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956 lines
31 KiB
956 lines
31 KiB
// TITLE("Alpha AXP Natural Logarithm")
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//++
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//
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// Copyright (c) 1993, 1994 Digital Equipment Corporation
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//
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// Module Name:
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//
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// log.s
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//
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// Abstract:
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//
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// This module implements a high-performance Alpha AXP specific routine
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// for IEEE double format natural logarithm.
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//
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// Author:
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//
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// Martha Jaffe
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//
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// Environment:
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//
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// User mode.
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//
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// Revision History:
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//
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// Thomas Van Baak (tvb) 7-Feb-1994
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//
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// Adapted for NT.
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//
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//--
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#include "ksalpha.h"
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//
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// Define DPML exception record for NT.
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//
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.struct 0
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ErErr: .space 4 // error code
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ErCxt: .space 4 // context
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ErPlat: .space 4 // platform
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ErEnv: .space 4 // environment
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ErRet: .space 4 // return value pointer
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ErName: .space 4 // function name
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ErType: .space 8 // flags and fill
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ErVal: .space 8 // return value
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ErArg0: .space 8 // arg 0
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ErArg1: .space 8 // arg 1
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ErArg2: .space 8 // arg 2
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ErArg3: .space 8 // arg 3
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DpmlExceptionLength:
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//
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// Define stack frame.
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//
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.struct 0
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Temp: .space 8 // save argument
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ExRec: .space DpmlExceptionLength // exception record
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.space 0 // for 16-byte stack alignment
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FrameLength:
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//
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// Define lower and upper 32-bit parts of 64-bit double.
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//
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#define LowPart 0x0
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#define HighPart 0x4
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SBTTL("Natural Log")
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//++
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//
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// double
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// log (
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// IN double x
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// )
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//
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// Routine Description:
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//
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// This function returns the natural log of the given double argument.
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//
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// Arguments:
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//
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// x (f16) - Supplies the argument value.
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//
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// Return Value:
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//
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// The double log result is returned as the function value in f0.
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//
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//--
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NESTED_ENTRY(log, FrameLength, ra)
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lda sp, -FrameLength(sp) // allocate stack frame
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mov ra, t7 // save return address
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PROLOGUE_END
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stt f16, Temp(sp)
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ldl t1, Temp + HighPart(sp)
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lda t0, _log_table
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ldah v0, 0x3fee(zero)
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subl t1, v0, v0
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ldt f1, 0(t0)
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ldah t2, 3(zero)
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cmpult v0, t2, v0
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bne v0, 80f
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sra t1, 20, v0
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sra t1, 8, t2
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cpyse f1, f16, f10
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subl v0, 1, t4
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lda t5, 0x7fe(zero)
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lda t3, 0xfe0(zero)
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cmpult t4, t5, t4
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and t2, t3, t2
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beq t4, 10f
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lda t6, 0x3ff(zero)
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subl v0, t6, t6
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br zero, 70f
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//
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// abnormal x
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//
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10: ldah t5, -0x8000(zero)
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ldah t4, 0x7ff0(zero)
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and t1, t5, t5
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and t1, t4, v0
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beq t5, 50f
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lda t6, logName
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bne v0, 30f
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ldah v0, 0x800(zero)
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ldt f10, Two53
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lda v0, 0x31(v0)
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cpyse f10, f16, f0
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subt f0, f10, f0
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fbne f0, 20f
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//
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// call exception dispatcher log(zero)
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//
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stt f16, ExRec + ErArg0(sp)
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stl t6, ExRec + ErName(sp)
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stl v0, ExRec + ErErr(sp)
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lda v0, ExRec(sp)
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bsr ra, __dpml_exception
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ldt f0, 0(v0)
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br zero, done
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//
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// call exception dispatcher log(neg)
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//
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20: ldah ra, 0x800(zero)
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stt f16, ExRec + ErArg0(sp)
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lda t6, logName
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stl t6, ExRec + ErName(sp)
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lda ra, 0x30(ra)
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stl ra, ExRec + ErErr(sp)
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lda v0, ExRec(sp)
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bsr ra, __dpml_exception
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ldt f0, 0(v0)
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br zero, done
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//
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// check for nan
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//
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30: stt f16, Temp(sp)
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ldl ra, Temp(sp)
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ldah v0, 0x10(zero)
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ldl t2, Temp + HighPart(sp)
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lda v0, -1(v0)
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and t2, v0, v0
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bis v0, ra, v0
