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1155 lines
35 KiB
1155 lines
35 KiB
// TITLE("Alpha AXP Square Root")
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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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// sqrt.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 square root.
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//
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// Author:
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//
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// Bill Gray (rtl::gray) 30-Jun-1993
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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) 4-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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SBTTL("Square Root")
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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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Temp0: .space 8 // save argument
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Temp1: .space 8 //
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ExRec: .space DpmlExceptionLength // exception record
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.space 8 // 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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//++
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//
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// double
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// sqrt (
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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 square root 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 square root result is returned in f0.
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//
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//--
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NESTED_ENTRY(sqrt, FrameLength, ra)
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lda sp, -FrameLength(sp) // allocate stack frame
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mov ra, a0 // save return address
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PROLOGUE_END
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//
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// Get the high 32 bits of x in an integer register
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// while isolating the fraction field, f.
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//
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stt f16, Temp0(sp)
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ldl v0, Temp0 + HighPart(sp)
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ldt f1, One
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lda t1, __sqrt_t_table
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sra v0, 13 t0
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cpyse f1, f16, f10
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//
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// Isolate exponent bits and compute index into
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// polynomial table
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//
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ldah t4, 0x3fe0(zero)
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and t0, 0xff, t0
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addl t0, t0, t0
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s8addl t0, zero, t0
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addl t1, t0, t0
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//
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// Evaluate a + b*f + c*(f*f).
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//
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lds f0, 4(t0)
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lds f11, 0(t0)
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ldt f12, 8(t0)
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mult f0, f10, f0
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ldah t0, -0x7fe0(zero)
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mult f10, f10, f10
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lda t0, -1(t0)
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and v0, t0, t2
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xor v0, t2, t3
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addl t3, t4, t3
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zapnot t3, 0xf, t3
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addt f12, f0, f0
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bis t2, t4, t2
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mult f10, f11, f10
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sll t3, 31, t3
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stq t3, Temp1(sp)
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ldah t3, 0x10(zero)
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stl t2, Temp0 + HighPart(sp)
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//
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// Compute final scale factor and branch if original
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// argument was abnormal
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//
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subl v0, t3, v0
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ldt f11, Temp0(sp)
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ldah t2, 0x7fe0(zero)
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ldt f12, Temp1(sp)
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cmpult v0, t2, v0
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addt f10, f0, f0
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beq v0, 10f
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//
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// Incorporate scale factor and perform Newton's iteration
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//
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mult f0, f11, f11
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mult f11, f0, f0
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mult f11, f12, f11
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ldt f12, Lsb
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subt f1, f0, f0
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addt f11, f11, f10
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mult f11, f0, f0
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mult f11, f12, f11
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//
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// Do Tuckerman's rounding
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//
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addt f10, f0, f0
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subt f0, f11, f12
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addt f0, f11, f11
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multc f0, f12, f10
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multc f0, f11, f13
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cmptle f16, f10, f10
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cmptlt f13, f16, f13
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fcmoveq f10, f0, f12
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fcmoveq f13, f12, f11
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cpys f11, f11, f0
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br zero, done
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//
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// The following code classifies the argument. I.e. t3 <-- F_CLASSIFY(x).
