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978 lines
24 KiB
978 lines
24 KiB
// TITLE("Alpha AXP Sine")
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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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// sin.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 sine.
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//
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// Author:
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//
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// Bob Hanek 1-Oct-1991
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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) 12-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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SaveS0: .space 8 //
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SaveS1: .space 8 //
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SaveRa: .space 8 //
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SaveF2: .space 8 //
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SaveF3: .space 8 //
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SaveF4: .space 8 //
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SaveF5: .space 8 //
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SaveF6: .space 8 //
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SaveF7: .space 8 //
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SaveF8: .space 8 //
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SaveF9: .space 8 //
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Temp0: .space 8 //
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Temp1: .space 8 //
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Temp2: .space 8 //
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Temp3: .space 8 //
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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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//
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// Define argument ranges.
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//
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#define BIG_X_HI 0x4169 // upper bound of medium argument range
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#define BIG_X_LO 0x21fb
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#define SMALL_X_HI 0x3e40 // lower bound of medium argument range
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#define SMALL_X_LO 0x0000
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#define EXP_WORD_OF_TWO_PI_HI 0x4019
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#define EXP_WORD_OF_TWO_PI_LO 0x21fb
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//
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// Define offsets into table.
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//
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#define D_2_POW_K_OVER_PI_OVER_4 0x0
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#define PI_OVER_4_OVER_2_POW_K_0 0x08
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#define PI_OVER_4_OVER_2_POW_K_1 0x10
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#define PI_OVER_4_OVER_2_POW_K_2 0x18
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#define PI_OVER_4_OVER_2_POW_K_3 0x20
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#define PI_OVER_4_OVER_2_POW_K_4 0x28
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#define PI_OVER_2_HI 0x30
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#define PI_OVER_2_LO 0x38
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#define PI_HI 0x40
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#define PI_LO 0x48
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#define THREE_PI_OVER_2_HI 0x50
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#define THREE_PI_OVER_2_LO 0x58
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#define TWO_PI_HI 0x60
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#define TWO_PI_LO 0x68
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#define TWO_POW_K_OVER_PI_OVER_4 0x70
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#define C_POLY0 0xb8
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#define C_POLY1 C_POLY0 + 8
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#define C_POLY2 C_POLY1 + 8
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#define C_POLY3 C_POLY2 + 8
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#define C_POLY4 C_POLY3 + 8
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#define P_POLY0 0x78
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#define P_POLY1 P_POLY0 + 8
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#define Q_POLY0 0x88
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#define Q_POLY1 Q_POLY0 + 8
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#define S_POLY0 0x98
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#define S_POLY1 S_POLY0 + 8
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#define S_POLY2 S_POLY1 + 8
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#define S_POLY3 S_POLY2 + 8
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#define SINCOS 0xe0
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#define SIN_A 0xe8
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#define COS_A 0xf0
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SBTTL("Sine")
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//++
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//
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// double
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// sin (
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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 sine 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 sine result is returned as the function value in f0.