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and t2, t4, t6
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cmpult zero, v0, v0
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cmpeq t6, t4, t4
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beq t4, 40f
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and t4, v0, t4
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bne t4, retarg
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//
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// call exception dispatcher log(neg)
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//
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40: ldah ra, 0x800(zero)
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stt f16, ExRec + ErArg0(sp)
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lda t6, logName
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stl t6, ExRec + ErName(sp)
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lda ra, 0x30(ra)
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stl ra, ExRec + ErErr(sp)
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lda v0, ExRec(sp)
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bsr ra, __dpml_exception
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ldt f16, 0(v0)
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retarg: cpys f16, f16, f0
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br zero, done
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//
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// check for denorm
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//
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50: ldah t4, 0x7ff0(zero)
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and t1, t4, t1
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bne t1, retarg
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ldah t2, 0x800(zero)
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ldt f10, Two53
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lda t2, 0x31(t2)
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lda ra, logName
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cpyse f10, f16, f0
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lda v0, ExRec(sp)
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subt f0, f10, f11
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fbne f11, 60f
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//
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// call exception dispatcher log(zero)
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//
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stt f16, ExRec + ErArg0(sp)
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stl t2, ExRec + ErErr(sp)
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stl ra, ExRec + ErName(sp)
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bsr ra, __dpml_exception
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ldt f0, 0(v0)
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br zero, done
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//
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// fix up denorms
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//
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60: stt f11, Temp(sp)
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cpyse f1, f11, f10
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ldl t1, Temp + HighPart(sp)
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lda t2, 0x832(zero)
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sra t1, 8, t5
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sra t1, 20, t1
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and t5, t3, t3
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subl t1, t2, t6
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mov t3, t2
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//
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// rejoin normal path
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//
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70: addl t0, t2, t2
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ldt f1, 0x98(t0) // load away from 1 coefs
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ldt f16, 0xd8(t2) // LOG_F_TABLE_TWOP
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ldt f0, 0xe0(t2)
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stq t6, Temp(sp)
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subt f10, f16, f10
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ldt f16, Temp(sp)
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ldt f12, 0x90(t0)
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ldt f15, 0x88(t0) // POLY_ADDRESS_TWOP_AWAY
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cvtqt f16, f16
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ldt f17, 0xa0(t0)
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mult f10, f0, f0
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ldt f10, 0xa8(t0)
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mult f0, f0, f11
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mult f1, f0, f1
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mult f10, f0, f10
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mult f11, f11, f13
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mult f11, f0, f14
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addt f12, f1, f1
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ldt f12, 0xd0(t0) // LOG2_LO_TWOP
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mult f11, f15, f11
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addt f17, f10, f10
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ldt f15, 0xf0(t2)
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ldt f17, 0xe8(t2)
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mult f12, f16, f12
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mult f13, f0, f13
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mult f14, f1, f1
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ldt f14, 0xc8(t0) // LOG2_HI_TWOP
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addt f12, f15, f12
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mult f13, f10, f10
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addt f11, f1, f1
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mult f16, f14, f14
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addt f12, f0, f0
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addt f1, f10, f1
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addt f14, f17, f14
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addt f0, f1, f0
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addt f0, f14, f0
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br zero, done
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//
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// near one case
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//
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80: subt f16, f1, f1
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ldt f10, 0x18(t0) // load near 1 poly coefs
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ldt f14, 0x28(t0)
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ldt f21, 0x20(t0)
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ldt f16, Two29
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ldt f19, 0x38(t0) // LOG2_LO_ONEP
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mult f1, f1, f15
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mult f1, f10, f10
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mult f1, f14, f14
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cpys f1, f16, f18
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ldt f16, 0x10(t0)
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cpys f1, f1, f20
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mult f1, f19, f19
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mult f15, f1, f13
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mult f15, f15, f11
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addt f10, f16, f10
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addt f14, f21, f14
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ldt f16, 0x30(t0) // LOG2_HI_ONEP
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ldt f21, 0x48(t0)
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addt f20, f18, f20
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mult f15, f13, f17
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mult f11, f1, f12
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mult f13, f11, f0
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mult f11, f15, f15
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mult f13, f10, f10
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ldt f13, 0x58(t0)
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addt f19, f16, f16
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ldt f19, 0x40(t0) // LOG_F_TABLE_ONEP
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mult f1, f21, f21
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mult f17, f14, f14
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mult f12, f11, f12
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ldt f17, 0x50(t0)
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mult f15, f1, f15
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mult f1, f13, f13
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subt f20, f18, f18
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mult f0, f16, f0
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addt f21, f19, f19
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ldt f21, Half
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addt f10, f14, f10
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mult f15, f11, f11
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addt f13, f17, f13
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subt f1, f18, f20
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addt f1, f18, f16
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mult f12, f19, f12
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addt f10, f0, f0
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mult f18, f18, f18
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mult f11, f13, f11
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mult f16, f20, f16
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addt f0, f12, f0
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mult f18, f21, f18
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mult f16, f21, f16
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addt f0, f11, f0
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subt f1, f18, f1
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subt f0, f16, f0
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addt f0, f1, f0
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//
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// Return with result in f0.
