[aandrejevic] 67894: [FAST486] Fix the implementation of FSIN and FCOS: First of all, 4 steps for a Maclaurin series is not enough. Second, the angle should be normalized to the [-pi/2, pi/2] range.
25 May
2015
25 May
'15
3:23 a.m.
Author: aandrejevic
Date: Mon May 25 03:23:40 2015
New Revision: 67894
URL: http://svn.reactos.org/svn/reactos?rev=67894&view=rev
Log:
[FAST486]
Fix the implementation of FSIN and FCOS:
First of all, 4 steps for a Maclaurin series is not enough.
Second, the angle should be normalized to the [-pi/2, pi/2] range.
Modified:
trunk/reactos/lib/fast486/fpu.c
Modified: trunk/reactos/lib/fast486/fpu.c
URL:
http://svn.reactos.org/svn/reactos/trunk/reactos/lib/fast486/fpu.c?rev=6789…
==============================================================================
--- trunk/reactos/lib/fast486/fpu.c [iso-8859-1] (original)
+++ trunk/reactos/lib/fast486/fpu.c [iso-8859-1] Mon May 25 03:23:40 2015
@@ -55,6 +55,9 @@
/* 2.00 */
static const FAST486_FPU_DATA_REG FpuTwo = {0x8000000000000000ULL, FPU_REAL10_BIAS + 1,
FALSE};
+
+/* Pi / 2 */
+static const FAST486_FPU_DATA_REG FpuHalfPi = {0xC90FDAA22168C235ULL, FPU_REAL10_BIAS,
FALSE};
static const FAST486_FPU_DATA_REG FpuInverseNumber[INVERSE_NUMBERS_COUNT] =
{
@@ -110,6 +113,114 @@
{0xA3D70A3D70A3D70AULL, FPU_REAL10_BIAS - 6, FALSE}, /* 1 / 50 */
};
+static const FAST486_FPU_DATA_REG FpuInverseNumberSine[INVERSE_NUMBERS_COUNT] =
+{
+ {0xAAAAAAAAAAAAAAAAULL, FPU_REAL10_BIAS - 3, FALSE}, /* 1 / 6 */
+ {0xCCCCCCCCCCCCCCCCULL, FPU_REAL10_BIAS - 5, FALSE}, /* 1 / 20 */
+ {0xC30C30C30C30C30CULL, FPU_REAL10_BIAS - 6, FALSE}, /* 1 / 42 */
+ {0xE38E38E38E38E38EULL, FPU_REAL10_BIAS - 7, FALSE}, /* 1 / 72 */
+ {0x94F2094F2094F209ULL, FPU_REAL10_BIAS - 7, FALSE}, /* 1 / 110 */
+ {0xD20D20D20D20D20DULL, FPU_REAL10_BIAS - 8, FALSE}, /* 1 / 156 */
+ {0x9C09C09C09C09C09ULL, FPU_REAL10_BIAS - 8, FALSE}, /* 1 / 210 */
+ {0xF0F0F0F0F0F0F0F0ULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 272 */
+ {0xBFA02FE80BFA02FEULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 342 */
+ {0x9C09C09C09C09C09ULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 420 */
+ {0x81848DA8FAF0D277ULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 506 */
+ {0xDA740DA740DA740DULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 600 */
+ {0xBAB656100BAB6561ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 702 */
+ {0xA16B312EA8FC377CULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 812 */
+ {0x8CF008CF008CF008ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 930 */
+ {0xF83E0F83E0F83E0FULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1056 */
+ {0xDC4A00DC4A00DC4AULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1190 */
+ {0xC4CE07B00C4CE07BULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1332 */
+ {0xB0E2A2600B0E2A26ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1482 */
+ {0x9FD809FD809FD809ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1640 */
+ {0x9126D6E4802449B5ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1806 */
+ {0x84655D9BAB2F1008ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1980 */
+ {0xF2805AF0221A0CC9ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2162 */
+ {0xDEE95C4CA037BA57ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2352 */
+ {0xCD9A673400CD9A67ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2550 */