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//
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//--
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NESTED_ENTRY(sin, FrameLength, ra)
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lda sp, -FrameLength(sp) // allocate stack frame
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stq s0, SaveS0(sp)
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stq s1, SaveS1(sp)
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stq ra, SaveRa(sp)
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stt f2, SaveF2(sp)
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stt f3, SaveF3(sp)
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stt f4, SaveF4(sp)
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stt f5, SaveF5(sp)
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stt f6, SaveF6(sp)
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stt f7, SaveF7(sp)
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stt f8, SaveF8(sp)
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stt f9, SaveF9(sp)
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PROLOGUE_END
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ornot zero, zero, t0
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srl t0, 33, t0
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ldah t1, SMALL_X_HI(zero)
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ldah t2, BIG_X_HI - SMALL_X_HI(zero)
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stt f16, Temp2(sp)
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cpys f31, f16, f2
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ldl v0, Temp2 + HighPart(sp)
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lda t2, BIG_X_LO - SMALL_X_LO(t2)
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cpys f16, f16, f3
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and v0, t0, v0 // the exponent field of the argument
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subl v0, t1, t0 // if v0 - small <= big - small
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cmpult t0, t2, t0 // we've got an abnormal (but not nessarily bad) argument
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beq t0, abnormal_argument
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ldah t2, EXP_WORD_OF_TWO_PI_HI(zero) // if (j >= EXP_WORD_OF_TWO_PI)
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lda t2, EXP_WORD_OF_TWO_PI_LO(t2) // we have a medium argument
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cmplt v0, t2, t2
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beq t2, medium_argument
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//
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// small argument reduction
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//
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// reduce the argument X to ( 8 * N + I ) * pi / 4 + y
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// and let the reduced argument be y' where
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// y' = X - floor( ( 8 * N + I + 1 ) / 2 ) * pi / 4
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// the low 3 bits of I are the octant
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//
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lda t0, __trig_cons
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ldt f0, TWO_POW_K_OVER_PI_OVER_4(t0)
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mult f2, f0, f0
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cvttqc f0, f1
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stt f1, Temp2(sp)
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ldl t2, Temp2(sp)
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sra t2, 7, t4
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cmpule t4, 7, t12
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beq t12, small_cos // if octant > 7; shouldn't happen
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// dispatch on octant
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lda t12, Switch2
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s4addl t4, 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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// 1st octant; compute sin(y')
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//
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Switch20:
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and t2, 127, t5
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subl t5, 27, t5
