aboutsummaryrefslogtreecommitdiff
path: root/keymaps/onekey/stm32f411/qfplib/qfplib.s
diff options
context:
space:
mode:
Diffstat (limited to 'keymaps/onekey/stm32f411/qfplib/qfplib.s')
-rw-r--r--keymaps/onekey/stm32f411/qfplib/qfplib.s825
1 files changed, 401 insertions, 424 deletions
diff --git a/keymaps/onekey/stm32f411/qfplib/qfplib.s b/keymaps/onekey/stm32f411/qfplib/qfplib.s
index f21812a..e035472 100644
--- a/keymaps/onekey/stm32f411/qfplib/qfplib.s
+++ b/keymaps/onekey/stm32f411/qfplib/qfplib.s
@@ -1,26 +1,5 @@
-@ Copyright 2015-2020 Mark Owen
-@ http://www.quinapalus.com
-@
-@ This file is free software: you can redistribute it and/or modify
-@ it under the terms of version 2 of the GNU General Public License
-@ as published by the Free Software Foundation.
-@
-@ This file is distributed in the hope that it will be useful,
-@ but WITHOUT ANY WARRANTY; without even the implied warranty of
-@ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-@ GNU General Public License for more details.
-@
-@ You should have received a copy of the GNU General Public License
-@ along with this file. If not, see <http://www.gnu.org/licenses/> or
-@ write to the Free Software Foundation, Inc., 51 Franklin Street,
-@ Fifth Floor, Boston, MA 02110-1301, USA.
-
-@ Thanks to Li Ling for optimisation suggestions and discussion.
-
[email protected] include_faster,0 @ include fast divide and square root?
[email protected] include_conversions,1 @ include float <-> fixed point conversion functions?
[email protected] include_scientific,1 @ include trignometic, exponential etc. functions?
+// Copyright 2015 Mark Owen ([email protected])
+// SPDX-License-Identifier: GPL-2.0-or-later
.ifndef include_faster
.equ include_faster,1
@@ -42,8 +21,6 @@
.cpu cortex-m0
.thumb
-@ exported symbols
-
.global qfp_fadd
.global qfp_fsub
.global qfp_fmul
@@ -74,15 +51,15 @@
.global qfp_fsqrt_fast
.endif
-@ exchange r0<->r1, r2<->r3
+// exchange r0<->r1, r2<->r3
xchxy:
push {r0,r2,r14}
mov r0,r1
mov r2,r3
pop {r1,r3,r15}
-@ IEEE single precision floats in r0,r1-> mantissae in r1,r0 exponents in r3,r2 *respectively*
-@ trashes r4
+// IEEE single precision floats in r0,r1-> mantissae in r1,r0 exponents in r3,r2 *respectively*
+// trashes r4
unpackxy:
push {r14}
bl unpackx
@@ -90,192 +67,192 @@ unpackxy:
pop {r4}
mov r14,r4
-@ IEEE single in r0-> signed (two's complemennt) mantissa in r0 9Q23 (24 significant bits), signed exponent (bias removed) in r2
-@ trashes r4; zero, denormal -> mantissa=+/-1, exponent=-380; Inf, NaN -> mantissa=+/-1, exponent=+640
+// IEEE single in r0-> signed (two's complemennt) mantissa in r0 9Q23 (24 significant bits), signed exponent (bias removed) in r2
+// trashes r4; zero, denormal -> mantissa=+/-1, exponent=-380; Inf, NaN -> mantissa=+/-1, exponent=+640
unpackx:
- lsrs r2,r0,#23 @ save exponent and sign
- lsls r0,#9 @ extract mantissa
+ lsrs r2,r0,#23 // save exponent and sign
+ lsls r0,#9 // extract mantissa
lsrs r0,#9
movs r4,#1
lsls r4,#23
- orrs r0,r4 @ reinstate implied leading 1
- cmp r2,#255 @ test sign bit
- uxtb r2,r2 @ clear it
- bls 1f @ branch on positive
- rsbs r0,#0 @ negate mantissa
+ orrs r0,r4 // reinstate implied leading 1
+ cmp r2,#255 // test sign bit
+ uxtb r2,r2 // clear it
+ bls 1f // branch on positive
+ rsbs r0,#0 // negate mantissa
1:
subs r2,#1
- cmp r2,#254 @ zero/denormal/Inf/NaN?
+ cmp r2,#254 // zero/denormal/Inf/NaN?
bhs 2f
- subs r2,#126 @ remove exponent bias: can now be -126..+127
+ subs r2,#126 // remove exponent bias: can now be -126..+127
bx r14
-2: @ here with special-case values
+2: // here with special-case values
cmp r0,#0
- mov r0,r4 @ set mantissa to +1
+ mov r0,r4 // set mantissa to +1
bpl 3f
- rsbs r0,#0 @ zero/denormal/Inf/NaN: mantissa=+/-1
+ rsbs r0,#0 // zero/denormal/Inf/NaN: mantissa=+/-1
3:
- subs r2,#126 @ zero/denormal: exponent -> -127; Inf, NaN: exponent -> 128
- lsls r2,#2 @ zero/denormal: exponent -> -508; Inf, NaN: exponent -> 512
- adds r2,#128 @ zero/denormal: exponent -> -380; Inf, NaN: exponent -> 640
+ subs r2,#126 // zero/denormal: exponent -> -127; Inf, NaN: exponent -> 128
+ lsls r2,#2 // zero/denormal: exponent -> -508; Inf, NaN: exponent -> 512
+ adds r2,#128 // zero/denormal: exponent -> -380; Inf, NaN: exponent -> 640
bx r14
-@ normalise and pack signed mantissa in r0 nominally 3Q29, signed exponent in r2-> IEEE single in r0
-@ trashes r4, preserves r1,r3
-@ r5: "sticky bits", must be zero iff all result bits below r0 are zero for correct rounding
+// normalise and pack signed mantissa in r0 nominally 3Q29, signed exponent in r2-> IEEE single in r0
+// trashes r4, preserves r1,r3
+// r5: "sticky bits", must be zero iff all result bits below r0 are zero for correct rounding
packx:
- lsrs r4,r0,#31 @ save sign bit
- lsls r4,r4,#31 @ sign now in b31
- bpl 2f @ skip if positive
+ lsrs r4,r0,#31 // save sign bit
+ lsls r4,r4,#31 // sign now in b31
+ bpl 2f // skip if positive
cmp r5,#0
beq 11f
- adds r0,#1 @ fiddle carry in to following rsb if sticky bits are non-zero
+ adds r0,#1 // fiddle carry in to following rsb if sticky bits are non-zero
11:
- rsbs r0,#0 @ can now treat r0 as unsigned
+ rsbs r0,#0 // can now treat r0 as unsigned
packx0:
- bmi 3f @ catch r0=0x80000000 case
+ bmi 3f // catch r0=0x80000000 case
2:
- subs r2,#1 @ normalisation loop
+ subs r2,#1 // normalisation loop
adds r0,r0
- beq 1f @ zero? special case
- bpl 2b @ normalise so leading "1" in bit 31
+ beq 1f // zero? special case
+ bpl 2b // normalise so leading "1" in bit 31
3:
- adds r2,#129 @ (mis-)offset exponent
- bne 12f @ special case: highest denormal can round to lowest normal
- adds r0,#0x80 @ in special case, need to add 256 to r0 for rounding
- bcs 4f @ tripped carry? then have leading 1 in C as required
+ adds r2,#129 // (mis-)offset exponent
+ bne 12f // special case: highest denormal can round to lowest normal
+ adds r0,#0x80 // in special case, need to add 256 to r0 for rounding
+ bcs 4f // tripped carry? then have leading 1 in C as required
12:
- adds r0,#0x80 @ rounding
- bcs 4f @ tripped carry? then have leading 1 in C as required (and result is even so can ignore sticky bits)
+ adds r0,#0x80 // rounding
+ bcs 4f // tripped carry? then have leading 1 in C as required (and result is even so can ignore sticky bits)
cmp r5,#0
- beq 7f @ sticky bits zero?
