/* ieee754-df.S double-precision floating point support for ARM
Copyright (C) 2003, 2004 Free Software Foundation, Inc.
Contributed by Nicolas Pitre (nico@cam.org)
This file is free software Free Software Foundation
In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file. (The General Public License restrictions
do apply in other respects executable.)
This file is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program Boston, MA 02111-1307, USA. */
/*
* Notes:
*
* The goal of this code is to be as fast as possible. This is
* not meant to be easy to understand for the casual reader.
* For slightly simpler code please see the single precision version
* of this file.
*
* Only the default rounding mode is intended for best performances.
* Exceptions aren't supported yet, but that can be added quite easily
* if necessary without impacting performances.
*/
@ For FPA, float words are always big-endian.
@ For VFP, floats words follow the memory system mode.
#if defined(__VFP_FP__) && !defined(__ARMEB__)
#define xl r0
#define xh r1
#define yl r2
#define yh r3
#else
#define xh r0
#define xl r1
#define yh r2
#define yl r3
#endif
#ifdef L_negdf2
ARM_FUNC_START negdf2
@ flip sign bit
eor xh, xh, #0x80000000
RET
FUNC_END negdf2
#endif
#ifdef L_addsubdf3
ARM_FUNC_START subdf3
@ flip sign bit of second arg
eor yh, yh, #0x80000000
#if defined(__thumb__) && !defined(__THUMB_INTERWORK__)
b 1f @ Skip Thumb-code prologue
#endif
ARM_FUNC_START adddf3
1: @ Compare both args, return zero if equal but the sign.
teq xl, yl
eoreq ip, xh, yh
teqeq ip, #0x80000000
beq LSYM(Lad_z)
@ If first arg is 0 or -0, return second arg.
@ If second arg is 0 or -0, return first arg.
orrs ip, xl, xh, lsl #1
moveq xl, yl
moveq xh, yh
orrnes ip, yl, yh, lsl #1
RETc(eq)
stmfd sp!, {r4, r5, lr}
@ Mask out exponents.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r4, xh, ip
and r5, yh, ip
@ If either of them is 0x7ff, result will be INF or NAN
teq r4, ip
teqne r5, ip
beq LSYM(Lad_i)
@ Compute exponent difference. Make largest exponent in r4,
@ corresponding arg in xh-xl, and positive exponent difference in r5.
subs r5, r5, r4
rsblt r5, r5, #0
ble 1f
add r4, r4, r5
eor yl, xl, yl
eor yh, xh, yh
eor xl, yl, xl
eor xh, yh, xh
eor yl, xl, yl
eor yh, xh, yh
1:
@ If exponent difference is too large, return largest argument
@ already in xh-xl. We need up to 54 bit to handle proper rounding
@ of 0x1p54 - 1.1.
cmp r5, #(54 << 20)
RETLDM "r4, r5" hi
@ Convert mantissa to signed integer.
tst xh, #0x80000000
bic xh, xh, ip, lsl #1
orr xh, xh, #0x00100000
beq 1f
rsbs xl, xl, #0
rsc xh, xh, #0
1:
tst yh, #0x80000000
bic yh, yh, ip, lsl #1
orr yh, yh, #0x00100000
beq 1f
rsbs yl, yl, #0
rsc yh, yh, #0
1:
@ If exponent == difference, one or both args were denormalized.
@ Since this is not common case, rescale them off line.
teq r4, r5
beq LSYM(Lad_d)
LSYM(Lad_x):
@ Scale down second arg with exponent difference.
@ Apply shift one bit left to first arg and the rest to second arg
@ to simplify things later, but only if exponent does not become 0.
mov ip, #0
movs r5, r5, lsr #20
beq 3f
teq r4, #(1 << 20)
beq 1f
movs xl, xl, lsl #1
adc xh, ip, xh, lsl #1
sub r4, r4, #(1 << 20)
subs r5, r5, #1
beq 3f
@ Shift yh-yl right per r5, keep leftover bits into ip.
1: rsbs lr, r5, #32
blt 2f
mov ip, yl, lsl lr
mov yl, yl, lsr r5
orr yl, yl, yh, lsl lr
mov yh, yh, asr r5
b 3f
2: sub r5, r5, #32
add lr, lr, #32
cmp yl, #1
adc ip, ip, yh, lsl lr
mov yl, yh, asr r5
mov yh, yh, asr #32
3:
@ the actual addition
adds xl, xl, yl
adc xh, xh, yh
@ We now have a result in xh-xl-ip.
