ref: 023884d2b02ea11670031c8a0cf0c22f4b6bc911
parent: 3567faf395cdc93d859692eb3c0421b0cdcf702d
author: Rangi <[email protected]>
date: Thu Sep 29 00:57:29 EDT 2022
Redefine the trig functions to divide circles into 1.0 turns (#1060) This makes their behavior consistent across Q settings Fixes #1059
--- a/man/rgbasm.5
+++ b/man/rgbasm.5
@@ -57,8 +57,8 @@
.Ql */ .
It can be split across multiple lines, or occur in the middle of an expression:
.Bd -literal -offset indent
-X = /* the value of x
- should be 3 */ 3
+DEF X = /* the value of x
+ should be 3 */ 3
.Ed
.Pp
Sometimes lines can be too long and it may be necessary to split them.
@@ -168,20 +168,20 @@
Examples:
.Bd -literal -offset indent
SECTION "Test", ROM0[2]
-X: ;\ This works with labels **whose address is known**
-Y = 3 ;\ This also works with variables
-SUM equ X + Y ;\ And likewise with numeric constants
+X: ;\ This works with labels **whose address is known**
+DEF Y = 3 ;\ This also works with variables
+DEF SUM EQU X + Y ;\ And likewise with numeric constants
; Prints "%0010 + $3 == 5"
PRINTLN "{#05b:X} + {#x:Y} == {d:SUM}"rsset 32
-PERCENT rb 1 ;\ Same with offset constants
-VALUE = 20
-RESULT = MUL(20.0, 0.32)
+DEF PERCENT rb 1 ;\ Same with offset constants
+DEF VALUE = 20
+DEF RESULT = MUL(20.0, 0.32)
; Prints "32% of 20 = 6.40"
PRINTLN "{d:PERCENT}% of {d:VALUE} = {f:RESULT}"-WHO equs STRLWR("WORLD")+DEF WHO EQUS STRLWR("WORLD"); Prints "Hello world!"
PRINTLN "Hello {s:WHO}!".Ed
@@ -350,18 +350,18 @@
.Ic SIN ,
.Ic COS ,
.Ic TAN ,
-etc) are defined in terms of a circle divided into 65535.0 degrees.
+etc) are defined in terms of a circle divided into 1.0 "turns" (equal to 2pi radians or 360 degrees).
.Pp
These functions are useful for automatic generation of various tables.
For example:
.Bd -literal -offset indent
-; Generate a 256-byte sine table with values in the range [0, 128]
-; (shifted and scaled from the range [-1.0, 1.0])
-ANGLE = 0.0
- REPT 256
- db (MUL(64.0, SIN(ANGLE)) + 64.0) >> 16
-ANGLE = ANGLE + 256.0 ; 256.0 = 65536 degrees / 256 entries
- ENDR
+; Generate a table of sine values from sin(0.0) to sin(1.0), with
+; amplitude scaled from [-1.0, 1.0] to [0.0, 128.0]
+DEF turns = 0.0
+REPT 256
+ db MUL(64.0, SIN(turns) + 1.0) >> 16
+ DEF turns += 1.0 / 256
+ENDR
.Ed
.Ss String expressions
The most basic string expression is any number of characters contained in double quotes
@@ -1011,7 +1011,7 @@
DEF COUNT = 2
DEF COUNT = 3
DEF COUNT = ARRAY_SIZE + COUNT
-COUNT = COUNT*2
+DEF COUNT *= 2
;\ COUNT now has the value 14
.Ed
.Pp
@@ -1753,13 +1753,12 @@
.Ic REPT
to generate tables on the fly:
.Bd -literal -offset indent
-; Generate a 256-byte sine table with values in the range [0, 128]
-; (shifted and scaled from the range [-1.0, 1.0])