+ beq 7f // sticky bits zero?
8:
- lsls r0,#1 @ remove leading 1
+ lsls r0,#1 // remove leading 1
9:
- subs r2,#1 @ compensate exponent on this path
+ subs r2,#1 // compensate exponent on this path
4:
cmp r2,#254
- bge 5f @ overflow?
- adds r2,#1 @ correct exponent offset
- ble 10f @ denormal/underflow?
- lsrs r0,#9 @ align mantissa
- lsls r2,#23 @ align exponent
- orrs r0,r2 @ assemble exponent and mantissa
+ bge 5f // overflow?
+ adds r2,#1 // correct exponent offset
+ ble 10f // denormal/underflow?
+ lsrs r0,#9 // align mantissa
+ lsls r2,#23 // align exponent
+ orrs r0,r2 // assemble exponent and mantissa
6:
- orrs r0,r4 @ apply sign
+ orrs r0,r4 // apply sign
1:
bx r14
5:
- movs r0,#0xff @ create infinity
+ movs r0,#0xff // create infinity
lsls r0,#23
b 6b
10:
- movs r0,#0 @ create zero
+ movs r0,#0 // create zero
bx r14
-7: @ sticky bit rounding case
- lsls r5,r0,#24 @ check bottom 8 bits of r0
- bne 8b @ in rounding-tie case?
- lsrs r0,#9 @ ensure even result
+7: // sticky bit rounding case
+ lsls r5,r0,#24 // check bottom 8 bits of r0
+ bne 8b // in rounding-tie case?
+ lsrs r0,#9 // ensure even result
lsls r0,#10
b 9b
-@ unpack two arguments (r0,r1) and shift one down to have common exponent, returned in r2; note that arguments are exchanged
-@ sticky bits shifted off bottom of smaller argument in r5
-@ following code is unnecessarily general for fadd, but is shared with atan2
+// unpack two arguments (r0,r1) and shift one down to have common exponent, returned in r2; note that arguments are exchanged
+// sticky bits shifted off bottom of smaller argument in r5
+// following code is unnecessarily general for fadd, but is shared with atan2
unpackxyalign:
push {r14}
bl unpackxy
- lsls r0,r0,#6 @ Q29
- lsls r1,r1,#6 @ Q29
- subs r4,r2,r3 @ calculate shift
- bge 1f @ x>=y?
- mov r2,r3 @ no: take common exponent from y
- mov r5,r0 @ potential sticky bits from x
- rsbs r4,#0 @ make shift positive
+ lsls r0,r0,#6 // Q29
+ lsls r1,r1,#6 // Q29
+ subs r4,r2,r3 // calculate shift
+ bge 1f // x>=y?
+ mov r2,r3 // no: take common exponent from y
+ mov r5,r0 // potential sticky bits from x
+ rsbs r4,#0 // make shift positive
asrs r0,r4
cmp r4,#32
blo 2f
- movs r0,#0 @ large shift, so all bits are sticky and result is zero
+ movs r0,#0 // large shift, so all bits are sticky and result is zero
pop {r15}
1:
- mov r5,r1 @ common exponent from x; potential sticky bits from y
+ mov r5,r1 // common exponent from x; potential sticky bits from y
asrs r1,r4
cmp r4,#32
blo 2f
- movs r1,#0 @ large shift, so all bits are sticky and result is zero
+ movs r1,#0 // large shift, so all bits are sticky and result is zero
pop {r15}
2:
rsbs r4,#0
adds r4,#32
- lsls r5,r4 @ extract sticky bits
+ lsls r5,r4 // extract sticky bits
pop {r15}
.thumb_func
qfp_fsub:
- movs r2,#1 @ subtract: flip sign bit of second argument and fall through to fadd
+ movs r2,#1 // subtract: flip sign bit of second argument and fall through to fadd
lsls r2,#31
eors r1,r2
.thumb_func
qfp_fadd:
push {r4,r5,r14}
bl unpackxyalign
- adds r0,r1 @ do addition
- bne 2f @ not in Inf-Inf case?
+ adds r0,r1 // do addition
+ bne 2f // not in Inf-Inf case?