@ Keep absolute value in xh-xl-ip, sign in r5.
ands r5, xh, #0x80000000
bpl LSYM(Lad_p)
rsbs ip, ip, #0
rscs xl, xl, #0
rsc xh, xh, #0
@ Determine how to normalize the result.
LSYM(Lad_p):
cmp xh, #0x00100000
bcc LSYM(Lad_l)
cmp xh, #0x00200000
bcc LSYM(Lad_r0)
cmp xh, #0x00400000
bcc LSYM(Lad_r1)
@ Result needs to be shifted right.
movs xh, xh, lsr #1
movs xl, xl, rrx
movs ip, ip, rrx
orrcs ip, ip, #1
add r4, r4, #(1 << 20)
LSYM(Lad_r1):
movs xh, xh, lsr #1
movs xl, xl, rrx
movs ip, ip, rrx
orrcs ip, ip, #1
add r4, r4, #(1 << 20)
@ Our result is now properly aligned into xh-xl, remaining bits in ip.
@ Round with MSB of ip. If halfway between two numbers, round towards
@ LSB of xl = 0.
LSYM(Lad_r0):
adds xl, xl, ip, lsr #31
adc xh, xh, #0
teq ip, #0x80000000
biceq xl, xl, #1
@ One extreme rounding case may add a new MSB. Adjust exponent.
@ That MSB will be cleared when exponent is merged below.
tst xh, #0x00200000
addne r4, r4, #(1 << 20)
@ Make sure we did not bust our exponent.
adds ip, r4, #(1 << 20)
bmi LSYM(Lad_o)
@ Pack final result together.
LSYM(Lad_e):
bic xh, xh, #0x00300000
orr xh, xh, r4
orr xh, xh, r5
RETLDM "r4, r5"
LSYM(Lad_l):
@ Result must be shifted left and exponent adjusted.
@ No rounding necessary since ip will always be 0.
#if __ARM_ARCH__ < 5
teq xh, #0
movne r3, #-11
moveq r3, #21
moveq xh, xl
moveq xl, #0
mov r2, xh
movs ip, xh, lsr #16
moveq r2, r2, lsl #16
addeq r3, r3, #16
tst r2, #0xff000000
moveq r2, r2, lsl #8
addeq r3, r3, #8
tst r2, #0xf0000000
moveq r2, r2, lsl #4
addeq r3, r3, #4
tst r2, #0xc0000000
moveq r2, r2, lsl #2
addeq r3, r3, #2
tst r2, #0x80000000
addeq r3, r3, #1
#else
teq xh, #0
moveq xh, xl
moveq xl, #0
clz r3, xh
addeq r3, r3, #32
sub r3, r3, #11
#endif
@ determine how to shift the value.
subs r2, r3, #32
bge 2f
adds r2, r2, #12
ble 1f
@ shift value left 21 to 31 bits, or actually right 11 to 1 bits
@ since a register switch happened above.
add ip, r2, #20
rsb r2, r2, #12
mov xl, xh, lsl ip
mov xh, xh, lsr r2
b 3f
@ actually shift value left 1 to 20 bits, which might also represent
@ 32 to 52 bits if counting the register switch that happened earlier.
1: add r2, r2, #20
2: rsble ip, r2, #32
mov xh, xh, lsl r2
orrle xh, xh, xl, lsr ip
movle xl, xl, lsl r2
@ adjust exponent accordingly.
3: subs r4, r4, r3, lsl #20
bgt LSYM(Lad_e)
@ Exponent too small, denormalize result.
@ Find out proper shift value.
mvn r4, r4, asr #20
subs r4, r4, #30
bge 2f
adds r4, r4, #12
bgt 1f
@ shift result right of 1 to 20 bits, sign is in r5.
add r4, r4, #20
rsb r2, r4, #32
mov xl, xl, lsr r4
orr xl, xl, xh, lsl r2
orr xh, r5, xh, lsr r4
RETLDM "r4, r5"
@ shift result right of 21 to 31 bits, or left 11 to 1 bits after
@ a register switch from xh to xl.
1: rsb r4, r4, #12
rsb r2, r4, #32
mov xl, xl, lsr r2
orr xl, xl, xh, lsl r4
mov xh, r5
RETLDM "r4, r5"
@ Shift value right of 32 to 64 bits, or 0 to 32 bits after a switch
@ from xh to xl.
2: mov xl, xh, lsr r4
mov xh, r5
RETLDM "r4, r5"
@ Adjust exponents for denormalized arguments.