+ {0xBE3C310B84A4F832ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2756 */
+ {0xB087277A39941560ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2970 */
+ {0xA44029100A440291ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3192 */
+ {0x9936034AA9121AA1ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3422 */
+ {0x8F3F82A86DACA008ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3660 */
+ {0x8639F00218E7C008ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3906 */
+ {0xFC0FC0FC0FC0FC0FULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4160 */
+ {0xED208916CF412FD1ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4422 */
+ {0xDF7B4EC93886702DULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4692 */
+ {0xD2FB287C7224E167ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4970 */
+ {0xC78031E00C78031EULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5256 */
+ {0xBCEEBFB33F021F2EULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5550 */
+ {0xB32EB86E96D5D441ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5852 */
+ {0xAA2B0A62E08248F3ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6162 */
+ {0xA1D139855F7268EDULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6480 */
+ {0x9A1100604AA03C2EULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6806 */
+ {0x92DC0092DC0092DCULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 7140 */
+ {0x8C258008C258008CULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 7482 */
+ {0x85E230A32BAB46DDULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 7832 */
+ {0x8008008008008008ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 8190 */
+ {0xF51BE2CC2D7AAC94ULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 8556 */
+ {0xEAD7EC46DDA80C62ULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 8930 */
+ {0xE135A9C97500E135ULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9312 */
+ {0xD8281B71177BDB7BULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9702 */
+ {0xCFA3892CE9FFCC17ULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 10100 */
+};
+
+static const FAST486_FPU_DATA_REG FpuInverseNumberCosine[INVERSE_NUMBERS_COUNT] =
+{
+ {0x8000000000000000ULL, FPU_REAL10_BIAS - 1, FALSE}, /* 1 / 2 */
+ {0xAAAAAAAAAAAAAAAAULL, FPU_REAL10_BIAS - 4, FALSE}, /* 1 / 12 */
+ {0x8888888888888888ULL, FPU_REAL10_BIAS - 5, FALSE}, /* 1 / 30 */
+ {0x9249249249249249ULL, FPU_REAL10_BIAS - 6, FALSE}, /* 1 / 56 */
+ {0xB60B60B60B60B60BULL, FPU_REAL10_BIAS - 7, FALSE}, /* 1 / 90 */
+ {0xF83E0F83E0F83E0FULL, FPU_REAL10_BIAS - 8, FALSE}, /* 1 / 132 */
+ {0xB40B40B40B40B40BULL, FPU_REAL10_BIAS - 8, FALSE}, /* 1 / 182 */
+ {0x8888888888888888ULL, FPU_REAL10_BIAS - 8, FALSE}, /* 1 / 240 */
+ {0xD62B80D62B80D62BULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 306 */
+ {0xAC7691840AC76918ULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 380 */
+ {0x8DDA520237694808ULL, FPU_REAL10_BIAS - 9, FALSE}, /* 1 / 462 */
+ {0xED7303B5CC0ED730ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 552 */
+ {0xC9A633FCD967300CULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 650 */
+ {0xAD602B580AD602B5ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 756 */
+ {0x96A850096A850096ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 870 */
+ {0x8421084210842108ULL, FPU_REAL10_BIAS - 10, FALSE}, /* 1 / 992 */