cmp r2,#200
blt 2f
movs r0,#1
- lsls r0,#29 @ for Inf-Inf, set mantissa to +1 to prevent zero result
+ lsls r0,#29 // for Inf-Inf, set mantissa to +1 to prevent zero result
2:
-packret: @ common return point: "pack and return"
+packret: // common return point: "pack and return"
bl packx
pop {r4,r5,r15}
-@ signed multiply r0 1Q23 by r1 4Q23, result in r0 7Q25, sticky bits in r5
-@ trashes r3,r4
+// signed multiply r0 1Q23 by r1 4Q23, result in r0 7Q25, sticky bits in r5
+// trashes r3,r4
mul0:
- uxth r3,r0 @ Q23
- asrs r4,r1,#16 @ Q7
- muls r3,r4 @ L*H, Q30 signed
- asrs r4,r0,#16 @ Q7
- uxth r5,r1 @ Q23
- muls r4,r5 @ H*L, Q30 signed
- adds r3,r4 @ sum of middle partial products
+ uxth r3,r0 // Q23
+ asrs r4,r1,#16 // Q7
+ muls r3,r4 // L*H, Q30 signed
+ asrs r4,r0,#16 // Q7
+ uxth r5,r1 // Q23
+ muls r4,r5 // H*L, Q30 signed
+ adds r3,r4 // sum of middle partial products
uxth r4,r0
- muls r4,r5 @ L*L, Q46 unsigned
- lsls r5,r4,#16 @ initialise sticky bits from low half of low partial product
- lsrs r4,#16 @ Q25
- adds r3,r4 @ add high half of low partial product to sum of middle partial products
- @ (cannot generate carry by limits on input arguments)
- asrs r0,#16 @ Q7
- asrs r1,#16 @ Q7
- muls r0,r1 @ H*H, Q14 signed
- lsls r0,#11 @ high partial product Q25
- lsls r1,r3,#27 @ sticky
- orrs r5,r1 @ collect further sticky bits
- asrs r1,r3,#5 @ middle partial products Q25
- adds r0,r1 @ final result
+ muls r4,r5 // L*L, Q46 unsigned
+ lsls r5,r4,#16 // initialise sticky bits from low half of low partial product
+ lsrs r4,#16 // Q25
+ adds r3,r4 // add high half of low partial product to sum of middle partial products
+ // (cannot generate carry by limits on input arguments)
+ asrs r0,#16 // Q7
+ asrs r1,#16 // Q7
+ muls r0,r1 // H*H, Q14 signed
+ lsls r0,#11 // high partial product Q25
+ lsls r1,r3,#27 // sticky
+ orrs r5,r1 // collect further sticky bits
+ asrs r1,r3,#5 // middle partial products Q25
+ adds r0,r1 // final result
bx r14
.thumb_func
qfp_fcmp:
- movs r2,#1 @ initialise result
- lsls r3,r2,#31 @ r3=0x80000000
- tst r0,r3 @ check sign of first argument
+ movs r2,#1 // initialise result
+ lsls r3,r2,#31 // r3=0x80000000
+ tst r0,r3 // check sign of first argument
beq 1f
- subs r0,r3,r0 @ convert to 2's complement form for direct comparison
+ subs r0,r3,r0 // convert to 2's complement form for direct comparison
1:
- tst r1,r3 @ repeat for second argument
+ tst r1,r3 // repeat for second argument
beq 2f
subs r1,r3,r1
2:
- subs r0,r1 @ perform comparison
- beq 4f @ equal? return 0
- bgt 3f @ r0>r1? return +1
- rsbs r2,#0 @ r0<r1: return -1
+ subs r0,r1 // perform comparison
+ beq 4f // equal? return 0
+ bgt 3f // r0>r1? return +1
+ rsbs r2,#0 // r0<r1: return -1
3:
mov r0,r2
4:
@@ -285,8 +262,8 @@ qfp_fcmp:
qfp_fmul:
push {r4,r5,r14}
bl unpackxy
- add r2,r3 @ sum exponents
- adds r2,#4 @ adjust exponent for pack which expects Q29
+ add r2,r3 // sum exponents
+ adds r2,#4 // adjust exponent for pack which expects Q29
fmul0:
bl mul0
b packret
@@ -296,56 +273,56 @@ qfp_fdiv:
push {r4,r5,r14}
fdiv_n:
bl unpackxy
- movs r5,#1 @ result cannot fall exactly half-way between two representable numbers (exercise for reader - note that
- @ we do not handle denormals) so there will always be sticky bits
- cmp r0,#0 @ check divisor sign
+ movs r5,#1 // result cannot fall exactly half-way between two representable numbers (exercise for reader - note that
+ // we do not handle denormals) so there will always be sticky bits
+ cmp r0,#0 // check divisor sign
bpl 1f
- rsbs r0,#0 @ ensure divisor positive
- rsbs r1,#0 @ preserve sign of result
+ rsbs r0,#0 // ensure divisor positive
+ rsbs r1,#0 // preserve sign of result
1:
movs r4,#0
- cmp r1,#0 @ check sign of dividend
+ cmp r1,#0 // check sign of dividend
bpl 2f
- rsbs r1,#0 @ result will be negative
- mvns r4,r4 @ save sign as 0x00000000 or 0xffffffff
-2: @ now do unsigned division on unpacked values {r1,r3}/{r0,r2}
- cmp r3,#200 @ dividend is an infinity? return it
+ rsbs r1,#0 // result will be negative
+ mvns r4,r4 // save sign as 0x00000000 or 0xffffffff
+2: // now do unsigned division on unpacked values {r1,r3}/{r0,r2}
+ cmp r3,#200 // dividend is an infinity? return it
bge 3f
rsbs r2,#0
- cmp r2,#200 @ divisor is zero? return infinity
+ cmp r2,#200 // divisor is zero? return infinity
bge 3f
- adds r2,r3 @ difference of exponents
- movs r3,#0x40 @ termination marker (calculate enough bits to do rounding correctly)
-2: @ division loop
- subs r1,r0 @ trial subtraction
+ adds r2,r3 // difference of exponents
+ movs r3,#0x40 // termination marker (calculate enough bits to do rounding correctly)
+2: // division loop
+ subs r1,r0 // trial subtraction
bcs 1f
- add r1,r0 @ restore if failed
+ add r1,r0 // restore if failed
1:
- adcs r3,r3 @ shift in result bit
- add r1,r1 @ shift up dividend
- bcc 2b @ loop until marker appears in carry
- lsls r0,r3,#4 @ align for packing
+ adcs r3,r3 // shift in result bit
+ add r1,r1 // shift up dividend
+ bcc 2b // loop until marker appears in carry
+ lsls r0,r3,#4 // align for packing
4:
- eors r0,r4 @ apply sign
+ eors r0,r4 // apply sign
b packret
infret:
movs r4,#0
3:
mov r0,r1
- movs r2,#255 @ return infinity
+ movs r2,#255 // return infinity
b 4b
.if include_faster
-@ The fast divide routine uses an initial approximation to the reciprocal of the divisor based on the top four bits of the mantissa
-@ followed by three Newton-Raphson iterations, resulting in about 27 bits of accuracy. This reciprocal is then multiplied by
-@ the dividend.
-@ The (fixed-point) reciprocal calculation is carefully implemented to preserve the necessary accuracy throughout. In places
-@ the implied binary point is not within the stored value. For example where "Q47" is shown below it means that the least
-@ significant bit of the value has significance 2^-47 and hence the most significant bit has significance 2^-16. In these
-@ cases the value is known to be very close to an integer (usually 1) and so the bits of greater significance do not need
-@ to be stored.
-@ The reciprocal calculation has been tested for all possible input mantissa values.
+// The fast divide routine uses an initial approximation to the reciprocal of the divisor based on the top four bits of the mantissa
+// followed by three Newton-Raphson iterations, resulting in about 27 bits of accuracy. This reciprocal is then multiplied by
+// the dividend.
