page.title=Dalvik bytecode @jd:body

In this document

General design

Summary of bytecode set

Op & Format Mnemonic / Syntax Arguments Description
00 10x nop   Waste cycles.

Note: Data-bearing pseudo-instructions are tagged with this opcode, in which case the high-order byte of the opcode unit indicates the nature of the data. See "packed-switch-payload Format", "sparse-switch-payload Format", and "fill-array-data-payload Format" below.

01 12x move vA, vB A: destination register (4 bits)
B: source register (4 bits)
Move the contents of one non-object register to another.
02 22x move/from16 vAA, vBBBB A: destination register (8 bits)
B: source register (16 bits)
Move the contents of one non-object register to another.
03 32x move/16 vAAAA, vBBBB A: destination register (16 bits)
B: source register (16 bits)
Move the contents of one non-object register to another.
04 12x move-wide vA, vB A: destination register pair (4 bits)
B: source register pair (4 bits)
Move the contents of one register-pair to another.

Note: It is legal to move from vN to either vN-1 or vN+1, so implementations must arrange for both halves of a register pair to be read before anything is written.

05 22x move-wide/from16 vAA, vBBBB A: destination register pair (8 bits)
B: source register pair (16 bits)
Move the contents of one register-pair to another.

Note: Implementation considerations are the same as move-wide, above.

06 32x move-wide/16 vAAAA, vBBBB A: destination register pair (16 bits)
B: source register pair (16 bits)
Move the contents of one register-pair to another.

Note: Implementation considerations are the same as move-wide, above.

07 12x move-object vA, vB A: destination register (4 bits)
B: source register (4 bits)
Move the contents of one object-bearing register to another.
08 22x move-object/from16 vAA, vBBBB A: destination register (8 bits)
B: source register (16 bits)
Move the contents of one object-bearing register to another.
09 32x move-object/16 vAAAA, vBBBB A: destination register (16 bits)
B: source register (16 bits)
Move the contents of one object-bearing register to another.
0a 11x move-result vAA A: destination register (8 bits) Move the single-word non-object result of the most recent invoke-kind into the indicated register. This must be done as the instruction immediately after an invoke-kind whose (single-word, non-object) result is not to be ignored; anywhere else is invalid.
0b 11x move-result-wide vAA A: destination register pair (8 bits) Move the double-word result of the most recent invoke-kind into the indicated register pair. This must be done as the instruction immediately after an invoke-kind whose (double-word) result is not to be ignored; anywhere else is invalid.
0c 11x move-result-object vAA A: destination register (8 bits) Move the object result of the most recent invoke-kind into the indicated register. This must be done as the instruction immediately after an invoke-kind or filled-new-array whose (object) result is not to be ignored; anywhere else is invalid.
0d 11x move-exception vAA A: destination register (8 bits) Save a just-caught exception into the given register. This must be the first instruction of any exception handler whose caught exception is not to be ignored, and this instruction must only ever occur as the first instruction of an exception handler; anywhere else is invalid.
0e 10x return-void   Return from a void method.
0f 11x return vAA A: return value register (8 bits) Return from a single-width (32-bit) non-object value-returning method.
10 11x return-wide vAA A: return value register-pair (8 bits) Return from a double-width (64-bit) value-returning method.
11 11x return-object vAA A: return value register (8 bits) Return from an object-returning method.
12 11n const/4 vA, #+B A: destination register (4 bits)
B: signed int (4 bits)
Move the given literal value (sign-extended to 32 bits) into the specified register.
13 21s const/16 vAA, #+BBBB A: destination register (8 bits)
B: signed int (16 bits)
Move the given literal value (sign-extended to 32 bits) into the specified register.
14 31i const vAA, #+BBBBBBBB A: destination register (8 bits)
B: arbitrary 32-bit constant
Move the given literal value into the specified register.
15 21h const/high16 vAA, #+BBBB0000 A: destination register (8 bits)
B: signed int (16 bits)
Move the given literal value (right-zero-extended to 32 bits) into the specified register.
16 21s const-wide/16 vAA, #+BBBB A: destination register (8 bits)
B: signed int (16 bits)
Move the given literal value (sign-extended to 64 bits) into the specified register-pair.
17 31i const-wide/32 vAA, #+BBBBBBBB A: destination register (8 bits)
B: signed int (32 bits)
Move the given literal value (sign-extended to 64 bits) into the specified register-pair.
18 51l const-wide vAA, #+BBBBBBBBBBBBBBBB A: destination register (8 bits)
B: arbitrary double-width (64-bit) constant
Move the given literal value into the specified register-pair.
19 21h const-wide/high16 vAA, #+BBBB000000000000 A: destination register (8 bits)
B: signed int (16 bits)
Move the given literal value (right-zero-extended to 64 bits) into the specified register-pair.
1a 21c const-string vAA, string@BBBB A: destination register (8 bits)
B: string index
Move a reference to the string specified by the given index into the specified register.
1b 31c const-string/jumbo vAA, string@BBBBBBBB A: destination register (8 bits)
B: string index
Move a reference to the string specified by the given index into the specified register.
1c 21c const-class vAA, type@BBBB A: destination register (8 bits)
B: type index
Move a reference to the class specified by the given index into the specified register. In the case where the indicated type is primitive, this will store a reference to the primitive type's degenerate class.
1d 11x monitor-enter vAA A: reference-bearing register (8 bits) Acquire the monitor for the indicated object.
1e 11x monitor-exit vAA A: reference-bearing register (8 bits) Release the monitor for the indicated object.

