](http://www.jacques-laporte.org/expx.htm) using the same constants as the logarithm algorithm.
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- Exponentials are calculated similar to the HP 35 algorithm, as described [here](http://www.jacques-laporte.org/expx.htm) using the same constants as the logarithm algorithm.
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- see `src/decn/proto/exp.cpp` for initial prototyping development work
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- see `src/decn/proto/exp.cpp` for initial prototyping development work
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- Powers are calculated using the identity y^x = e^(x*ln(y))
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- Powers are calculated using the identity y^x = e^(x*ln(y))
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- Square roots are calculated using the identity sqrt(x) = e^(0.5*ln(x))
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- Square roots are calculated using a fixed number of Newton-Raphson iterations to calculatie 1/sqrt(x) and then multiplying by x.
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- the iteration for 1/sqrt(x) is new_estimate = 0.5*estimate * (3 - x * estimate * estimate)
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- see `src/decn/proto/recip_sqrt.cpp for initial prototyping development work
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- Trigonometric functions are calculated using algorithms similar to the [sinclair scientific](http://files.righto.com/calculator/sinclair_scientific_simulator.html), and are fairly slow and inaccurate.
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- Trigonometric functions are calculated using algorithms similar to the [sinclair scientific](http://files.righto.com/calculator/sinclair_scientific_simulator.html), and are fairly slow and inaccurate.
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## TODO
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## TODO
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@ -1,391 +0,0 @@
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:2022D600838FF0C007C006C005C004C0021213CCE582D002D004D005D006D00760071222F3
|
|
||||||
:2022F600A5758200228D708E718F7290005375F000C004C002120E7690005375F00012103F
|
|
||||||
:2023160047D002D004900055E0700F90001F7430F0900020E4F075820022900053E0FEA332
|
|
||||||
:20233600E0FF30E70890001F742DF07C0190005375F000C004C002120EF2AE82AF83D002B8
|
|
||||||
:20235600D004902E25E493FDF8790018B8FF0119C3E89EE964808FF063F08095F0400AEEBD
|
|
||||||
:2023760094FDEF6480947F50027A01EA7057EF30E753EC241FF582E43400F5837430F00C23
|
|
||||||
:202396008C010CE9241FF582E43400F583742EF0C3E49EF8E49FF918B8FF01198C62C3E492
|
|
||||||
:2023B60098748089F063F08095F05017E562241FF582E43400F5837430F0056218B8FF01E7
|
|
||||||
:2023D6001980DBAC62EC241FF8E43400F9900055E075F00A842430FB88828983F00CEA60CA
|
|
||||||
:2023F600128C030CEB241FF582E43400F583742EF08019EE4F70108C030CEB241FF582E4D9
|
|
||||||
:202416003400F583742EF01EBEFF011FEC241FF9E43400FB900055E075F00A84A8F074303E
|
|
||||||
:2024360028F889828B83F0900055E0FB75F00A84E5F0700AEA7004EF30E7037561010CEA27
|
|
||||||
:202456007019EE4F70108C030CEB241FF582E43400F583742EF01EBEFF011FEDC313FD758E
|
|
||||||
:202476006001C3E5609D400302255CEC241FF8E43400F9E5602455F582E43400F583E07528
|
|
||||||
:20249600F00A842430FB88828983F00CEA7019EE4F70108C030CEB241FF582E43400F58347
|
|
||||||
:2024B600742EF01EBEFF011FEC241FF9E43400FBE5602455F582E43400F583E075F00A84A6
|
|
||||||
:2024D600A8F0743028F889828B83F00CEA7019EE4F70108C030CEB241FF582E43400F58375
|
|
||||||
:2024F600742EF01EBEFF011FE5602455F9E43400FB89828B83E07025EA7004EF30E71EEA75