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// Start with check on 0 or denormal
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//
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10: stt f16, Temp1(sp)
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ldl t3, Temp1 + HighPart(sp)
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ldah v0, 0x7ff0(zero)
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zapnot t3, 0xf, t2
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and t3, v0, t5
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srl t2, 31, t2
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cmpult t5, v0, v0
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and t2, 1, t2
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beq t5, 40f
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//
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// Branch if NaN's or Infinity
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//
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addl t2, 4, t6
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beq v0, 20f
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br zero, 50f
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//
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// Distinguish between NaN's and Infinities
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//
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20: ldah v0, 0x10(zero)
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ldl t5, Temp1(sp)
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lda v0, -1(v0)
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and t3, v0, v0
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bis v0, t5, t5
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stl v0, Temp1 + HighPart(sp)
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beq t5, 30f
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srl v0, 19 v0
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and v0, 1, t6
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br zero, 50f
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//
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// Was Infinity
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//
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30: addl t2, 2, t6
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br zero, 50f
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//
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// Distinguish between 0 and denorm
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//
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40: ldl t7, Temp1(sp)
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ldah t5, 0x10(zero)
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lda t5, -1(t5)
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and t3, t5, t3
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bis t3, t7, t7
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stl t3, Temp1 + HighPart(sp)
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mov 6, v0
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cmoveq t7, 8, v0
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addl t2, v0, t6
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//
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// Switch on class
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//
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50: cmpule t6, 9, t12
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beq t12, denorm
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lda t12, Switch
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s4addl t6, t12, t12
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ldl t12, 0(t12)
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jmp zero, (t12)
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//
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// Nan, +Inf or zero. Just return argument
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//
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retarg:
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cpys f16, f16, f0
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br zero, done
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//
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// Argument was negative. Dispatch error
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//
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error:
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lda t3, FunctionName
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ldah t2, 0x800(zero)
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stl t3, ExRec + ErName(sp)
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stt f16, ExRec + ErArg0(sp)
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lda t2, 0x5e(t2)
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stl t2, 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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// Denormalized argument. Scale up and take sqrt
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//
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denorm:
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ldah t7, 0x6b0(zero)
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stl t7, Temp1 + HighPart(sp)
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stl zero, Temp1(sp)
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ldt f10, Temp1(sp)
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cpyse f10, f16, f11
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subt f11, f10, f10
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stt f10, Temp0(sp)
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ldl ra, Temp0 + HighPart(sp)
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cpyse f1, f10, f13
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sra ra, 13, v0
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and ra, t0, t0
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and v0, 0xff, v0
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sll v0, 4, v0
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mult f13, f13, f16
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bis t0, t4, t3
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addl t1, v0, v0
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stl t3, Temp0 + HighPart(sp)
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xor ra, t0, t0
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lds f12, 4(v0)
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lds f0, 0(v0)
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addl t0, t4, t0
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ldt f11, 8(v0)
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zapnot t0, 0xf, t0
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mult f12, f13, f12
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ldt f13, Temp0(sp)
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mult f16, f0, f0
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sll t0, 31, t0
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stq t0, Temp0(sp)
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ldah t3, 0x350(zero)
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ldt f16, Temp0(sp)
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addt f11, f12, f11
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addt f0, f11, f0
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ldt f11, Lsb
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mult f0, f13, f13
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mult f13, f0, f0
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mult f13, f16, f13
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subt f1, f0, f0
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addt f13, f13, f12
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mult f13, f11, f11
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mult f13, f0, f0
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addt f12, f0, f0
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subt f0, f11, f16
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addt f0, f11, f11
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multc f0, f16, f1
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multc f0, f11, f13
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cmptle f10, f1, f1
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cmptlt f13, f10, f10
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fcmoveq f1, f0, f16
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fcmoveq f10, f16, f11
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stt f11, Temp0(sp)
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ldl v0, Temp0 + HighPart(sp)
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subl v0, t3, v0
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stl v0, Temp0 + HighPart(sp)
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ldt f0, Temp0(sp)
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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, (a0) // return through saved ra in a0
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.end sqrt
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.rdata
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.align 3
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Lsb: .quad 0x3cb4000000000000 // lsb factor: 5*2^-54
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One: .double 1.0
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//
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// Jump table indexed by F_CLASS(x)
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//
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Switch:
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.long retarg
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.long retarg
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.long retarg
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.long error
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.long denorm
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.long error
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.long denorm
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.long error
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.long retarg
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.long retarg
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//
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// Function name for __dpml_exception.
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//
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FunctionName:
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.ascii "sqrt\0"
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//
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// 256 entry square root table.