+// The (fixed-point) reciprocal calculation is carefully implemented to preserve the necessary accuracy throughout. In places
+// the implied binary point is not within the stored value. For example where "Q47" is shown below it means that the least
+// significant bit of the value has significance 2^-47 and hence the most significant bit has significance 2^-16. In these
+// cases the value is known to be very close to an integer (usually 1) and so the bits of greater significance do not need
+// to be stored.
+// The reciprocal calculation has been tested for all possible input mantissa values.
.thumb_func
qfp_fdiv_fast:
push {r4,r5,r14}
@@ -354,115 +331,115 @@ fdiv_fast_n:
cmp r0,#0
bpl 1f
rsbs r0,#0
- rsbs r1,#0 @ ensure divisor positive
+ rsbs r1,#0 // ensure divisor positive
1:
cmp r3,#200
- bge infret @ dividend is an infinity? return it
+ bge infret // dividend is an infinity? return it
rsbs r2,#0
- cmp r2,#200 @ divisor is zero?
- bge infret @ return infinity
- adds r2,r3 @ difference of exponents
- adr r4,rcpapp-8 @ the first 8 elements of the table are never accessed because of the mantissa's leading 1
- lsrs r3,r0,#20 @ y Q23; y>>20 Q7
- ldrb r4,[r4,r3] @ m=rcpapp[(y>>20)&7]; // Q8, .5<m<1
-
- lsls r3,r4,#2 @ m<<2 // Q10 first Newton-Raphson iteration
- muls r3,r0 @ s=y*(m<<2); // Q33
- lsls r4,#8 @ m<<=8; // Q16
- asrs r3,#21 @ s>>=21; // Q12
- muls r3,r4 @ s*=m; // Q28
- asrs r3,#12 @ s>>=12; // Q16
- subs r4,r3 @ m=m-s; // Q16
-
- mov r3,r4 @ s=y*m // Q39 second Newton-Raphson iteration
- muls r4,r0 @ ...
- asrs r4,#16 @ s>>=16; // Q23
- muls r4,r3 @ s*=m; // Q39
- lsls r3,#8 @ m<<=8; // Q24
- asrs r4,#15 @ s>>=15; // Q24
- subs r3,r4 @ m=m-s; // Q24
-
- lsls r4,r3,#7 @ \/ s=y*m; // Q47 third Newton-Raphson iteration
- muls r3,r0 @ /\ m<<=7; // Q31
- asrs r3,#15 @ s>>=15; // Q32
- lsrs r0,r4,#16 @ s*=(m>>16); // Q47
- muls r3,r0 @ ...
- asrs r3,#16 @ s>>=16; // Q31
- subs r0,r4,r3 @ m=m-s; // Q31
+ cmp r2,#200 // divisor is zero?
+ bge infret // return infinity
+ adds r2,r3 // difference of exponents
+ adr r4,rcpapp-8 // the first 8 elements of the table are never accessed because of the mantissa's leading 1
+ lsrs r3,r0,#20 // y Q23; y>>20 Q7
+ ldrb r4,[r4,r3] // m=rcpapp[(y>>20)&7]; // Q8, .5<m<1
+
+ lsls r3,r4,#2 // m<<2 // Q10 first Newton-Raphson iteration
+ muls r3,r0 // s=y*(m<<2); // Q33
+ lsls r4,#8 // m<<=8; // Q16
+ asrs r3,#21 // s>>=21; // Q12
+ muls r3,r4 // s*=m; // Q28
+ asrs r3,#12 // s>>=12; // Q16
+ subs r4,r3 // m=m-s; // Q16
+
+ mov r3,r4 // s=y*m // Q39 second Newton-Raphson iteration
+ muls r4,r0 // ...
+ asrs r4,#16 // s>>=16; // Q23
+ muls r4,r3 // s*=m; // Q39
+ lsls r3,#8 // m<<=8; // Q24
+ asrs r4,#15 // s>>=15; // Q24
+ subs r3,r4 // m=m-s; // Q24
+
+ lsls r4,r3,#7 // \/ s=y*m; // Q47 third Newton-Raphson iteration
+ muls r3,r0 // /\ m<<=7; // Q31
+ asrs r3,#15 // s>>=15; // Q32
+ lsrs r0,r4,#16 // s*=(m>>16); // Q47
+ muls r3,r0 // ...
+ asrs r3,#16 // s>>=16; // Q31
+ subs r0,r4,r3 // m=m-s; // Q31
div0:
- adds r0,#7 @ rounding; reduce systematic error
- lsrs r0,#4 @ Q27
- b fmul0 @ drop into multiplication code to calculate result
-
-@ The fast square root routine uses an initial approximation to the reciprocal of the square root of the argument based
-@ on the top four bits of the mantissa (possibly shifted one place to make the exponent even). It then performs three
-@ Newton-Raphson iterations, resulting in about 28-29 bits of accuracy. This reciprocal is then multiplied by
-@ the original argument to produce the result.
-@ Again, the fixed-point calculation is carefully implemented to preserve accuracy, and similar comments to those
-@ made above on the fast division routine apply.
-@ The reciprocal square root calculation has been tested for all possible (possibly shifted) input mantissa values.
+ adds r0,#7 // rounding; reduce systematic error
+ lsrs r0,#4 // Q27
+ b fmul0 // drop into multiplication code to calculate result
+
+// The fast square root routine uses an initial approximation to the reciprocal of the square root of the argument based
+// on the top four bits of the mantissa (possibly shifted one place to make the exponent even). It then performs three
+// Newton-Raphson iterations, resulting in about 28-29 bits of accuracy. This reciprocal is then multiplied by
+// the original argument to produce the result.
+// Again, the fixed-point calculation is carefully implemented to preserve accuracy, and similar comments to those
+// made above on the fast division routine apply.
+// The reciprocal square root calculation has been tested for all possible (possibly shifted) input mantissa values.