LSYM(Lad_d):
teq r4, #0
eoreq xh, xh, #0x00100000
addeq r4, r4, #(1 << 20)
eor yh, yh, #0x00100000
subne r5, r5, #(1 << 20)
b LSYM(Lad_x)
@ Result is x - x = 0, unless x = INF or NAN.
LSYM(Lad_z):
sub ip, ip, #0x00100000 @ ip becomes 0x7ff00000
and r2, xh, ip
teq r2, ip
orreq xh, ip, #0x00080000
movne xh, #0
mov xl, #0
RET
@ Overflow: return INF.
LSYM(Lad_o):
orr xh, r5, #0x7f000000
orr xh, xh, #0x00f00000
mov xl, #0
RETLDM "r4, r5"
@ At least one of x or y is INF/NAN.
@ if xh-xl != INF/NAN: return yh-yl (which is INF/NAN)
@ if yh-yl != INF/NAN: return xh-xl (which is INF/NAN)
@ if either is NAN: return NAN
@ if opposite sign: return NAN
@ return xh-xl (which is INF or -INF)
LSYM(Lad_i):
teq r4, ip
movne xh, yh
movne xl, yl
teqeq r5, ip
RETLDM "r4, r5" ne
orrs r4, xl, xh, lsl #12
orreqs r4, yl, yh, lsl #12
teqeq xh, yh
orrne xh, r5, #0x00080000
movne xl, #0
RETLDM "r4, r5"
FUNC_END subdf3
FUNC_END adddf3
ARM_FUNC_START floatunsidf
teq r0, #0
moveq r1, #0
RETc(eq)
stmfd sp!, {r4, r5, lr}
mov r4, #(0x400 << 20) @ initial exponent
add r4, r4, #((52-1) << 20)
mov r5, #0 @ sign bit is 0
mov xl, r0
mov xh, #0
b LSYM(Lad_l)
FUNC_END floatunsidf
ARM_FUNC_START floatsidf
teq r0, #0
moveq r1, #0
RETc(eq)
stmfd sp!, {r4, r5, lr}
mov r4, #(0x400 << 20) @ initial exponent
add r4, r4, #((52-1) << 20)
ands r5, r0, #0x80000000 @ sign bit in r5
rsbmi r0, r0, #0 @ absolute value
mov xl, r0
mov xh, #0
b LSYM(Lad_l)
FUNC_END floatsidf
ARM_FUNC_START extendsfdf2
movs r2, r0, lsl #1
beq 1f @ value is 0.0 or -0.0
mov xh, r2, asr #3 @ stretch exponent
mov xh, xh, rrx @ retrieve sign bit
mov xl, r2, lsl #28 @ retrieve remaining bits
ands r2, r2, #0xff000000 @ isolate exponent
beq 2f @ exponent was 0 but not mantissa
teq r2, #0xff000000 @ check if INF or NAN
eorne xh, xh, #0x38000000 @ fixup exponent otherwise.
RET
1: mov xh, r0
mov xl, #0
RET
2: @ value was denormalized. We can normalize it now.
stmfd sp!, {r4, r5, lr}
mov r4, #(0x380 << 20) @ setup corresponding exponent
add r4, r4, #(1 << 20)
and r5, xh, #0x80000000 @ move sign bit in r5
bic xh, xh, #0x80000000
b LSYM(Lad_l)
FUNC_END extendsfdf2
#endif /* L_addsubdf3 */
#ifdef L_muldivdf3
ARM_FUNC_START muldf3
stmfd sp!, {r4, r5, r6, lr}
@ Mask out exponents.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r4, xh, ip
and r5, yh, ip
@ Trap any INF/NAN.
teq r4, ip
teqne r5, ip
beq LSYM(Lml_s)
@ Trap any multiplication by 0.
orrs r6, xl, xh, lsl #1
orrnes r6, yl, yh, lsl #1
beq LSYM(Lml_z)
@ Shift exponents right one bit to make room for overflow bit.
@ If either of them is 0, scale denormalized arguments off line.
@ Then add both exponents together.
movs r4, r4, lsr #1
teqne r5, #0
beq LSYM(Lml_d)
LSYM(Lml_x):
add r4, r4, r5, asr #1
@ Preserve final sign in r4 along with exponent for now.
teq xh, yh
orrmi r4, r4, #0x8000
@ Convert mantissa to unsigned integer.
bic xh, xh, ip, lsl #1
bic yh, yh, ip, lsl #1
orr xh, xh, #0x00100000
orr yh, yh, #0x00100000
#if __ARM_ARCH__ < 4
@ Well, no way to make it shorter without the umull instruction.