|
|
||||||
:20251600700BC3EE94FEEF6480947F500605610561802EBEFE2BBFFF2805618024E56024F1
|
|
||||||
:2025360055F582E43400F583E0FB75F00A84E5F0700CEA7004EF30E7057561018003756171
|
|
||||||
:20255600000560022478EA700EC3E49E74808FF063F08095F04005ECC39561FCEC241FF5E0
|
|
||||||
:2025760082E43400F583E4F090005375F000C002120EF2AE82AF83D002EA6023C374809E4D
|
|
||||||
:2025960074808FF063F08095F0400AEE9480EF6480947F50071222A5758200228E82227538
|
|
||||||
:0325B6008200227E
|
|
||||||
:202E25001000000A0000000000000000000017023A325C63282D440080FF7F451F2F1205EE
|
|
||||||
:202E45003B5E3509FE7F5F1F014F502B185600FD7F633221083510505254FC7F635F00218F
|
|
||||||
:202E65001E53351F43FB7F636332002121082121FA7F63635F000021211D5FF97F6363634A
|
|
||||||
:1C2E8500320000210523F87F6363635F0000024C28F77F6363636332000F62415B
|
|
||||||
:08007E00756300756400C20205
|
|
||||||
:2025B9007403556475F00BA42474FE740035F0FF7D0074032564540375F00BA42474FB74A1
|
|
||||||
:2025D9000035F0FC8B708C718D728E828F838DF0120E76056422AE82AF83E5637002156475
|
|
||||||
:2025F9009000A0E0FCA3E0FD90003BECF0EDA3F08E828F831211477403556475F00BA4241B
|
|
||||||
:2026190074FE740035F0FF7D0075702D8D717572408E828F838DF0020E767403556475F029
|
|
||||||
:202639000BA42474FE740035F0FF7D008E828F838DF002136C7403556475F00BA42474F536
|
|
||||||
:2026590082740035F0F58322E56404540375F00BA42474F582740035F0F58322AE82AF8350
|
|
||||||
:20267900E56404540375F00BA42474FC740035F0FD7B008C828D838BF0C007C0061213CCCD
|
|
||||||
:20269900E582D006D00770277403556475F00BA42474FC740035F0FD7B008C828D838BF0F4
|
|
||||||
:2026B900C007C0061213CCE582D006D007601FE56404540375F00BA42474FC740035F0FD0E
|
|
||||||
:2026D9007B008C828D838BF01214150227837403556475F00BA42474FC740035F0FD8C707C
|
|
||||||
:2026F9008D7175720090006975F000C007C006120E76E56404540375F00BA42474FC74009B
|
|
||||||
:2027190035F0FD8C708D7175720090002D75F040120E767403556475F00BA42474FC740059
|
|
||||||
:2027390035F0FD8C708D7175720090009E75F040120E76D006D007C007C0068E828F8312A6
|
|
||||||
:202759000011D006D007E56404540375F00BA42474FE740035F0FF7D0075702D8D71757248
|
|
||||||
:20277900408E828F838DF0120E760225B9AE82AF837403556475F00BA42474FC740035F018
|
|
||||||
:20279900FD7B008C828D838BF0C007C0061213CCE582D006D0076001227403556475F00B5A
|
|
||||||
:2027B900A42474FC740035F0FD8C708D7175720090006975F000C007C006120E7674035504
|
|
||||||
:2027D9006475F00BA42474FC740035F0FD8C708D7175720090002D75F040120E76D006D0BF
|
|
||||||
:2027F90007C007C0068E828F83120011D006D0077403556475F00BA42474FE740035F0FFC8
|
|
||||||
:202819007D0075702D8D717572408E828F838DF0020E76B20222AF82C007120E73D007BFCF
|
|
||||||
:202839002A030228D0BF2B028055BF2D030228D6BF2E0302298CBF2F03022900BF340302ED
|
|
||||||
:202859002B86BF3503022B8FBF3603022B9CBF3703022BC3BF3803022BB6BF3903022BA9A3
|
|
||||||
:20287900BF3C030229CEBF3D03022906BF63030229B3BF6D03022B83BF7203022AE22230A2
|
|
||||||
:20289900022F7401B56302800215647403556475F00BA42474FE740035F0FF7D0075706927
|
|
||||||
:2028B9007571008D728E828F838DF0120E76C20222901697022675901920022675740355F3
|
|
||||||
:2028D9006475F00BA42474FE740035F0FF7D008E828F838DF0121448901697122675900035
|
|
||||||
:2028F9006975F000021448901C0B02267530022F7401B56302800215647403556475F00BB4
|
|
||||||
:20291900A42474FE740035F0FF7D0075705E7571008D728E828F838DF0120E76C202227498
|
|
||||||
:2029390003556475F00BA42474FE740035F0FF7D008E828F838DF01213CCE5826001221574
|
|
||||||
:20295900647403556475F00BA42474FE740035F0FF7D00E56404540375F00BA42474FB744C
|
|
||||||
:202979000035F0FC8B708C718D728E828F838DF0020E76200201227403556475F00BA42454
|
|
||||||
:2029990074FE740035F0FF8E708F7175720090005E75F000120E76C202227403556475F0CB
|
|
||||||