.thumb_func
qfp_fsqrt_fast:
push {r4,r5,r14}
bl unpackx
movs r1,r0
- bmi infret @ negative? return -Inf
- asrs r0,r2,#1 @ check LSB of exponent
+ bmi infret // negative? return -Inf
+ asrs r0,r2,#1 // check LSB of exponent
bcc 1f
- lsls r1,#1 @ was odd: double mantissa; mantissa y now 1..4 Q23
+ lsls r1,#1 // was odd: double mantissa; mantissa y now 1..4 Q23
1:
- adds r2,#4 @ correction for packing
- adr r4,rsqrtapp-4@ first four table entries are never accessed because of the mantissa's leading 1
- lsrs r3,r1,#21 @ y>>21 Q2
- ldrb r4,[r4,r3] @ initial approximation to reciprocal square root m Q8
-
- lsrs r0,r1,#7 @ y>>7 // Q16 first Newton-Raphson iteration
- muls r0,r4 @ m*y
- muls r0,r4 @ s=m*y*y // Q32
- asrs r0,#12 @ s>>12
- muls r0,r4 @ m*s // Q28
- asrs r0,#13 @ m*s // Q15
- lsls r4,#8 @ m // Q16
- subs r4,r0 @ m=(m<<8)-(s>>13) // Q16-Q15/2 -> Q16
-
- mov r0,r4 @ // second Newton-Raphson iteration
- muls r0,r0 @ u=m*m // Q32
- lsrs r0,#16 @ u>>16 // Q16
- lsrs r3,r1,#7 @ y>>7 // Q16
- muls r0,r3 @ s=u*(y>>7) // Q32
- asrs r0,#12 @ s>>12 // Q20
- muls r0,r4 @ s*m // Q36
- asrs r0,#21 @ s*m // Q15
- subs r4,r0 @ m=m-s // Q16-Q15/2
-
- mov r0,r4 @ // third Newton-Raphson iteration
- muls r0,r0 @ u=m*m // Q32
- lsrs r3,r0,#12 @ now multiply u and y in two parts: u>>12
- muls r3,r1 @ first partial product (u>>12)*y Q43
+ adds r2,#4 // correction for packing
+ adr r4,rsqrtapp-4// first four table entries are never accessed because of the mantissa's leading 1
+ lsrs r3,r1,#21 // y>>21 Q2
+ ldrb r4,[r4,r3] // initial approximation to reciprocal square root m Q8
+
+ lsrs r0,r1,#7 // y>>7 // Q16 first Newton-Raphson iteration
+ muls r0,r4 // m*y
+ muls r0,r4 // s=m*y*y // Q32
+ asrs r0,#12 // s>>12
+ muls r0,r4 // m*s // Q28
+ asrs r0,#13 // m*s // Q15
+ lsls r4,#8 // m // Q16
+ subs r4,r0 // m=(m<<8)-(s>>13) // Q16-Q15/2 -> Q16
+
+ mov r0,r4 // // second Newton-Raphson iteration
+ muls r0,r0 // u=m*m // Q32
+ lsrs r0,#16 // u>>16 // Q16
+ lsrs r3,r1,#7 // y>>7 // Q16
+ muls r0,r3 // s=u*(y>>7) // Q32
+ asrs r0,#12 // s>>12 // Q20
+ muls r0,r4 // s*m // Q36
+ asrs r0,#21 // s*m // Q15
+ subs r4,r0 // m=m-s // Q16-Q15/2
+
+ mov r0,r4 // // third Newton-Raphson iteration
+ muls r0,r0 // u=m*m // Q32
+ lsrs r3,r0,#12 // now multiply u and y in two parts: u>>12
+ muls r3,r1 // first partial product (u>>12)*y Q43
lsls r0,#20
- lsrs r0,#20 @ u&0xfff
- lsrs r5,r1,#12 @ y>>12
- muls r0,r5 @ second partial product (u&0xfff)*(y>>12) Q43
- add r0,r3 @ s=u*y // Q43
- asrs r0,#15 @ s>>15 // Q28
- muls r0,r4 @ (s>>15)*m // Q44
- lsls r4,#13 @ m<<13 // Q29
- asrs r0,#16 @ s>>16 // Q28
- subs r0,r4,r0 @ // Q29-Q28/2
-
- asrs r2,#1 @ halve exponent
- bcc div0 @ was y shifted?
+ lsrs r0,#20 // u&0xfff
+ lsrs r5,r1,#12 // y>>12
+ muls r0,r5 // second partial product (u&0xfff)*(y>>12) Q43
+ add r0,r3 // s=u*y // Q43
+ asrs r0,#15 // s>>15 // Q28
+ muls r0,r4 // (s>>15)*m // Q44
+ lsls r4,#13 // m<<13 // Q29
+ asrs r0,#16 // s>>16 // Q28
+ subs r0,r4,r0 // // Q29-Q28/2
+
+ asrs r2,#1 // halve exponent
+ bcc div0 // was y shifted?
lsrs r0,#1
- lsls r1,#1 @ shift y back
- b div0 @ round and complete with multiplication
+ lsls r1,#1 // shift y back
+ b div0 // round and complete with multiplication
.align 2
-@ round(2^15./[136:16:248])
+// round(2^15./[136:16:248])
rcpapp:
.byte 0xf1,0xd8,0xc3,0xb2, 0xa4,0x98,0x8d,0x84
-@ round(sqrt(2^22./[72:16:248]))
+// round(sqrt(2^22./[72:16:248]))
rsqrtapp:
.byte 0xf1,0xda,0xc9,0xbb, 0xb0,0xa6,0x9e,0x97, 0x91,0x8b,0x86,0x82
@@ -470,86 +447,86 @@ rsqrtapp:
.if include_conversions
-@ convert float to signed int, rounding towards -Inf, clamping
+// convert float to signed int, rounding towards -Inf, clamping
.thumb_func
qfp_float2int:
- movs r1,#0 @ fall through
+ movs r1,#0 // fall through
-@ convert float in r0 to signed fixed point in r0, clamping
+// convert float in r0 to signed fixed point in r0, clamping
.thumb_func
qfp_float2fix:
push {r4,r14}
bl unpackx
- add r2,r1 @ incorporate binary point position into exponent
- subs r2,#23 @ r2 is now amount of left shift required
- blt 1f @ requires right shift?
- cmp r2,#7 @ overflow?
+ add r2,r1 // incorporate binary point position into exponent
+ subs r2,#23 // r2 is now amount of left shift required
+ blt 1f // requires right shift?
+ cmp r2,#7 // overflow?
ble 4f
-3: @ overflow
- asrs r1,r0,#31 @ +ve:0 -ve:0xffffffff
- mvns r1,r1 @ +ve:0xffffffff -ve:0
+3: // overflow
+ asrs r1,r0,#31 // +ve:0 -ve:0xffffffff
+ mvns r1,r1 // +ve:0xffffffff -ve:0
movs r0,#1
lsls r0,#31
5:
- eors r0,r1 @ +ve:0x7fffffff -ve:0x80000000 (unsigned path: 0xffffffff)
+ eors r0,r1 // +ve:0x7fffffff -ve:0x80000000 (unsigned path: 0xffffffff)
pop {r4,r15}
1:
- rsbs r2,#0 @ right shift for r0, >0
+ rsbs r2,#0 // right shift for r0, >0
cmp r2,#32
- blt 2f @ more than 32 bits of right shift?