@ We must perform that 53 x 53 bit multiplication by hand.
stmfd sp!, {r7, r8, r9, sl, fp}
mov r7, xl, lsr #16
mov r8, yl, lsr #16
mov r9, xh, lsr #16
mov sl, yh, lsr #16
bic xl, xl, r7, lsl #16
bic yl, yl, r8, lsl #16
bic xh, xh, r9, lsl #16
bic yh, yh, sl, lsl #16
mul ip, xl, yl
mul fp, xl, r8
mov lr, #0
adds ip, ip, fp, lsl #16
adc lr, lr, fp, lsr #16
mul fp, r7, yl
adds ip, ip, fp, lsl #16
adc lr, lr, fp, lsr #16
mul fp, xl, sl
mov r5, #0
adds lr, lr, fp, lsl #16
adc r5, r5, fp, lsr #16
mul fp, r7, yh
adds lr, lr, fp, lsl #16
adc r5, r5, fp, lsr #16
mul fp, xh, r8
adds lr, lr, fp, lsl #16
adc r5, r5, fp, lsr #16
mul fp, r9, yl
adds lr, lr, fp, lsl #16
adc r5, r5, fp, lsr #16
mul fp, xh, sl
mul r6, r9, sl
adds r5, r5, fp, lsl #16
adc r6, r6, fp, lsr #16
mul fp, r9, yh
adds r5, r5, fp, lsl #16
adc r6, r6, fp, lsr #16
mul fp, xl, yh
adds lr, lr, fp
mul fp, r7, sl
adcs r5, r5, fp
mul fp, xh, yl
adc r6, r6, #0
adds lr, lr, fp
mul fp, r9, r8
adcs r5, r5, fp
mul fp, r7, r8
adc r6, r6, #0
adds lr, lr, fp
mul fp, xh, yh
adcs r5, r5, fp
adc r6, r6, #0
ldmfd sp!, {r7, r8, r9, sl, fp}
#else
@ Here is the actual multiplication: 53 bits * 53 bits -> 106 bits.
umull ip, lr, xl, yl
mov r5, #0
umlal lr, r5, xl, yh
umlal lr, r5, xh, yl
mov r6, #0
umlal r5, r6, xh, yh
#endif
@ The LSBs in ip are only significant for the final rounding.
@ Fold them into one bit of lr.
teq ip, #0
orrne lr, lr, #1
@ Put final sign in xh.
mov xh, r4, lsl #16
bic r4, r4, #0x8000
@ Adjust result if one extra MSB appeared (one of four times).
tst r6, #(1 << 9)
beq 1f
add r4, r4, #(1 << 19)
movs r6, r6, lsr #1
movs r5, r5, rrx
movs lr, lr, rrx
orrcs lr, lr, #1
1:
@ Scale back to 53 bits.
@ xh contains sign bit already.
orr xh, xh, r6, lsl #12
orr xh, xh, r5, lsr #20
mov xl, r5, lsl #12
orr xl, xl, lr, lsr #20
@ Apply exponent bias, check range for underflow.
sub r4, r4, #0x00f80000
subs r4, r4, #0x1f000000
ble LSYM(Lml_u)
@ Round the result.
movs lr, lr, lsl #12
bpl 1f
adds xl, xl, #1
adc xh, xh, #0
teq lr, #0x80000000
biceq xl, xl, #1
@ Rounding may have produced an extra MSB here.
@ The extra bit is cleared before merging the exponent below.
tst xh, #0x00200000
addne r4, r4, #(1 << 19)
1:
@ Check exponent for overflow.
adds ip, r4, #(1 << 19)
tst ip, #(1 << 30)
bne LSYM(Lml_o)
@ Add final exponent.
bic xh, xh, #0x00300000
orr xh, xh, r4, lsl #1
RETLDM "r4, r5, r6"
@ Result is 0, but determine sign anyway.
LSYM(Lml_z):
eor xh, xh, yh
LSYM(Ldv_z):
bic xh, xh, #0x7fffffff
mov xl, #0
RETLDM "r4, r5, r6"
@ Check if denormalized result is possible, otherwise return signed 0.
LSYM(Lml_u):
cmn r4, #(53 << 19)
movle xl, #0
bicle xh, xh, #0x7fffffff
RETLDM "r4, r5, r6" le
@ Find out proper shift value.