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blt t5, small_sin
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s4subl t5, t5, t5
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s8addl t5, t0, t5
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ldt f0, SINCOS(t5)
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ldt f5, SIN_A(t5)
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ldt f6, COS_A(t5)
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subt f2, f0, f4
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br zero, pos_tab_eval
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small_sin:
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mult f2, f2, f1
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ldt f10, S_POLY3(t0)
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ldt f0, S_POLY1(t0)
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ldt f5, S_POLY2(t0)
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ldt f11, S_POLY0(t0)
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mult f10, f1, f10
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mult f1, f1, f6
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mult f0, f1, f0
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mult f2, f1, f1
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addt f10, f5, f5
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addt f0, f11, f0
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mult f5, f6, f5
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addt f5, f0, f0
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mult f1, f0, f0
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subt f2, f0, f7
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fbge f3, adjust_sign
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br zero, change_sign
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//
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// 2nd octant; compute cos(y')
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//
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Switch21:
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ldt f10, PI_OVER_2_HI(t0)
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ornot zero, t2, t4
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and t4, 127, t4
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ldt f11, PI_OVER_2_LO(t0)
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subl t4, 27, t4
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subt f2, f10, f10
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blt t4, pos_cos_1
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s4subl t4, t4, t4
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s8addl t4, t0, t4
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ldt f6, SINCOS(t4)
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ldt f5, COS_A(t4)
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addt f10, f6, f6
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subt f6, f11, f4
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ldt f6, SIN_A(t4)
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br zero, pos_tab_eval
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//
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// 3rd octant; compute cos(y')
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//
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Switch22:
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ldt f1, PI_OVER_2_HI(t0)
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and t2, 127, t3
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ldt f11, PI_OVER_2_LO(t0)
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subl t3, 27, t3
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subt f2, f1, f10
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blt t3, pos_cos_1
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s4subl t3, t3, t3
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s8addl t3, t0, t3
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ldt f0, SINCOS(t3)
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ldt f6, SIN_A(t3)
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ldt f5, COS_A(t3)
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subt f10, f0, f0
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subt f11, f0, f4
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br zero, pos_tab_eval
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pos_cos_1:
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subt f10, f11, f10