Note: If this instruction needs to throw an exception, it must do so as if the pc has already advanced past the instruction. It may be useful to think of this as the instruction successfully executing (in a sense), and the exception getting thrown after the instruction but before the next one gets a chance to run. This definition makes it possible for a method to use a monitor cleanup catch-all (e.g., finally) block as the monitor cleanup for that block itself, as a way to handle the arbitrary exceptions that might get thrown due to the historical implementation of Thread.stop(), while still managing to have proper monitor hygiene.

1f 21c check-cast vAA, type@BBBB A: reference-bearing register (8 bits)
B: type index (16 bits)
Throw a ClassCastException if the reference in the given register cannot be cast to the indicated type.

Note: Since A must always be a reference (and not a primitive value), this will necessarily fail at runtime (that is, it will throw an exception) if B refers to a primitive type.

20 22c instance-of vA, vB, type@CCCC A: destination register (4 bits)
B: reference-bearing register (4 bits)
C: type index (16 bits)
Store in the given destination register 1 if the indicated reference is an instance of the given type, or 0 if not.

Note: Since B must always be a reference (and not a primitive value), this will always result in 0 being stored if C refers to a primitive type.

21 12x array-length vA, vB A: destination register (4 bits)
B: array reference-bearing register (4 bits)
Store in the given destination register the length of the indicated array, in entries
22 21c new-instance vAA, type@BBBB A: destination register (8 bits)
B: type index
Construct a new instance of the indicated type, storing a reference to it in the destination. The type must refer to a non-array class.
23 22c new-array vA, vB, type@CCCC A: destination register (8 bits)
B: size register
C: type index
Construct a new array of the indicated type and size. The type must be an array type.
24 35c filled-new-array {vC, vD, vE, vF, vG}, type@BBBB A: array size and argument word count (4 bits)
B: type index (16 bits)
C..G: argument registers (4 bits each)
Construct an array of the given type and size, filling it with the supplied contents. The type must be an array type. The array's contents must be single-word (that is, no arrays of long or double, but reference types are acceptable). The constructed instance is stored as a "result" in the same way that the method invocation instructions store their results, so the constructed instance must be moved to a register with an immediately subsequent move-result-object instruction (if it is to be used).
25 3rc filled-new-array/range {vCCCC .. vNNNN}, type@BBBB A: array size and argument word count (8 bits)
B: type index (16 bits)
C: first argument register (16 bits)
N = A + C - 1
Construct an array of the given type and size, filling it with the supplied contents. Clarifications and restrictions are the same as filled-new-array, described above.
26 31t fill-array-data vAA, +BBBBBBBB (with supplemental data as specified below in "fill-array-data-payload Format") A: array reference (8 bits)
B: signed "branch" offset to table data pseudo-instruction (32 bits)
Fill the given array with the indicated data. The reference must be to an array of primitives, and the data table must match it in type and must contain no more elements than will fit in the array. That is, the array may be larger than the table, and if so, only the initial elements of the array are set, leaving the remainder alone.
27 11x throw vAA A: exception-bearing register (8 bits)
Throw the indicated exception.
28 10t goto +AA A: signed branch offset (8 bits) Unconditionally jump to the indicated instruction.