:2029B9000BA42474FE740035F0FF7D008E828F838DF002136C100203022AA77403556475F7
|
|
||||||
:2029D900F00BA42474FE740035F0FF7D008E828F838DF012139CE5826001227403556475A5
|
|
||||||
:2029F900F00BA42474FE740035F0FF7D008E828F838DF01213CCE582600122740355647555
|
|
||||||
:202A1900F00BA42474FE740035F0FF8E708F7175720090006975F000120E76740355647552
|
|
||||||
:202A3900F00BA42474FE740035F0FF8E708F7175720090002D75F040120E76E52E30E71B8E
|
|
||||||
:202A59007403556475F00BA42474FE740035F0FF7D008E828F838DF002141590009E75F011
|
|
||||||
:202A79004012136C78A076051222437403556475F00BA42474FE740035F0FF7D0075702D61
|
|
||||||
:202A99008D717572408E828F838DF0020E767403556475F00BA42474FE740035F0FF7D00E4
|
|
||||||
:202AB9008E828F838DF01213CCE5826001227403556475F00BA42474FE740035F0FF7D0094
|
|
||||||
:202AD9008E828F838DF00214481002028006901AFB0227867403556475F00BA42474FE74A4
|
|
||||||
:202AF9000035F0FF7D008E828F838DF01213CCE5826001227403556475F00BA42474FE7454
|
|
||||||
:202B19000035F0FF8E708F7175720090006575F040120E767403556475F00BA42474FE7415
|
|
||||||
:202B39000035F0FF7D00E56404540375F00BA42474FB740035F0FC8B708C718D728E828F65
|
|
||||||
:202B5900838DF0120E76E56404540375F00BA42474FE740035F0FF7D007570658D71757234
|
|
||||||
:202B7900408E828F838DF0020E7602282C200201220564C2022220020122901F88122786B2
|
|
||||||
:202B9900C202222002012290222B122786C2022220020122901F37122786C202222002017C
|
|
||||||
:202BB90022901C47122786C20222E56404540375F00BA42474FE740035F0FF7D008E828F40
|
|
||||||
:202BD900838DF01213CCE582701F7403556475F00BA42474FE740035F0FF7D008E828F83E4
|
|
||||||
:202BF9008DF01213CCE582601FE56404540375F00BA42474FE740035F0FF7D008E828F83E3
|
|
||||||
:202C19008DF0121415022CA97403556475F00BA42474FE740035F0FF8E708F717572009025
|
|
||||||
:202C3900006975F000120E76E56404540375F00BA42474FE740035F0FF8E708F717572004C
|
|
||||||
:202C590090002D75F040120E767403556475F00BA42474FE740035F0FF8E708F717572000C
|
|
||||||
:202C790090009E75F040120E76122243E56404540375F00BA42474FE740035F0FF7D007583
|
|
||||||
:162C9900702D8D717572408E828F838DF0120E761225B9C2022258
|
|
||||||
:202CAF007A10E4FBFCE58225E0F582E58333F583EB33FBEC33FCEB9570F5F0EC9571400669
|
|
||||||
:092CCF00FCABF0438201DADD22C6
|
|
||||||
:06004200E478FFF6D8FD92
|
|
||||||
:200020007900E94400601B7A00902EA178A275A000E493F2A308B8000205A0D9F4DAF27516
|
|
||||||
:02004000A0FF1F
|
|
||||||
:1B2CD80020F71130F6138883A88220F509F6A8837583002280FEF280F5F022FB
|
|
||||||
:1D2CF300E5828570F0A4C582C0F08571F0A4D0F025F0C5838570F0A42583F583226B
|
|
||||||
:202D1000E570457160467A01E57025E0F570E571334012F571E5829570E583957140030A50
|
|
||||||
:202D300080E6C3E57113F571E57013F570C3E5829570F5F0E58395714005F58385F082C3C5
|
|
||||||
:0D2D5000E57113F571E57013F570DAE122FD
|
|
||||||
:200048007800E84400600A790175A000E4F309D8FC78A1E84400600C7901900001E4F0A314
|
|
||||||
:04006800D8FCD9FAED
|
|
||||||
:0F001100E4737581C9122DE7E582600302000ECA
|
|
||||||
:1C2D5D0020F71430F6148883A88220F507E6A88375830022E280F7E49322E02285
|
|
||||||
:202D7900C2D5E58330E70DD2D5E4C39582F582E49583F583E57130E70BE4C39570F570E45A
|
|
||||||
:162D99009571F571122D1030D50BE4C39582F582E49583F583228E
|
|
||||||
:202DAF00C2D5E58330E70DD2D5E4C39582F582E49583F583E57130E70DB2D5E4C39570F5EF
|
|
||||||
:182DCF0070E49571F571122CAF30D50BE4C39582F582E49583F5832264
|
|
||||||
:042DE70075820022CF
|
|
||||||
:00000001FF
|
|
||||||
11
src/calc.c
11
src/calc.c
@ -253,16 +253,7 @@ void process_cmd(char cmd){
|
|||||||
} break;
|
} break;
|
||||||
//////////
|
//////////
|
||||||
case '7':{ //y^x
|
case '7':{ //y^x
|
||||||
if (decn_is_nan(&stack(STACK_Y)) || decn_is_nan(&stack(STACK_X))){
|
do_binary_op(pow_decn);
|
||||||
set_dec80_NaN(&stack(STACK_Y));