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ldt f1, C_POLY1(t0)
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ldt f2, C_POLY4(t0)
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ldt f0, C_POLY2(t0)
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ldt f4, C_POLY0(t0)
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ldt f6, C_POLY3(t0)
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ldt f11, One
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mult f10, f10, f10
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mult f10, f10, f7
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mult f10, f1, f1
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mult f2, f10, f2
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mult f0, f7, f0
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addt f1, f4, f1
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mult f7, f10, f7
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addt f2, f6, f2
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addt f1, f0, f0
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mult f7, f2, f2
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addt f0, f2, f0
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mult f10, f0, f0
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subt f11, f0, f7
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fbge f3, adjust_sign
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br zero, change_sign
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//
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// 4th octant; compute -sin(y')
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//
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Switch23:
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ldt f6, PI_HI(t0)
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ornot zero, t2, t5
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and t5, 127, t5
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ldt f10, PI_LO(t0)
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subl t5, 27, t5
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subt f2, f6, f1
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blt t5, neg_sin_1
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s4subl t5, t5, t5
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s8addl t5, t0, t5
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ldt f0, SINCOS(t5)
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ldt f5, SIN_A(t5)
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ldt f6, COS_A(t5)
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addt f1, f0, f0
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subt f10, f0, f4
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br zero, pos_tab_eval
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//
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// 5th octant; compute -sin(y')
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//
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Switch24:
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ldt f11, PI_HI(t0)
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and t2, 127, t4
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ldt f10, PI_LO(t0)
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subl t4, 27, t4
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subt f2, f11, f1
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blt t4, neg_sin_1
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s4subl t4, t4, t4
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s8addl t4, t0, t4
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ldt f0, SINCOS(t4)
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ldt f5, SIN_A(t4)
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ldt f6, COS_A(t4)
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subt f1, f0, f0
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subt f0, f10, f4
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br zero, neg_tab_eval
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neg_sin_1:
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subt f1, f10, f2
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ldt f7, S_POLY3(t0)
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ldt f0, S_POLY1(t0)
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ldt f4, S_POLY2(t0)
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ldt f12, S_POLY0(t0)
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mult f2, f2, f11
