65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
70 {infinityD, infinityD},
71 {-infinityD, -1.0},
72 {-0.0, -0.0},
73 {+0.0, +0.0},
74 };
75
76 // Test special cases
77 for(int i = 0; i < testCases.length; i++) {
78 failures += testExpm1CaseWithUlpDiff(testCases[i][0],
79 testCases[i][1], 0, null);
80 }
81
82
83 // For |x| < 2^-54 expm1(x) ~= x
84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
85 double d = FpUtils.scalb(2, i);
86 failures += testExpm1Case(d, d);
87 failures += testExpm1Case(-d, -d);
88 }
89
90
91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).
92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x)
93 // overflows for x > ~= 709.8
94
95 // Use a 2-ulp error threshold to account for errors in the
96 // exp implementation; the increments of d in the loop will be
97 // exact.
98 for(double d = 37.5; d <= 709.5; d += 1.0) {
99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);
100 }
101
102 // For x > 710, expm1(x) should be infinity
103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) {
104 double d = FpUtils.scalb(2, i);
105 failures += testExpm1Case(d, infinityD);
106 }
107
108 // By monotonicity, once the limit is reached, the
109 // implemenation should return the limit for all smaller
110 // values.
111 boolean reachedLimit [] = {false, false};
112
113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;
114 // The greatest such y is ln(2^-53) ~= -36.7368005696771.
115 for(double d = -36.75; d >= -127.75; d -= 1.0) {
116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,
117 reachedLimit);
118 }
119
120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) {
121 double d = -FpUtils.scalb(2, i);
122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
123 }
124
125 // Test for monotonicity failures near multiples of log(2).
126 // Test two numbers before and two numbers after each chosen
127 // value; i.e.
128 //
129 // pcNeighbors[] =
130 // {nextDown(nextDown(pc)),
131 // nextDown(pc),
132 // pc,
133 // nextUp(pc),
134 // nextUp(nextUp(pc))}
135 //
136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])
137 {
138 double pcNeighbors[] = new double[5];
139 double pcNeighborsExpm1[] = new double[5];
140 double pcNeighborsStrictExpm1[] = new double[5];
141
142 for(int i = -50; i <= 50; i++) {
143 double pc = StrictMath.log(2)*i;
144
145 pcNeighbors[2] = pc;
146 pcNeighbors[1] = FpUtils.nextDown(pc);
147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]);
148 pcNeighbors[3] = FpUtils.nextUp(pc);
149 pcNeighbors[4] = FpUtils.nextUp(pcNeighbors[3]);
150
151 for(int j = 0; j < pcNeighbors.length; j++) {
152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]);
153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);
154 }
155
156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) {
157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) {
158 failures++;
159 System.err.println("Monotonicity failure for Math.expm1 on " +
160 pcNeighbors[j] + " and " +
161 pcNeighbors[j+1] + "\n\treturned " +
162 pcNeighborsExpm1[j] + " and " +
163 pcNeighborsExpm1[j+1] );
164 }
165
166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) {
167 failures++;
168 System.err.println("Monotonicity failure for StrictMath.expm1 on " +
169 pcNeighbors[j] + " and " +
|
65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
70 {infinityD, infinityD},
71 {-infinityD, -1.0},
72 {-0.0, -0.0},
73 {+0.0, +0.0},
74 };
75
76 // Test special cases
77 for(int i = 0; i < testCases.length; i++) {
78 failures += testExpm1CaseWithUlpDiff(testCases[i][0],
79 testCases[i][1], 0, null);
80 }
81
82
83 // For |x| < 2^-54 expm1(x) ~= x
84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
85 double d = Math.scalb(2, i);
86 failures += testExpm1Case(d, d);
87 failures += testExpm1Case(-d, -d);
88 }
89
90
91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).
92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x)
93 // overflows for x > ~= 709.8
94
95 // Use a 2-ulp error threshold to account for errors in the
96 // exp implementation; the increments of d in the loop will be
97 // exact.
98 for(double d = 37.5; d <= 709.5; d += 1.0) {
99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);
100 }
101
102 // For x > 710, expm1(x) should be infinity
103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) {
104 double d = Math.scalb(2, i);
105 failures += testExpm1Case(d, infinityD);
106 }
107
108 // By monotonicity, once the limit is reached, the
109 // implemenation should return the limit for all smaller
110 // values.
111 boolean reachedLimit [] = {false, false};
112
113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;
114 // The greatest such y is ln(2^-53) ~= -36.7368005696771.
115 for(double d = -36.75; d >= -127.75; d -= 1.0) {
116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,
117 reachedLimit);
118 }
119
120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) {
121 double d = -Math.scalb(2, i);
122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
123 }
124
125 // Test for monotonicity failures near multiples of log(2).
126 // Test two numbers before and two numbers after each chosen
127 // value; i.e.
128 //
129 // pcNeighbors[] =
130 // {nextDown(nextDown(pc)),
131 // nextDown(pc),
132 // pc,
133 // nextUp(pc),
134 // nextUp(nextUp(pc))}
135 //
136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])
137 {
138 double pcNeighbors[] = new double[5];
139 double pcNeighborsExpm1[] = new double[5];
140 double pcNeighborsStrictExpm1[] = new double[5];
141
142 for(int i = -50; i <= 50; i++) {
143 double pc = StrictMath.log(2)*i;
144
145 pcNeighbors[2] = pc;
146 pcNeighbors[1] = FpUtils.nextDown(pc);
147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]);
148 pcNeighbors[3] = Math.nextUp(pc);
149 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
150
151 for(int j = 0; j < pcNeighbors.length; j++) {
152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]);
153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);
154 }
155
156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) {
157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) {
158 failures++;
159 System.err.println("Monotonicity failure for Math.expm1 on " +
160 pcNeighbors[j] + " and " +
161 pcNeighbors[j+1] + "\n\treturned " +
162 pcNeighborsExpm1[j] + " and " +
163 pcNeighborsExpm1[j+1] );
164 }
165
166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) {
167 failures++;
168 System.err.println("Monotonicity failure for StrictMath.expm1 on " +
169 pcNeighbors[j] + " and " +
|