|
|
||||||
} else {
|
|
||||||
copy_decn(&LastX, &stack(STACK_X)); //save LastX
|
|
||||||
copy_decn(&AccDecn, &stack(STACK_Y));
|
|
||||||
copy_decn(&BDecn, &stack(STACK_X));
|
|
||||||
pow_decn();
|
|
||||||
copy_decn(&stack(STACK_Y), &AccDecn);
|
|
||||||
}
|
|
||||||
pop();
|
|
||||||
} break;
|
} break;
|
||||||
//////////
|
//////////
|
||||||
} //switch(cmd)
|
} //switch(cmd)
|
||||||
|
|||||||
199
src/decn/decn.c
199
src/decn/decn.c
@ -35,6 +35,7 @@
|
|||||||
// #define DEBUG_LOG_ALL //even more verbose
|
// #define DEBUG_LOG_ALL //even more verbose
|
||||||
// #define DEBUG_EXP
|
// #define DEBUG_EXP
|
||||||
// #define DEBUG_EXP_ALL //even more verbose
|
// #define DEBUG_EXP_ALL //even more verbose
|
||||||
|
// #define DEBUG_SQRT
|
||||||
|
|
||||||
#ifndef DESKTOP
|
#ifndef DESKTOP
|
||||||
//#undef EXTRA_CHECKS
|
//#undef EXTRA_CHECKS
|
||||||
@ -47,6 +48,7 @@
|
|||||||
#undef DEBUG_LOG_ALL
|
#undef DEBUG_LOG_ALL
|
||||||
#undef DEBUG_EXP
|
#undef DEBUG_EXP
|
||||||
#undef DEBUG_EXP_ALL
|
#undef DEBUG_EXP_ALL
|
||||||
|
#undef DEBUG_SQRT
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
#ifdef DESKTOP
|
#ifdef DESKTOP
|
||||||
@ -68,8 +70,8 @@ static const uint8_t num_digits_display = 16;
|
|||||||
dec80 AccDecn;
|
dec80 AccDecn;
|
||||||
__idata dec80 BDecn;
|
__idata dec80 BDecn;
|
||||||
__idata dec80 TmpDecn; //used by add_decn() and mult_decn() and sqrt_decn()
|
__idata dec80 TmpDecn; //used by add_decn() and mult_decn() and sqrt_decn()
|
||||||
__idata dec80 Tmp2Decn; //used by recip_decn() and ln_decn() and sincos_decn() and sqrt_decn()
|
__idata dec80 Tmp2Decn; //used by recip_decn(), ln_decn(), exp_decn(), sqrt_decn(), and sincos_decn()
|
||||||
__xdata dec80 Tmp3Decn; //used by recip_decn() and ln_decn() and sincos_decn() and sqrt_decn()
|
__idata dec80 Tmp3Decn; //used by ln_decn(), exp_decn(), sqrt_decn(), and sincos_decn()
|
||||||
__xdata dec80 Tmp4Decn; //used by sincos_decn()
|
__xdata dec80 Tmp4Decn; //used by sincos_decn()
|
||||||
|
|
||||||
__xdata dec80 TmpStackDecn[4];
|
__xdata dec80 TmpStackDecn[4];
|
||||||
@ -78,11 +80,6 @@ __idata uint8_t TmpStackPtr;
|
|||||||
|
|
||||||
__xdata char Buf[DECN_BUF_SIZE];
|
__xdata char Buf[DECN_BUF_SIZE];
|
||||||
|
|
||||||
//1 constant
|
|
||||||
const dec80 DECN_1 = {
|
|
||||||
0, {10, 0}
|
|
||||||
};
|
|
||||||
|
|
||||||
//ln(10) constant
|
//ln(10) constant
|
||||||
const dec80 DECN_LN_10 = {
|
const dec80 DECN_LN_10 = {
|
||||||
0, {23, 2, 58, 50, 92, 99, 40, 45, 68}
|
0, {23, 2, 58, 50, 92, 99, 40, 45, 68}
|
||||||
@ -425,6 +422,11 @@ void set_dec80_zero(dec80* dest){
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
void set_decn_one(dec80* dest){
|
||||||
|
set_dec80_zero(dest);
|
||||||
|
dest->lsu[0] = 10;
|
||||||
|
}
|
||||||
|
|
||||||
uint8_t decn_is_zero(const dec80* x){
|
uint8_t decn_is_zero(const dec80* x){
|
||||||
uint8_t i;
|
uint8_t i;
|
||||||
for (i = 0; i < DEC80_NUM_LSU; i++){
|
for (i = 0; i < DEC80_NUM_LSU; i++){
|
||||||
@ -872,14 +874,12 @@ void recip_decn(void){
|
|||||||
} else {
|
} else {
|
||||||
CURR_RECIP.lsu[0] = 10; //0.1 with implicit point and exponent
|
CURR_RECIP.lsu[0] = 10; //0.1 with implicit point and exponent
|
||||||
}
|
}
|
||||||
for (i = 1; i < DEC80_NUM_LSU; i++){
|
zero_remaining_dec80(&CURR_RECIP, 1);
|
||||||
CURR_RECIP.lsu[i] = 0;
|
|
||||||
}
|
|
||||||
copy_decn(&AccDecn, &CURR_RECIP);
|
copy_decn(&AccDecn, &CURR_RECIP);
|
||||||
//do newton raphson iterations
|
//do newton-raphson iterations
|
||||||
for (i = 0; i < 6; i++){ //just fix number of iterations for now
|
for (i = 0; i < 6; i++){ //just fix number of iterations for now
|
||||||
#ifdef DEBUG_DIV
|
