📄 libm.inc
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;-----------------------------------------------------------------------;
; libm.inc: Math Library Include File
;
; This file is part of the compact math library for the dsPIC30.
; (c) Microchip Technology. 2003.
;
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Macro for defining long (32-bit) constants.
;
; LCONST name,value
;
; Equates the constant <name> to <value>,
; the constant <name>LO to the lower 16-bits of <value>, and
; the constant <name>HI to the upper 16-bits of <value>.
;-----------------------------------------------------------------------;
.macro LCONST,name,value
.equ &name,&value
.equ &name&LO,(&value) & 0xFFFF
.equ &name&HI,((&value)>>16) & 0xFFFF
.endm
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Debug Macro: Halt the simulator
;-----------------------------------------------------------------------;
.macro HALT
.pword 0xDA4000
.endm
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Status register
;-----------------------------------------------------------------------;
.equ SR_CBIT, 0 ; Carry
.equ SR_SZBIT, 1 ; Sticky Zero
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Standard C Library <errno> values
;-----------------------------------------------------------------------;
.equ _EDOM,33 ; Domain error
.equ _ERANGE,34 ; Range Error
;-----------------------------------------------------------------------;
; Floating-point Number Classification
;-----------------------------------------------------------------------;
.equ ZEROBIT, 0
.equ FINITEBIT, 1
.equ INFBIT, 2
.equ NANBIT, 7
.equ ZEROTYPE, (1 << ZEROBIT)
.equ FINITETYPE, (1 << FINITEBIT)
.equ INFTYPE, (1 << INFBIT)
.equ NANTYPE, (1 << NANBIT)
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Characteristics of single-precision floating-point numbers
;-----------------------------------------------------------------------;
.equ FLT_BIAS, 127 ; exponent bias
.equ FLT_SMIN, -149 ; min unbiased subnormal exponent
.equ FLT_EMIN, -126 ; min unbiased normal exponent
.equ FLT_EMAX, 127 ; max unbiased normal exponent
.equ FLT_PREC, 24 ; precision
.equ FLT_QNAN, 22 ; bit number for quiet NaN
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Characteristics of double-precision floating-point numbers
;-----------------------------------------------------------------------;
.equ DBL_BIAS, 1023 ; exponent bias
.equ DBL_SMIN, -1074 ; min unbiased subnormal exponent
.equ DBL_EMIN, -1022 ; min unbiased normal exponent
.equ DBL_EMAX, 1023 ; max unbiased normal exponent
.equ DBL_PREC, 53 ; precision
.equ DBL_QNAN, 51 ; bit number for quiet NaN
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Unpacked double-precision structure
;-----------------------------------------------------------------------;
.equ DTYP, 0 ; floating-point type
.equ DEXP, 2 ; biased exponent
.equ DFLT, 4 ; operand
.equ DFLT0, DFLT+0 ; *
.equ DFLT1, DFLT+2 ; *
.equ DFLT2, DFLT+4 ; *
.equ DFLT3, DFLT+6 ; *
.equ DSIG, 12 ; significand
.equ DSIZ, 20 ; sizeof(struct DUNPACK)
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Useful constants
;-----------------------------------------------------------------------;
.equ DP_HALF3, 0x3FE0 ; +0.5
.equ DP_HALF2, 0x0000 ; *
.equ DP_HALF1, 0x0000 ; *
.equ DP_HALF0, 0x0000 ; *
.equ DP_SQRTHALF3, 0x3FE6 ; Sqrt[+0.5]
.equ DP_SQRTHALF2, 0xA09E
.equ DP_SQRTHALF1, 0x667F
.equ DP_SQRTHALF0, 0x3BCD
.equ DP_ZERO3, 0x0000 ; +0.0
.equ DP_ONE3, 0x3FF0 ; +1.0
.equ DP_ONE2, 0x0000 ; *
.equ DP_ONE1, 0x0000 ; *
.equ DP_ONE0, 0x0000 ; *
.equ DP_NEGONE3, 0xBFF0 ; -1.0
.equ DP_NEGONE2, 0x0000 ; *
.equ DP_NEGONE1, 0x0000 ; *
.equ DP_NEGONE0, 0x0000 ; *
.equ DP_NEGTWO3, 0xC000 ; -2.0
.equ DP_NEGTWO2, 0x0000 ; *
.equ DP_NEGTWO1, 0x0000 ; *
.equ DP_NEGTWO0, 0x0000 ; *
.equ DP_PI3, 0x4009 ; +Pi
.equ DP_PI2, 0x21FB ; *