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//
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.align 3
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.globl __sqrt_t_table
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__sqrt_t_table:
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.float 5.25192082e-001
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.float -1.75747597e+000
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.double 2.6464974462692763e+000
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.float 5.15111804e-001
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.float -1.73715818e+000
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.double 2.6362593054537453e+000
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.float 5.05300283e-001
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.float -1.71722889e+000
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.double 2.6261391341915705e+000
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.float 4.95748460e-001
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.float -1.69767773e+000
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.double 2.6161345458522471e+000
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.float 4.86447543e-001
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.float -1.67849493e+000
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.double 2.6062435780891402e+000
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.float 4.77389067e-001
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.float -1.65967047e+000
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.double 2.5964637691802634e+000
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.float 4.68565017e-001
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.float -1.64119542e+000
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.double 2.5867933778763708e+000
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.float 4.59967613e-001
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.float -1.62306046e+000
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.double 2.5772301172720726e+000
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.float 4.51589465e-001
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.float -1.60525715e+000
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.double 2.5677722316823841e+000
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.float 4.43423420e-001
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.float -1.58777702e+000
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.double 2.5584177809840178e+000
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.float 4.35462624e-001
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.float -1.57061172e+000
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.double 2.5491646878882950e+000
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.float 4.27700490e-001
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.float -1.55375361e+000
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.double 2.5400114102036593e+000
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.float 4.20130670e-001
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.float -1.53719485e+000
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.double 2.5309559425202091e+000
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.float 4.12747115e-001
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.float -1.52092814e+000
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.double 2.5219966432800311e+000
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.float 4.05543953e-001
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.float -1.50494635e+000
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.double 2.5131318561302742e+000
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.float 3.98515552e-001
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.float -1.48924243e+000
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.double 2.5043598307294976e+000
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.float 3.91656518e-001
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.float -1.47380984e+000
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.double 2.4956791166576457e+000
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.float 3.84961635e-001
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.float -1.45864189e+000
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.double 2.4870879666367363e+000
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.float 3.78425866e-001
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.float -1.44373238e+000
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.double 2.4785850040822726e+000
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.float 3.72044414e-001
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.float -1.42907512e+000
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.double 2.4701686028111789e+000
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.float 3.65812600e-001
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.float -1.41466427e+000
|
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.double 2.4618374464189174e+000
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.float 3.59725922e-001
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.float -1.40049386e+000
|
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.double 2.4535898984567197e+000
|
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.float 3.53780121e-001
|
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.float -1.38655853e+000
|
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.double 2.4454247451516906e+000
|
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.float 3.47970992e-001
|
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.float -1.37285280e+000
|
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.double 2.4373406056097546e+000
|
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.float 3.42294544e-001
|
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.float -1.35937130e+000
|
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.double 2.4293359988624310e+000
|
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.float 3.36746901e-001
|
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.float -1.34610915e+000
|
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.double 2.4214098911341502e+000
|
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.float 3.31324309e-001
|
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.float -1.33306122e+000
|
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.double 2.4135608443300902e+000
|
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.float 3.26023191e-001
|
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.float -1.32022274e+000
|
|
.double 2.4057876358548973e+000
|
|
.float 3.20840031e-001
|
|
.float -1.30758882e+000
|
|
.double 2.3980888548975567e+000
|
|
.float 3.15771550e-001
|
|
.float -1.29515541e+000
|
|
.double 2.3904637987369988e+000
|
|
.float 3.10814440e-001
|
|
.float -1.28291762e+000
|
|
.double 2.3829108308987554e+000
|
|
.float 3.05965573e-001
|
|
.float -1.27087140e+000
|
|
.double 2.3754291107716869e+000
|
|
.float 3.01221997e-001
|
|
.float -1.25901258e+000
|
|
.double 2.3680174165800736e+000
|
|
.float 2.96580702e-001
|
|
.float -1.24733686e+000
|
|
.double 2.3606745061532881e+000
|
|
.float 2.92038947e-001
|
|
.float -1.23584068e+000
|
|
.double 2.3533996524278131e+000
|
|
.float 2.87593961e-001
|
|
.float -1.22451997e+000
|
|
.double 2.3461916115767520e+000
|
|
.float 2.83243120e-001
|
|
.float -1.21337104e+000
|
|
.double 2.3390493874647480e+000
|
|
.float 2.78983861e-001
|
|
.float -1.20239019e+000
|
|
.double 2.3319719207388188e+000
|
|
.float 2.74813741e-001
|
|
.float -1.19157410e+000
|
|
.double 2.3249584500223111e+000
|
|
.float 2.70730376e-001
|
|
.float -1.18091917e+000
|
|
.double 2.3180078386470857e+000
|
|
.float 2.66731441e-001
|
|
.float -1.17042208e+000
|
|
.double 2.3111191896320209e+000
|
|
.float 2.62814730e-001
|
|
.float -1.16007960e+000
|
|
.double 2.3042915890976596e+000
|
|
.float 2.58978039e-001
|
|
.float -1.14988852e+000
|
|
.double 2.2975241538422528e+000
|
|
.float 2.55219340e-001
|
|
.float -1.13984573e+000
|
|
.double 2.2908158724885475e+000
|
|
.float 2.51536548e-001
|
|
.float -1.12994838e+000
|
|
.double 2.2841661874688031e+000
|
|
.float 2.47927740e-001
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//
|
|
// End of table.
|
|
//
|