#ifdef DEBUG_DIV
|
||||||
decn_to_str_complete(&curr_recip);
|
decn_to_str_complete(&CURR_RECIP);
|
||||||
printf("%2d: %s\n", i, Buf);
|
printf("%2d: %s\n", i, Buf);
|
||||||
#endif
|
#endif
|
||||||
//Accum *= x_copy
|
//Accum *= x_copy
|
||||||
@ -892,7 +892,7 @@ void recip_decn(void){
|
|||||||
//Accum *= -1
|
//Accum *= -1
|
||||||
negate_decn(&AccDecn);
|
negate_decn(&AccDecn);
|
||||||
//Accum += 1
|
//Accum += 1
|
||||||
copy_decn(&BDecn, &DECN_1);
|
set_decn_one(&BDecn);
|
||||||
add_decn();
|
add_decn();
|
||||||
#ifdef DEBUG_DIV
|
#ifdef DEBUG_DIV
|
||||||
decn_to_str_complete(&AccDecn);
|
decn_to_str_complete(&AccDecn);
|
||||||
@ -962,7 +962,7 @@ void ln_decn(void){
|
|||||||
printf("ln() accum scaled between 1,10: %s\n", Buf);
|
printf("ln() accum scaled between 1,10: %s\n", Buf);
|
||||||
#endif
|
#endif
|
||||||
//get initial estimate (accum = 10 - A)
|
//get initial estimate (accum = 10 - A)
|
||||||
copy_decn(&BDecn, &DECN_1);
|
set_decn_one(&BDecn);
|
||||||
BDecn.exponent = 1; //BDecn = 10
|
BDecn.exponent = 1; //BDecn = 10
|
||||||
negate_decn(&AccDecn);
|
negate_decn(&AccDecn);
|
||||||
add_decn();
|
add_decn();
|
||||||
@ -1139,7 +1139,7 @@ void exp_decn(void){
|
|||||||
//initial b = -10*ln(10)
|
//initial b = -10*ln(10)
|
||||||
copy_decn(&BDecn, &DECN_LN_10); //b=ln(10)
|
copy_decn(&BDecn, &DECN_LN_10); //b=ln(10)
|
||||||
copy_decn(&SAVED, &AccDecn); //save = accum
|
copy_decn(&SAVED, &AccDecn); //save = accum
|
||||||
copy_decn(&AccDecn, &DECN_1);
|
set_decn_one(&AccDecn);
|
||||||
AccDecn.exponent = 1; //accum = 10
|
AccDecn.exponent = 1; //accum = 10
|
||||||
mult_decn(); //accum = 10*ln(10)
|
mult_decn(); //accum = 10*ln(10)
|
||||||
copy_decn(&BDecn, &AccDecn); //b = 10*ln(10)
|
copy_decn(&BDecn, &AccDecn); //b = 10*ln(10)
|
||||||
@ -1208,10 +1208,10 @@ void exp_decn(void){
|
|||||||
//build final value
|
//build final value
|
||||||
// (currently accum = save = remainder)
|
// (currently accum = save = remainder)
|
||||||
// calculate 1+remainder
|
// calculate 1+remainder
|
||||||
copy_decn(&BDecn, &DECN_1);
|
set_decn_one(&BDecn);
|
||||||
add_decn();
|
add_decn();
|
||||||
//get initial multiplier (10) for ln(10)
|
//get initial multiplier (10) for ln(10)
|
||||||
copy_decn(&BDecn, &DECN_1);
|
set_decn_one(&BDecn);
|
||||||
BDecn.exponent = 1; //BDecn = 10
|
BDecn.exponent = 1; //BDecn = 10
|
||||||
//do multiplies
|
//do multiplies
|
||||||
j = UINT8_MAX; //becomes 0 after incrementing to start (1 + 10^-j) series
|
j = UINT8_MAX; //becomes 0 after incrementing to start (1 + 10^-j) series
|
||||||
@ -1273,7 +1273,7 @@ void exp10_decn(void){
|
|||||||
|
|
||||||
void pow_decn(void) {
|
void pow_decn(void) {
|
||||||
if (decn_is_zero(&BDecn)) {
|
if (decn_is_zero(&BDecn)) {
|
||||||
copy_decn(&AccDecn, &DECN_1);
|
set_decn_one(&AccDecn);
|
||||||
return;
|
return;
|
||||||
}
|
}
|
||||||
if (decn_is_zero(&AccDecn)) {
|
if (decn_is_zero(&AccDecn)) {
|
||||||
@ -1288,6 +1288,144 @@ void pow_decn(void) {
|
|||||||
exp_decn();
|
exp_decn();
|
||||||
}
|
}
|
||||||
|
|
||||||
|
#ifdef USE_POW_SQRT_IMPL
|
||||||
|
void sqrt_decn(void) {
|
||||||
|
if (decn_is_zero(&AccDecn)) {
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
if (decn_is_nan(&AccDecn)) {
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
if (AccDecn.exponent < 0){ //negative
|
||||||
|
set_dec80_NaN(&AccDecn);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
st_push_decn(&BDecn); // sqrt should behave like an unary operation
|
||||||
|
//b = 0.5
|
||||||
|
set_dec80_zero(&BDecn);
|
||||||
|
BDecn.lsu[0] = 5;
|
||||||
|
pow_decn();
|
||||||
|
st_pop_decn(&BDecn);
|
||||||
|
}
|
||||||
|
#else
|
||||||