-ANGLE = 0.0
- REPT 256
- db (MUL(64.0, SIN(ANGLE)) + 64.0) >> 16
-ANGLE = ANGLE + 256.0 ; 256.0 = 65536 degrees / 256 entries
- ENDR
+; Generate a table of square values from 0**2 = 0 to 100**2 = 10000
+DEF x = 0
+REPT 101
+ dw x * x
+ DEF x += 1
+ENDR
.Ed
.Pp
As in macros, you can also use the escape sequence
--- a/src/asm/fixpoint.c
+++ b/src/asm/fixpoint.c
@@ -24,9 +24,9 @@
#define fix2double(i) ((double)((i) / fix_PrecisionFactor()))
#define double2fix(d) ((int32_t)round((d) * fix_PrecisionFactor()))
-// pi*2 radians == 2**fixPrecision fixed-point "degrees"
-#define fdeg2rad(f) ((f) * (M_PI * 2) / fix_PrecisionFactor())
-#define rad2fdeg(r) ((r) * fix_PrecisionFactor() / (M_PI * 2))
+// 2*pi radians == 1 turn
+#define turn2rad(f) ((f) * (M_PI * 2))
+#define rad2turn(r) ((r) / (M_PI * 2))
uint8_t fixPrecision;
@@ -51,37 +51,37 @@
int32_t fix_Sin(int32_t i)
{- return double2fix(sin(fdeg2rad(fix2double(i))));
+ return double2fix(sin(turn2rad(fix2double(i))));
}
int32_t fix_Cos(int32_t i)
{- return double2fix(cos(fdeg2rad(fix2double(i))));
+ return double2fix(cos(turn2rad(fix2double(i))));
}
int32_t fix_Tan(int32_t i)
{- return double2fix(tan(fdeg2rad(fix2double(i))));
+ return double2fix(tan(turn2rad(fix2double(i))));
}
int32_t fix_ASin(int32_t i)
{- return double2fix(rad2fdeg(asin(fix2double(i))));
+ return double2fix(rad2turn(asin(fix2double(i))));
}
int32_t fix_ACos(int32_t i)
{- return double2fix(rad2fdeg(acos(fix2double(i))));
+ return double2fix(rad2turn(acos(fix2double(i))));
}
int32_t fix_ATan(int32_t i)
{- return double2fix(rad2fdeg(atan(fix2double(i))));
+ return double2fix(rad2turn(atan(fix2double(i))));
}
int32_t fix_ATan2(int32_t i, int32_t j)
{- return double2fix(rad2fdeg(atan2(fix2double(i), fix2double(j))));
+ return double2fix(rad2turn(atan2(fix2double(i), fix2double(j))));
}
int32_t fix_Mul(int32_t i, int32_t j)
--- /dev/null
+++ b/test/asm/trigonometry.asm
@@ -1,0 +1,38 @@
+for Q, 2, 31
+ OPT Q.{d:Q}+
+ assert sin(0.25) == 1.0
+ assert asin(1.0) == 0.25
+
+ assert sin(0.0) == 0.0
+ assert asin(0.0) == 0.0
+
+ assert cos(0.0) == 1.0
+ assert acos(1.0) == 0.0
+
+ if Q > 2 ; can't represent 0.125 in Q.2
+ assert tan(0.125) == 1.0
+ assert atan(1.0) == 0.125
+ else
+ assert tan(0.0) == 0.0
+ assert atan(0.0) == 0.0
+ endc
+endr
+
+SECTION "sine", ROM0[0]
+OPT Q.16
+; Generate a table of sine values from sin(0.0) to sin(1.0), with
+; amplitude scaled from [-1.0, 1.0] to [0.0, 128.0]
+DEF turns = 0.0
+REPT 256
+ db MUL(64.0, SIN(turns) + 1.0) >> 16
+ DEF turns += 1.0 / 256
+ENDR
+
+
+SECTION "cosine", ROM0[256]
+OPT Q.8
+; 32 samples of cos(x) from x=0 to x=pi radians=0.5 turns
+for x, 0.0, 0.5, 0.5 / 32
+ dw cos(x)
+endr
binary files /dev/null b/test/asm/trigonometry.out.bin differ