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//
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done:
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lda sp, FrameLength(sp) // deallocate stack frame
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ret zero, (t7) // return through saved ra in t7
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.end log
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.align 3
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.rdata
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//
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// Define floating point constants.
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//
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Half: .double 0.5
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One: .double 1.0
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Two29: .double 536870912.0 // 2^29
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Two53: .double 9007199254740992.0 // 2^53
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//
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// Function name for dpml_exception.
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//
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logName:
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.ascii "log\0"
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//
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// log data table
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//
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.align 3
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_log_table:
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// 1.0 in working precision
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.double 1.0000000000000000e+000
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// poly coeffs near 1
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.double -5.0000000000000000e-001
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.double 3.3333333333333581e-001
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.double -2.5000000000000555e-001
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.double 1.9999999999257809e-001
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.double -1.6666666665510016e-001
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.double 1.4285715095862653e-001
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.double -1.2500001025849336e-001
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.double 1.1110711557933650e-001
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.double -9.9995589399147614e-002
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.double 9.1816350893696136e-002
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.double -8.4241019625172817e-002
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// poly coeffs quotient, near 1
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.double 8.3333333333333953e-002
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.double 1.2499999999536091e-002
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.double 2.2321429837356640e-003
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.double 4.3401216971065997e-004
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.double 8.9664418510783172e-005
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// poly coeffs away from 1
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.double -5.0000000000000000e-001
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.double 3.3333333331462339e-001
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.double -2.4999999997583292e-001
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.double 2.0000326978572527e-001
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.double -1.6666993645814179e-001
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// poly coeffs quotient, away from 1
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.double 8.3333333333334911e-002
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.double 1.2499999967659360e-002
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.double 2.2323547997135616e-003
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// log of 2 in hi and lo parts
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.double 6.9314718055989033e-001
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.double 5.4979230187083712e-014
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// Table of F, 1/F, and hi and lo log of F; (128 * 4 entries)
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.double 1.0039062500000000e+000
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.double 9.9610894941634243e-001
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.double 3.8986404156275967e-003
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.double 2.9726346900928951e-014
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.double 1.0117187500000000e+000
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.double 9.8841698841698844e-001
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.double 1.1650617220084314e-002
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.double -1.0903974971735932e-013
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.double 1.0195312500000000e+000
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.double 9.8084291187739459e-001
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.double 1.9342962843211353e-002
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.double -8.0418538505225864e-014
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.double 1.0273437500000000e+000
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.double 9.7338403041825095e-001
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.double 2.6976587698300136e-002
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.double -9.8060505168431766e-014
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.double 1.0351562500000000e+000
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.double 9.6603773584905661e-001
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.double 3.4552381506728125e-002
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.double -6.8391397423287774e-014
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.double 1.0429687500000000e+000
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.double 9.5880149812734083e-001
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.double 4.2071213920735318e-002