|
void sqrt_decn(void){
|
||||||
|
#define CURR_EST Tmp2Decn //holds current 1/sqrt(x) estimate
|
||||||
|
#define X_2 Tmp3Decn //holds copy of original x / 2
|
||||||
|
uint8_t i;
|
||||||
|
exp_t initial_exp;
|
||||||
|
if (decn_is_nan(&AccDecn)) {
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
if (AccDecn.exponent < 0){ //negative
|
||||||
|
set_dec80_NaN(&AccDecn);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
//normalize
|
||||||
|
remove_leading_zeros(&AccDecn);
|
||||||
|
#ifdef DEBUG_SQRT
|
||||||
|
decn_to_str_complete(&AccDecn);
|
||||||
|
printf("sqrt in: %s\n", Buf);
|
||||||
|
#endif
|
||||||
|
//store copy of x
|
||||||
|
st_push_decn(&AccDecn);
|
||||||
|
//calculate x_orig / 2
|
||||||
|
set_dec80_zero(&BDecn);
|
||||||
|
BDecn.lsu[0] = 5;
|
||||||
|
mult_decn();
|
||||||
|
copy_decn(&X_2, &AccDecn);
|
||||||
|
//restore x
|
||||||
|
st_load_decn(&AccDecn);
|
||||||
|
//get initial estimate for 1/sqrt(x) == 10^(-0.5 * log(x)):
|
||||||
|
// approximate significand == 10^(-0.5 * log(x_signif))
|
||||||
|
// with linear approximation: -0.18 * x_signif + 2.5
|
||||||
|
// new exponent part is (10^(-0.5 * log(10^x_exp)))
|
||||||
|
// == 10^(-0.5 * x^exp)
|
||||||
|
initial_exp = get_exponent(&AccDecn);
|
||||||
|
set_exponent(&AccDecn, 0, 0); //clear exponent (Acc is not negative)
|
||||||
|
#ifdef DEBUG_SQRT
|
||||||
|
printf("sqrt exponent %d ", initial_exp);
|
||||||
|
#endif
|
||||||
|
if (initial_exp & 0x1){ //odd
|
||||||
|
#ifdef DEBUG_SQRT
|
||||||
|
printf("(odd) ");
|
||||||
|
#endif
|
||||||
|
//increment x_exp and
|
||||||
|
initial_exp++;
|
||||||
|
//approximate estimated significand as (-0.056*x_signif + 0.79) * 10^0.5
|
||||||
|
// == -0.18 * x_signif + 2.5
|
||||||
|
//b = -0.18
|
||||||
|
BDecn.lsu[0] = 18;
|
||||||
|
BDecn.exponent = -1; //negative, and exponent = -1
|
||||||
|
//a = -0.18 * x_signif
|
||||||
|
mult_decn();
|
||||||
|
//b = 2.5
|
||||||
|
BDecn.lsu[0] = 25;
|
||||||
|
BDecn.exponent = 0;
|
||||||
|
//a = -0.18 * x_signif + 2.5
|
||||||
|
add_decn();
|
||||||
|
} else { //even
|
||||||
|
//keep x_exp as is and approximate estimated significand as
|
||||||
|
// -0.056*x_signif + 0.79
|
||||||
|
//b = -0.056
|
||||||
|
BDecn.lsu[0] = 56;
|
||||||
|
set_exponent(&BDecn, -2, 1);
|
||||||
|
//a = -0.056 * x_signif
|
||||||
|
mult_decn();
|
||||||
|
//b = 0.79
|
||||||
|
BDecn.lsu[0] = 7;
|
||||||
|
BDecn.lsu[1] = 90;
|
||||||
|
BDecn.exponent = 0;
|
||||||
|
//a = -0.056*x_signif + 0.79
|
||||||
|
add_decn();
|
||||||
|
}
|
||||||
|
//est_exp = -x_exp / 2;
|
||||||
|
initial_exp = -initial_exp / 2;
|
||||||
|
//est_exp-- if AccDecn exponent is negative
|
||||||
|
// (AccDecn exponent is either 0 or -1, and AccDecn is positive)
|
||||||
|
if (AccDecn.exponent != 0){
|
||||||
|
initial_exp--;
|
||||||
|
}
|
||||||
|
set_exponent(&AccDecn, initial_exp, 0); //(initial estimate is never negative)
|
||||||
|
copy_decn(&CURR_EST, &AccDecn);
|
||||||
|
#ifdef DEBUG_SQRT
|
||||||
|
printf(" -> %d\n", initial_exp);
|
||||||
|
#endif
|
||||||
|
//do newton-raphson iterations
|
||||||
|
for (i = 0; i < 6; i++){ //just fix number of iterations for now
|
||||||
|
#ifdef DEBUG_SQRT
|
||||||
|
decn_to_str_complete(&CURR_EST);
|
||||||
|
printf("sqrt %2d: %s\n", i, Buf);
|
||||||
|
#endif
|
||||||
|
//accum = est * est;
|
||||||
|
copy_decn(&BDecn, &AccDecn);
|
||||||
|
mult_decn();
|
||||||
|
//accum *= x_orig_2; //accum = x/2 * est * est
|
||||||
|
copy_decn(&BDecn, &X_2);
|
||||||
|
mult_decn();
|
||||||
|
//accum = - x/2 * est * est
|
||||||
|
negate_decn(&AccDecn);
|
||||||
|
//b = 3/2
|
||||||
|
set_dec80_zero(&BDecn);
|
||||||
|
BDecn.lsu[0] = 15;
|
||||||