+ {0xE9A3D25E00E9A3D2ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1122 */
+ {0xD00D00D00D00D00DULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1260 */
+ {0xBA7258200BA72582ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1406 */
+ {0xA80A80A80A80A80AULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1560 */
+ {0x983B773A92E16009ULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1722 */
+ {0x8A8DCD1FEEAE465CULL, FPU_REAL10_BIAS - 11, FALSE}, /* 1 / 1892 */
+ {0xFD477B6C956529CDULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2070 */
+ {0xE865AC7B7603A196ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2256 */
+ {0xD5FEBF01E17D2DC4ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2450 */
+ {0xC5B200C5B200C5B2ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2652 */
+ {0xB7307B1492B1D28FULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 2862 */
+ {0xAA392F35DC17F00AULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3080 */
+ {0x9E96394D47B46C68ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3306 */
+ {0x941A9CC82BF7E68BULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3540 */
+ {0x8AA08EF5936D4008ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 3782 */
+ {0x8208208208208208ULL, FPU_REAL10_BIAS - 12, FALSE}, /* 1 / 4032 */
+ {0xF46C5E0BB22F800FULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4290 */
+ {0xE6271BA5329217D3ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4556 */
+ {0xD918B2EF5B7B4866ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 4830 */
+ {0xCD1ED923A7DCBEB2ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5112 */
+ {0xC21BDD800C21BDD8ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5402 */
+ {0xB7F5F08CD84C2BD5ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 5700 */
+ {0xAE968C517F46800AULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6006 */
+ {0xA5E9F6ED347F0721ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6320 */
+ {0x9DDEDA75A1CD4726ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6642 */
+ {0x9665EE14DB2283E4ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 6972 */
+ {0x8F71AD362448008FULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 7310 */
+ {0x88F61A371B048C2BULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 7656 */
+ {0x82E88A942AB2D933ULL, FPU_REAL10_BIAS - 13, FALSE}, /* 1 / 8010 */
+ {0xFA7EF5D91AC9538AULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 8372 */
+ {0xEFE4D31416B96CFEULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 8742 */
+ {0xE5F36CB00E5F36CBULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9120 */
+ {0xDC9D0ECFCB6E9378ULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9506 */
+ {0xD3D56292AB7E800DULL, FPU_REAL10_BIAS - 14, FALSE}, /* 1 / 9900 */
+};
+
/* PRIVATE FUNCTIONS **********************************************************/
#ifndef FAST486_NO_FPU
@@ -1202,7 +1313,8 @@
PCFAST486_FPU_DATA_REG FirstOperand,
PCFAST486_FPU_DATA_REG SecondOperand,
BOOLEAN RoundToNearest,
- PFAST486_FPU_DATA_REG Result)
+ PFAST486_FPU_DATA_REG Result,
+ PLONGLONG Quotient OPTIONAL)
{
BOOLEAN Success = FALSE;
INT OldRoundingMode = State->FpuControl.Rc;
@@ -1219,6 +1331,7 @@
if (!Fast486FpuMultiply(State, &Temp, SecondOperand, &Temp)) goto Cleanup;
if (!Fast486FpuSubtract(State, FirstOperand, &Temp, Result)) goto Cleanup;
+ if (Quotient) *Quotient = Integer;