LSYM(Lml_r):
mvn r4, r4, asr #19
subs r4, r4, #30
bge 2f
adds r4, r4, #12
bgt 1f
@ shift result right of 1 to 20 bits, preserve sign bit, round, etc.
add r4, r4, #20
rsb r5, r4, #32
mov r3, xl, lsl r5
mov xl, xl, lsr r4
orr xl, xl, xh, lsl r5
movs xh, xh, lsl #1
mov xh, xh, lsr r4
mov xh, xh, rrx
adds xl, xl, r3, lsr #31
adc xh, xh, #0
teq lr, #0
teqeq r3, #0x80000000
biceq xl, xl, #1
RETLDM "r4, r5, r6"
@ shift result right of 21 to 31 bits, or left 11 to 1 bits after
@ a register switch from xh to xl. Then round.
1: rsb r4, r4, #12
rsb r5, r4, #32
mov r3, xl, lsl r4
mov xl, xl, lsr r5
orr xl, xl, xh, lsl r4
bic xh, xh, #0x7fffffff
adds xl, xl, r3, lsr #31
adc xh, xh, #0
teq lr, #0
teqeq r3, #0x80000000
biceq xl, xl, #1
RETLDM "r4, r5, r6"
@ Shift value right of 32 to 64 bits, or 0 to 32 bits after a switch
@ from xh to xl. Leftover bits are in r3-r6-lr for rounding.
2: rsb r5, r4, #32
mov r6, xl, lsl r5
mov r3, xl, lsr r4
orr r3, r3, xh, lsl r5
mov xl, xh, lsr r4
bic xh, xh, #0x7fffffff
bic xl, xl, xh, lsr r4
add xl, xl, r3, lsr #31
orrs r6, r6, lr
teqeq r3, #0x80000000
biceq xl, xl, #1
RETLDM "r4, r5, r6"
@ One or both arguments are denormalized.
@ Scale them leftwards and preserve sign bit.
LSYM(Lml_d):
mov lr, #0
teq r4, #0
bne 2f
and r6, xh, #0x80000000
1: movs xl, xl, lsl #1
adc xh, lr, xh, lsl #1
tst xh, #0x00100000
subeq r4, r4, #(1 << 19)
beq 1b
orr xh, xh, r6
teq r5, #0
bne LSYM(Lml_x)
2: and r6, yh, #0x80000000
3: movs yl, yl, lsl #1
adc yh, lr, yh, lsl #1
tst yh, #0x00100000
subeq r5, r5, #(1 << 20)
beq 3b
orr yh, yh, r6
b LSYM(Lml_x)
@ One or both args are INF or NAN.
LSYM(Lml_s):
orrs r6, xl, xh, lsl #1
orrnes r6, yl, yh, lsl #1
beq LSYM(Lml_n) @ 0 * INF or INF * 0 -> NAN
teq r4, ip
bne 1f
orrs r6, xl, xh, lsl #12
bne LSYM(Lml_n) @ NAN * <anything> -> NAN
1: teq r5, ip
bne LSYM(Lml_i)
orrs r6, yl, yh, lsl #12
bne LSYM(Lml_n) @ <anything> * NAN -> NAN
@ Result is INF, but we need to determine its sign.
LSYM(Lml_i):
eor xh, xh, yh
@ Overflow: return INF (sign already in xh).
LSYM(Lml_o):
and xh, xh, #0x80000000
orr xh, xh, #0x7f000000
orr xh, xh, #0x00f00000
mov xl, #0
RETLDM "r4, r5, r6"
@ Return NAN.
LSYM(Lml_n):
mov xh, #0x7f000000
orr xh, xh, #0x00f80000
RETLDM "r4, r5, r6"
FUNC_END muldf3
ARM_FUNC_START divdf3
stmfd sp!, {r4, r5, r6, lr}
@ Mask out exponents.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r4, xh, ip
and r5, yh, ip
@ Trap any INF/NAN or zeroes.
teq r4, ip
teqne r5, ip
orrnes r6, xl, xh, lsl #1
orrnes r6, yl, yh, lsl #1
beq LSYM(Ldv_s)
@ Shift exponents right one bit to make room for overflow bit.
@ If either of them is 0, scale denormalized arguments off line.
@ Then substract divisor exponent from dividend''s.
movs r4, r4, lsr #1
teqne r5, #0
beq LSYM(Ldv_d)
LSYM(Ldv_x):
sub r4, r4, r5, asr #1
@ Preserve final sign into lr.
eor lr, xh, yh
@ Convert mantissa to unsigned integer.