|
//accum = 3/2 - x/2 * est * est
|
||||||
|
add_decn();
|
||||||
|
//accum *= est; //accum = 0.5 * est * (3 - x * est * est)
|
||||||
|
copy_decn(&BDecn, &CURR_EST);
|
||||||
|
mult_decn();
|
||||||
|
//est = accum;
|
||||||
|
copy_decn(&CURR_EST, &AccDecn);
|
||||||
|
}
|
||||||
|
|
||||||
|
//calc sqrt from recip_sqrt
|
||||||
|
st_pop_decn(&BDecn);
|
||||||
|
mult_decn();
|
||||||
|
|
||||||
|
#undef CURR_EST
|
||||||
|
#undef X_COPY
|
||||||
|
}
|
||||||
|
#endif //USE_POW_SQRT_IMPL
|
||||||
|
|
||||||
|
|
||||||
// see W.E. Egbert, "Personal Calculator Algorithms II: Trigonometric functions"
|
// see W.E. Egbert, "Personal Calculator Algorithms II: Trigonometric functions"
|
||||||
void project_decn_into_0_2pi(void) {
|
void project_decn_into_0_2pi(void) {
|
||||||
const uint8_t is_negative = (AccDecn.exponent < 0);
|
const uint8_t is_negative = (AccDecn.exponent < 0);
|
||||||
@ -1333,11 +1471,11 @@ void sincos_decn(const uint8_t sincos_arctan) {
|
|||||||
set_dec80_zero(&THETA);
|
set_dec80_zero(&THETA);
|
||||||
if (is_negative) negate_decn(&AccDecn);
|
if (is_negative) negate_decn(&AccDecn);
|
||||||
copy_decn(&COS, &AccDecn);
|
copy_decn(&COS, &AccDecn);
|
||||||
copy_decn(&SIN, &DECN_1);
|
set_decn_one(&SIN);
|
||||||
} else {
|
} else {
|
||||||
project_decn_into_0_2pi();
|
project_decn_into_0_2pi();
|
||||||
copy_decn(&THETA, &AccDecn);
|
copy_decn(&THETA, &AccDecn);
|
||||||
copy_decn(&COS, &DECN_1);
|
set_decn_one(&COS);
|
||||||
set_dec80_zero(&SIN);
|
set_dec80_zero(&SIN);
|
||||||
// 0.0 00 5
|
// 0.0 00 5
|
||||||
SIN.lsu[2] = 50;
|
SIN.lsu[2] = 50;
|
||||||
@ -1409,7 +1547,7 @@ void arcsin_decn(void) {
|
|||||||
copy_decn(&BDecn, &AccDecn);
|
copy_decn(&BDecn, &AccDecn);
|
||||||
mult_decn();
|
mult_decn();
|
||||||
negate_decn(&AccDecn);
|
negate_decn(&AccDecn);
|
||||||
copy_decn(&BDecn, &DECN_1);
|
set_decn_one(&BDecn);
|
||||||
add_decn();
|
add_decn();
|
||||||
sqrt_decn();
|
sqrt_decn();
|
||||||
recip_decn();
|
recip_decn();
|
||||||
@ -1446,25 +1584,6 @@ void pi_decn(void) {
|
|||||||
mult_decn();
|
mult_decn();
|
||||||
}
|
}
|
||||||
|
|
||||||
void sqrt_decn(void) {
|
|
||||||
if (decn_is_zero(&AccDecn)) {
|
|
||||||
return;
|
|
||||||
}
|
|
||||||
if (decn_is_nan(&AccDecn)) {
|
|
||||||
return;
|
|
||||||
}
|
|
||||||
if (AccDecn.exponent < 0){ //negative
|
|
||||||
set_dec80_NaN(&AccDecn);
|
|
||||||
return;
|
|
||||||
}
|
|
||||||
st_push_decn(&BDecn); // sqrt should behave like an unary operation
|
|
||||||
//b = 0.5
|
|
||||||
set_dec80_zero(&BDecn);
|
|
||||||
BDecn.lsu[0] = 5;
|
|
||||||
pow_decn();
|
|
||||||
st_pop_decn(&BDecn);
|
|
||||||
}
|
|
||||||
|
|
||||||
static void set_str_error(void){
|
static void set_str_error(void){
|
||||||
Buf[0] = 'E';
|
Buf[0] = 'E';
|
||||||
Buf[1] = 'r';
|
Buf[1] = 'r';
|
||||||
|
|||||||
@ -69,6 +69,7 @@ extern __idata uint8_t TmpStackPtr;
|
|||||||
void build_dec80(__xdata const char* signif_str, __xdata exp_t exponent);
|
void build_dec80(__xdata const char* signif_str, __xdata exp_t exponent);
|
||||||
|
|
||||||
void set_dec80_zero(dec80* dest);
|
void set_dec80_zero(dec80* dest);
|
||||||
|
void set_decn_one(dec80* dest);
|
||||||
void set_dec80_NaN(dec80* dest);
|
void set_dec80_NaN(dec80* dest);
|
||||||
uint8_t decn_is_zero(const dec80* x);
|
uint8_t decn_is_zero(const dec80* x);
|
||||||
uint8_t decn_is_nan(const dec80* x);
|
uint8_t decn_is_nan(const dec80* x);
|
||||||
|
|||||||
@ -341,6 +341,51 @@ TEST_CASE("division"){
|
|||||||
);
|
);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
static void sqrt_test(const char* x_str, int x_exp)
|
||||||
|
{
|
||||||
|
CAPTURE(x_str); CAPTURE(x_exp);
|
||||||
|