Note: The branch offset must not be 0. (A spin loop may be legally constructed either with goto/32 or by including a nop as a target before the branch.)

29 20t goto/16 +AAAA A: signed branch offset (16 bits)
Unconditionally jump to the indicated instruction.

Note: The branch offset must not be 0. (A spin loop may be legally constructed either with goto/32 or by including a nop as a target before the branch.)

2a 30t goto/32 +AAAAAAAA A: signed branch offset (32 bits)
Unconditionally jump to the indicated instruction.
2b 31t packed-switch vAA, +BBBBBBBB (with supplemental data as specified below in "packed-switch-payload Format") A: register to test
B: signed "branch" offset to table data pseudo-instruction (32 bits)
Jump to a new instruction based on the value in the given register, using a table of offsets corresponding to each value in a particular integral range, or fall through to the next instruction if there is no match.
2c 31t sparse-switch vAA, +BBBBBBBB (with supplemental data as specified below in "sparse-switch-payload Format") A: register to test
B: signed "branch" offset to table data pseudo-instruction (32 bits)
Jump to a new instruction based on the value in the given register, using an ordered table of value-offset pairs, or fall through to the next instruction if there is no match.
2d..31 23x cmpkind vAA, vBB, vCC
2d: cmpl-float (lt bias)
2e: cmpg-float (gt bias)
2f: cmpl-double (lt bias)
30: cmpg-double (gt bias)
31: cmp-long
A: destination register (8 bits)
B: first source register or pair
C: second source register or pair
Perform the indicated floating point or long comparison, setting a to 0 if b == c, 1 if b > c, or -1 if b < c. The "bias" listed for the floating point operations indicates how NaN comparisons are treated: "gt bias" instructions return 1 for NaN comparisons, and "lt bias" instructions return -1.

For example, to check to see if floating point x < y it is advisable to use cmpg-float; a result of -1 indicates that the test was true, and the other values indicate it was false either due to a valid comparison or because one of the values was NaN.

32..37 22t if-test vA, vB, +CCCC
32: if-eq
33: if-ne
34: if-lt
35: if-ge
36: if-gt
37: if-le
A: first register to test (4 bits)
B: second register to test (4 bits)
C: signed branch offset (16 bits)
Branch to the given destination if the given two registers' values compare as specified.

Note: The branch offset must not be 0. (A spin loop may be legally constructed either by branching around a backward goto or by including a nop as a target before the branch.)

38..3d 21t if-testz vAA, +BBBB
38: if-eqz
39: if-nez
3a: if-ltz
3b: if-gez
3c: if-gtz
3d: if-lez
A: register to test (8 bits)
B: signed branch offset (16 bits)
Branch to the given destination if the given register's value compares with 0 as specified.

Note: The branch offset must not be 0. (A spin loop may be legally constructed either by branching around a backward goto or by including a nop as a target before the branch.)

3e..43 10x (unused)   (unused)
44..51 23x arrayop vAA, vBB, vCC
44: aget
45: aget-wide
46: aget-object
47: aget-boolean
48: aget-byte
49: aget-char
4a: aget-short
4b: aput
4c: aput-wide
4d: aput-object
4e: aput-boolean
4f: aput-byte
50: aput-char
51: aput-short
A: value register or pair; may be source or dest (8 bits)
B: array register (8 bits)
C: index register (8 bits)
Perform the identified array operation at the identified index of the given array, loading or storing into the value register.
52..5f 22c iinstanceop vA, vB, field@CCCC
52: iget
53: iget-wide
54: iget-object
55: iget-boolean
56: iget-byte
57: iget-char
58: iget-short
59: iput
5a: iput-wide
5b: iput-object
5c: iput-boolean
5d: iput-byte
5e: iput-char
5f: iput-short
A: value register or pair; may be source or dest (4 bits)
B: object register (4 bits)
C: instance field reference index (16 bits)
Perform the identified object instance field operation with the identified field, loading or storing into the value register.

Note: These opcodes are reasonable candidates for static linking, altering the field argument to be a more direct offset.