@ Dividend -> r5-r6, divisor -> yh-yl.
mov r5, #0x10000000
mov yh, yh, lsl #12
orr yh, r5, yh, lsr #4
orr yh, yh, yl, lsr #24
movs yl, yl, lsl #8
mov xh, xh, lsl #12
teqeq yh, r5
beq LSYM(Ldv_1)
orr r5, r5, xh, lsr #4
orr r5, r5, xl, lsr #24
mov r6, xl, lsl #8
@ Initialize xh with final sign bit.
and xh, lr, #0x80000000
@ Ensure result will land to known bit position.
cmp r5, yh
cmpeq r6, yl
bcs 1f
sub r4, r4, #(1 << 19)
movs yh, yh, lsr #1
mov yl, yl, rrx
1:
@ Apply exponent bias, check range for over/underflow.
add r4, r4, #0x1f000000
add r4, r4, #0x00f80000
cmn r4, #(53 << 19)
ble LSYM(Ldv_z)
cmp r4, ip, lsr #1
bge LSYM(Lml_o)
@ Perform first substraction to align result to a nibble.
subs r6, r6, yl
sbc r5, r5, yh
movs yh, yh, lsr #1
mov yl, yl, rrx
mov xl, #0x00100000
mov ip, #0x00080000
@ The actual division loop.
1: subs lr, r6, yl
sbcs lr, r5, yh
subcs r6, r6, yl
movcs r5, lr
orrcs xl, xl, ip
movs yh, yh, lsr #1
mov yl, yl, rrx
subs lr, r6, yl
sbcs lr, r5, yh
subcs r6, r6, yl
movcs r5, lr
orrcs xl, xl, ip, lsr #1
movs yh, yh, lsr #1
mov yl, yl, rrx
subs lr, r6, yl
sbcs lr, r5, yh
subcs r6, r6, yl
movcs r5, lr
orrcs xl, xl, ip, lsr #2
movs yh, yh, lsr #1
mov yl, yl, rrx
subs lr, r6, yl
sbcs lr, r5, yh
subcs r6, r6, yl
movcs r5, lr
orrcs xl, xl, ip, lsr #3
orrs lr, r5, r6
beq 2f
mov r5, r5, lsl #4
orr r5, r5, r6, lsr #28
mov r6, r6, lsl #4
mov yh, yh, lsl #3
orr yh, yh, yl, lsr #29
mov yl, yl, lsl #3
movs ip, ip, lsr #4
bne 1b
@ We are done with a word of the result.
@ Loop again for the low word if this pass was for the high word.
tst xh, #0x00100000
bne 3f
orr xh, xh, xl
mov xl, #0
mov ip, #0x80000000
b 1b
2:
@ Be sure result starts in the high word.
tst xh, #0x00100000
orreq xh, xh, xl
moveq xl, #0
3:
@ Check if denormalized result is needed.
cmp r4, #0
ble LSYM(Ldv_u)
@ Apply proper rounding.
subs ip, r5, yh
subeqs ip, r6, yl
adcs xl, xl, #0
adc xh, xh, #0
teq ip, #0
biceq xl, xl, #1
@ Add exponent to result.
bic xh, xh, #0x00100000
orr xh, xh, r4, lsl #1
RETLDM "r4, r5, r6"
@ Division by 0x1p*: shortcut a lot of code.
LSYM(Ldv_1):
and lr, lr, #0x80000000
orr xh, lr, xh, lsr #12
add r4, r4, #0x1f000000
add r4, r4, #0x00f80000
cmp r4, ip, lsr #1
bge LSYM(Lml_o)
cmp r4, #0
orrgt xh, xh, r4, lsl #1
RETLDM "r4, r5, r6" gt
cmn r4, #(53 << 19)
ble LSYM(Ldv_z)
orr xh, xh, #0x00100000
mov lr, #0
b LSYM(Lml_r)
@ Result must be denormalized: put remainder in lr for
@ rounding considerations.
LSYM(Ldv_u):
orr lr, r5, r6
b LSYM(Lml_r)
@ One or both arguments are denormalized.
@ Scale them leftwards and preserve sign bit.
LSYM(Ldv_d):
mov lr, #0
teq r4, #0
bne 2f
and r6, xh, #0x80000000
1: movs xl, xl, lsl #1
adc xh, lr, xh, lsl #1
tst xh, #0x00100000
subeq r4, r4, #(1 << 19)
beq 1b
orr xh, xh, r6
teq r5, #0
bne LSYM(Ldv_x)
2: and r6, yh, #0x80000000
3: movs yl, yl, lsl #1
adc yh, lr, yh, lsl #1
tst yh, #0x00100000
subeq r5, r5, #(1 << 20)
beq 3b
orr yh, yh, r6
b LSYM(Ldv_x)
@ One or both arguments is either INF, NAN or zero.