+ blt 2f // more than 32 bits of right shift?
movs r2,#32
2:
asrs r0,r0,r2
pop {r4,r15}
-@ unsigned version
+// unsigned version
.thumb_func
qfp_float2uint:
- movs r1,#0 @ fall through
+ movs r1,#0 // fall through
.thumb_func
qfp_float2ufix:
push {r4,r14}
bl unpackx
- add r2,r1 @ incorporate binary point position into exponent
+ add r2,r1 // incorporate binary point position into exponent
movs r1,r0
- bmi 5b @ negative? return zero
- subs r2,#23 @ r2 is now amount of left shift required
- blt 1b @ requires right shift?
- mvns r1,r0 @ ready to return 0xffffffff
- cmp r2,#8 @ overflow?
+ bmi 5b // negative? return zero
+ subs r2,#23 // r2 is now amount of left shift required
+ blt 1b // requires right shift?
+ mvns r1,r0 // ready to return 0xffffffff
+ cmp r2,#8 // overflow?
bgt 5b
4:
- lsls r0,r0,r2 @ result fits, left shifted
+ lsls r0,r0,r2 // result fits, left shifted
pop {r4,r15}
-@ convert signed int to float, rounding
+// convert signed int to float, rounding
.thumb_func
qfp_int2float:
- movs r1,#0 @ fall through
+ movs r1,#0 // fall through
-@ convert signed fix to float, rounding; number of r0 bits after point in r1
+// convert signed fix to float, rounding; number of r0 bits after point in r1
.thumb_func
qfp_fix2float:
push {r4,r5,r14}
1:
movs r2,#29
- subs r2,r1 @ fix exponent
-packretns: @ pack and return, sticky bits=0
+ subs r2,r1 // fix exponent
+packretns: // pack and return, sticky bits=0
movs r5,#0
b packret
-@ unsigned version
+// unsigned version
.thumb_func
qfp_uint2float:
- movs r1,#0 @ fall through
+ movs r1,#0 // fall through
.thumb_func
qfp_ufix2float:
push {r4,r5,r14}
cmp r0,#0
- bge 1b @ treat <2^31 as signed
+ bge 1b // treat <2^31 as signed
movs r2,#30
- subs r2,r1 @ fix exponent
- lsls r5,r0,#31 @ one sticky bit
+ subs r2,r1 // fix exponent
+ lsls r5,r0,#31 // one sticky bit
lsrs r0,#1
b packret
@@ -557,207 +534,207 @@ qfp_ufix2float:
.if include_scientific
-@ All the scientific functions are implemented using the CORDIC algorithm. For notation,
-@ details not explained in the comments below, and a good overall survey see
-@ "50 Years of CORDIC: Algorithms, Architectures, and Applications" by Meher et al.,
-@ IEEE Transactions on Circuits and Systems Part I, Volume 56 Issue 9.
-
-@ Register use:
-@ r0: x
-@ r1: y
-@ r2: z/omega
-@ r3: coefficient pointer
-@ r4,r12: m
-@ r5: i (shift)
-
-cordic_start: @ initialisation
- movs r5,#0 @ initial shift=0
+// All the scientific functions are implemented using the CORDIC algorithm. For notation,
+// details not explained in the comments below, and a good overall survey see
+// "50 Years of CORDIC: Algorithms, Architectures, and Applications" by Meher et al.,
+// IEEE Transactions on Circuits and Systems Part I, Volume 56 Issue 9.
+
+// Register use:
+// r0: x
+// r1: y
+// r2: z/omega
+// r3: coefficient pointer
+// r4,r12: m
+// r5: i (shift)
+
+cordic_start: // initialisation
+ movs r5,#0 // initial shift=0
mov r12,r4
b 5f
-cordic_vstep: @ one step of algorithm in vector mode
- cmp r1,#0 @ check sign of y
+cordic_vstep: // one step of algorithm in vector mode
+ cmp r1,#0 // check sign of y
bgt 4f
b 1f
-cordic_rstep: @ one step of algorithm in rotation mode
- cmp r2,#0 @ check sign of angle
+cordic_rstep: // one step of algorithm in rotation mode
+ cmp r2,#0 // check sign of angle
bge 1f
4:
- subs r1,r6 @ negative rotation: y=y-(x>>i)
+ subs r1,r6 // negative rotation: y=y-(x>>i)
rsbs r7,#0
- adds r2,r4 @ accumulate angle
+ adds r2,r4 // accumulate angle
b 2f
1:
- adds r1,r6 @ positive rotation: y=y+(x>>i)
- subs r2,r4 @ accumulate angle
+ adds r1,r6 // positive rotation: y=y+(x>>i)
+ subs r2,r4 // accumulate angle
2:
mov r4,r12
- muls r7,r4 @ apply sign from m
- subs r0,r7 @ finish rotation: x=x{+/-}(y>>i)
+ muls r7,r4 // apply sign from m
+ subs r0,r7 // finish rotation: x=x{+/-}(y>>i)
5:
- ldmia r3!,{r4} @ fetch next angle from table and bump pointer
- lsrs r4,#1 @ repeated angle?
+ ldmia r3!,{r4} // fetch next angle from table and bump pointer
+ lsrs r4,#1 // repeated angle?