60..6d 21c sstaticop vAA, field@BBBB
60: sget
61: sget-wide
62: sget-object
63: sget-boolean
64: sget-byte
65: sget-char
66: sget-short
67: sput
68: sput-wide
69: sput-object
6a: sput-boolean
6b: sput-byte
6c: sput-char
6d: sput-short
A: value register or pair; may be source or dest (8 bits)
B: static field reference index (16 bits)
Perform the identified object static field operation with the identified static field, loading or storing into the value register.

Note: These opcodes are reasonable candidates for static linking, altering the field argument to be a more direct offset.

6e..72 35c invoke-kind {vC, vD, vE, vF, vG}, meth@BBBB
6e: invoke-virtual
6f: invoke-super
70: invoke-direct
71: invoke-static
72: invoke-interface
A: argument word count (4 bits)
B: method reference index (16 bits)
C..G: argument registers (4 bits each)
Call the indicated method. The result (if any) may be stored with an appropriate move-result* variant as the immediately subsequent instruction.

invoke-virtual is used to invoke a normal virtual method (a method that is not private, static, or final, and is also not a constructor).

invoke-super is used to invoke the closest superclass's virtual method (as opposed to the one with the same method_id in the calling class). The same method restrictions hold as for invoke-virtual.

invoke-direct is used to invoke a non-static direct method (that is, an instance method that is by its nature non-overridable, namely either a private instance method or a constructor).

invoke-static is used to invoke a static method (which is always considered a direct method).

invoke-interface is used to invoke an interface method, that is, on an object whose concrete class isn't known, using a method_id that refers to an interface.

Note: These opcodes are reasonable candidates for static linking, altering the method argument to be a more direct offset (or pair thereof).

73 10x (unused)   (unused)
74..78 3rc invoke-kind/range {vCCCC .. vNNNN}, meth@BBBB
74: invoke-virtual/range
75: invoke-super/range
76: invoke-direct/range
77: invoke-static/range
78: invoke-interface/range
A: argument word count (8 bits)
B: method reference index (16 bits)
C: first argument register (16 bits)
N = A + C - 1
Call the indicated method. See first invoke-kind description above for details, caveats, and suggestions.
79..7a 10x (unused)   (unused)
7b..8f 12x unop vA, vB
7b: neg-int
7c: not-int
7d: neg-long
7e: not-long
7f: neg-float
80: neg-double
81: int-to-long
82: int-to-float
83: int-to-double
84: long-to-int
85: long-to-float
86: long-to-double
87: float-to-int
88: float-to-long
89: float-to-double
8a: double-to-int
8b: double-to-long
8c: double-to-float
8d: int-to-byte
8e: int-to-char
8f: int-to-short
A: destination register or pair (4 bits)
B: source register or pair (4 bits)
Perform the identified unary operation on the source register, storing the result in the destination register.
90..af 23x binop vAA, vBB, vCC
90: add-int
91: sub-int
92: mul-int
93: div-int
94: rem-int
95: and-int
96: or-int
97: xor-int
98: shl-int
99: shr-int
9a: ushr-int
9b: add-long
9c: sub-long
9d: mul-long
9e: div-long
9f: rem-long
a0: and-long
a1: or-long
a2: xor-long
a3: shl-long
a4: shr-long
a5: ushr-long
a6: add-float
a7: sub-float
a8: mul-float
a9: div-float
aa: rem-float
ab: add-double
ac: sub-double
ad: mul-double
ae: div-double
af: rem-double
A: destination register or pair (8 bits)
B: first source register or pair (8 bits)
C: second source register or pair (8 bits)
Perform the identified binary operation on the two source registers, storing the result in the destination register.
b0..cf 12x binop/2addr vA, vB
b0: add-int/2addr
b1: sub-int/2addr
b2: mul-int/2addr
b3: div-int/2addr
b4: rem-int/2addr
b5: and-int/2addr
b6: or-int/2addr
b7: xor-int/2addr
b8: shl-int/2addr
b9: shr-int/2addr
ba: ushr-int/2addr
bb: add-long/2addr
bc: sub-long/2addr
bd: mul-long/2addr
be: div-long/2addr
bf: rem-long/2addr
c0: and-long/2addr
c1: or-long/2addr
c2: xor-long/2addr
c3: shl-long/2addr
c4: shr-long/2addr
c5: ushr-long/2addr
c6: add-float/2addr
c7: sub-float/2addr
c8: mul-float/2addr
c9: div-float/2addr
ca: rem-float/2addr
cb: add-double/2addr
cc: sub-double/2addr
cd: mul-double/2addr
ce: div-double/2addr
cf: rem-double/2addr
A: destination and first source register or pair (4 bits)
B: second source register or pair (4 bits)
Perform the identified binary operation on the two source registers, storing the result in the first source register.
d0..d7 22s binop/lit16 vA, vB, #+CCCC
d0: add-int/lit16
d1: rsub-int (reverse subtract)
d2: mul-int/lit16
d3: div-int/lit16
d4: rem-int/lit16
d5: and-int/lit16
d6: or-int/lit16
d7: xor-int/lit16
A: destination register (4 bits)
B: source register (4 bits)
C: signed int constant (16 bits)
Perform the indicated binary op on the indicated register (first argument) and literal value (second argument), storing the result in the destination register.