.equ DP_PI1, 0x5444 ; *
.equ DP_PI0, 0x2D18 ; *
.equ DP_TWOPI3, 0x4019 ; 2 Pi
.equ DP_TWOPI2, 0x21FB ; *
.equ DP_TWOPI1, 0x5444 ; *
.equ DP_TWOPI0, 0x2D18 ; *
.equ DP_TWOoverPI3, 0x3FE4 ; 2/Pi
.equ DP_TWOoverPI2, 0x5F30 ; *
.equ DP_TWOoverPI1, 0x6DC9 ; *
.equ DP_TWOoverPI0, 0xC883 ; *
.equ DP_PIOVER23, 0x3FF9 ; +Pi/2
.equ DP_PIOVER22, 0x21FB ; *
.equ DP_PIOVER21, 0x5444 ; *
.equ DP_PIOVER20, 0x2D18 ; *
.equ DP_PIOVER33, 0x3FF0 ; +Pi/3
.equ DP_PIOVER32, 0xC152 ; *
.equ DP_PIOVER31, 0x382D ; *
.equ DP_PIOVER30, 0x7366 ; *
.equ DP_PIOVER63, 0x3FE0 ; +Pi/6
.equ DP_PIOVER62, 0xC152 ; *
.equ DP_PIOVER61, 0x382D ; *
.equ DP_PIOVER60, 0x7366 ; *
.equ DP_INV_PI3, 0x3FD4 ; 1/Pi
.equ DP_INV_PI2, 0x5F30 ; *
.equ DP_INV_PI1, 0x6DC9 ; *
.equ DP_INV_PI0, 0xC883 ; *
.equ DP_LOGe3, 0x3FDB ; log10(e)
.equ DP_LOGe2, 0xCB7B ; *
.equ DP_LOGe1, 0x1526 ; *
.equ DP_LOGe0, 0xE50E ; *
.equ DP_LN23, 0x3FE6 ; ln(2)
.equ DP_LN22, 0x2E42 ; *
.equ DP_LN21, 0xFEFA ; *
.equ DP_LN20, 0x39EF ; *
.equ DP_POSINF3, 0x7FF0 ; +Infinity
.equ DP_POSINF2, 0x0000 ; *
.equ DP_NEGINF3, 0xFFF0 ; -Infinity
LCONST HALF, 0x3F000000 ; +0.5
LCONST ONE, 0x3F800000 ; +1.0
LCONST NEGONE, 0xBF800000 ; -1.0
LCONST NEGTWO, 0xC0000000 ; -2.0
LCONST POSINF, 0x7F800000 ; +Infinity
LCONST NEGINF, 0xFF800000 ; -Infinity
LCONST NaN, 0x7FFFFFFF ; Quiet NaN
;------ Minimum signed 32-bit integer: -2^31
LCONST LONG_MIN, (1<<31) | ((31+FLT_BIAS)<<23)
;------ Minimum signed 64-bit integer: -2^63
LCONST LLONG_MIN, (1<<31) | ((63+FLT_BIAS)<<23)
.equ LLONG_MIN64, (1<<15) | ((63+DBL_BIAS)<<4)
LCONST SQRTHALF,0x3F3504F3 ; sqrt(1/2)
LCONST LOGe, 0x3EDE5BD9 ; log10(e)
LCONST LN2, 0x3F317218 ; ln(2)
LCONST PI, 0x40490FDB ; Pi
LCONST PIOVER2,0x3FC90FDB ; Pi/2
LCONST PIOVER3,0x3F860A92 ; Pi/3
LCONST PIOVER6,0x3F060A92 ; Pi/6
LCONST TWOPI, 0x40C90FDB ; 2 Pi
LCONST TWOoverPI,0x3F22F983 ; 2/Pi
LCONST INV_PI, 0x3EA2F983 ; 1/Pi
;-----------------------------------------------------------------------;
; Extended-precision constants for argument reduction
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Extended-precision constant for ln(2)
;-----------------------------------------------------------------------;
; C = ln(2)
; = 0.693147
; 355
; C1 = ---
; 512
; = 0.693359
; C2 = C - C1
; = -2.12194E-04
;-----------------------------------------------------------------------;
LCONST LN2C1, 0x3F318000
LCONST LN2C2, 0xB95E8083
.equ DP_LN2C13, 0x3FE6
.equ DP_LN2C12, 0x3000
.equ DP_LN2C23, 0xBF2B
.equ DP_LN2C22, 0xD010
.equ DP_LN2C21, 0x5C61
.equ DP_LN2C20, 0x0CA8
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Extended-precision constant for Pi
;-----------------------------------------------------------------------;
; C = Pi
; = 3.14159265358979324
; 201
; C1 = ---
; 64
; = 3.140625
; C2 = C - C1
; = 9.67653589793E-4
;-----------------------------------------------------------------------;
LCONST PI_C1, 0x40490000
LCONST PI_C2, 0x3A7DAA22
.equ DP_PI_C13, 0x4009
.equ DP_PI_C12, 0x2000
.equ DP_PI_C23, 0x3F4F
.equ DP_PI_C22, 0xB544
.equ DP_PI_C21, 0x42D1
.equ DP_PI_C20, 0x846A
;-----------------------------------------------------------------------;
;-----------------------------------------------------------------------;
; Extended-precision constant for Pi/2
;-----------------------------------------------------------------------;
; C = Pi/2
; = 1.57079632679489662
; 201
; C1 = ---
; 128
; = 1.570312500
; C2 = C - C1
; = 4.83826794897e-4f
;-----------------------------------------------------------------------;
LCONST PIOVER2_C1, 0x3FC90000
LCONST PIOVER2_C2, 0x39FDAA22
.equ DP_PIOVER2_C13, 0x3FF9
.equ DP_PIOVER2_C12, 0x2000
.equ DP_PIOVER2_C23, 0x3F3F
.equ DP_PIOVER2_C22, 0xB544
.equ DP_PIOVER2_C21, 0x42D1
.equ DP_PIOVER2_C20, 0x846A
;-----------------------------------------------------------------------;
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