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mult f7, f11, f7
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mult f11, f11, f6
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mult f0, f11, f0
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mult f2, f11, f2
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addt f7, f4, f4
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addt f0, f12, f0
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mult f4, f6, f4
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addt f4, f0, f0
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mult f2, f0, f0
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addt f10, f0, f0
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subt f0, f1, f7
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fbge f3, adjust_sign
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br zero, change_sign
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//
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// 6th octant; compute -cos(y')
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//
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Switch25:
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ldt f12, THREE_PI_OVER_2_HI(t0)
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ornot zero, t2, t3
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and t3, 127, t3
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ldt f11, THREE_PI_OVER_2_LO(t0)
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subl t3, 27, t3
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subt f2, f12, f12
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blt t3, neg_cos_1
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s4subl t3, t3, t3
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s8addl t3, t0, t3
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ldt f6, SINCOS(t3)
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ldt f5, COS_A(t3)
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addt f12, f6, f6
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subt f6, f11, f4
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ldt f6, SIN_A(t3)
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br zero, neg_tab_eval
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//
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// 7th octant; compute -cos(y')
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//
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Switch26:
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ldt f10, THREE_PI_OVER_2_HI(t0)
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and t2, 127, t5
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ldt f11, THREE_PI_OVER_2_LO(t0)
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subl t5, 27, t5
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subt f2, f10, f12
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blt t5, neg_cos_1
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s4subl t5, t5, t5
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s8addl t5, t0, t5
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ldt f0, SINCOS(t5)
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ldt f6, SIN_A(t5)
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ldt f5, COS_A(t5)
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subt f12, f0, f0
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subt f11, f0, f4
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br zero, neg_tab_eval
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neg_cos_1:
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subt f12, f11, f11
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ldt f1, C_POLY1(t0)
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ldt f2, C_POLY4(t0)
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ldt f7, C_POLY2(t0)
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ldt f0, C_POLY0(t0)
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ldt f4, C_POLY3(t0)
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ldt f6, One
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mult f11, f11, f11
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mult f11, f11, f10
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mult f11, f1, f1
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mult f2, f11, f2
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mult f7, f10, f7
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addt f1, f0, f0