build_dec80(x_str, x_exp);
|
||||||
|
// decn_to_str_complete(&AccDecn);
|
||||||
|
// printf(" acc: %s\n", Buf);
|
||||||
|
sqrt_decn();
|
||||||
|
decn_to_str_complete(&AccDecn);
|
||||||
|
CAPTURE(Buf); // sqrt(x)
|
||||||
|
|
||||||
|
//calculate actual result
|
||||||
|
bmp::mpfr_float::default_precision(50);
|
||||||
|
std::string x_full_str(x_str);
|
||||||
|
x_full_str += "e" + std::to_string(x_exp);
|
||||||
|
CAPTURE(x_full_str);
|
||||||
|
bmp::mpfr_float x_actual(x_full_str);
|
||||||
|
CAPTURE(x_actual);
|
||||||
|
if (decn_is_nan(&AccDecn)){
|
||||||
|
//check that NaN is from result of sqrt(-)
|
||||||
|
CHECK(x_actual <= 0);
|
||||||
|
} else if (decn_is_zero(&AccDecn)){
|
||||||
|
//check actual is also 0
|
||||||
|
CHECK(x_actual == 0);
|
||||||
|
} else {
|
||||||
|
x_actual = sqrt(x_actual);
|
||||||
|
bmp::mpfr_float calculated(Buf);
|
||||||
|
bmp::mpfr_float rel_diff = abs((x_actual - calculated) / x_actual);
|
||||||
|
CHECK(rel_diff < 3e-16); //TODO
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
TEST_CASE("sqrt"){
|
||||||
|
sqrt_test("0", 0);
|
||||||
|
sqrt_test("2", 0);
|
||||||
|
sqrt_test("-1", 0);
|
||||||
|
sqrt_test("0.155", 0);
|
||||||
|
sqrt_test("10", 0);
|
||||||
|
sqrt_test("1.1", 10);
|
||||||
|
sqrt_test("2.02", -10);
|
||||||
|
sqrt_test("2.02", 0);
|
||||||
|
sqrt_test("1.5", 0);
|
||||||
|
sqrt_test("9", 99);
|
||||||
|
sqrt_test("123", 12345);
|
||||||
|
}
|
||||||
|
|
||||||
static void log_test(
|
static void log_test(
|
||||||
//input
|
//input
|
||||||
const char* x_str, int x_exp,
|
const char* x_str, int x_exp,
|
||||||
|
|||||||
@ -23,7 +23,7 @@
|
|||||||
#include <boost/multiprecision/mpfr.hpp>
|
#include <boost/multiprecision/mpfr.hpp>
|
||||||
using namespace boost::multiprecision;
|
using namespace boost::multiprecision;
|
||||||
|
|
||||||
// #define DEBUG
|
#define DEBUG
|
||||||
|
|
||||||
using std::cout;
|
using std::cout;
|
||||||
using std::endl;
|
using std::endl;
|
||||||
@ -51,7 +51,7 @@ int main(void){
|
|||||||
|
|
||||||
//loop through values to test
|
//loop through values to test
|
||||||
#ifdef DEBUG
|
#ifdef DEBUG
|
||||||
mpfr_float x(0.1, CALC_PRECISION);
|
mpfr_float x(2.0, CALC_PRECISION);
|
||||||
{
|
{
|
||||||
#else
|
#else
|
||||||
for (mpfr_float x(1e-99, CALC_PRECISION); x < 1e99; x *= 1.03){
|
for (mpfr_float x(1e-99, CALC_PRECISION); x < 1e99; x *= 1.03){
|
||||||
@ -87,7 +87,7 @@ int main(void){
|
|||||||
x_exp++;
|
x_exp++;
|
||||||
est_signif = -0.18 * x_signif + 2.5;
|
est_signif = -0.18 * x_signif + 2.5;
|
||||||
} else { //even
|
} else { //even
|
||||||
//keep x_exp as is and approximate estimate significand as
|
//keep x_exp as is and approximate estimated significand as
|
||||||
// -0.056*x_signif + 0.79
|
// -0.056*x_signif + 0.79
|
||||||
est_signif = -0.056 * x_signif + 0.79;
|
est_signif = -0.056 * x_signif + 0.79;
|
||||||
}
|
}
|
||||||
|
|||||||
@ -3,6 +3,8 @@
|
|||||||
"""
|
"""
|
||||||
Created on Wed Dec 11 00:56:01 2019
|
Created on Wed Dec 11 00:56:01 2019
|
||||||
|
|
||||||
|
Calculate constants used for "0x5F3759DF" reciprocal sqrt
|
||||||
|
|
||||||
@author: jeffrey
|
@author: jeffrey
|
||||||
"""
|
"""
|
||||||
|
|
||||||
|
|||||||
@ -140,7 +140,7 @@ static void latch_on(void)
|
|||||||
|
|
||||||
__xdata char EntryBuf[MAX_CHARS_PER_LINE + 1];
|
__xdata char EntryBuf[MAX_CHARS_PER_LINE + 1];
|
||||||
__xdata uint8_t ExpBuf[2];
|
__xdata uint8_t ExpBuf[2];
|
||||||
__code const char VER_STR[32+1] = "STC RPN Calculator v1.11";
|
__code const char VER_STR[32+1] = "STC RPN Calculator v1.12";
|
||||||
|
|
||||||
|
|
||||||
enum {
|
enum {
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user