Note: rsub-int does not have a suffix since this version is the main opcode of its family. Also, see below for details on its semantics.

d8..e2 22b binop/lit8 vAA, vBB, #+CC
d8: add-int/lit8
d9: rsub-int/lit8
da: mul-int/lit8
db: div-int/lit8
dc: rem-int/lit8
dd: and-int/lit8
de: or-int/lit8
df: xor-int/lit8
e0: shl-int/lit8
e1: shr-int/lit8
e2: ushr-int/lit8
A: destination register (8 bits)
B: source register (8 bits)
C: signed int constant (8 bits)
Perform the indicated binary op on the indicated register (first argument) and literal value (second argument), storing the result in the destination register.

Note: See below for details on the semantics of rsub-int.

e3..ff 10x (unused)   (unused)

packed-switch-payload format

Name Format Description
ident ushort = 0x0100 identifying pseudo-opcode
size ushort number of entries in the table
first_key int first (and lowest) switch case value
targets int[] list of size relative branch targets. The targets are relative to the address of the switch opcode, not of this table.

Note: The total number of code units for an instance of this table is (size * 2) + 4.

sparse-switch-payload format

Name Format Description
ident ushort = 0x0200 identifying pseudo-opcode
size ushort number of entries in the table
keys int[] list of size key values, sorted low-to-high
targets int[] list of size relative branch targets, each corresponding to the key value at the same index. The targets are relative to the address of the switch opcode, not of this table.

Note: The total number of code units for an instance of this table is (size * 4) + 2.

fill-array-data-payload format

Name Format Description
ident ushort = 0x0300 identifying pseudo-opcode
element_width ushort number of bytes in each element
size uint number of elements in the table
data ubyte[] data values

Note: The total number of code units for an instance of this table is (size * element_width + 1) / 2 + 4.

Mathematical operation details

Note: Floating point operations must follow IEEE 754 rules, using round-to-nearest and gradual underflow, except where stated otherwise.

