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|
|
| stan.sa 3.3 7/29/91
|
| The entry point stan computes the tangent of
| an input argument;
| stand does the same except for denormalized input.
|
| Input: Double-extended number X in location pointed to
| by address register a0.
|
| Output: The value tan(X) returned in floating-point register Fp0.
|
| Accuracy and Monotonicity: The returned result is within 3 ulp in
| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
| result is subsequently rounded to double precision. The
| result is provably monotonic in double precision.
|
| Speed: The program sTAN takes approximately 170 cycles for
| input argument X such that |X| < 15Pi, which is the usual
| situation.
|
| Algorithm:
|
| 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
|
| 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
| k = N mod 2, so in particular, k = 0 or 1.
|
| 3. If k is odd, go to 5.
|
| 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a
| rational function U/V where
| U = r + r*s*(P1 + s*(P2 + s*P3)), and
| V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r.
| Exit.
|
| 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a
| rational function U/V where
| U = r + r*s*(P1 + s*(P2 + s*P3)), and
| V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r,
| -Cot(r) = -V/U. Exit.
|
| 6. If |X| > 1, go to 8.
|
| 7. (|X|<2**(-40)) Tan(X) = X. Exit.
|
| 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
|
| Copyright (C) Motorola, Inc. 1990
| All Rights Reserved
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|STAN idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
#include "fpsp.h"
BOUNDS1: .long 0x3FD78000,0x4004BC7E
TWOBYPI: .long 0x3FE45F30,0x6DC9C883
TANQ4: .long 0x3EA0B759,0xF50F8688
TANP3: .long 0xBEF2BAA5,0xA8924F04
TANQ3: .long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000
TANP2: .long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000
TANQ2: .long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000
TANP1: .long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000
TANQ1: .long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000
INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000
TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
|--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
|--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
|--MOST 69 BITS LONG.
.global PITBL
PITBL:
.long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000
.long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000
.long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000
.long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000
.long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000
.long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000
.long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000
.long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000
.long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000
.long 0xC0040000,0x90836524,0x88034B96,0x20B00000
.long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000
.long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000
.long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000
.long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000
.long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000
.long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000
.long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000
.long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000
.long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000
.long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000
.long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000
.long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000
.long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000
.long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000
.long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000
.long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000
.long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000
.long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000
.long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000
.long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000
.long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000
.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000
.long 0x00000000,0x00000000,0x00000000,0x00000000
.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000
.long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000
.long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000
.long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000
.long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000
.long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000
.long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000
.long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000
.long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000
.long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000
.long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000
.long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000
.long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000
.long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000
.long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000
.long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000
.long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000
.long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000
.long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000
|