LSYM(Ldv_s):
teq r4, ip
teqeq r5, ip
beq LSYM(Lml_n) @ INF/NAN / INF/NAN -> NAN
teq r4, ip
bne 1f
orrs r4, xl, xh, lsl #12
bne LSYM(Lml_n) @ NAN / <anything> -> NAN
b LSYM(Lml_i) @ INF / <anything> -> INF
1: teq r5, ip
bne 2f
orrs r5, yl, yh, lsl #12
bne LSYM(Lml_n) @ <anything> / NAN -> NAN
b LSYM(Lml_z) @ <anything> / INF -> 0
2: @ One or both arguments are 0.
orrs r4, xl, xh, lsl #1
bne LSYM(Lml_i) @ <non_zero> / 0 -> INF
orrs r5, yl, yh, lsl #1
bne LSYM(Lml_z) @ 0 / <non_zero> -> 0
b LSYM(Lml_n) @ 0 / 0 -> NAN
FUNC_END divdf3
#endif /* L_muldivdf3 */
#ifdef L_cmpdf2
ARM_FUNC_START gtdf2
ARM_FUNC_ALIAS gedf2 gtdf2
mov ip, #-1
b 1f
ARM_FUNC_START ltdf2
ARM_FUNC_ALIAS ledf2 ltdf2
mov ip, #1
b 1f
ARM_FUNC_START cmpdf2
ARM_FUNC_ALIAS nedf2 cmpdf2
ARM_FUNC_ALIAS eqdf2 cmpdf2
mov ip, #1 @ how should we specify unordered here?
1: stmfd sp!, {r4, r5, lr}
@ Trap any INF/NAN first.
mov lr, #0x7f000000
orr lr, lr, #0x00f00000
and r4, xh, lr
and r5, yh, lr
teq r4, lr
teqne r5, lr
beq 3f
@ Test for equality.
@ Note that 0.0 is equal to -0.0.
2: orrs ip, xl, xh, lsl #1 @ if x == 0.0 or -0.0
orreqs ip, yl, yh, lsl #1 @ and y == 0.0 or -0.0
teqne xh, yh @ or xh == yh
teqeq xl, yl @ and xl == yl
moveq r0, #0 @ then equal.
RETLDM "r4, r5" eq
@ Check for sign difference.
teq xh, yh
movmi r0, xh, asr #31
orrmi r0, r0, #1
RETLDM "r4, r5" mi
@ Compare exponents.
cmp r4, r5
@ Compare mantissa if exponents are equal.
moveq xh, xh, lsl #12
cmpeq xh, yh, lsl #12
cmpeq xl, yl
movcs r0, yh, asr #31
mvncc r0, yh, asr #31
orr r0, r0, #1
RETLDM "r4, r5"
@ Look for a NAN.
3: teq r4, lr
bne 4f
orrs xl, xl, xh, lsl #12
bne 5f @ x is NAN
4: teq r5, lr
bne 2b
orrs yl, yl, yh, lsl #12
beq 2b @ y is not NAN
5: mov r0, ip @ return unordered code from ip
RETLDM "r4, r5"
FUNC_END gedf2
FUNC_END gtdf2
FUNC_END ledf2
FUNC_END ltdf2
FUNC_END nedf2
FUNC_END eqdf2
FUNC_END cmpdf2
#endif /* L_cmpdf2 */
#ifdef L_unorddf2
ARM_FUNC_START unorddf2
str lr, [sp, #-4]!
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and lr, xh, ip
teq lr, ip
bne 1f
orrs xl, xl, xh, lsl #12
bne 3f @ x is NAN
1: and lr, yh, ip
teq lr, ip
bne 2f
orrs yl, yl, yh, lsl #12
bne 3f @ y is NAN
2: mov r0, #0 @ arguments are ordered.
RETLDM
3: mov r0, #1 @ arguments are unordered.
RETLDM
FUNC_END unorddf2
#endif /* L_unorddf2 */
#ifdef L_fixdfsi
ARM_FUNC_START fixdfsi
orrs ip, xl, xh, lsl #1
beq 1f @ value is 0.
mov r3, r3, rrx @ preserve C flag (the actual sign)
@ check exponent range.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r2, xh, ip
teq r2, ip
beq 2f @ value is INF or NAN
bic ip, ip, #0x40000000
cmp r2, ip
bcc 1f @ value is too small
add ip, ip, #(31 << 20)
cmp r2, ip
bcs 3f @ value is too large
rsb r2, r2, ip
mov ip, xh, lsl #11
orr ip, ip, #0x80000000
orr ip, ip, xl, lsr #21
mov r2, r2, lsr #20
tst r3, #0x80000000 @ the sign bit
mov r0, ip, lsr r2
rsbne r0, r0, #0
RET
1: mov r0, #0
RET
2: orrs xl, xl, xh, lsl #12
bne 4f @ r0 is NAN.