bcs 3f
- adds r5,#1 @ adjust shift if not
+ adds r5,#1 // adjust shift if not
3:
mov r6,r0
- asrs r6,r5 @ x>>i
+ asrs r6,r5 // x>>i
mov r7,r1
- asrs r7,r5 @ y>>i
- lsrs r4,#1 @ shift end flag into carry
+ asrs r7,r5 // y>>i
+ lsrs r4,#1 // shift end flag into carry
bx r14
-@ CORDIC rotation mode
+// CORDIC rotation mode
cordic_rot:
push {r6,r7,r14}
- bl cordic_start @ initialise
+ bl cordic_start // initialise
1:
bl cordic_rstep
- bcc 1b @ step until table finished
- asrs r6,r0,#14 @ remaining small rotations can be linearised: see IV.B of paper referenced above
+ bcc 1b // step until table finished
+ asrs r6,r0,#14 // remaining small rotations can be linearised: see IV.B of paper referenced above
asrs r7,r1,#14
asrs r2,#3
- muls r6,r2 @ all remaining CORDIC steps in a multiplication
+ muls r6,r2 // all remaining CORDIC steps in a multiplication
muls r7,r2
mov r4,r12
muls r7,r4
asrs r6,#12
asrs r7,#12
- subs r0,r7 @ x=x{+/-}(yz>>k)
- adds r1,r6 @ y=y+(xz>>k)
+ subs r0,r7 // x=x{+/-}(yz>>k)
+ adds r1,r6 // y=y+(xz>>k)
cordic_exit:
pop {r6,r7,r15}
-@ CORDIC vector mode
+// CORDIC vector mode
cordic_vec:
push {r6,r7,r14}
- bl cordic_start @ initialise
+ bl cordic_start // initialise
1:
bl cordic_vstep
- bcc 1b @ step until table finished
+ bcc 1b // step until table finished
4:
- cmp r1,#0 @ continue as in cordic_vstep but without using table; x is not affected as y is small
- bgt 2f @ check sign of y
- adds r1,r6 @ positive rotation: y=y+(x>>i)
- subs r2,r4 @ accumulate angle
+ cmp r1,#0 // continue as in cordic_vstep but without using table; x is not affected as y is small
+ bgt 2f // check sign of y
+ adds r1,r6 // positive rotation: y=y+(x>>i)
+ subs r2,r4 // accumulate angle
b 3f
2:
- subs r1,r6 @ negative rotation: y=y-(x>>i)
- adds r2,r4 @ accumulate angle
+ subs r1,r6 // negative rotation: y=y-(x>>i)
+ adds r2,r4 // accumulate angle
3:
asrs r6,#1
- asrs r4,#1 @ next "table entry"
+ asrs r4,#1 // next "table entry"
bne 4b
b cordic_exit
.thumb_func
-qfp_fsin: @ calculate sin and cos using CORDIC rotation method
+qfp_fsin: // calculate sin and cos using CORDIC rotation method
push {r4,r5,r14}
movs r1,#24
- bl qfp_float2fix @ range reduction by repeated subtraction/addition in fixed point
+ bl qfp_float2fix // range reduction by repeated subtraction/addition in fixed point
ldr r4,pi_q29
- lsrs r4,#4 @ 2pi Q24
+ lsrs r4,#4 // 2pi Q24
1:
subs r0,r4
bge 1b
1:
adds r0,r4
- bmi 1b @ now in range 0..2pi
- lsls r2,r0,#2 @ z Q26
- lsls r5,r4,#1 @ pi Q26 (r4=pi/2 Q26)
- ldr r0,=#0x136e9db4 @ initialise CORDIC x,y with scaling
+ bmi 1b // now in range 0..2pi
+ lsls r2,r0,#2 // z Q26
+ lsls r5,r4,#1 // pi Q26 (r4=pi/2 Q26)
+ ldr r0,=#0x136e9db4 // initialise CORDIC x,y with scaling
movs r1,#0
1:
- cmp r2,r4 @ >pi/2?
+ cmp r2,r4 // >pi/2?
blt 2f
- subs r2,r5 @ reduce range to -pi/2..pi/2
- rsbs r0,#0 @ rotate vector by pi
+ subs r2,r5 // reduce range to -pi/2..pi/2
+ rsbs r0,#0 // rotate vector by pi
b 1b
2:
- lsls r2,#3 @ Q29
- adr r3,tab_cc @ circular coefficients
- movs r4,#1 @ m=1
+ lsls r2,#3 // Q29
+ adr r3,tab_cc // circular coefficients
+ movs r4,#1 // m=1
bl cordic_rot
- adds r1,#9 @ fiddle factor to make sin(0)==0
- movs r2,#0 @ exponents to zero
+ adds r1,#9 // fiddle factor to make sin(0)==0
+ movs r2,#0 // exponents to zero
movs r3,#0
- movs r5,#0 @ no sticky bits
- bl packx @ pack cosine
+ movs r5,#0 // no sticky bits
+ bl packx // pack cosine
bl xchxy
- b packretns @ pack sine
+ b packretns // pack sine
.thumb_func
qfp_fcos:
push {r14}
bl qfp_fsin
- mov r0,r1 @ extract cosine result
+ mov r0,r1 // extract cosine result
pop {r15}
.thumb_func
qfp_ftan:
push {r4,r5,r14}
- bl qfp_fsin @ sine in r0/r2, cosine in r1/r3
+ bl qfp_fsin // sine in r0/r2, cosine in r1/r3
.if include_faster
- b fdiv_fast_n @ sin/cos
+ b fdiv_fast_n // sin/cos
.else
b fdiv_n
.endif
.thumb_func
-qfp_fexp: @ calculate cosh and sinh using rotation method; add to obtain exp
+qfp_fexp: // calculate cosh and sinh using rotation method; add to obtain exp
push {r4,r5,r14}
movs r1,#24
- bl qfp_float2fix @ Q24: covers entire valid input range
- asrs r1,r0,#16 @ Q8
- ldr r2,=#5909 @ log_2(e) Q12
- muls r1,r2 @ estimate exponent of result Q20
- asrs r1,#19 @ Q1
- adds r1,#1 @ rounding
- asrs r1,#1 @ rounded estimate of exponent of result
- push {r1} @ save for later
- lsls r2,r0,#5 @ Q29
- ldr r0,=#0x162e42ff @ ln(2) Q29
- muls r1,r0 @ accurate contribution of estimated exponent
- subs r2,r1 @ residual to be exponentiated, approximately -.5..+.5 Q29
- ldr r0,=#0x2c9e15ca @ initialise CORDIC x,y with scaling
+ bl qfp_float2fix // Q24: covers entire valid input range
+ asrs r1,r0,#16 // Q8
+ ldr r2,=#5909 // log_2(e) Q12
+ muls r1,r2 // estimate exponent of result Q20
+ asrs r1,#19 // Q1
+ adds r1,#1 // rounding
+ asrs r1,#1 // rounded estimate of exponent of result
+ push {r1} // save for later
+ lsls r2,r0,#5 // Q29
+ ldr r0,=#0x162e42ff // ln(2) Q29
+ muls r1,r0 // accurate contribution of estimated exponent
+ subs r2,r1 // residual to be exponentiated, approximately -.5..+.5 Q29
+ ldr r0,=#0x2c9e15ca // initialise CORDIC x,y with scaling
movs r1,#0
- adr r3,tab_ch @ hyperbolic coefficients
- mvns r4,r1 @ m=-1
- bl cordic_rot @ calculate cosh and sinh
- add r0,r1 @ exp=cosh+sinh
- pop {r2} @ recover exponent
- b packretns @ pack result
+ adr r3,tab_ch // hyperbolic coefficients
+ mvns r4,r1 // m=-1
+ bl cordic_rot // calculate cosh and sinh
+ add r0,r1 // exp=cosh+sinh
+ pop {r2} // recover exponent
+ b packretns // pack result
.thumb_func
-qfp_fsqrt: @ calculate sqrt and ln using vector method
+qfp_fsqrt: // calculate sqrt and ln using vector method
push {r4,r5,r14}
bl unpackx
- movs r1,r0 @ -ve argument?
- bmi 3f @ return -Inf, -Inf
- ldr r1,=#0x0593C2B9 @ scale factor for CORDIC
- bl mul0 @ Q29
- asrs r1,r2,#1 @ halve exponent
+ movs r1,r0 // -ve argument?