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mult f10, f11, f10
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addt f2, f4, f2
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addt f0, f7, f0
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mult f10, f2, f2
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addt f0, f2, f0
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mult f11, f0, f0
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subt f0, f6, f7
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fbge f3, adjust_sign
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br zero, change_sign
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//
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// 8th octant; compute sin(y')
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//
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Switch27:
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ldt f12, TWO_PI_HI(t0)
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ornot zero, t2, t2
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and t2, 127, t2
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ldt f1, TWO_PI_LO(t0)
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subl t2, 27, t2
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subt f2, f12, f2
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blt t2, pos_sin_1
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s4subl t2, t2, t2
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s8addl t2, t0, t2
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ldt f10, SINCOS(t2)
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ldt f5, SIN_A(t2)
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ldt f6, COS_A(t2)
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addt f2, f10, f10
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subt f1, f10, f4
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br zero, neg_tab_eval
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pos_sin_1:
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subt f2, f1, f11
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ldt f12, S_POLY3(t0)
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ldt f7, S_POLY1(t0)
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ldt f10, S_POLY2(t0)
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ldt f6, S_POLY0(t0)
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mult f11, f11, f0
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mult f12, f0, f12
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mult f0, f0, f4
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mult f7, f0, f7
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mult f11, f0, f0
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addt f12, f10, f10
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addt f7, f6, f6
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mult f10, f4, f4
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addt f4, f6, f4
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mult f0, f4, f0
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addt f1, f0, f0
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subt f2, f0, f7
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fbge f3, adjust_sign
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br zero, change_sign
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small_cos:
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mult f2, f2, f12
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ldt f10, C_POLY1(t0)
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ldt f6, C_POLY4(t0)
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ldt f1, C_POLY2(t0)
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ldt f0, C_POLY0(t0)
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ldt f5, C_POLY3(t0)
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mult f12, f12, f11
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mult f12, f10, f10
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mult f6, f12, f6
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mult f1, f11, f1
|
|
addt f10, f0, f0
|
|
mult f11, f12, f11
|
|
ldt f10, One
|
|
addt f6, f5, f5
|
|
addt f0, f1, f0
|
|
mult f11, f5, f5
|
|
addt f0, f5, f0
|
|
mult f12, f0, f0
|
|
subt f10, f0, f7
|
|
fbge f3, adjust_sign
|
|
br zero, change_sign
|
|
|
|
//
|
|
// a medium argument
|
|
//
|
|
medium_argument:
|
|
lda t5, __trig_cons // reduce the argument with extra precision
|
|
ldt f6, D_2_POW_K_OVER_PI_OVER_4(t5)
|
|
mult f2, f6, f6
|
|
cvttqc f6, f1