Success = TRUE;
Cleanup:
@@ -1236,14 +1349,43 @@
PFAST486_FPU_DATA_REG Result)
{
INT i;
- FAST486_FPU_DATA_REG TempResult = *Operand;
- FAST486_FPU_DATA_REG OperandSquared = *Operand;
- FAST486_FPU_DATA_REG SeriesElement = *Operand;
+ ULONGLONG Quadrant;
+ FAST486_FPU_DATA_REG Normalized = *Operand;
+ FAST486_FPU_DATA_REG TempResult;
+ FAST486_FPU_DATA_REG OperandSquared;
+ FAST486_FPU_DATA_REG SeriesElement;
+ PCFAST486_FPU_DATA_REG Inverse;
+
+ if (!Fast486FpuRemainder(State,
+ Operand,
+ &FpuHalfPi,
+ FALSE,
+ &Normalized,
+ (PLONGLONG)&Quadrant))
+ {
+ return FALSE;
+ }
+
+ /* Normalize the quadrant number */
+ Quadrant &= 3;
+
+ if (!(Quadrant & 1))
+ {
+ /* This is a sine */
+ Inverse = FpuInverseNumberSine;
+ TempResult = SeriesElement = Normalized;
+ }
+ else
+ {
+ /* This is a cosine */
+ Inverse = FpuInverseNumberCosine;
+ TempResult = SeriesElement = FpuOne;
+ }
/* Calculate the square of the operand */
- if (!Fast486FpuMultiply(State, Operand, Operand, &OperandSquared)) return FALSE;
-
- for (i = 2; (i * (i + 1)) <= INVERSE_NUMBERS_COUNT; i += 2)
+ if (!Fast486FpuMultiply(State, &Normalized, &Normalized,
&OperandSquared)) return FALSE;
+
+ for (i = 0; i < INVERSE_NUMBERS_COUNT; i++)
{
if (!Fast486FpuMultiply(State, &SeriesElement, &OperandSquared,
&SeriesElement))
{
@@ -1253,7 +1395,7 @@
if (!Fast486FpuMultiply(State,
&SeriesElement,
- &FpuInverseNumber[i * (i + 1) - 1],
+ &Inverse[i],
&SeriesElement))
{
/* An exception occurred */
@@ -1269,6 +1411,9 @@
return FALSE;
}
}
+
+ /* Flip the sign for the third and fourth quadrant */
+ if (Quadrant >= 2) TempResult.Sign = !TempResult.Sign;
*Result = TempResult;
return TRUE;
@@ -1283,43 +1428,13 @@
PFAST486_FPU_DATA_REG Operand,
PFAST486_FPU_DATA_REG Result)
{
- INT i;
- FAST486_FPU_DATA_REG TempResult = FpuOne;
- FAST486_FPU_DATA_REG OperandSquared = *Operand;
- FAST486_FPU_DATA_REG SeriesElement = FpuOne;
-
- /* Calculate the square of the operand */
- if (!Fast486FpuMultiply(State, Operand, Operand, &OperandSquared)) return FALSE;
-
- for (i = 1; (i * (i + 1)) <= INVERSE_NUMBERS_COUNT; i += 2)
- {
- if (!Fast486FpuMultiply(State, &SeriesElement, &OperandSquared,
&SeriesElement))
- {
- /* An exception occurred */
- return FALSE;
- }
-
- if (!Fast486FpuMultiply(State,
- &SeriesElement,
- &FpuInverseNumber[i * (i + 1) - 1],
- &SeriesElement))
- {
- /* An exception occurred */
- return FALSE;
- }
-
- /* Toggle the sign of the series element */
- SeriesElement.Sign = !SeriesElement.Sign;
-
- if (!Fast486FpuAdd(State, &TempResult, &SeriesElement, &TempResult))
- {
- /* An exception occurred */
- return FALSE;
- }
- }
-
- *Result = TempResult;
- return TRUE;
+ FAST486_FPU_DATA_REG Value = *Operand;
+
+ /* Add pi / 2 */
+ if (!Fast486FpuAdd(State, &Value, &FpuHalfPi, &Value)) return FALSE;
+
+ /* Calculate the sine */
+ return Fast486FpuCalculateSine(State, &Value, Result);
}
static inline VOID FASTCALL
@@ -2090,7 +2205,7 @@
break;
}
- Fast486FpuRemainder(State, &FPU_ST(0), &FPU_ST(1), TRUE,
&FPU_ST(0));
+ Fast486FpuRemainder(State, &FPU_ST(0), &FPU_ST(1), TRUE,
&FPU_ST(0), NULL);
FPU_UPDATE_TAG(0);
break;
@@ -2121,7 +2236,7 @@
break;
}
- Fast486FpuRemainder(State, &FPU_ST(0), &FPU_ST(1), FALSE,
&FPU_ST(0));
+ Fast486FpuRemainder(State, &FPU_ST(0), &FPU_ST(1), FALSE,
&FPU_ST(0), NULL);
FPU_UPDATE_TAG(0);
break;
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