+ bmi 3f // return -Inf, -Inf
+ ldr r1,=#0x0593C2B9 // scale factor for CORDIC
+ bl mul0 // Q29
+ asrs r1,r2,#1 // halve exponent
bcc 1f
- adds r1,#1 @ was odd: add 1 and shift mantissa
+ adds r1,#1 // was odd: add 1 and shift mantissa
asrs r0,#1
1:
- push {r1} @ save exponent/2 for later
+ push {r1} // save exponent/2 for later
mov r1,r0
- ldr r3,=#0x0593C2B9 @ re-use constant
+ ldr r3,=#0x0593C2B9 // re-use constant
lsls r3,#2
- adds r0,r3 @ "a+1"
- subs r1,r3 @ "a-1"
+ adds r0,r3 // "a+1"
+ subs r1,r3 // "a-1"
movs r2,#0
- adr r3,tab_ch @ hyperbolic coefficients
- mvns r4,r2 @ m=-1
+ adr r3,tab_ch // hyperbolic coefficients
+ mvns r4,r2 // m=-1
bl cordic_vec
- mov r1,r2 @ keep ln result
- pop {r2} @ retrieve exponent/2
+ mov r1,r2 // keep ln result
+ pop {r2} // retrieve exponent/2
2:
movs r3,r2
- b packretns @ pack sqrt result
+ b packretns // pack sqrt result
3:
movs r2,#255
@@ -766,59 +743,59 @@ qfp_fsqrt: @ calculate sqrt and ln using vector method
.thumb_func
qfp_fln:
push {r4,r5,r14}
- bl qfp_fsqrt @ get unpacked ln in r1/r3; exponent has been halved
- cmp r3,#70 @ ln(Inf)?
- bgt 3b @ return Inf
+ bl qfp_fsqrt // get unpacked ln in r1/r3; exponent has been halved
+ cmp r3,#70 // ln(Inf)?
+ bgt 3b // return Inf
rsbs r3,#0
cmp r3,#70
- bgt 1f @ ln(0)? return -Inf
- ldr r0,=#0x0162e430 @ ln(4) Q24
- muls r0,r3 @ contribution from negated, halved exponent
- adds r1,#8 @ round result of ln
- asrs r1,#4 @ Q24
- subs r0,r1,r0 @ add in contribution from (negated) exponent
- movs r2,#5 @ pack expects Q29
+ bgt 1f // ln(0)? return -Inf
+ ldr r0,=#0x0162e430 // ln(4) Q24
+ muls r0,r3 // contribution from negated, halved exponent
+ adds r1,#8 // round result of ln
+ asrs r1,#4 // Q24
+ subs r0,r1,r0 // add in contribution from (negated) exponent
+ movs r2,#5 // pack expects Q29
b packretns
1:
- mvns r0,r0 @ make result -Inf
+ mvns r0,r0 // make result -Inf
b 3b
.thumb_func
qfp_fatan2:
push {r4,r5,r14}
- bl unpackxyalign @ convert to fixed point (ensure common exponent, which is discarded)
+ bl unpackxyalign // convert to fixed point (ensure common exponent, which is discarded)
asrs r0,#1
asrs r1,#1
- movs r2,#0 @ initial angle
- cmp r0,#0 @ x negative
+ movs r2,#0 // initial angle
+ cmp r0,#0 // x negative
bge 5f
- rsbs r0,#0 @ rotate to 1st/4th quadrants
+ rsbs r0,#0 // rotate to 1st/4th quadrants
rsbs r1,#0
- ldr r2,pi_q29 @ pi Q29
+ ldr r2,pi_q29 // pi Q29
5:
- adr r3,tab_cc @ circular coefficients
- movs r4,#1 @ m=1
- bl cordic_vec @ also produces magnitude (with scaling factor 1.646760119), which is discarded
- mov r0,r2 @ result here is -pi/2..3pi/2 Q29
- ldr r2,pi_q29 @ pi Q29
- adds r4,r0,r2 @ attempt to fix -3pi/2..-pi case
- bcs 6f @ -pi/2..0? leave result as is
- subs r4,r0,r2 @ <pi? leave as is
+ adr r3,tab_cc // circular coefficients
+ movs r4,#1 // m=1
+ bl cordic_vec // also produces magnitude (with scaling factor 1.646760119), which is discarded
+ mov r0,r2 // result here is -pi/2..3pi/2 Q29
+ ldr r2,pi_q29 // pi Q29
+ adds r4,r0,r2 // attempt to fix -3pi/2..-pi case
+ bcs 6f // -pi/2..0? leave result as is
+ subs r4,r0,r2 // <pi? leave as is
bmi 6f
- subs r0,r4,r2 @ >pi: take off 2pi
+ subs r0,r4,r2 // >pi: take off 2pi
6:
- subs r0,#1 @ fiddle factor so atan2(0,1)==0
- movs r2,#0 @ exponent for pack
+ subs r0,#1 // fiddle factor so atan2(0,1)==0
+ movs r2,#0 // exponent for pack
b packretns
.align 2
.ltorg
-@ first entry in following table is pi Q29
+// first entry in following table is pi Q29
pi_q29:
-@ circular CORDIC coefficients: atan(2^-i), b0=flag for preventing shift, b1=flag for end of table
+// circular CORDIC coefficients: atan(2^-i), b0=flag for preventing shift, b1=flag for end of table
tab_cc:
-.word 0x1921fb54*4+1 @ no shift before first iteration
+.word 0x1921fb54*4+1 // no shift before first iteration
.word 0x0ed63383*4+0
.word 0x07d6dd7e*4+0
.word 0x03fab753*4+0
@@ -830,16 +807,16 @@ tab_cc:
.word 0x000fffff*4+0
.word 0x0007ffff*4+0
.word 0x00040000*4+0
-.word 0x00020000*4+0+2 @ +2 marks end
+.word 0x00020000*4+0+2 // +2 marks end
-@ hyperbolic CORDIC coefficients: atanh(2^-i), flags as above
+// hyperbolic CORDIC coefficients: atanh(2^-i), flags as above
tab_ch:
.word 0x1193ea7b*4+0
-.word 0x1193ea7b*4+1 @ repeat i=1
+.word 0x1193ea7b*4+1 // repeat i=1
.word 0x082c577d*4+0
.word 0x04056247*4+0
.word 0x0200ab11*4+0
-.word 0x0200ab11*4+1 @ repeat i=4
+.word 0x0200ab11*4+1 // repeat i=4
.word 0x01001559*4+0
.word 0x008002ab*4+0
.word 0x00400055*4+0
@@ -848,7 +825,7 @@ tab_ch:
.word 0x00080001*4+0
.word 0x00040000*4+0
.word 0x00020000*4+0
-.word 0x00020000*4+1+2 @ repeat i=12
+.word 0x00020000*4+1+2 // repeat i=12
.endif