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.double -4.8263140005511282e-014
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.double 1.0507812500000000e+000
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.double 9.5167286245353155e-001
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.double 4.9533935122326511e-002
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.double -4.9880309107981426e-014
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.double 1.0585937500000000e+000
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.double 9.4464944649446492e-001
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.double 5.6941376400118315e-002
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.double 2.0109399435564958e-014
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.double 1.0664062500000000e+000
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.double 9.3772893772893773e-001
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.double 6.4294350705495162e-002
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.double -9.7905185119902161e-014
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.double 1.0742187500000000e+000
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.double 9.3090909090909091e-001
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.double 7.1593653186937445e-002
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.double 7.1373082253431780e-014
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.double 1.0820312500000000e+000
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.double 9.2418772563176899e-001
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.double 7.8840061707751374e-002
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.double 2.4650189061766119e-014
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.double 1.0898437500000000e+000
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.double 9.1756272401433692e-001
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.double 8.6034337341743594e-002
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.double 5.9559229876256426e-014
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.double 1.0976562500000000e+000
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.double 9.1103202846975084e-001
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.double 9.3177224854116503e-002
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.double 6.6787085171628983e-014
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.double 1.1054687500000000e+000
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.double 9.0459363957597172e-001
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.double 1.0026945316371894e-001
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.double -4.3786376170783979e-014
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.double 1.1132812500000000e+000
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.double 8.9824561403508774e-001
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.double 1.0731173578915332e-001
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.double -6.5266788027310712e-014
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.double 1.1210937500000000e+000
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.double 8.9198606271777003e-001
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.double 1.1430477128010352e-001
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.double -4.4889533522386993e-014
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.double 1.1289062500000000e+000
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.double 8.8581314878892736e-001
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.double 1.2124924363297396e-001
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.double -1.0427241278273008e-013
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.double 1.1367187500000000e+000
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.double 8.7972508591065290e-001
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.double 1.2814582269197672e-001
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.double -4.6680314039457961e-014
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.double 1.1445312500000000e+000
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.double 8.7372013651877134e-001
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.double 1.3499516453748583e-001
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.double 1.8996158041578768e-014
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.double 1.1523437500000000e+000
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.double 8.6779661016949150e-001
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.double 5.2566735112936347e-001
|
|
.double 6.4308667860314017e-001
|
|
.double -1.1285622521565641e-013
|
|
.double 1.9101562500000000e+000
|
|
.double 5.2351738241308798e-001
|
|
.double 6.4718504499523988e-001
|
|
.double 6.9672514647224776e-014
|
|
.double 1.9179687500000000e+000
|
|
.double 5.2138492871690423e-001
|
|
.double 6.5126668331504334e-001
|
|
.double -8.5234246813161544e-014
|
|
.double 1.9257812500000000e+000
|
|
.double 5.1926977687626774e-001
|
|
.double 6.5533172956315866e-001
|
|
.double -3.1028217233522746e-014
|
|
.double 1.9335937500000000e+000
|
|
.double 5.1717171717171717e-001
|
|
.double 6.5938031808923370e-001
|
|
.double -1.0587069463342906e-013
|
|
.double 1.9414062500000000e+000
|
|
.double 5.1509054325955739e-001
|
|
.double 6.6341258161696715e-001
|
|
.double 9.9105859809946792e-014
|
|
.double 1.9492187500000000e+000
|
|
.double 5.1302605210420837e-001
|
|
.double 6.6742865127184814e-001
|
|
.double 1.0805094338364667e-013
|
|
.double 1.9570312500000000e+000
|
|
.double 5.1097804391217561e-001
|
|
.double 6.7142865660525786e-001
|
|
.double 4.4466890378487691e-014
|
|
.double 1.9648437500000000e+000
|
|
.double 5.0894632206759438e-001
|
|
.double 6.7541272562016275e-001
|
|
.double 1.3985026783782165e-014
|
|
.double 1.9726562500000000e+000
|
|
.double 5.0693069306930694e-001
|
|
.double 6.7938098479589826e-001
|
|
.double -1.0090714198118343e-013
|
|
.double 1.9804687500000000e+000
|
|
.double 5.0493096646942803e-001
|
|
.double 6.8333355911158833e-001
|
|
.double 3.2359204011502443e-014
|
|
.double 1.9882812500000000e+000
|
|
.double 5.0294695481335949e-001
|
|
.double 6.8727057207092912e-001
|
|
.double 3.1147551503113092e-014
|
|
.double 1.9960937500000000e+000
|
|
.double 5.0097847358121328e-001
|
|
.double 6.9119214572424426e-001
|
|
.double -1.0229682936814195e-013
|
|
|
|
//
|
|
// End of table.
|
|
//
|