Opcode C Semantics Notes
neg-int int32 a;
int32 result = -a;
Unary twos-complement.
not-int int32 a;
int32 result = ~a;
Unary ones-complement.
neg-long int64 a;
int64 result = -a;
Unary twos-complement.
not-long int64 a;
int64 result = ~a;
Unary ones-complement.
neg-float float a;
float result = -a;
Floating point negation.
neg-double double a;
double result = -a;
Floating point negation.
int-to-long int32 a;
int64 result = (int64) a;
Sign extension of int32 into int64.
int-to-float int32 a;
float result = (float) a;
Conversion of int32 to float, using round-to-nearest. This loses precision for some values.
int-to-double int32 a;
double result = (double) a;
Conversion of int32 to double.
long-to-int int64 a;
int32 result = (int32) a;
Truncation of int64 into int32.
long-to-float int64 a;
float result = (float) a;
Conversion of int64 to float, using round-to-nearest. This loses precision for some values.
long-to-double int64 a;
double result = (double) a;
Conversion of int64 to double, using round-to-nearest. This loses precision for some values.
float-to-int float a;
int32 result = (int32) a;
Conversion of float to int32, using round-toward-zero. NaN and -0.0 (negative zero) convert to the integer 0. Infinities and values with too large a magnitude to be represented get converted to either 0x7fffffff or -0x80000000 depending on sign.
float-to-long float a;
int64 result = (int64) a;
Conversion of float to int64, using round-toward-zero. The same special case rules as for float-to-int apply here, except that out-of-range values get converted to either 0x7fffffffffffffff or -0x8000000000000000 depending on sign.
float-to-double float a;
double result = (double) a;
Conversion of float to double, preserving the value exactly.
double-to-int double a;
int32 result = (int32) a;
Conversion of double to int32, using round-toward-zero. The same special case rules as for float-to-int apply here.
double-to-long double a;
int64 result = (int64) a;
Conversion of double to int64, using round-toward-zero. The same special case rules as for float-to-long apply here.
double-to-float double a;
float result = (float) a;
Conversion of double to float, using round-to-nearest. This loses precision for some values.
int-to-byte int32 a;
int32 result = (a << 24) >> 24;
Truncation of int32 to int8, sign extending the result.
int-to-char int32 a;
int32 result = a & 0xffff;
Truncation of int32 to uint16, without sign extension.
int-to-short int32 a;
int32 result = (a << 16) >> 16;
Truncation of int32 to int16, sign extending the result.
add-int int32 a, b;
int32 result = a + b;
Twos-complement addition.
sub-int int32 a, b;
int32 result = a - b;
Twos-complement subtraction.
rsub-int int32 a, b;
int32 result = b - a;
Twos-complement reverse subtraction.
mul-int int32 a, b;
int32 result = a * b;
Twos-complement multiplication.
div-int int32 a, b;
int32 result = a / b;
Twos-complement division, rounded towards zero (that is, truncated to integer). This throws ArithmeticException if b == 0.
rem-int int32 a, b;
int32 result = a % b;
Twos-complement remainder after division. The sign of the result is the same as that of a, and it is more precisely defined as result == a - (a / b) * b. This throws ArithmeticException if b == 0.
and-int int32 a, b;
int32 result = a & b;
Bitwise AND.
or-int int32 a, b;
int32 result = a | b;
Bitwise OR.
xor-int int32 a, b;
int32 result = a ^ b;
Bitwise XOR.
shl-int int32 a, b;
int32 result = a << (b & 0x1f);
Bitwise shift left (with masked argument).
shr-int int32 a, b;
int32 result = a >> (b & 0x1f);
Bitwise signed shift right (with masked argument).
ushr-int uint32 a, b;
int32 result = a >> (b & 0x1f);
Bitwise unsigned shift right (with masked argument).
add-long int64 a, b;
int64 result = a + b;
Twos-complement addition.
sub-long int64 a, b;
int64 result = a - b;
Twos-complement subtraction.
mul-long int64 a, b;
int64 result = a * b;
Twos-complement multiplication.
div-long int64 a, b;
int64 result = a / b;
Twos-complement division, rounded towards zero (that is, truncated to integer). This throws ArithmeticException if b == 0.
rem-long int64 a, b;
int64 result = a % b;
Twos-complement remainder after division. The sign of the result is the same as that of a, and it is more precisely defined as result == a - (a / b) * b. This throws ArithmeticException if b == 0.
and-long int64 a, b;
int64 result = a & b;
Bitwise AND.
or-long int64 a, b;
int64 result = a | b;
Bitwise OR.
xor-long int64 a, b;
int64 result = a ^ b;
Bitwise XOR.
shl-long int64 a, b;
int64 result = a << (b & 0x3f);
Bitwise shift left (with masked argument).
shr-long int64 a, b;
int64 result = a >> (b & 0x3f);
Bitwise signed shift right (with masked argument).
ushr-long uint64 a, b;
int64 result = a >> (b & 0x3f);
Bitwise unsigned shift right (with masked argument).
add-float float a, b;
float result = a + b;
Floating point addition.
sub-float float a, b;
float result = a - b;
Floating point subtraction.
mul-float float a, b;
float result = a * b;
Floating point multiplication.
div-float float a, b;
float result = a / b;
Floating point division.
rem-float float a, b;
float result = a % b;
Floating point remainder after division. This function is different than IEEE 754 remainder and is defined as result == a - roundTowardZero(a / b) * b.
add-double double a, b;
double result = a + b;
Floating point addition.
sub-double double a, b;
double result = a - b;
Floating point subtraction.
mul-double double a, b;
double result = a * b;
Floating point multiplication.
div-double double a, b;
double result = a / b;
Floating point division.
rem-double double a, b;
double result = a % b;
Floating point remainder after division. This function is different than IEEE 754 remainder and is defined as result == a - roundTowardZero(a / b) * b.