|
|
stt f1, Temp2(sp)
|
|
ldl s0, Temp2(sp)
|
|
addl s0, 0x80, t2
|
|
bic t2, 0xff, t2
|
|
stq t2, Temp3(sp)
|
|
ldt f5, Temp3(sp)
|
|
ldt f0, PI_OVER_4_OVER_2_POW_K_0(t5)
|
|
ldt f10, PI_OVER_4_OVER_2_POW_K_1(t5)
|
|
cvtqt f5, f5
|
|
ldt f6, PI_OVER_4_OVER_2_POW_K_2(t5)
|
|
mult f5, f0, f0
|
|
mult f5, f10, f10
|
|
mult f5, f6, f6
|
|
subt f2, f0, f0
|
|
subt f0, f10, f1
|
|
subt f1, f0, f0
|
|
addt f10, f0, f0
|
|
addt f6, f0, f8
|
|
subt f1, f8, f9
|
|
cmpteq f9, f1, f11
|
|
fbne f11, evaluate
|
|
|
|
subt f9, f1, f1
|
|
ldt f12, PI_OVER_4_OVER_2_POW_K_3(t5)
|
|
mult f5, f12, f12
|
|
addt f8, f1, f1
|
|
addt f12, f1, f8
|
|
subt f9, f8, f10
|
|
cmpteq f10, f9, f0
|
|
fbne f0, evaluate
|
|
|
|
subt f10, f9, f9
|
|
ldt f6, PI_OVER_4_OVER_2_POW_K_4(t5)
|
|
mult f5, f6, f5
|
|
addt f8, f9, f8
|
|
addt f5, f8, f8
|
|
subt f10, f8, f9
|
|
cmpteq f9, f10, f11
|
|
fbne f11, evaluate
|
|
|
|
subt f9, f10, f10
|
|
addt f8, f10, f8
|
|
br zero, evaluate
|
|
|
|
//
|
|
// process an abnormal argument
|
|
// it's either very small, very big, a NaN or an Inf
|
|
//
|
|
abnormal_argument:
|
|
cmple v0, t1, t1
|
|
beq t1, big_NaN_or_Inf
|
|
|
|
cpys f3, f2, f0 // very small argument; simply return it.
|
|
br zero, done
|
|
|
|
//
|
|
// Process big arguments or NaNs or Infs
|
|
//
|
|
big_NaN_or_Inf:
|
|
ldah s1, 0x7ff0(zero) // mask is 0x7ff00000
|
|
and v0, s1, v0
|
|
xor v0, s1, v0
|
|
beq v0, NaN_or_Inf // NaN or an infinity
|
|
|
|
cpys f2, f2, f16 // reduce the very big argument
|
|
mov zero, a1 // very carefully
|
|
lda a2, Temp1(sp)
|
|
lda a3, Temp0(sp)
|
|
bsr ra, __trig_reduce
|
|
mov v0, s0
|
|
ldt f8, Temp0(sp)
|
|
ldt f9, Temp1(sp)
|
|
|
|
//
|
|
// evaluate the function
|
|
//
|
|
evaluate:
|
|
sra s0, 7, t2
|
|
and t2, 7, t2
|
|
cmpule t2, 7, t12
|
|
beq t12, pos_sin_2
|
|
|
|
lda t12, Switch1 // dispatch on the octant
|
|
s4addl t2, t12, t12
|
|
ldl t12, 0(t12)
|
|
jmp zero, (t12)
|
|
|
|
//
|
|
// 1st octant; compute sin(y')
|
|
//
|
|
Switch10:
|
|
and s0, 127, t4
|
|
subl t4, 27, t4
|
|
blt t4, pos_sin_2
|
|
|
|
s4subl t4, t4, t4
|
|
lda t5, __trig_cons
|
|
s8addl t4, t5, t4
|
|
ldt f6, SINCOS(t4)
|
|
ldt f5, SIN_A(t4)
|
|
subt f9, f6, f6
|
|
subt f6, f8, f4
|
|
ldt f6, COS_A(t4)
|
|
br zero, pos_tab_eval
|
|
|
|
//
|
|
// 2nd octant; compute cos(y')
|
|
//
|
|
Switch11:
|
|
ornot zero, s0, t7
|
|
and t7, 127, t7
|
|
subl t7, 27, t7
|
|
blt t7, pos_cos_2
|
|
|
|
s4subl t7, t7, t7
|
|
lda a0, __trig_cons
|
|
s8addl t7, a0, t7
|
|
ldt f0, SINCOS(t7)
|
|
ldt f6, SIN_A(t7)
|
|
ldt f5, COS_A(t7)
|
|
addt f9, f0, f0
|
|
subt f0, f8, f4
|
|
br zero, pos_tab_eval
|
|
|
|
//
|
|
// 3rd octant; compute cos(y')
|
|
//
|
|
Switch12:
|
|
and s0, 127, a2
|
|
subl a2, 27, a2
|
|
blt a2, pos_cos_2
|
|
|
|
s4subl a2, a2, a2
|
|
lda a3, __trig_cons
|
|
s8addl a2, a3, a2
|
|
ldt f1, SINCOS(a2)
|
|
ldt f6, SIN_A(a2)
|
|
ldt f5, COS_A(a2)
|
|
subt f9, f1, f1
|
|
subt f8, f1, f4
|
|
br zero, pos_tab_eval
|
|
|
|
pos_cos_2:
|
|
mult f9, f9, f10
|
|
lda a5, __trig_cons
|
|
ldt f11, C_POLY1(a5)
|
|
ldt f12, C_POLY4(a5)
|
|
ldt f14, C_POLY2(a5)
|
|
mult f10, f10, f13
|
|
mult f10, f11, f11
|
|
ldt f15, C_POLY0(a5)
|
|
mult f12, f10, f12
|
|
ldt f16, C_POLY3(a5)
|
|
ldt f17, One
|
|
mult f14, f13, f14
|
|
addt f11, f15, f11
|
|
mult f13, f10, f13
|
|
addt f12, f16, f12
|
|
addt f11, f14, f11
|
|
mult f13, f12, f12
|
|
addt f11, f12, f11
|
|
mult f10, f11, f10
|
|
subt f17, f10, f7
|
|
fbge f3, adjust_sign
|
|
br zero, change_sign
|
|
|
|
//
|
|
// 4th octant; compute -sin(y')
|
|
//
|
|
Switch13:
|
|
ornot zero, s0, t8
|
|
and t8, 127, t8
|
|
subl t8, 27, t8
|
|
blt t8, neg_sin_2
|
|
|
|
s4subl t8, t8, t8
|
|
lda t9, __trig_cons
|
|
s8addl t8, t9, t8
|
|
ldt f18, SINCOS(t8)
|
|
ldt f5, SIN_A(t8)
|
|
ldt f6, COS_A(t8)
|
|
addt f9, f18, f18
|
|
subt f8, f18, f4
|
|
br zero, pos_tab_eval
|
|
|
|
//
|
|
// 5th octant; compute -sin(y')
|
|
//
|
|
Switch14:
|
|
and s0, 127, t11
|
|
subl t11, 27, t11
|
|
blt t11, neg_sin_2
|
|
|
|
s4subl t11, t11, t11
|
|
lda ra, __trig_cons
|
|
s8addl t11, ra, t11
|
|
ldt f19, SINCOS(t11)
|
|
ldt f5, SIN_A(t11)
|
|
ldt f6, COS_A(t11)
|
|
subt f9, f19, f19
|
|
subt f19, f8, f4
|
|
br zero, neg_tab_eval
|
|
|
|
neg_sin_2:
|
|
mult f9, f9, f20
|
|
lda v0, __trig_cons
|
|
ldt f21, S_POLY3(v0)
|
|
ldt f22, S_POLY1(v0)
|
|
ldt f23, S_POLY2(v0)
|
|
mult f21, f20, f21
|
|
ldt f25, S_POLY0(v0)
|
|
mult f20, f20, f24
|
|
mult f22, f20, f22
|
|
mult f9, f20, f20
|
|
addt f21, f23, f21
|
|
addt f22, f25, f22
|
|
mult f21, f24, f21
|
|
addt f21, f22, f21
|
|
mult f20, f21, f20
|
|
addt f8, f20, f8