3: ands r0, r3, #0x80000000 @ the sign bit
moveq r0, #0x7fffffff @ maximum signed positive si
RET
4: mov r0, #0 @ How should we convert NAN?
RET
FUNC_END fixdfsi
#endif /* L_fixdfsi */
#ifdef L_fixunsdfsi
ARM_FUNC_START fixunsdfsi
orrs ip, xl, xh, lsl #1
movcss r0, #0 @ value is negative
RETc(eq) @ or 0 (xl, xh overlap r0)
@ check exponent range.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r2, xh, ip
teq r2, ip
beq 2f @ value is INF or NAN
bic ip, ip, #0x40000000
cmp r2, ip
bcc 1f @ value is too small
add ip, ip, #(31 << 20)
cmp r2, ip
bhi 3f @ value is too large
rsb r2, r2, ip
mov ip, xh, lsl #11
orr ip, ip, #0x80000000
orr ip, ip, xl, lsr #21
mov r2, r2, lsr #20
mov r0, ip, lsr r2
RET
1: mov r0, #0
RET
2: orrs xl, xl, xh, lsl #12
bne 4f @ value is NAN.
3: mov r0, #0xffffffff @ maximum unsigned si
RET
4: mov r0, #0 @ How should we convert NAN?
RET
FUNC_END fixunsdfsi
#endif /* L_fixunsdfsi */
#ifdef L_truncdfsf2
ARM_FUNC_START truncdfsf2
orrs r2, xl, xh, lsl #1
moveq r0, r2, rrx
RETc(eq) @ value is 0.0 or -0.0
@ check exponent range.
mov ip, #0x7f000000
orr ip, ip, #0x00f00000
and r2, ip, xh
teq r2, ip
beq 2f @ value is INF or NAN
bic xh, xh, ip
cmp r2, #(0x380 << 20)
bls 4f @ value is too small
@ shift and round mantissa
1: movs r3, xl, lsr #29
adc r3, r3, xh, lsl #3
@ if halfway between two numbers, round towards LSB = 0.
mov xl, xl, lsl #3
teq xl, #0x80000000
biceq r3, r3, #1
@ rounding might have created an extra MSB. If so adjust exponent.
tst r3, #0x00800000
addne r2, r2, #(1 << 20)
bicne r3, r3, #0x00800000
@ check exponent for overflow
mov ip, #(0x400 << 20)
orr ip, ip, #(0x07f << 20)
cmp r2, ip
bcs 3f @ overflow
@ adjust exponent, merge with sign bit and mantissa.
movs xh, xh, lsl #1
mov r2, r2, lsl #4
orr r0, r3, r2, rrx
eor r0, r0, #0x40000000
RET
2: @ chech for NAN
orrs xl, xl, xh, lsl #12
movne r0, #0x7f000000
orrne r0, r0, #0x00c00000
RETc(ne) @ return NAN
3: @ return INF with sign
and r0, xh, #0x80000000
orr r0, r0, #0x7f000000
orr r0, r0, #0x00800000
RET
4: @ check if denormalized value is possible
subs r2, r2, #((0x380 - 24) << 20)
andle r0, xh, #0x80000000 @ too small, return signed 0.
RETc(le)
@ denormalize value so we can resume with the code above afterwards.
orr xh, xh, #0x00100000
mov r2, r2, lsr #20
rsb r2, r2, #25
cmp r2, #20
bgt 6f
rsb ip, r2, #32
mov r3, xl, lsl ip
mov xl, xl, lsr r2
orr xl, xl, xh, lsl ip
movs xh, xh, lsl #1
mov xh, xh, lsr r2
mov xh, xh, rrx
5: teq r3, #0 @ fold r3 bits into the LSB
orrne xl, xl, #1 @ for rounding considerations.
mov r2, #(0x380 << 20) @ equivalent to the 0 float exponent
b 1b
6: rsb r2, r2, #(12 + 20)
rsb ip, r2, #32
mov r3, xl, lsl r2
mov xl, xl, lsr ip
orr xl, xl, xh, lsl r2
and xh, xh, #0x80000000
b 5b
FUNC_END truncdfsf2
#endif /* L_truncdfsf2 */