arch/m68k/fpsp040/satan.S

Source file repositories/reference/linux-study-clean/arch/m68k/fpsp040/satan.S

File Facts

System
Linux kernel
Corpus path
arch/m68k/fpsp040/satan.S
Extension
.S
Size
15961 bytes
Lines
478
Domain
Architecture Layer
Bucket
arch/m68k
Inferred role
Architecture Layer: arch/m68k
Status
atlas-only

Why This File Exists

CPU and platform-specific kernel glue: boot entry, traps, syscall entry, interrupts, page tables, context switch, and low-level barriers.

Dependency Surface

Detected Declarations

Annotated Snippet

|
|	satan.sa 3.3 12/19/90
|
|	The entry point satan computes the arctangent of an
|	input value. satand does the same except the input value is a
|	denormalized number.
|
|	Input: Double-extended value in memory location pointed to by address
|		register a0.
|
|	Output:	Arctan(X) returned in floating-point register Fp0.
|
|	Accuracy and Monotonicity: The returned result is within 2 ulps in
|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|		result is subsequently rounded to double precision. The
|		result is provably monotonic in double precision.
|
|	Speed: The program satan takes approximately 160 cycles for input
|		argument X such that 1/16 < |X| < 16. For the other arguments,
|		the program will run no worse than 10% slower.
|
|	Algorithm:
|	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
|
|	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
|		Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
|		of X with a bit-1 attached at the 6-th bit position. Define u
|		to be u = (X-F) / (1 + X*F).
|
|	Step 3. Approximate arctan(u) by a polynomial poly.
|
|	Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
|		calculated beforehand. Exit.
|
|	Step 5. If |X| >= 16, go to Step 7.
|
|	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
|
|	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
|		Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
|

|		Copyright (C) Motorola, Inc. 1990
|			All Rights Reserved
|
|       For details on the license for this file, please see the
|       file, README, in this same directory.

|satan	idnt	2,1 | Motorola 040 Floating Point Software Package

	|section	8

#include "fpsp.h"

BOUNDS1:	.long 0x3FFB8000,0x4002FFFF

ONE:	.long 0x3F800000

	.long 0x00000000

ATANA3:	.long 0xBFF6687E,0x314987D8
ATANA2:	.long 0x4002AC69,0x34A26DB3

ATANA1:	.long 0xBFC2476F,0x4E1DA28E
ATANB6:	.long 0x3FB34444,0x7F876989

ATANB5:	.long 0xBFB744EE,0x7FAF45DB
ATANB4:	.long 0x3FBC71C6,0x46940220

ATANB3:	.long 0xBFC24924,0x921872F9

Annotation

Implementation Notes