|
|
subt f8, f9, f7
|
|
fbge f3, adjust_sign
|
|
br zero, change_sign
|
|
|
|
//
|
|
// 6th octant; compute -cos(y')
|
|
//
|
|
Switch15:
|
|
ornot zero, s0, t0
|
|
and t0, 127, t0
|
|
subl t0, 27, t0
|
|
blt t0, neg_cos_2
|
|
|
|
s4subl t0, t0, t0
|
|
lda t1, __trig_cons
|
|
s8addl t0, t1, t0
|
|
ldt f26, SINCOS(t0)
|
|
ldt f6, SIN_A(t0)
|
|
ldt f5, COS_A(t0)
|
|
addt f9, f26, f26
|
|
subt f26, f8, f4
|
|
br zero, neg_tab_eval
|
|
|
|
//
|
|
// 7th octant; compute -cos(y')
|
|
//
|
|
Switch16:
|
|
and s0, 127, t3
|
|
subl t3, 27, t3
|
|
blt t3, neg_cos_2
|
|
|
|
s4subl t3, t3, t3
|
|
lda t5, __trig_cons
|
|
s8addl t3, t5, t3
|
|
ldt f27, SINCOS(t3)
|
|
ldt f6, SIN_A(t3)
|
|
ldt f5, COS_A(t3)
|
|
subt f9, f27, f27
|
|
subt f8, f27, f4
|
|
br zero, neg_tab_eval
|
|
|
|
neg_cos_2:
|
|
mult f9, f9, f28
|
|
lda t6, __trig_cons
|
|
ldt f29, C_POLY1(t6)
|
|
ldt f30, C_POLY4(t6)
|
|
ldt f1, C_POLY2(t6)
|
|
mult f28, f28, f0
|
|
mult f28, f29, f29
|
|
ldt f15, C_POLY0(t6)
|
|
mult f30, f28, f30
|
|
ldt f16, C_POLY3(t6)
|
|
ldt f14, One
|
|
mult f1, f0, f1
|
|
addt f29, f15, f15
|
|
mult f0, f28, f0
|
|
addt f30, f16, f16
|
|
addt f15, f1, f1
|
|
mult f0, f16, f0
|
|
addt f1, f0, f0
|
|
mult f28, f0, f0
|
|
subt f0, f14, f7
|
|
fbge f3, adjust_sign
|
|
br zero, change_sign
|
|
|
|
//
|
|
// 8th octant; compute sin(y')
|
|
//
|
|
Switch17:
|
|
ornot zero, s0, s0
|
|
and s0, 127, s0
|
|
subl s0, 27, s0
|
|
blt s0, pos_sin_2
|
|
|
|
s4subl s0, s0, s0
|
|
lda a0, __trig_cons
|
|
s8addl s0, a0, s0
|
|
ldt f13, SINCOS(s0)
|
|
ldt f5, SIN_A(s0)
|
|
ldt f6, COS_A(s0)
|
|
addt f9, f13, f13
|
|
subt f8, f13, f4
|
|
|
|
neg_tab_eval:
|
|
cpysn f3, f3, f3
|
|
|
|
pos_tab_eval:
|
|
mult f4, f4, f12 // evalutate p_poly & q_poly
|
|
lda a1, __trig_cons
|
|
ldt f11, P_POLY1(a1)
|
|
ldt f17, P_POLY0(a1)
|
|
ldt f10, Q_POLY1(a1)
|
|
mult f11, f12, f11
|
|
ldt f19, Q_POLY0(a1)
|
|
mult f4, f12, f18
|
|
mult f10, f12, f10
|
|
addt f11, f17, f11
|
|
addt f10, f19, f10
|
|
mult f18, f11, f11
|
|
mult f12, f10, f10
|
|
subt f4, f11, f4
|
|
mult f5, f10, f10
|
|
mult f6, f4, f4
|
|
subt f10, f4, f4
|
|
subt f5, f4, f7
|
|
fbge f3, adjust_sign
|
|
br zero, change_sign
|
|
|
|
pos_sin_2:
|
|
mult f9, f9, f23
|
|
lda a3, __trig_cons
|
|
ldt f25, S_POLY3(a3)
|
|
ldt f24, S_POLY1(a3)
|
|
ldt f22, S_POLY2(a3)
|
|
mult f25, f23, f25
|
|
ldt f20, S_POLY0(a3)
|
|
mult f23, f23, f21
|
|
mult f24, f23, f24
|
|
mult f9, f23, f23
|
|
addt f25, f22, f22
|
|
addt f24, f20, f20
|
|
mult f22, f21, f21
|
|
addt f21, f20, f20
|
|
mult f23, f20, f20
|
|
addt f8, f20, f8
|
|
subt f9, f8, f7
|
|
fbge f3, adjust_sign
|
|
|
|
br zero, change_sign
|
|
|
|
//
|
|
// Determine if we have a NaN or an Inf
|
|
//
|
|
NaN_or_Inf:
|
|
stt f2, Temp2(sp)
|
|
ldl a4, Temp2 + HighPart(sp)
|
|
and a4, s1, a5
|
|
cmpeq a5, s1, s1
|
|
beq s1, NaN_or_Inf1
|
|
|
|
ldl t9, Temp2(sp)
|
|
ldah t8, 0x10(zero) // mask = 0x000fffff
|
|
lda t8, -1(t8)
|
|
and a4, t8, a4
|
|
bis a4, t9, a4
|
|
cmpult zero, a4, a4
|
|
and s1, a4, s1
|
|
bne s1, NaN_or_Inf2
|
|
|
|
//
|
|
// report an exception
|
|
//
|
|
NaN_or_Inf1:
|
|
lda t10, sinName
|
|
stl t10, ExRec + ErName(sp)
|
|
ldah t12, 0x800(zero)
|
|
stt f2, ExRec + ErArg0(sp)
|
|
lda t12, 0x55(t12)
|
|
stl t12, ExRec + ErErr(sp)
|
|
lda v0, ExRec(sp)
|
|
bsr ra, __dpml_exception
|
|
ldt f2, 0(v0)
|
|
|
|
//
|
|
// return the argument
|
|
//
|
|
NaN_or_Inf2:
|
|
cpys f2, f2, f0
|
|
br zero, done
|
|
|
|
change_sign:
|
|
cpysn f7, f7, f7
|
|
adjust_sign:
|
|
cpys f7, f7, f0
|
|
|
|
//
|
|
// Restore registers and return with result in f0.
|
|
//
|
|
|
|
done: ldq s0, SaveS0(sp)
|
|
ldq s1, SaveS1(sp)
|
|
ldq ra, SaveRa(sp)
|
|
ldt f2, SaveF2(sp)
|
|
ldt f3, SaveF3(sp)
|
|
ldt f4, SaveF4(sp)
|
|
ldt f5, SaveF5(sp)
|
|
ldt f6, SaveF6(sp)
|
|
ldt f7, SaveF7(sp)
|
|
ldt f8, SaveF8(sp)
|
|
ldt f9, SaveF9(sp)
|
|
lda sp, FrameLength(sp) // deallocate stack frame
|
|
ret zero, (ra) // return
|
|
|
|
.end sin
|
|
|
|
.rdata
|
|
.align 3
|
|
|
|
//
|
|
// Define floating point constants.
|
|
//
|
|
|
|
One: .double 1.0
|
|
|
|
//
|
|
// dispatch on octant
|
|
//
|
|
|
|
Switch1:
|
|
.long Switch10
|
|
.long Switch11
|
|
.long Switch12
|
|
.long Switch13
|
|
.long Switch14
|
|
.long Switch15
|
|
.long Switch16
|
|
.long Switch17
|
|
|
|
//
|
|
// dispatch on octant
|
|
//
|
|
|
|
Switch2:
|
|
.long Switch20
|
|
.long Switch21
|
|
.long Switch22
|
|
.long Switch23
|
|
.long Switch24
|
|
.long Switch25
|
|
.long Switch26
|
|
.long Switch27
|
|
|
|
//
|
|
// Function name for dpml_exception.
|
|
//
|
|
|
|
sinName:
|
|
.ascii "sin\0"
|